This page
intentionally left
blank
Copyright © 2006, New Age International (P) Ltd., Publishers
Published by New Age International (P) Ltd., Publishers
All rights reserved.
No part of this ebook may be reproduced in any form, by photostat, microfilm, xerography,
or any other means, or incorporated into any information retrieval system, electronic or
mechanical, without the written permission of the publisher. All inquiries should be
emailed to rights@newagepublishers.com
ISBN (13) : 978-81-224-2841-4
PUBLISHING FOR ONE WORLD
NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS
4835/24, Ansari Road, Daryaganj, New Delhi - 110002
Visit us at www.newagepublishers.com
Preface
Rivers have been the focus of human activity since the early civilizations. Even in modern times a
large number of activities of the engineers such as water supply, irrigation, water quality control,
power generation, flood control, river regulation, navigation and recreation are centered around
rivers. Hence considerable interest has been evinced in the society about various aspects of rivers
such as their formation, hydraulics and sediment transport, erosion and sedimentation, and effect of
natural and human interferences on rivers.
Books have been written on rivers by geologists, geomorphologists, hydraulic engineers,
hydrologists and geographers. Even though all of them have attempted to understand the behaviour
of rivers that have carved their channels through the material deposited by them, the emphasis of
each one of them is different from that of the other depending on his background, objectives of
writing the book and the targeted readership. Yet fewer attempts seem to have been made to
synthesize the contributions of these scientists into a coherent text that takes a balanced view of the
subject of river morphology. To fill this gap is the objective in writing this book. Hence, the text
covers history of fluvial hydraulics and geomorphology, drainage basin characteristics, erosion,
fluvial morphology, hydraulics of alluvial and gravel-bed rivers, river bed and channel changes,
fluvial palaeo hydrology, analytical and numerical modeling of fluvial processes, morphology of
some Indian rivers, rivers and environment, and data needs for morphological studies. The text can
be used for teaching a course on river morphology to graduate and undergraduate students in civil
engineering and geology, and as a reference material for engineers engaged in planning and
management of rivers.
My interest and involvement in the study of alluvial rivers and associated problems started with
late Prof. E.W. Lane, and Profs. M.L. Albertson, D.B. Simons and E.V. Richardson of the Colorado
State University, Fort Collins (U.S.A.). Over four decades of teaching and research in fluvial
hydraulics, and association with colleagues at the University of Roorkee (now I.I.T. Roorkee) India,
have helped me in looking at rivers in a much broader perspective. My association with Central
Water and Power Research Station at Pune over the last decade further enriched my association
with the rivers problems.
While preparing the manuscript of the book, valuable assistance has been rendered by my
former colleagues Profs. K.G. Ranga Raju and U.C. Kothyari who have gone through the draft of
the book and given valuable suggestions for its improvement; most of these have been incorporated.
I am indebted to Profs. Rajiv Sinha of I.I.T. Kanpur, Brahma Parkash and Pradeep Kumar of I.I.T.
Roorkee, and V.S. Kale of the University of Poona for making their publications available to me. I
vi
Preface
am thankful to Dr. Z.S. Tarapore and subsequent directors of CWPRS for allowing me to work at the
research station for the past thirteen years. I am particularly thankful to M.S. Shitole, Joint Director,
D.N. Deshmukh, J.D. Prayag, R.A. Oak, Hradaya Prakash, Pradeep Kumar, Mukund Deshpande,
Y.N. Karanjikar and others whose assistance has been valuable in finalizing the manuscript of the
book. Lastly, I am thankful to my wife Vidya and daughter Rashmi for the patience shown by them
while I was preparing the manuscript.
December 2005
R-1 Sankul Condominium
Near Deenanath Hospital
Evandavane, Pune-411004
R. J. Garde
List of Symbols
a1,a2,a3
A
Ab
Af
Au
coefficients/exponents
area of cross-section, area of basin
area at bankful stage, area corresponding to bed
area of fan
area of basin of order u
Au
Aw
b
B
BI
C
Ca
CD
CL
mean area of basin of order u
area of corresponding to wall
exponent
width of rectangular channel
Brice braiding index
Chezy’s coefficient, suspended sediment concentration at a point, climate index
reference suspended sediment concentration
drag coefficient
lift coefficient
CB , C
d*
d, d50
d16, d50, d84, d90
da
di
dmax
D
DC
Dd
Dmax
E
ER
f
bed material concentration in ppm by wt., total load concentration
dimensionless sediment size
median size of bed material, rain drop size
sediment size such that 16,50,84,90 percent material is finer than this size respectively
arithmetic mean size
any size fraction
maximum size of sediment
depth of flow (WD=A)
depth at the centre
drainage density
maximum depth
kinetic energy of storm
entrenchment ratio
Darcy-Weisbach resistance coefficient
viii
River Morphology
f¢
f ¢¢
f1
F
Fb
Fbo
FD
Fe
FL
friction factor corresponding to grain roughness
friction factor corresponding to form roughness
Lacey’s silt factor
stream frequency
Blench’s bed factor
value of Fb when bed load is negligible
drag force
erosion factor
lift force
Fr
Froude number (= U/ gD )
Fs
g
G
Ge
G¥
DG
hb
hs
H
i
I
I30
j
ks
K
Ko
l
L
ls
Lu
Blench’s side factor
gravitational acceleration
transport rate of any section
equilibrium transport rate
sediment transport rate at infinity
change in G
head loss in bend
saltation height
average height at ripple or dunes, bars; relief
index
intensity of rain fall
maximum 30 minute intensity during storm
index
roughness parameter
erodibility index, diffusion coefficient, wave number (= 2pD/L)
theoretical diffusion coefficient
length, distance, length of aggradation
average length of ripples or dunes, length of stream up to drainage divide
saltation length
total length of streams of order u
Lu
mean length of streams of order u
exponent
percent of silt-clay in perimeter, Kramer’s uniformity coefficient, dimensionless
velocity bed or water wave
meander belt
meander length
meander width (MB-W)
m
M
Mb
ML
MW
ix
List of Symbols
n
nb
ns
Nu
nw
pi
P
Pmax
q
qb
qBv
qc
qs
qT
qTv
index, exponent, Manning’s n
Manning’s n with respect to bed
Strickler’s n
number of streams of order u
Manning’s n with respect to wall
per cent
perimeter, annual rainfall
average monthly maximum precipitation
discharge per unit width
bed load transport rate in weight/width
volumetric bed load transport rate per unit width
critical water discharge per unit width
suspended load transport rate per unit width
total sediment transport rate in volume per unit width
total volumetric sediment transport rate per unit width
q*
dimensionless discharge (= q/ gd 3 )
q¢
Q, Qw
lateral inflow per unit length on both sides
water discharge
Q1
= Qb/d2 gd
Q2
= Qb S/d2 gd
Q3
= Qb/d2 gd S
Q2.33
Qb
QB
Qma
Qmaf
Qr
QS
QT
r
rc
ri, ro
R
RA
Rb
flood discharge of return period 2.33 years
bankful discharge
bed-load discharge
mean annual discharge
mean annual flood discharge
runoff rate per unit area
suspended load discharge
total sediment transport rate in weight or volume
radius
centre line radius of bend
inner and outer radius of bend
hydraulic radius, annul run off, run off parameter
area ratio
hydraulic radius corresponding to bed, bifurcation ratio
x
River Morphology
Rb¢, Rb¢¢
Re
RL
Rm
Rb with respect to grain and form roughness respectively
Reynolds number
length ratio of Horton
mean radius of meander bends
Ro*2
= Dg s d 3 /r f n 2
Rs
RW
R*
S, So
S¢
S¢¢
Sa
Sf
Si
SW
bifurcation ratio for slope
hydraulic radius corresponding to walls
particle Reynolds number u* d/v
slope, bed slope, slope at x = o
slope corresponding to grain roughness
slope corresponding to form roughness
annual erosion rate in cm (absolute)
energy slope, fan slope
sinuosity
water surface slope
S
average catchment slope
Su
SDR
SE
tp
average slope of segments of order u
sediment delivery ratio
super-elevation
time to peak
T
TE
u
number of years, also dimensionless excess shear {= ( t' - t 0 c ) / t 0 c }
trap efficiency of reservoirs
local velocity in x direction, order of stream
u¢2
ud
udcr
r.m.s. value of velocity function in x direction
velocity at the top of particle
critical velocity at particle level
u*
shear velocity (= t 0 / r f )
u*¢
u*¢¢
U
Ucr
Ug
UW
v
shear velocity corresponding to grain roughness
shear velocity corresponding to form roughness
average velocity
average critical velocity
average velocity of particle moving as bed load
average velocity of bed form or wave
local velocity in y direction
xi
List of Symbols
v¢2
vq
vmax
vr
Vcp
w
w¢ 2
W
Wav
Wb
Wo
Ws
x
y
Y1
z
Z
Zo
a
a1, a2, a3
b
gs, gf
d
d¢
Dgs
Îm
Îs
h
q
k
k0
l
m
n
x
r.m.s. value of velocity fluctuations in y direction
velocity in q direction
maximum velocity at any vertical
velocity in r direction
average velocity in the vertical
local velocity in z direction, mean width of rib
r.m.s. value of velocity fluctuations in z direction
average width (WD = A); weight of the particle
average unit weight over T years
bankful width
unit weight value of sediment
water surface width
distance in x direction, a dimensionless coefficient
distance from the wall
hydraulic mean depth (=A/Ws)
lateral distance from the origin,
actual slope of suspended sediment distribution curve, elevation of bed at given x and
t; side slope of channel (Z hor.: 1 vert.)
theoretical value of suspended distribution curve; bed elevation at x = 0
energy correction coefficient
exponents
es /em ratio of sediment transfer coefficient to the momentum transfer coefficient
specific weights of sediment and fluid
lag distance
thickness of laminar sub-layer
difference in specific weights of sediment and fluid
momentum transfer coefficient
sediment transfer coefficient
dimensionless distance in the vertical
angle
Karman constant (actual)
Karman constant (clear water)
porosity, wave length
dynamic viscosity of fluid
kinematic viscosity of fluid
sheltering coefficient
xii
rf
rs
s
sg
t
to
t0c
tr, tq
t*
t*c
j
jB, jS, jT
y
y¢
w
w0
River Morphology
mass density of fluid
mass density of sediment
arithmetic standard deviation
geometric standard deviation
shear stress
average shear stress on the bed
critical shear stress for sediment
components of shear stress on the bed along r and q direction
dimensionless shear stress
dimensionless critical shear stress
angle of repose
dimensionless bed-load, suspended load and total load transport rate respectively
= Dgsd35/t0
= Dgsd35/t0¢
fall velocity
fall velocity under ideal conditions
Subscripts and superscripts
Subscripts
*
dimensionless quantity
c
pertaining to critical condition
pertaining to section 1, 2.
1, 2
Superscripts
'
corresponding to grain roughness
''
corresponding to form roughness
Glossary of Some Terms in
River Morphology
Below is given meaning of some terms occurring in the text. (adapted from Easterbrook 1969)
Abrasion: wearing away of particle due to friction
Aggradation: rise in bed level of the stream over large length
Alluvium: unconsolidated sediment deposited by river; sediment deposited in river bed, floodplains,
lakes, alluvial fans etc.
Alluvial fan: cone shaped accumulation of debris or sediment deposited by the stream as it descends
from steep slope to a plain where the material deposits in the form of a fan
Avalanche: mass of snow sliding down the mountain
Avulsion: shifting of a river course
Base level: the level below which a land surface cannot be reduced by running water
Bed-load: material moved on or near the bed due to tractive force of the flow
Bed-forms: features developed on the bed of the river due to interaction between flowing water and
river bed sediments
Bed-load: material moved on or near the bed due to tractive force of the flow
Bed material load: material transported by the stream which has the stream bed or banks as its origin
Beheaded stream: lower portion of the stream from which water has been diverted due to stream piracy
Braided stream: a stream divided into a number of channels by island formation, which may join and
bifurcate again and again
Cirque: a deep steep walled recess in a mountain caused by erosion due to glaciers
Colluvium: unconsolidated deposits, usually at the foot hills or cliff, brought down by gravity
Creep: slow down-slope movement of rock fragments and soil
Crevasse: a fissure formed in glacial ice due to various strains
Degradation: general lowering of stream bed over large length due to deficiency of sediment load as
compared to its sediment transport capacity
Delta: a triangular shaped alluvial deposit formed when a stream enters lake or sea
Diastrophism: the process or processes by which the crust of the earth’s surface is deformed
xiv
River Morphology
Divide: a ridge between the streams; a line of separation between drainage basins
Drainage basin: the area drained by a system of rivers
Eolian: deposits which are due to transporting action of the wind
Ephemeral stream: the stream which flows only in direct response to precipitation; it receives no water
from ground water
Escarpment: relatively steep slope or cliff separating gently sloping tracts
Eustatic: pertaining to simultaneous world wide changes in sea level
Floodplain: relatively flat land strip on one or both sides of a stream built by sediment deposits during
flooding. It is sometimes called active flood plain
Fluvial: produced by the action of rivers
Geomorphic cycle: erosion cycle during which land forms are evolved which change from youth to
maturity to old, each of which is characterized by distinctive features
Geologic structure: it includes not only folding, faulting and uplift of the crust but also includes other
factors related to the physical and chemical characteristics of rocks, relative resistance to
weathering, dip, strike, jointing, stratification etc.
Glacial drift: material transported by glaciers
Glacial trough: U-shaped valley produced by glacial erosion
Hanging valley: a tributary valley whose floor is higher than that of the main valley at the junction due
to degradation of the main valley
Incised meander or entrenched meander: a deep sinuous valley cut by a rejuvenated stream
Levee: natural or man-made embankment above the general level of floodplain which confines the
stream channel
Loess: fine sized particles deposited by wind
Mass-wasting: the down-slope movement of rock debris under the influence of gravity
Meander scar: crescent-shaped cut in a valley side made by lateral planation of the outer part of a
meander
Meandering stream: a stream that follows sinuous or crooked path
Misfit stream: a stream whose meanders are either too small or too large, compared to valley width
Monadnock: a residual hill or mountain standing above a peneplain
Oxbow: a crescent-shaped lake formed in an abandoned river bend by a meander cutoff
Palaeosol: a buried soil
Peneplain: a landscape of low relief formed by long continued erosion
Periglacial: region beyond the margin of a glacier
Piracy: diversion of one stream by the other
Pleistocene: the last Ice Age
Glossary of Some Terms in River Morphology
xv
Regimes of flow: characteristics of bed and water surface produced by water flowing on a loose alluvial
bed
Rejuvenation: activation of erosion of a stream by uplift, climatic changes or change in base level
Relief: the difference between high and low points of the land surface
Saltation load: material bouncing along the bed or moved directly or indirectly by the impact of
bouncing particles
Scour: local lowering of the bed of the stream usually due to presence of a hydraulic structure in the
stream
Suspended load: that part of the sediment load carried by the stream that is kept in suspension by
turbulent fluctuations
Talus: an accumulation of loose rock mass at the base of a cliff
Terrace: a flat or gently sloping surface bordered by an escarpment, it is composed of alluvium or bed
rock. It is flooded so rarely that it does not grow by sediment deposition
Underfit stream: a stream which is too small for the valley through which it flows
This page
intentionally left
blank
Contents
Preface
v
List of Symbols
vii
Glossary
xiii
1. INTRODUCTION
1.1 Introduction
1.2 Some Problems in River Morphology
1.3 Historical Developments in Fluvial Hydraulics
1.4 Historical Developments in Geomorphology
1.5 Scope
References
1
1
2
4
7
9
10
2. DRAINAGE BASINS AND CHANNEL NETWORKS
2.1 Introduction
2.2 Drainage Patterns and Texture
2.3 Stream Order
2.4 Horton’s Laws of Stream Numbers and Stream Lengths
2.5 Areas of Drainage Basins
2.6 Basin Shape
2.7 Lithology
2.8 Vegetation
2.9 Drainage Densities and Stream Frequency
2.10 Relief Aspects
2.11 Drainage Basin Characteristics and Hydrology
2.12 Random Walk Model
2.13 Concluding Remarks
References
11
11
12
14
16
19
21
21
22
24
26
29
29
31
31
3. SOIL EROSION AND SEDIMENT YIELD
3.1 Introduction
3.2 Global Erosion Rates
34
34
35
xviii
River Morphology
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
Types of Erosion
Factors Affecting Erosion
Mechanics of Sheet Erosion
Equations for Predicting Soil Loss from Agricultural Lands
Measurement of Sediment Yield
Sediment Delivery Ratio
Process Based Modelling of Erosion
Erosion Rates from Indian Catchments
References
39
41
44
48
50
56
60
64
67
4. FLUVIAL MORPHOLOGY
4.1 Geomorphology and Fluvial Morphology
4.2 Geomorphic Cycle (or Cycle of Erosion)
4.3 Rejuvenation of Erosion Cycle
4.4 Criticism of Geomorphic Cycle
4.5 Noncyclic Concept of Landscape Evolution
4.6 Geological Time Scale
4.7 Glaciation
4.8 Fluvial Morphology
4.9 Topography Produced by Streams
4.10 Variables in River Morphology
4.11 Neotectonics and Earthquakes
References
71
71
72
74
74
76
77
80
82
94
104
105
107
5. HYDRAULICS OF ALLUVIAL STREAMS
5.1 Introduction
5.2 Incipient Motion
5.3 Modes of Sediment Transport
5.4 Bed-Forms in Unidirectional Flow
5.5 Resistance to Flow in Alluvial Streams
5.6 Bed-Load Transport
5.7 Suspended Load Transport
5.8 Total Load Transport
References
110
110
110
120
124
137
145
150
158
164
6. HYDRAULIC GEOMETRY AND PLAN FORMS OF ALLUVIAL RIVERS
6.1 Introduction
6.2 Stable Channels Carrying Sediment
6.3 Hydraulic Geometry of Alluvial Streams
6.4 Empirical Relationships for Hydraulic Geometry
169
169
170
176
180
xix
Contents
6.5
6.6
6.7
6.8
6.9
6.10
Non-Dimensional Relations for Hydraulic Geometry
Flow Around Bends with Rigid and Alluvial Beds
Shear Direction Near Curved Stream Bed and Bed Topography
Braided Rivers
Meandering
Stability Analysis and Criteria for Plan-Forms
References
186
189
194
198
202
212
223
7. GRAVEL-BED RIVERS
7.1 Introduction
7.2 Data for Gravel-Bed Rivers
7.3 Bed Material
7.4 Pavement
7.5 Hydraulic Geometry
7.6 Bed Features in Gravel-Bed Rivers
7.7 Resistance to Flow in Gravel-Bed Rivers
7.8 Sediment Transport in Gravel-Bed Rivers
References
229
229
230
230
233
233
237
241
246
253
8. FLUVIAL PALAEO HYDROLOGY
8.1 Introduction
8.2 Objectives of Palaeo Hydrologic Studies
8.3 Basis of Analysis
8.4 Climatic Changes: Past and Future
8.5 Palaeo Hydrologic Estimates of Discharge and Velocity
8.6 Palaeo Hydrologic Studies in India
8.7 Fluvial Palaeo Hydrologic Studies in India
References
256
256
257
258
260
262
267
271
273
9. BED LEVEL VARIATION IN STREAMS
9.1 Introduction
Degradation
9.2 Types of Degradation
9.3 Downstream Progression Degradation
9.4 Upstream Progression Degradation
9.5 Effects of Degradation
9.6 Prediction of Depth of Degradation
9.7 Control of Degradation
Local Scour Around Bridge Piers
9.8 Factors Affecting Scour
275
275
277
277
282
285
285
286
286
286
288
xx
River Morphology
9.9
9.10
9.11
9.12
9.13
9.14
9.15
9.16
9.17
9.18
Equations for Predicting Scour Depth
Verification of Equations for Scour Depth
Scour in Gravelly Material
Scour in Cohesive Soils
Protection of Scour Around Bridge Piers
Aggradation
Occurrence of Aggradation
Reservoir Sedimentation
Sediment Inflow and Trap Efficiency
Movement and Sediment Deposition in Reservoirs
Modeling of Sediment Deposition
Methods for Preserving and Restoring Reservoir Capacity
References
291
293
295
296
296
296
297
301
302
304
306
310
311
10. RIVER CHANNEL CHANGES
10.1 Introduction
10.2 Avulsion
10.3 Stream Capture
10.4 Erosion at Bends
10.5 Natural and Artificial Cut-Offs
10.6 Channel Pattern Changes
10.7 Longitudinal Grain Sorting
References
315
315
315
321
323
326
329
331
334
11. ANALYTICAL MODELS OF RIVER MORPHOLOGY
11.1 Introduction
11.2 Basic One-Dimensional Equations
11.3 Analysis of Water Surfaces and Bed Waves
11.4 Analytical Models
11.5 Some Applications of Linear Models
References
337
337
338
342
343
346
357
12. NUMERICAL MODELS FOR MORPHOLOGICAL STUDIES
12.1 Introduction
12.2 One-Dimensional Equations
12.3 Numerical Schemes of Solution
12.4 Classification of One-Dimensional Models
12.5 Convergence and Stability
12.6 Boundary Conditions
359
359
360
362
363
366
367
xxi
Contents
12.7
12.8
12.9
12.10
12.11
Channel Cross-Sections and Method of Erosion or Deposition
Modeling of Armouring
HEC – 6
CRARIMA
Applications of HEC – 6
References
368
369
372
376
378
383
13. MORPHOLOGY OF SOME INDIAN RIVERS
13.1 River Systems in North India
Kosi
13.2 Introduction
13.3 Catchment Characteristics and Geology
13.4 Geotectonics
13.5 Hydrology
13.6 Sediment Size and Slope
13.7 Morphology of the Kosi
13.8 Management of the Kosi
13.9 Present Day Problems of the Kosi
Brahmaputra
13.10 Introduction
13.11 River Characteristics
13.12 Seismicity and Landslides
13.13 Climate and Hydrology
13.14 Resistance to Flow and Sediment Transport
13.15 Plan-Forms
13.16 Flooding and Flood Protection
13.17 Drainage of Hinter Lands
13.18 River Bed Changes in Brahmaputra
13.19 Development Plans
13.20 Role of Dredging
References
386
386
388
388
391
392
393
395
396
398
402
402
402
407
410
411
414
416
419
420
422
423
424
424
14. RIVERS AND ENVIRONMENT
14.1 Introduction
14.2 Actions Causing Disturbance in Stream System and Their Impacts
14.3 Environmental Effects of Hydraulic Structures
14.4 Dams and Reservoirs
14.5 Water Quality in Reservoirs
14.6 Thermal and Hydro-Power Plants
427
427
429
429
430
433
436
xxii
River Morphology
14.7
14.8
14.9
14.10
Recreation
Stream Pollution
River Action Plans
Stream Restoration
References
15. DATA REQUIREMENTS FOR MORPHOLOGICAL STUDIES
15.1 Introduction
15.2 Maps, Air-Photos, Satellite Imageries
15.3 Lithology and Tectonics
15.4 Vegetal Cover
15.5 Geomorphic Map
15.6 Basin Characteristics and Morphometry
15.7 Sea-Level Fluctuations, Climatic and Other Changes
15.8 Cross-Sections, Longitudinal Section and Plan-Form
15.9 Bed and Bank Material
15.10 Hydrologic Data
15.11 Sediment Load Data
15.12 Stratigraphic Studies
15.13 Water Quality Related Data
15.14 Catalogue of Information on Morphological Studies
References
437
437
438
439
440
442
442
442
445
446
446
449
450
451
453
454
455
456
458
459
459
Appendix A
462
Author Index
463
Subject Index
473
C H A P T E R
1
Introduction
1.1
INTRODUCTION
A river carries water, sediment and solute from the drainage area to the sea and is thus of interest to
hydraulic engineers, geomorphologists and sedimentologists. This is important to engineers because
water is used for a variety of purposes by humanity; water courses are used as navigation channels, and
also erosion, transportation and deposition of sediment cause a number of problems in the river and in
the catchment that must be solved pragmatically. The direct effect of transportation of sediment and
water from the geologist’s and geomorphologist’s point of view is that the structure and form of the river
and adjoining areas are continually changed due to erosion and sedimentation. The rates of this change
are variable. While geologists and geomorphologists are concerned about changes taking place in 103 to
106 years or more, engineers are concerned with changes in a river during a relatively short period, say
10–20 years to probably 50–100 years. These channel changes can be in the form of size, shape,
composition of bed material, slope and plan-form. The engineer’s primary objective is to understand the
basic mechanisms of erosion, transportation and deposition of sediment by flow in the river and develop
qualitative and quantitative methods for prediction of river behaviour. The approach followed by
engineers is called fluvial hydraulics or river dynamics and this approach has been developed during the
past 200–300 years.
The other approach taken by geologists and geomorphologists is primarily qualitative even though,
in recent years some quantitative methods have been used. Morphology is defined as the science of
structure or form. Hence according to Worcester (1948) geomorphology is the science of landforms; it is
the interpretive description of the relief features of the earth. It thus describes the surface of the
lithosphere, explains its origin and interprets its history. To understand geomorphology one should
know in detail the composition and structure of the rocks of the earth and the processes which act on it.
Geomorphology recognises that the earth’s surface has changed in the past and is changing at present
due to internal and external processes. The internal processes are those, which originate within the earth
itself and include diastrophism and volcanism. External processes shaping the earth’s surface include
running water, weathering, waves and shore currents, glaciers, avalanches, and plant, animal and human
2
River Morphology
activities. It may be mentioned that most of the changes taking place in the earth’s surface are slow, even
though a few may be catastrophic. Conventional texts in geomorphology would deal in detail about the
internal and external processes which cause changes in the landform and then deal with the topography
produced by streams in humid regions, by winds in arid and semiarid regions, glaciers, shore processes,
ground water, volcanoes etc. Geomorphology is sometimes called physiography. This latter term, as
used particularly in Europe, includes climatology, meteorology, oceanography and mathematical
geography. Inasmuch as these are not addressed in this book, the term geomorphology is preferred to
physiography.
The word “fluvial” means produced by river action. Hence fluvial morphology means the science of
landforms as produced by river action. It can also be called river morphology; it is a branch of
geomorphology and it would deal with form of the streams and adjoining areas as brought about by
erosion, transportation and deposition of sediment by the running water. Both river morphology and
geomorphology are descriptive sciences based mainly on careful observation and interpretation of
natural phenomena. In the last century hydraulic engineers, hydrologists and geographers have also
made contributions to river morphology.
1.2
SOME PROBLEMS IN RIVER MORPHOLOGY
Since the dawn of civilization, mankind has used rivers for supporting and sustaining life. This has been
done by harnessing and controlling rivers for the benefit of people. In doing so the regime or stability of
the river is invariably disturbed. In discussing these problems caused by disturbance in the stability of
rivers, it is desirable to define what geomorphologists call a graded stream (Mackin 1948). A graded
stream, poised stream, balanced stream or a stream in equilibrium is defined by Mackin as the one in
which channel dimensions and slope are so adjusted over a period of time that it carries incoming
sediment load and water without appreciable erosion or deposition.
In geologic time frame no river can be graded because of the natural tendency of land mass and
rivers to erode gradually towards sea level. In a true dynamic sense also no river can be in true
equilibrium since the discharge changes continuously. However, it may be mentioned that the changes
related to geomorphic erosion are very slow and hence if one considers a time period of a few years to
some decades, most of the streams can be considered to be in equilibrium, except a few rivers such as the
Kosi, the Brahmaputra and the Yellow river which are truly unstable.
This equilibrium of the stream is disturbed by natural or man-made interferences in one or more of
the conditions that maintain the equilibrium. A few of these instances are discussed below.
i. When a large dam is constructed across the river to store water for irrigation, water supply,
flood control, generation of water power, navigation or recreation, the sediment transport
capacity upstream of the dam is reduced thereby causing aggradation in the main reservoir and
also in the tributaries on the upstream. This has many undesirable effects including depletion of
reservoir capacity and flooding of the upstream areas. In some cases such as the Imperial dam
on the Colorado river and Bhakra dam on the Sutlej in India sediment deposition has been
found to occur 70-80 km upstream of the dam.
The water released from the reservoir is almost sediment free and hence it picks up sediment
from the bed and banks of the stream causing degradation over long reaches of the stream. It
Introduction
ii.
iii.
iv.
v.
vi.
vii.
viii.
3
may also lead to channel widening or change in the planform of the river. Needless to
emphasise, degradation has many undesirable effects.
It has long been recognized that water transport is comparatively much cheaper than road or rail
transport and hence many streams such as the Danube, the Volga, the Rhine, the Mississippi,
the Yangtze, the Ganga, the Brahmaputra and the Nile have been used for navigation since
ancient times. Making the river navigable year around involves construction of dams, locks,
channel widening, channel straightening and channel contraction using spurs or jetties and
bank stabilization. It may also involve dredging and releasing additional water during low
flows. These changes affect the stability of the river and hence executions of such changes need
consideration from hydraulic and morphologic points of view.
Barrages, canal head works, sediment excluders and extractors in irrigation canals are
constructed for withdrawing relatively sediment free water for irrigation and water supply
purposes. This disturbs the equilibrium of the stream causing aggradation in the downstream
reaches. Similarly, aggradation takes place when rivers are used for dumping mining wastes
hoping that the stream will safely carry the dumped material downstream. However, the stream
can carry this excess load only with increased slope, which is achieved by aggradation. This
happened, for example, on the Yuba river in California (U.S.A.) during gold-rush period in the
latter half of the 19th century.
Similarly, when sand and gravel are mined from the river bed to meet the ever increasing
demand of the construction industry, the river downstream is found to degrade creating many
problems in that reach. Such degradation in the river causes similar effects in the tributaries and
sub-tributaries on the downstream side.
In order to have equitable distribution of water throughout the country large scale transfer of
water from one basin to the other is either contemplated or is being executed. This is likely to
disturb the equilibrium of the streams because the balance between water distribution and
sediment load distribution is likely to be disturbed.
Construction of flood control works such as embankments, reservoirs, channel straightening,
meander cut-offs and channel improvement also tend to disturb the equilibrium of the stream
and needs careful study.
Large scale dredging carried out along the river for navigation purposes also disturbs the
sediment balance and hence the stream equilibrium.
There are other less obvious factors that affect the stability of the stream, i.e., they affect
channel slope, plan-form, cross-section, and alignment. Some of these are the following:
Change in drainage basin characteristics due to change in land use such as deforestation,
reforestation, agricultural land development, road construction, urbanization, and building of
dams and check-dams disturb the river equilibrium by changing runoff and sediment load and
trigger changes in the channel characteristics.
Ruhe (1971) has described the case where straightening of a channel had repercussions
throughout the basin. In the Willow river (Crawford County, Iowa, USA) straightening led to
channel deepening and widening. In addition, new deeply entrenched gullies extended for
many kilometres up the tributary system and developed hill slides, disrupting agricultural lands
and public roads.
4
River Morphology
When urbanization takes place large-scale changes are induced in the catchment, its
hydrological characteristics and the sediment yield. Because of breaking of new grounds,
removing of vegetation, and use of construction equipment, the runoff and storm flow increases
and hence land erosion is accelerated. As a result the sediment load of the streams is often
increased dramatically. Wolman and Schick (1967) recorded up to 50,000 tons/km2/yr sediment
load at one site, as compared to 80-200 tons/km2/yr under normal conditions.
After the urban area is developed, infiltration is reduced and ground water levels may be
lowered. Untreated waste including sewage may be discharged into the streams causing
pollution, which in turn, may be lethal for the aquatic life and detrimental to the use of the water
in downstream reaches for drinking and recreational purposes. Due to urbanization there is an
encroachment on the flood plain and hence channels are confined resulting in higher flood
levels.
ix. Long term changes in the climate or hydrologic regime lead to significant changes in discharge,
type of sediment load and its quality which lead to change in channel dimensions, change in
river course and/or change in plan-form or meander characteristics. In extreme case the river
can cease to exist.
x. Earthquakes and active tectonic movement such as subsidence or upheaval are found to
influence the river stability.
Earthquake of magnitude greater than 4 on Richter scale can trigger a number of landslides through
out the region and earthquake of magnitude 8 or larger is capable of triggering tens of thousands of land
slides throughout the region that extends to more than 400 km from the fault (Wilson and Keefer 1985).
Heavy rainfall following such landslides can bring enormous amount of material in the stream and can
change its regime. Gee (1951) has reported the damage caused by 15 August 1950 earthquake in
Brahmaputra valley that was of 8.6 intensity on Richter scale. He found that 75 percent of hills in 4 3000
km2 area were mutilated by landslides. Small and large rivers became blocked by material that fell in
them and some even ceased to flow. Flood following the earthquake burst these dams and large quantity
of sediment and rock material was carried downstream. The rivers Dibang and Subansiri twice changed
their courses. The Brahmaputra got considerably silted up near Dibrugarh, and the bed level rose by a
few metres; it took several years for the excess sediment to move downstream.
In engineering literature little attention has been paid to active neo-tectonic movement as a factor
influencing river morphology. The rates of surficial deformation in certain region may vary from less
than 10 mm/yr to more than 10 mm/yr for seismic deformation. When considered over a few decades
such deformation can affect valley slope enough to affect the river morphology. If at a particular section
along the river there is uplift there is aggradation on upstream and downstream side while in between
there is degradation.
1.3
HISTORICAL DEVELOPMENTS IN FLUVIAL HYDRAULICS
(GARDE 1995)
Even though mankind has been living with sediment problems for the past several centuries, relatively
little progress was made in our knowledge about sediment movement up to 16th century A.D. Earlier
civilizations in the valleys of the Indus, the Tigris, the Euphrates, the Nile and the Yellow rivers were
5
Introduction
using canals for supplying water for irrigation through unlined channels. These canals either took off
from a weir or they were inundation canals. The common problem with these canals was silting and
hence frequent sediment removal was necessary. Locating the canals on the outer side of the bend of a
stream to reduce sediment entry into canal seems to have been practised. The Chinese had made
considerable progress in controlling large rivers, flood diversion, and similar other problems. The
Romans had made progress in water supply and sewerage. The Greeks knew about the fall velocity of
different sediment particles.
During 1600–1800 A.D. relatively more progress was made in understanding the physics of flow in
open channels. The basic equations governing the flow, viz. the continuity equation and the equations of
motion were developed during this period. d¢ Alembert (1717–1783) gave the differential equation for
continuity of flow which was generalized by Leonard Euler (1707–1783). It was also during this period
that the equations of motion, commonly known as Euler’s equations were established. The French
engineer Chezy (1718–1798) gave the resistance equation U = C RS where U is the average velocity,
R the hydraulic radius, S the channel slope and C is Chezy coefficient. Some basic ideas about river
hydraulics were initiated by Dominico Guglielmini (1655–1710) and Paul Frizi; both wrote books on
rivers. Du Buat (1734–1809) gave scouring velocities for materials of different sizes.
Much more progress was made during 19th century. Bouniceau, Grass, Lechalas, Suchier and
Deacon conducted studies and critical velocities for different sized materials were recommended.
Brahm showed that the critical velocity is proportional to (submerged particle weight)1/6. D.F. duBoys
(1847-1924) gave a simple model for bed-load transport and reached the conclusion that qB ~
to (to – toc) were qB is the rate of bed-load transport, and to and toc are the average bed shear stress and
critical shear stress for given size of bed material respectively. During this period two new resistance
equations, which are now commonly used, were proposed. These are
Darcy-Weisbach equation:
hf =
fL U2
D 2g
Manning’s equation
U=
1 2 / 3 1/ 2
R S
n
and
...(1.1)
Here hf is the head loss in length L of pipe diameter D, R is the hydraulic radius, S is the slope and
f and n are friction factor and Manning’s roughness coefficient respectively. In the latter half of 19th
century O. Fargue (1827–1910) who was closely associated with the developmental work of the river
Garonne, gave what are popularly known as “Fargue’s rules” of river behaviour. Finally equations of
motion for laminar flow and turbulent flow, commonly known as Navier-Stokes equations and Reynolds
equations were developed. Similarly Sternberg gave his law for the reduction of sediment size along the
river by the combined action of grinding and sorting. It was also at the fag end of 19th century that
Kennedy proposed the method for design of stable channels based on canal data from India that was
later modified by Lacey and others.
The first half of the twentieth century witnessed all round progress in fluvial hydraulics. G.K.
Gilbert (1843–1918) performed extensive laboratory experiments and studied modes of sediment
6
River Morphology
transport, and observed various bed-forms. Different investigators later used the hydraulic data
collected by Gilbert to study resistance and sediment transport in channels. As regards channel
resistance, Strickler analysed Swiss river data and for plane beds with coarse material proposed the
equation
n = d 150/ 6 /21
...(1.2)
where d50 is expressed in metres. Exner tried to explain formation of bed undulations using the
equations of motion. During this period a number of investigators conducted experiments in the
laboratory and developed empirical equations for critical shear stress (i.e., shear stress at which
sediment of a given size just starts moving) as a function of sediment size d and the difference in specific
weight between sediment and water Dgs. However, the credit for developing the rational criterion for
incipient motion that is based on sound principles of fluid mechanics goes to A.F. Shields (1908–1974).
Using sediments of different relative densities and sizes, he obtained a unique curve between toc/Dgs d
and t oc / r f .d / n . Here toc is critical shear stress for sediment of size d and n is the kinematic viscosity
of fluid. The term
t oc / r f = u*c is known as critical shear velocity.
In a similar manner a number of empirical equations were developed by different investigators
relating rate of bed-load transport to (to – toc), (q – qc) or (U – Uc) where q is the discharge per unit
width, U is the average velocity of flow, and quantities with subscript c refer to their values at incipient
motion conditions. However, these equations were of limited use. In 1948 E. Meyer-Peter and R. Müller
proposed an empirical equation for bed-load transport which is based on a wide range of sediment sizes
and flow conditions and which is used often even today. A. Kalinske and H.A. Einstein developed bedload equations using statistical nature of sediment movement.
Simultaneously progress was made in developing the theory of suspended sediment transport. The
German meteorologist Schmidt gave the equation
w o C + Îs
dC
=0
dy
...(1.3)
for distribution of suspended sediment in the vertical. Here C is the concentration of sediment of fall
velocity wo at a distance y from the bed and Îs is sediment transfer coefficient. This equation was
integrated independently by Rouse and by Ippen using equation for velocity distribution obtained by
Karman and Prandtl, and the integrated form was verified by Vanoni and Ismail. Simultaneously, bedload and suspended load samplers were developed and tested in Europe and U.S.A., which greatly
helped in collecting valuable data on sediment transport by rivers.
As regards the resistance to flow, Karman and Prandtl’s equations for velocity distribution for
turbulent flow in pipes were adapted to open channel flow and velocity distribution laws for
hydrodynamically smooth and rough surfaces were established. Einstein (1904–1963) suggested a
method for separating grain resistance and form resistance of bed undulations while Einstein and
Barbarossa proposed a method for predicting resistance to flow in alluvial streams.
Lastly on the basis of a large volume of data from stable mobile bed alluvial channels and building
on the advances made by Kennedy, Lindley, King and others, G. Lacey (1887–1980) proposed a method
of channel design according to which for given Q and bed material size, the channel depth, width and
Introduction
7
slope are uniquely fixed. Also data were collected about the geometry of alluvial rivers and equations
have been developed to predict width and depth as a function of bankful discharge and sediment size.
The last half of the twentieth century has seen considerable progress in fluvial hydraulics. The
characteristics of different bed-forms have been studied and criteria for their prediction established. A
number of equations have been developed to predict the resistance and sediment transport rates of
uniform and non-uniform sediments.
Kennedy, Engelund, Hansen and Fredsoe, have studied stability of mobile bed subjected to small
disturbances to explain the formation of dunes, antidunes and plane bed. Similarly, Hansen, Callander,
Parker, Hayaski and Ozaki, Engelund and Skovgaard and others have carried out stability analysis to
determine the conditions under which streams meander.
And finally, with the availability of high speed computers the equations of motion in alluvial
streams have been solved to develop methods of prediction of bed levels in unsteady non-uniform flows
such as silting of reservoirs, aggradation caused by increase in sediment load or decrease in discharge
and degradation caused by increase in flow. Simultaneously field data are being collected to test various
softwares developed for solving such problems. Also experimental data are being collected to study
some basic problems such as armouring and pickup function.
There has also seen considerable activity in understanding the hydraulics of gravel-bed rivers, their
hydraulic geometry and sediment transport and scour.
1.4
HISTORICAL DEVELOPMENTS IN GEOMORPHOLOGY
(Tinkler, 1985)
From the Greek writings one can extract three basic principles regarding the rational investigations of
landforms; these are (i) the concept of infinite time, (ii) reality of denudation i.e., loss of mass or
material from the landscape and (iii) acceptance of the principle of conservation of mass. Herodotus
(485– 425 B.C.) recognized the importance of yearly increments of silt and clay deposition by the Nile.
He also anticipated the idea of changing sea levels that is of great significance in geomorphology.
Aristotle (384 – 322 B.C.) thought that rainfall might produce a temporary torrent, but doubted that it
could maintain flow in a river. Strabo (54 B.C.–25 A.D.) noted examples of local sinking and rise of the
land. He also mentioned about the effect of ebbs and tides on the growth of delta. Both Strabo and
Seneca (B.C.– 65 A.D.) recognized the role played by volcanic activity and earthquakes on the
landforms.
During the many centuries that followed the decline of the Roman Empire, there was little or no
progress of scientific thought in Europe; however, some learning process continued in Arabia. During
941–982 A.D. there is reference to erosion and transportation of sediment by the streams and wind and
weathering in the four-volume tretise on discourses of the Brothers of Purity.
Little progress was made in Europe between the first century and beginning of the 16th century.
During the fifteenth, sixteenth and seventeenth centuries landforms were explained by the philosophy of
catastrophism, according to which the features of the earth were created as a result of violent
catastrophic actions. Leonardo da Vinci (1452–1519 A.D.) had very advanced ideas about geologic
thinking for his time. He recognized that streams cut the valleys and that the streams carried sediment
from one part of the earth and deposited at other places. The Frenchman Baffon (1707–1788) thought
8
River Morphology
that erosion by streams would eventually reduce the land to the sea level. He was also the first to suggest
that the age of the earth was not to be measured in terms of a few thousand years. Another Frenchman
Guetthard (1715–1786) also discussed about the degradation of mountains by streams and emphasized
that not all the material removed by the stream would immediately be carried to the sea but a part would
also deposit on the flood plains. The Swiss De Saussure (1740–1799) recognized the ability of glaciers
to carry out erosional work.
James Hutton (1726–1797) who entered the university at the age of 14 to study humanities was
more interested in chemistry and geology. Finally, he was educated as a physician. However, instead of
practising medicine he gradually switched over to agriculture and travelled through Southern England
during which time he developed his interest in geology. Hutton is known for propounding the concept
that “the present is the key to the past”, thus establishing the doctrine of uniformitarianism. His writings
clearly express the concept of a river system and its geomorphic significance. Some other important
concepts introduced by Hutton are:
i. A vast portion of the present rocks is composed of bodies, animals, vegetables and minerals of
more ancient formation.
ii. All present rocks are going to decay and their material going to deposit in the sea.
iii. The morphological process requires indefinitely long geological time.
iv. There is a conceptual possibility of relative change between land and sea levels leading to
upheaval.
Hutton’s friend John Playfair (1748–1819) who was Professor of Mathematics and Philosophy at
Edinburgh was in contact with Hutton, Joseph Black, and Adam Smith. After the death of Hutton in
1797 Playfair published “Illustrations of Huttonian Theory of Earth” in 1802 for he had realized how
confused and repetitive were the writings of Hutton; Playfair’s work was smaller, cheaper, and precise
with great clarity and beauty of expression. Playfair presented Hutton’s ideas and conclusions clearly.
Playfair also proclaimed the ability of glaciers to erode their valleys deeply.
Sir Charles Lyell (1797–1875) wrote a number of textbooks to spread the geologic knowledge. He
was somewhat doubtful about the immense ability of running water to carve the valleys. It was during
19th century that there was recognition of an ice age during which much of North Europe was covered
with ice sheets. Playfair had sensed the possibility of large boulders being transported by glaciers. Louis
Agassiz (1807-1873), Venetz of Switzerland in 1821, Bernardi of Germany in 1832 and Jean de
Charpentier in 1836 supported this concept of glaciation in Europe. In the later part of 19th century
books were written to describe the principles of landform development. These were by Peschel,
Richthofen and A. Penck.
The basic foundation of geomorphology was laid in America in the later half of 19th century by
Major J.W. Powell (1834-1902), G.K. Gilbert (1843-1918) and C.E. Dutton (1841-1912). Powell’s
studies of Unita Mountains emphasized the importance of geologic structure in the classification of
landforms. He also introduced the concept of the limiting level to which the land-level would reduce and
called it the base level. Col. George Greenwood earlier used this concept in Europe in 1857. Powell
recognized that the process of erosion, if carried undisturbed on land, would reduce it eventually to a
level little above sea level. He was able to correctly interpret that various unconformities in rocks in the
Grand Canyon, Colorado (U.S.A.) correspond to ancient periods of land erosion.
Introduction
9
G.K. Gilbert’s contribution in experimental work carried out in California has already been
described. He was a pioneer in studying hydraulic mining and its effect on stream morphology. His other
contributions include recognizing the importance of lateral planation by streams in the development of
valleys and his explanation of Henry Mountains of Utah (U.S.A.) as the result of erosion of intrusive
bodies. Dutton gave a penetrating analysis of individual landforms. Gilbert and Dutton are given credit
for initiating the concept of erosional unloading of the earth’s crest technically known as isostasy. W.M.
Davis (1850–1934) had greater impact on the development of geomorphology than any one else. Of all
the contributions to geomorphology, Davis is remembered for introducing the concept of geomorphic
cycle. According to this concept in the evolution of landscapes there is a systematic sequence that
enables one to recognize the stages of development of landforms. This sequence is called by him as
youth, maturity and old age. These landsforms are explainable in terms of differences in geologic
structure, geomorphic processes and the stage of development. In the development of the idea of
geomorphic cycle Davis had assumed that there is a relatively rapid uplift due to diastrophism which is
followed by a relatively long period of standstill which permits the erosion cycle to run its course. W.
Penck and his followers questioned Davis’ idea of geomorphic cycle during 1920’s and 30’s. In spite of
these objections the Davisian geomorphic cycle is still considered a reasonable model primarily because
of the absence of a plausible reasonable alternative.
Recent Contributions
Since the end of the Second World War a large number of aspects about river morphology have been or
are being studied. These include channel geometry, mathematical modelling, effect of neo-tectonics and
mass movements on channels, fluvial systems, experimental fluvial morphology, palaeo climatic and
palaeo hydrologic effects and gravel-bed rivers. Scientists working at U.S. Geological Survey have
studied short-term morphology of river channels; they include W.B. Langbein, L.B. Leopold and M.G.
Wolman. S.A. Schumm, M.P. Mosley and W.E. Weaver studied fluvial systems and performed
experiments in the laboratory to study river morphology. J.R.L. Allen from U.K. has done extensive
work on the character and classification of bed forms and sedimentary structures with respect to deltas,
meanders and floodplains. Many investigators including K.J. Gregory, J. Lewin, V.R. Baker and L.
Starkel have studied Palaeo climatic and palaeo hydrologic effects on river channels. Geographers in
U.K. have given impetus to the research in gravel-bed rivers and this work is now continued in Canada,
U.S.A. and New Zealand.
1.5
SCOPE
The text takes a balanced view of the contributions made by engineers, geologists, geomorphologists
and geographers to fluvial morphology.
Introduction, morphologic problems, and history of fluvial hydraulics and geomorphology are
discussed in the first chapter. The second chapter is devoted to the discussion about drainage basin and
channel networks. The third chapter deals with erosion from the catchment in humid regions where
erosion due to water action predominates. The fourth chapter presents basic concepts from
geomorphology such as geomorphic cycle, stages of landform and rivers and discusses the erosional and
depositional features developed by rivers. Chapter five deals with the hydraulics of alluvial rivers while
chapter six deals with the hydraulic geometry and plan-forms in alluvial streams. The seventh chapter
10
River Morphology
deals with gravel-bed rivers. Chapter eight deals with fluvial paleo hydrology while chapters nine and
ten are devoted to changes in bed level and plan-form. Chapters eleven and twelve deal with analytical
and numerical models used in studying the transient flows in rivers. Chapter thirteen is devoted to the
discussion of morphology of the Kosi and the Brahmaputra rivers in India. Chapter fourteen deals with
rivers and environment, and the fifteenth chapter dicusses the data requirements for morphological
studies.
References
Garde, R.J. (1995) History of Fluvial Hydraulics. New Age International (P) Ltd., Publishers, New Delhi.
Gee, G.P. (1951) The Assam Earthquake of 1950. Jour. Bombay Natural History Society, Vol. 50, pp. 629–638.
Mackin, J.H. (1948) Concept of the Graded River. Bul. Geological Society of America, Vol. 59, pp. 463–512.
Ouchi, S. (1985) Response of Alluvial Rivers to Slow Active Tectonic Movement. Bul. Geological Society of
America, Vol. 96, Apr, pp. 504–513.
Ruhe, R.V. (1971) Stream Region and Man’s Manipulation - in Environmental Geomorphology (Ed. D.R. Coates).
Publication in Geomorphology, State University of New York, Binghamton, U.S.A.
Thornbury, W.D. (1969) Principles of Geomorphology. John Wiley and Sons Inc., New York, 2nd Ed. Chapter 1.
Tinkler, K.J. (1985) A Short History of Geomorphology. Croom Helm (P) Ltd., U.K., 1st Edition.
Wilson, R.C. and Keefer, D.K. (1985) Predicting Areal Limits of Earthquake–Induced Land Sliding. In Evaluating
Earthquake Hazards in the Los Angeles Region (Ed. Ziony, J.I.). USGS Professional Paper 1360, pp 317–345
Wolman, M.G. and Schick A.P. (1967) Effects of Construction on Fluvial Sediment Urban and Sub-urban Areas of
Maryland. Water Resources Research, Vol. 3, pp. 451–464.
Worcester, P.G. (1948) A Text Book of Geomorphology. D. Van Nostrand Co. Inc., New York, U.S.A., 2nd Edition.
C H A P T E R
2
Drainage Basins and Channel
Networks
2.1
INTRODUCTION
Drainage basin is an area drained by the stream and its tributaries. It is bounded by a divide. Drainage
basin is also sometimes called watershed or catchment area. It can be thought of as an open system that
receives energy or input from the atmosphere and sun over the basin and loses energy or output through
the water and sediment mainly through the basin mouth or outlet (Strahler 1964). The present form of
any drainage basin is the result of the processes that have operated in the past on the material available
locally. These processes at the basin level are the precipitation and runoff, sediment yield and rate of
erosion. However, these processes in the past may not be the same in their relative importance as the
ones that operate in the drainage basin at present. The importance of studying the drainage basin
characteristics derives from the need of studying forms of channels and channel networks as they are
related to physical characteristics of the drainage basin, and also from the need of relating physical
characteristics of the basin to flow characteristics and sediment yield.
The drainage pattern is the arrangement and length of small, medium and large streams in the basin.
Two aspects of the development of drainage basins have been studied. In earlier years, the drainage
pattern development in relation to the structure and lithology of the underlying rocks was studied. This
was essentially qualitative in nature. In the recent times drainage patterns have been treated more as
geometric patterns and attempts have been made to derive relationships for them (Horton 1945). The
drainage pattern acquired at any time is the result of the combined effect of lithology, precipitation
pattern and climate, and their variation with respect to space and time. Since the sediment eroded from
the drainage basin along with water causing erosion, flows through the tributaries and the main stream,
the drainage net is intimately associated with the hydraulic geometry of the stream channels and their
longitudinal profile. As suggested by Schumm (1977) the drainage basin is primarily a sediment
production area where climate, diastrophism and land use act as the upstream controls.
12
River Morphology
Glock (1932) assumed that the drainage pattern is initiated on an essentially smooth plane due to the
uplift. According to him the drainage pattern goes through the following developmental stages:
initiation, elongation (headward growth of the main stream), elaboration (filling in of the previously
undissected areas by small tributaries), maximum extension (the maximum development of the drainage
pattern) and abstraction (loss of tributaries as the elevation is reduced through time). This sequence
takes a long time in geologic sense. During this sequence the sediment yield first increases to a
maximum and then decreases. However, such erosional development cannot be observed. Hence several
drainage basins in different stages of development are studied at a given time. Thus what is to be
observed in time domain is studied in space domain assuming the process to be ergodic.
The topographic characteristics of the drainage basin can be visualised either for the basin or for the
drainage network. The most important topographic characteristics for the basin are its area, length,
shape and relief. The corresponding characteristics for the drainage network are area tributary to stream
channels, drainage density, stream length, network shape or drainage pattern, and network relief.
2.2
DRAINAGE PATTERNS AND TEXTURE
Drainage pattern is the general arrangement of channels in a drainage basin. Drainage patterns reflect
the influence of such factors as initial slope, inequalities in rock hardness, structural controls, recent
diastrophism, and recent geomorphic and geologic history of the drainage basin. Because drainage
patterns are influenced by many factors, they are quite useful in the interpretation of geomorphic
features and their study represents one of the more practical approaches to the understanding of the
structural and lithologic controls on landform evolution. Looking at them in the most general manner,
one can classify drainage patterns into the following categories:
Figure 2.1 (a) shows dendritic or branch-like pattern that is probably the most common drainage
pattern. This is characterised by irregular branching of tributary streams in many directions and at
almost any angle usually less than 90o. Dendritic patterns develop on rocks of uniform resistance and
indicate a complete lack of structural control. This pattern is more likely to be found on nearly
horizontal sedimentary rocks or on areas of massive igneous rocks. They may also be seen on complex
metamorphosed rocks.
Trellised or lattice-like pattern shown in Fig. 2.1 (b) displays a system of sub-parallel streams,
usually along the strike of the rock formations or between parallel or nearly parallel topographic
features recently deposited by wind or ice.
Radial pattern shown in Fig. 2.1 (c) is usually found on the flanks of domes or volcanoes and
various other types of isolated conical and sub conical hills.
Parallel drainage pattern shown in Fig. 2.1 (d) is usually found in regions of pronounced slope or
structural controls that lead to regular spacing of parallel or near parallel streams.
Rectangular drainage pattern shown in Fig. 2.1 (e) has the main stream and its tributaries
displaying right-angled bends. This is common in areas where joints and faults intersect at right angle.
The streams are thus adjusted to the underlying structure.
Deranged drainage pattern, see Fig. 2.1 (f) indicates a complete lack of structural or bed rock
control. Here the preglacial drainage has been affected by glaciation and new drainage has not had
enough time to develop any significant degree of integration. It is marked by irregular stream courses
that flow into and out of lakes and swamps and have only a few short tributaries.
13
Drainage Basins and Channel Networks
a) Dendritic pattern
c) Radial or concentric pattern
b) Trellis
Trelliedororlattice
latticelike
likepattern
pattern
d) Parallel pattern
e) Rectangular pattern
f) Deranged pattern
g) Centripetal pattern
h) Highly violent pattern
Fig. 2.1 Various drainage pattern
Centripetal pattern shown in Fig. 2.1 (g) is encountered locally. Here the drainage lines converge
into a central depression. These are found on sinkholes, craters and other basin like depressions.
Highly violent pattern shown in Fig. 2.1 (h) is characteristic of areas of complex geology.
The complex drainage patterns observed in nature are a result of differing lithology, regional slopes,
presence of joints and faults, and geologic activities such as glaciation, volcanism and limestone
solution. Zernitz (1932), Howard (1967) and Thornbury (1969) have given full description of
commonly occurring drainage patterns and their interpretation.
Drainage Texture
An important geomorphic concept about the drainage pattern is the drainage texture by which one
means relative spacing of drainage lines. Drainage texture is commonly expressed as fine, medium or
coarse. Climate affects the drainage texture both directly and indirectly. The amount and type of
precipitation influence directly the quantity and character of runoff. In areas where the precipitation
14
River Morphology
occurs primarily in the form of thunder showers, a larger percentage of rainfall will result in runoff
immediately and hence, other factors remaining the same, there will be more surface drainage lines. The
climate affects the drainage texture indirectly by its control on the amount and types of vegetation
present which, in turn, influences the amount and rate of surface runoff. With similar conditions of
lithology and geologic structure, semiarid regions have finer drainage structure than humid regions,
even though major streams may be more widely spaced in semiarid than in humid regions. It is also
noticed that drainage lines are more numerous over impermeable materials than over permeable areas.
The initial relief also affects drainage structure; drainage lines develop in larger number upon an
irregular surface than on the one that lacks conspicuous relief.
Bad-land topography promotes fine drainage structure. Impermeable clays and shales, sparse
vegetation and existence of thundershowers are responsible for very fine drainage structure. Coarse
drainage structure is in particular found on sand and gravel outwash plains. Gravel plains have fewer
drainage lines on them than adjacent till plains underlain by relatively impermeable clay till.
The drainage structure can be qualitatively related to a parameter known as drainage density (see
section 2.9) first defined by Horton (1932) as total length of streams per unit of drainage area. Drainage
density varies from about 0.93 km/km2 on steep impervious areas to nearly zero for highly permeable
basins. It varies from about 2.0 to 0.60 km/km2 in humid regions. As indicated by Smith (1950) and
Strahler (1957), coarse drainage structure corresponds to drainage density less than 5.0 km/km2,
medium drainage structure to drainage density value between 5 and 15 km/km 2 and fine drainage
structure to drainage density between 15 and 150 km/km2.
2.3
STREAM ORDER
A stream net or river net is the interrelated drainage pattern formed by a set of streams in a certain area.
A junction is the point where two channels meet. A link is any unbroken stretch of the river between two
junctions; this is then known as the interior link. If it is between the source and first junction, it is called
the exterior link.
Quantitative analysis of the stream network really started with Horton (1945). This analysis has
been developed to facilitate comparison between different drainage basins, to help obtain relations
between various aspects of drainage patterns, and to define certain useful properties of drainage basins
in significant terms.
According to Horton (1945) the main stream in the river net should be denoted by the same order
number all the way from its mouth to its headwaters. Thus, at every junction where the order changes,
one of the lower order streams is renumbered to the higher order and the process repeated. Thus in Fig.
2.2 (a) the main stream is shown as the fourth order stream right back to its source. The third order
streams which are tributary to the fourth order stream are also extended back to their farthest source as
the third order streams and so on. The streams joining the third order stream are second order stream and
they can be extended backward. It can be immediately realized that a certain amount of subjectivity is
involved in the ordering of streams according to Horton’s method.
In Strahler’s (1952) system, see Fig. 2.2 (b), the headwater streams that receive no tributary are
called first order streams. Two first order streams unite to give a second order stream. Two second order
streams unite to give a third order stream and so on. When two streams of different order unite, the
combined stream retains the order of the higher order stream. A combination of two streams of lower
15
Drainage Basins and Channel Networks
a) Horton (1945)
b) Strahler (1952)
c) Scheideggar (1965)
d) Shreve (1967)
Fig. 2.2
Systems of stream ordering
order, say (u – 1), with a stream of given order u increases the order of the latter by one integer, that is
(u + 1). The result of this system of ordering is that it does not reflect any increments except
approximately doubling the discharge if one assumes that streams of the same order in the same
drainage basin carry approximately equal discharges.
Scheideggar (1965) defines the order x after two streams of order u1 and u2 by
d
x = log2 2 u1 ´ 2 u2
i
...(2.1)
His system of ordering is shown in Fig. 2.2 (c).
Shreve (1967) has suggested a system of ordering streams in which, the order numbers of two
streams contributing to the junction are added to arrive at the order number below the junction, see Fig.
2.2 (d). Thus each exterior link or head tributary has a magnitude 1. If links of magnitude u1 and u2 join,
then the resultant downstream link has the order (u1 + u2). If we assume that the first order streams are
approximately of the same magnitude and that the discharge is neither lost nor gained from any source
other than the tributaries (which is not completely true) then Shreve number is roughly proportional to
the discharge in the segment of the stream. It may be mentioned that Strahler’s system of ordering has
been more commonly used than the other methods and the same is utilised herein. The analysis of
drainage basin considering stream orders is often known as morphometry.
The morphometric analysis of drainage basins carried out by Horton (1945), Strahler (1952),
Rzhanitsyn (1960) and others is based on the premise that for the given conditions of lithology, climate,
rainfall, and other relevant parameters in the basin, the river net, the slope and the surface relief tend to
reach a steady state in which the morphology is adjusted to transmit the sediment and excess flow
produced. If there are any major climatic or hydrologic changes in the region, the steady state
16
River Morphology
morphologic characteristics will naturally be modified. In other words, the river net is the definite
response of the drainage basin to the complex physical processes taking place over the drainage basin.
2.4
HORTON’S LAWS OF STREAM NUMBERS AND STREAM LENGTHS
Consider a river net in a drainage basin in which the highest order of the stream is K. Let u represent the
order of any segment and Nu represent the number of streams of the order u. It has been found by Horton
and other investigators that if log (Nu) is plotted against u for any river net the data fall on a single
straight line with Nu decreasing for increasing u, see Fig. 2.3. Hence the relation between Nu and u can
be expressed as
4
- Daddy's creek
- Alleghney river
- Sher river (India)
3
log Nu
Rb = 4.34
2
Rb = 4.12
1
Rb = 4.07
0
0
1
2
3
u
4
5
6
7
Fig. 2.3 Variation of log Nu with u (Horton’s ordering system)
Also
or
log Nu = a – bu
log N(u + 1) = a – b (u + 1)
log
Nu
= b from which one gets
N( u +1)
...(2.2)
...(2.3)
Nu
= 10b = Rb
N( u +1)
Here a and b are constants. The constant Rb is known as the bifurcation ratio. It is defined as the
number of streams of order u divided by number of streams of order (u – 1). Since Nk = 1
N(k – 1)/Nk = Rb or N(k – 1) = Rb
N(k – 2) = N(k – 1) ´ Rb = Rb2
Nu = Rb(k – u)
...(2.4)
17
Drainage Basins and Channel Networks
It may be mentioned that for small drainage basins the relation between log Nu and u has been found
to be slightly concave upwards thus deviating from the linear relationship expressed by Eq. (2.2);
however the deviation becomes smaller as u increases, see Smart (1967). Horton (1945) found that the
value of Rb varied from 2 to 4 for the river nets investigated by him, whereas Strahler (1964) found this
range to be from 3 to 5 for the drainage basins in which geologic structures do not distort the drainage
pattern. Mittal et al. (1974) found Rb to lie between 4.4 and 5.0 for sixty-two third order drainage basins
in Garhwal, Himalaya (India), where lithologic conditions were represented by limestones, quartzites,
phyllites, sand-shales and alluvium. This value ranged between 3.5 and 4.5 for sixth and seventh order
sub basins of the Narmada, see NIH (1995).
It has been found by some investigators that the bifurcation ratio Rb is not independent of the order
of stream, and hence in a particular drainage basin Rb should be calculated between streams of 1 order
lag with those of 2 order lag in order to reduce the difficulties introduced by order and the size of area
analysed. Schumm (1956) recommends the use of weighted Rb designated as WRb
WRb =
d
S Rb ( u , u + 1) Nu + N u + 1
SN
i
where Nu is the number of streams of u th order.
The principle embodied in Eqs. (2.2) and (2.3) is commonly known as Horton’s Law of Stream
Numbers which states that
“The number of streams of different order in a given drainage basin tends closely to
approximate an inverse geometric series in which the first term is unity and the ratio is the
bifurcation ratio”. (Horton 1945).
The fact that the bifurcation ratio remains fairly constant is interpreted to mean that the drainage
basins in homogenous materials tend to show geometric similarity. Strahler (1964) has emphasized that
there is a close relationship between the shape of the drainage basin, bifurcation ratio and the shape of
the unit hydrograph. A very elongated basin will have a very high value of Rb (of the order of 15 or so)
and will give a sustained unit graph with low peak. On the other hand a near circular drainage basin will
have a low Rb value (around 2.4 or so) and would yield a unit graph with high peak and small base
length.
It can be seen from Eq. (2.4) that
n
åN
u
i =1
= RbK - 1 + RbK - 2 + RbK - 3
d
U|
||
+ ..... + 1V
||
|W
= N1 + N2 + N3 + ..... N k
i
= RbK - 1 ( Rb - 1 ) .....
...(2.5)
If one measures the total length of streams of a given order u in a drainage basin and designates it Lu,
the mean length of the streams of order u, Lu will be
18
10
5
10
6
10
4
10
5
10
3
10
4
10
2
10
3
10
1
10
2
10
0
10
1
10
–1
10
0
10
–2
}u
Nu and }u km
2
Nu
øu
Sessquehanna
river basin (U.S.A.)
6
Fig. 2.4
2
4
6
u Order
8
10
10
Lukm
River Morphology
–1
Variation of Nu, Au , Lu with u
Lu = Lu/Nu
...(2.6)
If in any given basin log Lu is plotted against u one gets log Lu increasing linearly with u, thus
yielding a straight line, see Fig. 2.4. This means that
Lu / Lu – 1 = constant RL
...(2.7)
where RL is known as the Horton’s length ratio. It follows from Eq. (2.7) that
L2 = L1 RL, L3 = L2 RL = L1 RL2
and
...(2.8)
Lu = L1 RLu - 1
The principle embodied in Eqs. (2.7) and (2.8) is known as Horton’s Second Law of Stream
Lengths, which states that
“The average lengths of the streams of each of the different orders in a drainage basin tend
closely to approximate a direct geometric series in which the first term is the average length of
streams of first order”. (Horton 1945).
Morisawa (1962) has found that RL values ranged from 2 to 3 in Applachian Plateau Province
(U.S.A.), while its value ranged between 1.50 and 2.40 for four sub basins of Narmada.
These two laws of drainage composition have been substantiated by several investigators
irrespective of whether Horton’s or Strahler’s method of stream ordering is used. They include Chorely
(1957), Morisawa (1962) and Gregory (1966).
The total length of streams of order u will be Lu Nu. Substituting the value of Nu from Eq. (2.4) and
using Eq. (2.8) one gets
19
Drainage Basins and Channel Networks
Lu = Total length of streams of order u = Nu Lu
= L1 RL(u – 1) Rb(k – u)
Hence total length of the streams of Kth order basin will be
K
åL
u =
L1 Rbk - 1 + L1 RL RbK - 2 + L1 RL2 RbK - 3 + ... L1 RLK Rb- 2 + L1 RLK - 1
1
R| R F R I F R I
S|1 + R + GH R JK + GH R JK
T
2
=
L1 RbK -1
L
L
L
b
b
b
3
FR I
+ ... + G J
HR K
K -2
L
b
FR I
+G J
HR K
L
b
K -1
U|
V|
W
...(2.9)
Substituting RL/Rb = RLB one can simplify the above equation to the form
K
å
1
K -1
Lu = L1 Rb
dR
dR
K
LBI
K
LB
i
- 1i
-1
...(2.9)
Another length parameter introduced by Horton (1945) is the length of overland flow Lo which is
the length of flow path, projected to the horizontal, of non channel flow from the point of drainage
divide to the point on the adjacent stream channel. Length of overland flow is one of the most important
variables affecting the hydrologic and physiographic development of the drainage basin. During
evolution of the drainage basin Lo is approximately equal to half the reciprocal of the drainage density.
2.5
AREAS OF DRAINAGE BASINS
Basin area is hydrologically important because it directly affects the size of the storm hydrograph, and
the magnitude of mean and peak flows. Amount of sediment eroded from the drainage basin is also
related to the basin area. In fact, since almost every watershed characteristic is correlated with area, the
area is the most important parameter in the description of form and processes of the drainage basin.
The area Au of a basin of given order u is defined as the total area projected upon a horizontal plane,
which contributes overland flow to the channel segment of a given order and all the tributaries of the
lower order. Thus area of the basin of the third order, A3 will be the sum of areas of first and second order
basins, plus all additional areas, known as inter-basin areas, contributing directly to channels of order
higher than the first. Thus
A2 = S N1 A1 + S N1 Ao2
where Ao2 is the inter-basin area contributing to second order segments. In general one can write
Au = {S N1 A1 + SN1 A2 + SN1 A3 + ... S N1 Au – 1}
...(2.10)
+ {SN1 Ao1 + S N1 Ao2 + ... SN1 Aou }
Law of areas has been inferred by Horton (1945) and stated by Schumm (1956), according to which
the mean basin areas of stream of each order tend closely to approximate a direct geometric sequence in
which the first term is the mean area of the first order basin. Hence if log Au is plotted against u, a
straight line is obtained as shown in Fig. 2.4. From this one can deduce that
20
River Morphology
Au = A1 RAu- 1
...(2.11)
where Au is the mean area of basin of order u, A1 is mean area of first order basins, and RA is known as
the area ratio.
Some attempts have been made to relate stream lengths to basin areas. It is argued that according to
the laws of stream lengths and basin areas, both these parameters are related to the stream order. Hence
a relation of the type L ~ An should relate basin length to the basin area. On the basis of over 300
measurements made by Langbein (1947), Hack (1957) found that this relation is of the type
L = 1.16 A0.60
...(2.12)
L km
where L is the stream length in km measured up to the drainage divide and A is basin area in km2. For
geometrically similar basins one would expect L ~ A0.50. Since according to Hack L ~ A0.60, it means that
drainage basin changes its shape in the downstream direction; it tends to become longer and narrower as
it changes. Figure 2.5 shows variation of L with A for different regions as well as the enveloping curves.
10
3
10
2
10
1
10
0
10
–1
1.
2.
3.
4.
5.
6.
7.
8.
W. Malaysia
Deron
W. USA
Uganda
Wales
Australia
Nebraska (USA)
E. USA
Envelope curves
10
3
10
2
10
1
10
0
10
1
10
2
10
3
2
A km
Fig. 2.5 Variation of total stream length with basin area
Müller (see Gregory and Walling (1976)) defines three lengths to describe the stream length. These
are the length of the stream channel Le, the length of valley Lv and shortest distance between the mouth
and the source of stream Lm.
Hack has also shown that
Au = A1 RAu - 1
u
( RLB
- 1)
( RLB - 1)
...(2.13)
21
Drainage Basins and Channel Networks
2.6
BASIN SHAPE
Basin shape affects the hydrologic characteristics of the basin, namely hydrograph shape. As mentioned
earlier a long narrow basin having high bifurcation ratio gives a low but sustained peak whereas round
basins with low bifurcation ratio would give a sharply peaked hydrograph. Several shape factors have
been suggested to describe the shape of the basins, some of which are listed below:
Table 2.1
S.No.
Notation
Definition
Form factors for basins
Reference
Form factor Rf Basin area Au/(Basin
length)2
Circularity
Basin area Au/Area of circle
ratio C
with the same perimeter
Horton
(1932)
Miller
(1953)
3.
Elongation
ratio E
Schumm
(1956)
4.
Lamniscate
ratio K
1.
2.
(Diameter of a circle with
area of basin)/(Maximum
basin length)
(Basin length)2/4 (basin
area)
Chorely et al.
(1957)
Comments
Reciprocal of this is used by Corps of
Engineers (U.S.A.) in Hydrograph analysis
C = 0.6 to 0.7 for homogeneous basins of 1st and
2nd order. For non-homogenous basin C = 0.4 to
0.50
E = 0.6 to 1.0; lower value for areas with strong
relief and steep slope
—
The circularity and elongation ratios can be of practical utility in predicting certain hydrological
characteristics of the drainage basin. Elongation ratio has been used in the studies of sediment eroded
from the basins. In general drainage basins tend to become more elongated with strong relief and steep
slopes. Available data indicate that the drainage basin gets relatively elongated as its size increases.
2.7
LITHOLOGY
The lithology and rock structure in the basin play an important role in influencing the hydrologic,
erosional and other characteristics of the basin. The rock type and soil mantle affect the infiltration
capacity. Permeable soil or rock allows water to percolate into the ground which later may be discharged
into the stream. Hence the surface runoff is reduced. Basins with bed rock or soil which is relatively
impermeable produce high volume of surface runoff and very little ground water flow.
Rock type governs the character and rate weathering, the weathering products obtained and hence
the nature of sediment and solutes supplied to the stream. The nature and effect of vegetation is also
partly governed by rock type, which in turn governs the sediment supply. Hence sediment load vs water
discharge relationship would depend on rock type. Similarly alluvial fan area vs drainage area
relationship also depends on rock type.
The rock type also influences the shape of the valley and stream because it controls resistance to
erosion and also the runoff as discussed above. Morisawa (1968) found that valleys cut in
unconsolidated beach sands and gravels were V-shaped, while those cut in silts and muds were flat
bottomed. In the same manner Brush and Hack have found that the correlation between channel gradient
S and its length L depends on the lithology and rock type. If S = a Lb the slope decreased with increase
in L for all the rock types i.e., b was negative, but the rate of decrease varied with rock type. Lastly,
22
River Morphology
lithology and rock structure also affect the morphometry and geometry of the drainage basins. A flatlying resistant bed will cause increase in stream length and decrease in stream slope. Where the
sediments are folded, stream cutting across resistant strata will be short and steep with small drainage
areas. Similarly drainage pattern is also influenced by lithology. For flat and homogenous rock surface
drainage net tends to form at random and streams flowing in all directions i.e. dendritic pattern. In the
case of jointed or folded rocks streams tend to erode the channel along a weakness. If joints are the
weakness, their orientation determines the stream pattern. In tilted or folded strata streams tend to
develop along linear bands of outcropping weak rock. Therefore, a full understanding of lithology is
essential for the study of river morphology.
2.8
VEGETATION
Vegetation including grass, shrubs, and forests plays an important role in the hydrologic cycle and
catchment erosion. Hence, its effect is of prime importance to those working on river morphology and
river dynamics. Studies by various investigators have shown that water and sediment yield, flood peaks
and the time of their occurrence, and the velocity of travel of the flow peak are strongly influenced by
the nature and extent of vegetation.
When the pressure on the land, because of increase in the population and human activity, was not
heavy, there were marginal changes in the forests, and minor disturbances in their coverage were soon
made up naturally. However, because of increase in the population and industrial growth and
consequent increase in food, space and energy requirements of nations, there has been indiscriminate
deforestation in some parts of the world. In the early eighties, most of the tropical forests were estimated
as being altered by man at around 12 million hectares per year, see Bruijnzeel (1990). Many
investigators consider this as an underestimate. Deforestation includes cutting of trees for fuel, timber
and other industrial uses, deforestation caused by great and small forest fires, shifting of zoom
cultivation, construction activity related to logging such as creation of access roads, skid tracks and
landings, clearing areas for habitation and developing industry, surface mining and similar activities.
Generally speaking, a forest subjected to some of the above mentioned disturbances may recover to its
previous state if left alone for a sufficiently long period. However, this is not the case when the forest is
converted to permanent agriculture such as grazing, cropping or extractive tree crops.
The effects of partial or complete removal of forest on climate, water yield and its seasonal
distribution and on sediment production have been studied by many investigators. Below are given the
salient features of these effects, (see Bruijnzeel (1990)).
Rainfall and Water Yield
1. Tropical forests reflect about 12 percent of the incident short wave radiation while agricultural
crops reflect 15 to 20 percent. Hence a different partitioning of energy between warming up of
the boundary layer and evaporation is to be expected when tropical forests are converted to
grass lands or agricultural crops.
2. As a result of extensive studies during the past four decades, it is found that the extent of forests
has definite effect on rainfall.
3. It has been found that in humid tropics removal of natural forests cover may result in
considerable initial increase in water yield, the increase depending on the amount of rain
received.
Drainage Basins and Channel Networks
23
4. The initial increase in water yield, after removal of the forest cover, gradually decreases with
the passage of years and may return to pre cut flows in about eight years in case of natural
regrowth.
Stream Flow Regime
1. Geological, topographical and vegetative cover play an important role on floods and hence
isolation of effect of vegetation becomes rather difficult.
2. If geology is favourable, cutting vegetation shifts infiltration flow to surface flow and therefore
peaks will enhance.
3. Also in the absence of retarding effect, the peak is likely to occur earlier.
4. Change in evapo-transpiration and infiltration opportunities associated with change in forest
cover will govern the dry season flows. If infiltration opportunities after forest removal have
decreased to the extent that the increase in amount of water leaving the area as stream flow
exceeds the gain in base flow associated with reduced evapo-transpiration, then the dry season
flow is reduced. If on the other hand, the surface infiltration characteristics are maintained over
most of the area by deliberate soil conservation practices or by some other method, then the
effect of reduced evapo-transpiration after clearing will show up as increased base flow or dry
seasonal flow.
Sediment Production and Yield
When dealing with the effect of change in forest cover on erosion and sedimentation it is helpful to
distinguish between surface erosion (i.e., splash, sheet and rill erosion), gully erosion, and mass
movements because the ability of vegetation cover to control the various forms of erosion is rather
different. It is well known that only part of the material eroded from hill side will enter drainage
network, the rest may move into temporary storage such as depressions, foot slopes, small alluvial fans
or in small tributaries, behind debris basins or flood plains. The stored material may be released during
large storms or caught by vegetation, or form stable topographic elements. Since these storage
opportunities tend to increase with increase in area, sediment delivery ratio, which is defined as the
amount of sediment passing a given section during a given time divided by amount of sediment eroded
from upstream in the same time, is found to decrease with increase in catchment area. It may be years
before sediment stored in temporary storages is released and its effect felt several kilometers
downstream from the region of erosion. Sediment yield, which is rate of sediment passing a given
section, is discussed in detail, in Chapter–III. This was found to be the case on the Brahmaputra river in
Assam (India) after 1950 strong earthquake, see Goswami (1985). During August 1950 earthquake,
apparently one of the most severe ever recorded, massive landslides occurred which temporarily
blocked many major tributaries. Bursting of these dams after several days not only produced devastating
floods downstream, but also brought down enormous volume of sediment thereby raising the beds of
these rivers considerably. The mean annual suspended load and water discharge between 1955–1963
were 750 000 m3 and 16 530 m3/s as against 130 000 m3 and 14 850 m3/s during 1969–1976. Also
during the former period the river reach upstream of Pandu was aggrading, whilst it was degrading
during 1969–1976.
24
River Morphology
Surface and Gully Erosion
Studies by Wiersum (1984) have indicated that erosion is minimum (0.10 to 0.60 tonnes/km 2/year) in
those areas where soil surface is adequately protected by a well developed litter and herb layer. When
this layer is destroyed or removed, erosion rates rise dramatically to 500 to 5000 tonnes/km2/year. Hence
protection from tree stands lays not so much in the ability of tree canopy to break the power of rain drops
but rather in developing and maintaining a litter layer. When rills are formed and they grow into gullies,
their lateral and head ward extension through scouring, undercutting and subsequent collapse of walls
cause a large increase in sediment production.
Mass Wasting
Some of the highest reported natural erosion rates from rain-forested areas have been related to intense
mass wasting under conditions of steep topography, tectonic activity, and intense rainfall. In mass
wasting, steep slopes in combination with geological and climatic factors are more important than land
use. Prasad (1975) after ten years of observations of seismic activity, rainfall and occurrence of land
slides in eastern Nepal concluded that intense precipitation and associated saturation of soil were
apparently more important than seismic shocks. Starkel (1972) has opined that the role of vegetation in
preventing shallow slope failures (less than 3 m) is very important; Manandhar and Khanal (1988) have
confirmed this in south of Khatmandu. As regards the influence of tall vegetation on slope stability, the
net effect is considered positive, the major factor being the mechanical reinforcement of the soil by tree
roots.
2.9
DRAINAGE DENSITIES AND STREAM FREQUENCY
Drainage density is defined as the total length of streams in a basin divided by its area. Hence the
drainage density Dd is given by
Dd =
å å
K
N
1
1
Lu/A
...(2.14)
and will have dimension of km–1. Here N is the number of streams of order u and K is the order of the
river basin. Greater drainage density means more channels per unit area or more closeness of channel
spacing. Drainage density varies over a wide range from 2 km–1 to 800 km–1 or even more depending on
the character of subsoil material, vegetation and relief. Climate is equally important in determining the
drainage density since it controls discharge and indirectly the vegetation. Table 2.2 illustrates the effect
of these factors, namely lithology, climate and vegetation on the drainage density.
Drainage density does not seem to change regularly with stream order within basins. Investigations
by Morisawa (1968) indicate that drainage density of the whole basin tends to approximate the mean
drainage density of the 1st order basins in the watershed. Langbein appreciated the significance of
drainage density as a factor determining the time of travel of water. Since water and sediment flow
through the stream channels, annual sediment yield from the catchment is found to increase with
increase in drainage as sediment yield ~ Dd0.1 (Garde and Kothyari 1987). Osborn has found that mean
annual flood Q2.33 is proportional to Dd2.0 . Gregory and Walling (1976) have plotted total stream length
against drainage area for a large number of catchments and found that L ~ A0.378 up to 100 km2 area and
beyond that the exponent of A somewhat increases, see Fig. 2.5. Hence one can conclude that L/A i.e. Dd
would decrease as A increases.
25
Drainage Basins and Channel Networks
Table 2.2 Effect of lithology, climate and vegetation on drainage density
[Adapted from Selby 1967, NIH 1993]
Location
Lithology
Climate
Vegetation
Humid,
Continental
Deciduous forest
D d km–1
Pennsilvania
(U.S.A.)
Horizontal resistant
sand stone
2–2.5
Colorado (U.S.A.)
Granite, gneiss and schist
Humid, montane
Montane forest
2.5–5.6
Maryland (U.S.A.)
Shale
Humid, Continental
Coniferous and
deciduous forest
4.4
Volcanic Plateau
(New Zealand)
Pumice and ignimbrite
Temperate,
maritime
Scrub and grass
5.4
South Auckland
(New Zealand)
Graywacke overlain
by volcanic ash
Temperate,
maritime
Formerly green forest,
now pasture grass
15.7
South Dakota
(U.S.A.)
Clay and shale
Semiarid
Sparse bunch grasses
or none
50–160
Arizona (U.S.A.)
Horizontally bedded shale
Hot desert
None
106–220
New Jersey (U.S.A.)
Clay and sand fill
Humid continental
None
344-825
Bihar (India)
Alluvium to Granite,
Gneiss
Humid
59 per cent agriculture
and 41 percent forest etc.
0.377
Obtaining drainage density can be a tricky problem because a lot would depend on the scale of the
map used. Hence uniform scale needs to be used in the comparison of drainage densities of different
basins. Carlson and Langbein (1960) have recommended a more rapid method of estimation of the
drainage density. Draw a line of known length L on the contour map and count the number of streams n
which intersect this line. A minimum of 50 contour crossings is advocated to provide an adequate
sample. Then drainage density equals 1.41 n/L.
Strahler (1964) considered the drainage density Dd to be a variable dependent on runoff rate per unit
area Qr, erosion proportionately factor K (which is mass rate of erosion per unit area per unit eroding
force), relief H, mass density of fluid rf, dynamic viscosity m, and g.
\
Dd = f (Qr, K H, rf , m, g)
The above equation can be written in dimensionless form as
FG
H
Dd H = f KQr ,
Qr r f H Qr2
,
gH
m
IJ
K
The first term (Dd H) is known as the ruggedness number, (Qr K) is known as Horton number,
which expresses the relative intensity of erosion processes in the drainage basin, (Qr rf H/m) is Reynolds
number and (Qr2/g H) is Froude number.
Schumm (1956) has introduced a parameter called constant of channel maintenance C that
represents the area in km2 necessary to develop and maintain one kilometer of drainage channel. If Au is
plotted against Su1 Lu it is found that the two are related linearly as
26
River Morphology
Au = a + C Su1 Lu
...(2.15)
C being the constant of channel maintenance.
A basin with relatively impermeable strata requires a smaller drainage area to maintain a permanent
channel as compared to the basin with permeable strata. The constant of channel maintenance is taken as
a measure of erodibility of the basin.
Horton (1932) defines the stream frequency F as the number of stream segments of all orders within
a given basin of order K, divided by the basin area; or
F = Su1 Nu /Ak
...(2.16)
From the analysis of worldwide data Peltier (1962) found that for areas of comparable average
slope, stream frequency is greater in semi-arid regions; it is least in the arid regions and intermediate in
humid regions. High drainage densities or stream frequencies are a reflection of increased channel
development and hence should give high sediment yield, which is really the case. Melton (1958) has
analysed in detail the relationship between stream frequency and drainage density both of which
measure the texture of the drainage net, yet each treats the different aspect of it. According to him it is
possible to construct two hypothetical drainage basins having the same drainage density but different
stream frequency, and vice versa. However, in nature there is a good correlation between the two. From
the analysis of 156 drainage basins covering a wide range of climatic and lithological conditions,
Melton found the following relation
F = 0.434 Dd2
–2
where F is in km and Dd is in km
2.10
...(2.17)
–1
RELIEF ASPECTS
The relief is the difference in elevation between given points. Maximum basin relief is the difference in
elevation between the basin mouth and the highest point on the basin perimeter. Alternative definition of
maximum relief is the basin relief along the longest dimension of the basin parallel to the principal
drainage line. Relief ratio Rk is the ratio of maximum basin relief to the horizontal distance along the
longest dimension of basin parallel to the principal drainage line (Schumm 1956). Melton (1958)
defines the relative relief as the maximum relief H divided by the basin perimeter P while Maxwell
defines the relative relief as H divided to basin diameter. Use of the perimeter as the horizontal length
dimension solves the difficulty of locating a suitable axial line in the basin. Two other parameters
involving maximum relief have been defined by Strahler (1957). The ruggedness number is the product
of maximum relief H and the drainage density Dd i.e. (H Dd). The geometry number is defined as
(H Dd /S) where S is the ground slope. Both these parameters are dimensionless. Observed values of
ruggedness number vary from 0.05 to about 1. Strahler (1964) found that the geometry number varies
over a relatively narrow range viz. 0.40 to 1.0.
Schumm (1954) found that for six small drainage basins in Colorado Plateau Province (U.S.A.) the
relief ratio Rh correlated well with annual sediment loss giving a relationship of the form
log (annual sediment loss) ~ Rh
27
Drainage Basins and Channel Networks
Admittedly, relief ratio strongly influences the sediment loss since the force exerted on the surface
is directly related to Rh. However, climatic factors such as rainfall and vegetal cover also affect sediment
loss. Schumm’s data shown in Fig. 2.6 are taken from catchments in the same region; hence climatic
conditions were similar even though the lithology changed somewhat.
10
0
3
Schumm's data
Shale
Annual sediment loss Ha.m/km
2
8
6
2
Friable
sandstone
ak
roc
k
4
10
4
8
0
0.1
sis
8
1
Re
Conglomerate
sandstone
–1
tan
t to
we
2
5
0.2
0.3
0.4
0.5
0.6
Rh
Fig. 2.6 Relation between annual sediment loss and Rh (Schumm 1954)
Hypsometric Curves
Let “a” be the horizontal projected area of a drainage basin at an elevation h (see Fig. 2.7) and A be the
total projected area. Then one can prepare a curve between relative height h/H and relative area a/A as
shown in the Figure 2.7. Such a curve is known as hypsometric curve. The analysis of large drainage
basins using such curves was first done by Langbein (1947) and later used by Strahler and others. The
hypsometric curve, in general, will change with time because of the gradual erosion of areas at higher
levels and hence the relative position of the hypsometric curve on a/H vs h/H graph gives an idea about
the stage of development of the basin landscape. Figure 2.7 shows young and mature stages of
topography. This figure also shows monadnock phase in which the resistant rock in the basin may form
prominent hills at isolated places giving a distorted hypsometric curve. Sometimes the integral
z
1
f (x) dx where f (x) = h/H and x = a/A is used as an index of evolution of the topography of the basin.
o
This integral represents the rock mass that is still to be eroded. Young phase would correspond to a high
value of the integral while mature phase would correspond to a relatively small value. Strahler (1964)
has indicated that most of the hypsometric curves can be represented by an equation of the form
28
River Morphology
y
Divide
Entire basin
area A
1.0
Original land surface
Young
0.8
Mature
(Equilibrium)
0.6
Area a
h
H
0.4
Monadnock
(Prominent hills)
(x, y)
Summit
plane
H
0.2
h
y
a
0
Base plane
Fig. 2.7
0
0.2
0.4
0.6
0.8
1.0
a/A
Hypsometric curve
F d - x a IJ
y=G
H x d - aK
z
...(2.18)
Here y and x are as shown in Fig 2.7. The exponent z increases as the topography becomes more
mature. Hypsometric curves are also related to hydrologic characteristics of the drainage basin. Thus
distribution of elevation in a drainage basin is closely related to the amount of flood storage available,
the effect of which is to make the rising limb of hydrograph less steep, increase the time lag and make
the peak lower and less pronounced. Knowledge of hypsometric curve is also useful in better estimates
of rainfall, snowfall and evaporation in the basin.
Channel Slopes
A composite stream profile in a drainage basin can be prepared in the following way. For each first order
streams vertical drop and horizontal length of the segment is determined. From these data mean drop
and mean horizontal length are determined. This procedure is followed for streams of all orders. The
triangles for each order are connected in sequence to produce a composite profile. Since each segment
slope is governed by the average discharge and average sediment load, a segmented profile looks logical
even though we tend to draw a continuous curve through these points. If S u is the average slope of the
segments of order u, Horton (1945) expressed variation of S u by the law of stream slopes according to
which
Su = S1 RsK - u
where Rs is ratio similar to bifurcation ratio and can be called slope ratio.
...(2.19)
29
Drainage Basins and Channel Networks
2.11
DRAINAGE BASIN CHARACTERISTICS AND HYDROLOGY
Many times a need is felt to have hydrologic data at sites where gauging station data are not available.
Since there is a lack of data about precipitation (input) and stream flow (output), there is great difficulty
in testing input-output models unless severe simplifying assumptions are made. Hence, scientists have
worked on the premise that fluvial activity and form of the land must be related. This was reflected in
Strahler’s dimensional analysis presented earlier where runoff per unit area was related to erosion, relief
and drainage density. Bodhaine and Thomas (see Osborn 1980) obtained the following expression for
mean annual flood Q
Q = 0.638 A0.889 L– 0.037 R1.135 G
...(2.20)
where L is ratio of lake area to catchment area expressed in percent, G is the geologic factor and R is the
average annual runoff.
A number of studies conducted in the U.S.A. and other countries have shown that basic drainage
parameters such as stream length, basin length, basin relief area, drainage density, and slope are
adequate to obtain correlations with different flows from the basin. The ungauged flows for which the
methods have been developed are 7 day low flows of 2-yr and 20-yr return periods Q2 and Q20
respectively, average annual flow Qaa, two year and 50 year peak flows Q2p and Q50p and sediment flow
Qs. One flow is considered to be functionally related to another flow of same type of different return
period. Thus
Q2p = f (Q50p)
...(2.21)
For low flows this general relationship is
Q1L = f (Q2L)–n
...(2.22)
where n is positive. Some of the successful geomorphic parameters used are (L1 . H) (LT . H), (LT H0.5)
and (Dd . L1) L1, where L1 is the length of first order perennial streams, H is the relief, LT is the total
length of streams and Dd is the drainage density (Osborn, 1971). It may be noted that all these
parameters are dimensional.
Work done on the geomorphological instantaneous unit hydrograph has been summarised by
Rodriguez-Iturbe (1993). GIUH is defined as the probability density function for the time of arrival of a
randomly chosen drop to the gauging site and is related to Horton’s Rb, RL, RA, average velocity of the
stream flow v and length of the channel of highest order LW. The peak flow qp and time to peak tp are
given as
qp = 1.31 RL0.43 ULW– 1
tp
FR I
= 0.44 G J
HR K
B
...(2.23)
0.55
–1
RL–0.38 LWU
...(2.24)
A
Here qp is in hr–1, U in m/s, tp in hr and LW in km.
2.12
RANDOM WALK MODEL
The precipitation falling on a uniformly sloping plain develops an incipient set of rills near the
watershed divide; these are generally oriented downhill. As the rills deepen with time, cross grading
30
River Morphology
Uniform spacing at origin
Fig. 2.8
Random walk model for stream network
begins owing to overflow of shallow rills. The direction that the cross grading takes place and the micro
piracy of the incipient rills are postulated to be a matter of chance until the rills deepen sufficiently. This
randomness in the first stages of development of stream has led to formulation of random walk model
for drainage network.
To illustrate the basic ideas behind random walk model assume a row of equally spaced points on
the boundary of the drainage basin say at 1.5 cm apart; eight such points are shown in Fig. 2.8. They can
be considered as source of first order streams. Assume each point can move to the right, left or in the
forward direction through a fixed distance so that the motion is downhill. As a result, a series of
staggering paths will be generated and junctions may occur after which the joint path will be extended as
a single unit, see Leopold and Langbein (1962), Shreve (1966 and 1967). Such artificial networks have
properties and relationships closely approximating Horton’s laws. As a consequence, it has been
suggested that some of these relationships are attributes common to all systems of randomly developed
networks and are not really laws of orderly stream development. Of course it does not follow that stream
networks are generated at random, even though random walk models approximate to them in many
aspects. Some may even argue that streams do not develop from head downwards but do so from mouth
upwards. Leopold and Langbein found that for such a random walk model constructed, Lu + 1/Lu came
out to be 2.8, a figure which lies between 2.5 and 3.7 the range obtained by Horton (1945). Similarly,
from random walk model it is found that Lu ~ A0.64 which agrees well with Hack’s relation L = 1.16 A0.60
as given in Eq. (2.13).
One may argue that the development of drainage network is not so much a matter of chance but it is
influenced by lithology, climate, vegetation and antecedent conditions. The present streams may reflect
the effects of sequences of beds that have been eradicated by erosion during geologic past. Since
random walk model ignores all these factors one must view such a model with caution.
31
Drainage Basins and Channel Networks
2.13
CONCLUDING REMARKS
At the end it is pertinent to mention that most of the generalities developed in this chapter have been
obtained from the data on small basins in weak rocks in U.S.A. Such basins adjust rapidly to the
changing conditions. Therefore one may assume that some present property or properties are controlling
the stream geometry and slope which can be measured and statistical relations obtained. If variation in
lithology is great and erosional history complex, the drainage net analysis may become more involved
(Sparks 1972).
References
Bruijnzeel, L.A.(1990) Hydrology of Moist Tropical Forests and Effects of Conservation. A State of Knowledge
Review. Division of Water Sciences, IHP, UNESCO, Paris (France). 224 p.
Carlson, C.W. and Langbein, W.B. (1960). Rapid Approximation of Drainage Density: Line Intersection Method.
USGS Water Resources Division, Bull. 11, February 10.
Chorely, R.J. (1957). Illustrating the Laws of Morphometry. Geo. Mag. Vol. 94.
Chorely, R.J., Malm, D.E.G. and Pogorzelski, H.A. (1957) A New Standard for Estimating Basin Shape, Am. Jour.
Sci., Vol. 255, pp. 138– 141.
Garde, R.J. and Kothyari, U.C. (1987) Sediment Yield Estimation. JIP, CBIP, India, Vol. 44, No. 3.
Garde, R.J. and Kothyari, U.C. (1990) Flood Estimation in Indian Catchments. Jour. of Hydrology, Elsevier
Science Publications, Amsterdam, Netherlands, Vol. 113, pp. 135–146.
Goswami, D.C. (1985) Brahmaputra River, Assam, India: Physiography, Basin Denudation and Channel
Aggradation. WR Research, Vol. 21.
Gregory, K.J. (1966) Dry Valleys and Composition of the Drainage Net. Jour. Hydro. Vol. 4, pp. 327–340.
Gregory, K.J. and Walling, D.E. (1976) Drainage Basin Form and Processes:A Geomorphological Approach.
Edward Arnold (Publishers) Ltd., London, Paper-Back Edition, 458 p.
Glock, W.S. (1932) Available Relief as a Factor of Control in the Profile of Land Form. Jour. Geol., Vol. 40, pp.
74–83.
Hack, J.T. (1957) Studies of Longitudinal Stream Profiles in Virginia and Maryland. USGS Professional Paper
294 – B,. 53 p.
Horton, R.E. (1932) Drainage Basin Characteristics. Trans. AGU, Vol. 13, pp. 350–361.
Horton, R.E. (1945) Erosional Development of Stream Their Drainage Basins:Hydrological Approach to
Quantitative Morphology. Bull. Geol. Soc. Am. Vol. 50, pp. 275–370.
Howard, A.D. (1967) Drainage Analysis in Geologic Interpretation:A Summation. Am. Soc. Petroleum Geologists
Bull. Vol. 51, pp. 2246–2259.
Langbein, W.B. et al. (1947) Topographic Characteristics of Drainage Basins. USGS Water Supply Paper 968C.
Leopold, L.B. and Langbein, W.B. (1962) the Concept of Entropy in Landscape Evolution. Theoretical Papers in
Hydrologic and Geomorphic Sciences. USGS Professional Paper 500A. 20 p.
Manandhar, I.N. and Khanal, N.R. (1988) Study of Landscape Processes with Special Reference to Landslides in
Lele Watershed, Central Nepal. Unpublished Report, Dept. of Geology, Tribhuvan University, Khatmandu
(Nepal).
Melton, M.A. (1958) Geometrical Properties of Mature Drainage Systems and Their Representation in an E4
Phase. Jour. Geol. Vol. 66, pp. 35–54.
32
River Morphology
Miller, V.C. (1953) A Quantitative Geomorphic Study of Drainage Basin Characteristics in the Clinch Mountain
Area, Verginia and Tennessee, Project NR 389-042, Tech. Rept. No. 3, Columbia University, New York
(U.S.A.).
Mittal, R.S., Parkash, B. and Bajpai, I.P. (1974) Drainage Basin Morphometric Study of the Part of Garhwal
Himalaya. Himalayan Geology, Wadia Institute of Himalayan Geology.
Morisawa, M.E. (1962) Quantitative Geomorphology of Some Watersheds in Appalachian Plateau. Geol. Soc.
Am. Bull. Vol. 73, No. 9, pp. 1025–1046.
Morisawa, M.E. (1968) Streams–Their Dynamics and Morphology. Earth and Planetary Science Series, McGraw
Hill Book Company, N.Y. 175 pp
National Institute of Hydrology (1993) Geomorphological Characteristics of Punpun Basin of Ganga River
System, Roorkee (India), CS (AR) - 125.
National Institute of Hydrology (1995) Fluvial Geomorphological Characteristics of Four Sub-basins of Upper
Narmada, Roorkee (India), CS(AR) - 159.
Osborn, J.F. (1980) Drainage Basin Characteristics Applied to Hydraulic Design and Water Resources
Management, Chapter 8, In Geomorphology and Engineering (Ed. Coates, D.R.), George Allen and Unwin,
London, 1980, pp. 141– 172.
Peltier, L.C. (1962) Area Sampling for Terrain Analysis. Prof. Geogr. Vol. 14, pp. 24–28.
Prasad, R.C. (1975) The Landslide and Erosion Problems with Special Reference to the Kosi Catchment. Proc. of
the Seminar on Landslides and Toe Erosion Problems with Special Reference to Himalayan Region. Gangtok,
Sikkim.
Rodriguez - Iturbe, I. (1993) The Geomorphological Unit Hydrograph, Chapter 3 in Channel Network Hydrology
(Ed. Beven, K. and Kirkby, M.J.), John Willey and sons, New York, pp. 43–68.
Rzhanitsyn, N.A. (1960) Morphological and Hydrological Regularities of the Structure of the River Net.
Published by Gidrameterizdat, Leningrad (Translated into English by P.B. Kimgold, USDA, ARS, U.S.A.)
Scheideggar, A.E. (1965) The Algebra of Stream Order Numbers, USGS Prof. Paper 5258, pp. 187–189.
Schumm, S.A. (1954) The Relation of Drainage Basin Relief to Sediment Loss. International Union of Geodesy
and Geophysics; 10th General Assembly, Rome, IASH Publ. 36, Vol. 1, pp. 216–219.
Schumm, S.A. (1956) Evolution of Drainage Systems and Slopes in Badlands at Perth Amboy, New Jersey, Geol.
Soc. Am. Bulletin. 67, pp. 597–646.
Schumm, S.A. (1977) The Fluvial System. Wiley Interscience Publication. John Wiley and Sons., New York. 338
p.
Selby, M.J. (1967) Morphometry of Drainage Basins in Areas of Pumice Lithology. Proc. 5th New Zealand
Geography Conference, New Zealand Geogr. Soc., Auckland (N.Z.), pp. 169–174.
Shreve, R.L. (1966) Statistical Laws of Stream Numbers. Jour. Geo. Vol. 74, pp. 17–37.
Shreve, R.L. (1967) Infinite Topological Random Channel Networks. Jour. Geol. Vol. 75, No. 2, pp. 178–186.
Smart, J.S. (1967) A Comment on Horton’s Law of Stream Numbers. WR Research, Vol. 3, pp. 773–776.
Smith, K.G. (1950) Standards for Grading Texture of Erosional Topography. Am. Jour. Sci. Vol. 248, pp. 655–658.
Sparks, B.W. (1972) Geomorphology, Longman Group Ltd., London, Chapter 6, 2nd Ed.
Strahler, A.N. (1952) Dynamic Basins of Geomorphology, Bull. Geol. Soc. Am., Vol. 63, pp. 923–938.
Strahler, A.N. (1957) Quantitative Analysis of Watershed Geomorphology. Trans. AGU, Vol. 38, pp. 913–920.
Strahler, A.N. (1964) Quantitative Geomorphology of Drainage Basins and Channel Networks. Section 4-II in
Handbook of Applied Hydrology (Ed. V.T. Chow ) McGraw Hill Book Company Ltd., New York, pp. 4–39 to
4–76.
Drainage Basins and Channel Networks
33
Thornbury, W.D. (1969) Principles of Geomorphology. Wiley International Edition, John Wiley and Sons, Inc.,
2nd Edition.
Wiersum, K.F. (1984) Surface Erosion under Various Tropical Agroforestry Systems, in Proceedings Symposium
on Effects of Forest. Land use on Erosion and Slope Stability (Eds C.L. D’Loughlin and A.J. Pearce.).
IUFRO, Vienna and East-West Centre, Honolulu, (Hawaii).
Zernitz, E.R. (1932) Drainage Patterns and Their Significance. Jour. of Geol., Vol. 40, pp. 498–521.
C H A P T E R
3
Soil Erosion and Sediment Yield
3.1
INTRODUCTION
Soil can be eroded from its present state by the action of water, wind and glaciers; however in the
context of the theme of this book, attention is concentrated on soil erosion by water, which is by far the
most important in humid and semi-humid areas. Soil erosion by water is the process of detachment of
soil particles by the impact of rainfall and runoff, and its transport down the slope. Erosion from
mountainous areas and agricultural lands is the major source of sediment transported by the streams and
that deposited in reservoirs, flood plains, and deltas. Sediment load is also generated by erosion of bed
and banks of the streams, by the mass movements of sediment such as land slides, rockslides and mud
flows, and because of construction activity related to roads, buildings and dams. Part of the sediment
from the above-mentioned sources, which is carried by the stream, is stored in the valley bottom and on
flood plains and released later. Hence, erosion of sediment is discontinuous with time and it displays a
high degree of spatial variability.
Since part of the sediment eroded from an area can deposit in the lower reaches, the rate of erosion
is usually greater than the rate at which sediment is carried downstream at any section; the latter is
knows as the sediment yield. It may be mentioned that since landscape formation and changes in it are
due to differential erosion and deposition of sediment, erosion, sediment yield and landscape formation
are closely interrelated; therefore study of soil erosion and sediment yield assumes great importance in
river morphology. Excessive erosion rates in the catchments of the rivers Kosi and Brahmaputra in India
are responsible for the severe migration of the Kosi and change of river regime of the Brahmaputra.
Similar problems are also encountered in China on the Yellow river. Reservoirs constructed on streams
carrying sediment lose their capacity due to deposition of sediment in the reservoir. On an average
Indian reservoirs are losing their storage capacity between 0.05 to 5.0 percent per year. In Pakistan,
Mangla reservoir, which was planned to last 100 years, is now expected to last only 57 years due to
excessive sediment deposition (El-Swaify et al. 1982). Dendy (1968) opined that if the present rates of
sedimentation continue a large per cent of small reservoirs would lose about fifty percent capacity in the
next three decades.
35
Soil Erosion and Sediment Yield
Soil erosion is found to reduce crop productivity and large tracts of land are made unproductive
every year. Brown (1984) estimated that about 23 billion tons of soil from croplands in the world is
being lost every year. Accordingly to UNEP (1980), about 20 million-hectare areas in the world become
uneconomical for cropping each year due to soil erosion and erosion induced degradation.
3.2
GLOBAL EROSION RATES
Sediment going out of the catchment every year i.e., sediment yield gives a valuable idea about rates of
erosion and soil loss from the drainage basin. This information is also very useful in studying the
sediment problems and river behaviour. The sediment yield is made of suspended load and bed-load.
Except when the depth is small and material is coarse, it is rather difficult to measure the bed-load.
Hence most of available data on erosion rates only include suspended load, which is normally expressed
in tons/km2/year or tons/year.
The mean annual suspended sediment yield expressed as tons/km2/year varies over a very wide
range. Low sediment yield is generally associated with lowland areas or areas underlain by rocks that
are highly resistant to weathering and erosion, e.g., 1.0 ton/km2/year for many rivers in Poland, and 1.7
tons/km2/year for a river draining the Southern Table Lands and Highlands of New South Wales, see
Walling (1988). Some of the high values of sediment yield obtained are from highly erodible loess
region. Table 3.1 adapted from Walling (1988) lists some of the high sediment yield values.
Table 3.1 Maximum values of specific suspended sediment yield (Walling 1988)
Country
River
China
Dali
Taiwan
Kenya
North Island
New Zealand
Huangfuchuan
187
Tsengwen
Perkerra
Waiapu
Waingaromia
Drainage area
km2
Suspended sediment yield
tons/km2/year
3199
21 700
1000
1310
1378
175
55 500
—
28 000
19 520
19 970
17 340
High values of suspended sediment yield can be attributed to various factors such as underlying
geology, topography, climatic conditions, high erodibility of soils and land use. Steep slopes and high
intensity of rainfall can also cause high values of sediment yield. Holeman (1968) has given valuable
information on the sediment yield of major rivers of the world. Table 3.2 gives such data for some rivers
in the world, which discharge more than 104 tons of sediment each year into the sea.
Some idea about erosion rates observed in various continents would also be helpful in knowing
which regions contribute the highest and the lowest sediment load to the oceans. Table 3.3 is based on
the synthesis of data given by Strakov, and Milliman and Meade (1983).
Table 3.3 indicates that the highest sediment load is fed to the oceans every year by Asia and the
next in line would be South America and North and Central America. On the basis of whatever data that
were then available some investigators have produced maps of global suspended sediment yield. One
such map prepared by Walling (1988) is shown in Fig. 3.1. From the analysis of such data estimates are
36
River Morphology
Table 3.2
S.No
1.
Some rivers of the world discharging more than 104 tons/year sediment
to the sea (Holeman, Ref. p. 68 (1982)
River
Yellow
Location
Total drainage
area 103 km2
China
Average annual
sediment load
Average water
discharge 103 m3/s
103 tons
tons/km2
666
2080 000
2945
1.50
2.
Ganga
India
945
1600 000
1563
11.80
3.
Brahmaputra
Bangladesh
658
800 000
1445
12.20
4.
Yangtze
China
1920
550 000
547
21.80
5.
Indus
Pakistan
957
480 000
508
5.60
6.
Ching (tributary of
Yellow)
China
56
450 000
8008
0.057
7.
Amazon
Brazil
5709
400 000
67
181.40
8.
Mississippi
U.S.A.
3185
344 000
109
17.90
9.
Irrawaddy
Mynamar
425
330 000
914
15.60
10.
Missouri
U.S.A. (Missouri)
1354
240 000
176
2.00
11.
Lo (tributary of
Yellow)
China
26
210 000
7890
—
12.
Kosi
India
61
190 000
3117
1.80
13.
Mekong
Thailand
786
187 000
484
11.10
14.
Colorado
U.S.A.
630
149 000
422
0.16
15.
Red
Vietnam
118
143 000
1207
3.90
16.
Nile
Egypt
2944
122 000
39
2.80
Table 3.3
Continent
Mean erosion rates in different continents
Area 10 6 km2
Erosion rate tons/km2/year
Africa
29.81
35 - 72
Asia
44.89
208 - 229
Australia
7.86
43
North and Central America
20.44
84 - 113
South America
17.9
100 - 148
9.7
50 - 75
Europe
made of the total suspended sediment load transported to the ocean every year. Some of the estimates of
mean annual sediment load are given in Table 3.4.
The earlier data base was meagre whereas in the estimates made in 80 have been based on data from
over 2000 rivers spread over all the continents. Hence, these recent estimates are likely to be more
accurate than the older ones.
Soil Erosion and Sediment Yield
Sediment Yield
2
1
t.km yr
1000
750
500
250
100
50
Deserts and
permanent ice
Fig. 3.1 Suspended sediment yield on global basis (Walling 1988)
37
38
River Morphology
Table 3.4 Some estimates of the yearly-suspended sediment transport to oceans
Author
Year
Estimated mean annual load in 10 6 tons
Keunen
1950
32 500
Pechinov
1959
24 200
Fournier
1960
51 100
Mackenzie & Garrels
1966
8300
Holeman
1968
15 700
USSR National Committee for IHD
1974
15 000
Walling and Webb
1983
15 000
According to the concept of geomorphic cycle, material is continually eroded from higher elevation
areas and brought down to the low-lying areas and sea thereby reducing the slope of the terrain. Natural
agents such as rainfall and runoff, wind and glaciers cause this erosion. Geologists have made estimates
of such erosion. The time required to reduce the uplifted land surface to a gently undulating plain was
estimated by Davis to be 20–200 million years. Geomorphologists use four types of evidences to
estimate the rate of loss of material from the land. These are: (i) Method based on estimates of
suspended and dissolved material transported by rivers; this is obtained by sampling the sediment load
and discharge measurements. (ii) Measurement of sediment accumulated in reservoirs. (iii)
Measurement of surface processes on slopes including rates of soil creep, surface wash and landslides.
(iv) Comparison of known geological or radiocarbon dates with landform changes identified as
subsequent to them. Because of the different techniques used and also because of the fact that erosion
2000
Normal Relief
Steep relief
1000
Steep relief
200
100
Normal relief
50
10
1.5
20
R
S
P
2.5
Ground loss (mm/1000 yr)
500
G
R S P G
Fig. 3.2 Ranges of rates of lowering of land surfaces (Young 1969)
39
Soil Erosion and Sediment Yield
rates are governed by rock type, climate, vegetation, basin area, relative relief and steepness of slope the
reported erosion rates in different environments are not rigorously comparable.
Young (1969) has examined the then-available data on erosion rates and found it necessary to divide
the results into two classes of relief: normal relief including plains moderately dissected areas and gentle
to moderate slopes, and steep relief including mountainous areas and individual steep slopes. His results
are shown in Fig. 3.2. All data have been converted into mm/1000 years and are plotted on logarithmic
scale. For large variations the extreme limits are shown on the ordinate and on abscissa the method used
for measurement is indicated viz. R river load, S reservoir sedimentation, P surface process
measurements and G geological evidence. His analysis gives an average erosion rate of 500 mm/1000
years for steep relief and 46 mm/1000 years for normal relief. He has also mentioned that with respect to
rock type there are no marked differences in rates of erosion between igneous and metamorphic rocks,
siliceous sedimentaries and lime stones; unconsolidated rocks are eroded 10–1000 times faster than
consolidated rocks.
Schumm (1963) suggests that denudation rate of about 900 mm/1000 years be considered as an
average maximum rate for drainage basins of the order of 4000 km2. On the basis of suspended sediment
yield of the Kosi as reported by Khosla (1953), Schumm obtains nearly the same rate as quoted above.
On the other hand, he reports data by Zeuner, Gilluly, Stone and Gutenberg, which indicate that the
present maximum rates of uplift or orogeny are far in excess of rates of denudation in many areas. These
are 76 m/10 000 years in California, 30 m/10 000 years in Russia, 45 m/10 000 years in Japan and 100
m/10 000 years in the Gulf area. Even though average uplift rates may be 1/3 or 1/4 of the maximum
rates and further it is not known that uplift will continue at this rate, it does indicate that timeindependent landforms may not be obtained in some cases because the rates of denudation and uplift are
so different.
3.3
TYPES OF EROSION
Major types of soil erosion due to the action of water include sheet erosion, rill and inter-rill erosion,
concentrated flow erosion on gully erosion, and stream channel erosion. Sheet erosion is the erosion of
land surface caused by the impact of raindrops and transport of soil by overland flow. Sheet erosion is
more or less uniform removal of soil without development of water channels. Rill and inter-rill erosion
caused by surface runoff results in numerous small-eroded channels across the landscape. Rills are
Fig. 3.3 Formation of gullies
40
River Morphology
defined as eroded channels so small that tillage operations obliterate them every year. Both sheet erosion
and rill erosion are widespread over a field and according to Foster (1988) can exceed 20 000 tons/km2
in severe cases.
The topography of most fields causes surface runoff in a few major natural waterways before
leaving the fields. Erosion that occurs in these areas is called concentrated flow erosion; the impact of
this erosion is localized in and around the waterways.
When eroded channels in concentrated flow areas become so large that they cannot be easily
crossed they are called gullies. Gullies are steep sided water channels, which carry ephemeral flow
during storms. Formation of gullies is shown in Fig. 3.3. Gullies are associated with accelerated erosion
and hence with landscape instability. Gullies may not normally develop from rills; their development is
a complex process, which is not fully understood. Some observations indicate that small depressions
caused by weakening of vegetal cover get enlarged; several such depressions coalesce and form a
channel, which develops into a gully. Some gully action is found to occur due to subsidence of pipes or
tunnels formed underground due to subsurface flow. This normally happens in high sodium soils. In a
few cases gully action has been initiated where linear landslides leave deep steep sided scars, which may
be occupied by running water in subsequent storms (Morgan 1979). Discontinuous gullies represent
youthful stage while fused gullies are an early mature stage of development. The sediment removed
from the landscape due to formation, widening or deepening of gullies is known as gully erosion (Heede
1975, and Piest et al. 1975). Very little is known about rates of gully erosion.
It may be added that ephemeral streams are those streams, which do not flow continuously. They
respond only to the occurrence of precipitation. Other times they are almost dry. Perennial streams are
those streams which flow continuously, their water supply coming from rainfall, snow melt and ground
water. Stream channel erosion includes stream bank erosion, valley trenching, streambed lowering and
flood plain scour. It can also include the material carried by streams such as that from mine wastes and
construction activities (such as dams, tunnels and roads) along the banks of the channel.
In general, sheet erosion is the prime offender in humid regions, whereas in more arid parts where
the rainfall is experienced in short high intensity storms, channel erosion is more predominant. Material
derived from sheet erosion source is fine-grained material swept from fields and carried in suspension to
and through the conveyance system. Channel type erosion is a source of coarser material and this
material is obtained from the areas, which are already a part of the transportation system. In general
sheet erosion forms a major part of total erosion from a given area. Thus Roehl (1963) found that in
4300 km2 of well scattered area in South Eastern U.S.A. sheet erosion accounted for 66 to 100 percent
of the total erosion.
Mass movement includes large-scale erosion due to tectonic activity, landslides, creep rock flow or
mud flows; the eroded material is ultimately fed to the stream thereby increasing the sediment
concentration substantially. Gross Ventre landslide South of Yellow Stone Park U.S.A., which occurred
in 1925, produced 50 Mm3 rock materials forming a 68 m high dam in the valley. The lake formed by
this dam was 8.0 km long. Rockslide at Frank (B.C. Canada) in 1903 brought down 35 Mm 3 rock debris.
Such landslides are a common occurrence in the valleys of Himalaya in India.
Relative importance of sheet erosion, gully erosion, channel erosion, mass movement, and
accelerated erosion due to construction of roads etc. varies from one catchment to the other since it
depends on various factors. Robinson (1977) has given data on sediment sources and their total
contribution to the sediment in streams in U.S.A., (see Table 3.5).
41
Soil Erosion and Sediment Yield
Table 3.5 Sediment sources and their total contribution to sediment in streams in U.S.A. (Robinson 1977)
Sediment source
Total sediment in 106 tons/years
Agricultural lands
680
Percent of total
40
Stream bank erosion
450
26
Pasture and range land
210
12
Forest lands
130
7
Other federal lands
115
6
Urban
73
4
Roads
51
3
Mining
18
1
Other
14
1
3.4
FACTORS AFFECTING EROSION
Factors affecting erosion are briefly discussed below.
Rainfall and Temperature
Rainfall is the most important factor affecting erosion because of its power to detach the soil particles
and its ability to produce runoff, which causes erosion and transportation of the eroded material. Erosion
can be produced by a short duration high intensity storm during which the infiltration capacity is
exceeded. Prolonged low intensity storms can also cause erosion. In the case of erosion due to water, the
antecedent conditions of the soil with regard to soil moisture play an important role. If the soil is already
well soaked by previous storm a low intensity short duration storm can also cause significant erosion.
For each area one would expect a critical or threshold value of rainfall intensity above which significant
erosion would take place. Depending on geologic conditions this value varies from 10 mm/hr to 30 mm/
hr. The erosive ability of rainfall depends upon its intensity and duration and velocity and diameter of
the rain drops. For the same mean annual precipitation the annual erosion would depend on how this
precipitation is distributed over the year. Fournier (1949) found that the ratio (maximum monthly
rainfall/annual rainfall) is a better rainfall parameter for the study of erosion. Garde and Kothyari (1987)
have utilised this parameter in their analysis of erosion from the Indian catchments.
Temperature plays an important role in the process of weathering, especially mechanical
weathering, which leads to the disintegration of rocks. Alternate freezing and thawing, and alternate
heating and cooling are the processes involved in this disintegration. Rainfall is responsible for
chemical weathering as well as for transportation and deposition of the eroded material. Considering the
importance of rainfall and temperature in the process of erosion it is natural that mean annual
temperature and mean annual rainfall be used as the criteria for classifying modes of weathering and
transportation as done by Leopold, Wolman and Miller (1964), (see Fig. 3.4). For any given temperature
the erosion rate first increases with increase in precipitation, reaches a maximum and then significantly
reduces. This reduction is due to the growth of vegetation which protects the soil surface from direct
impact of rain drops, increases infiltration and gives direct protection from erosion due to foliage lying
on the ground. This is shown in Fig. 3.5.
42
River Morphology
Mean annual temp. °C
30
Mechanical
Chemical weathering
weathering
mass movement
wind
running water
20 running
water
Mechanical and
chemical weathering
running water
10
mass movement
Mechanical weathering
mass movement
running water
0
10
20
Wind
0
20 40 60 80 100 120 140 160 180 200
Mean annual rainfall, cm.
Fig. 3.4 Hypothetical morphogenic regions
160
Mean annual temp. 10°C
Effective precipitation cm
140
120
100
Forest
80
60
Grassland
40
Desert shrub
20
0
0
100
200
300
400
2
Sediment yield tons/Km . yr
Fig. 3.5
Sediment yield as related to precipitation and vegetation (Leopold et al. 1964)
Soil Characteristics
The erodibility of soil depends on its texture, aggregate stability, shear strength, infiltration capacity,
and organic and chemical contents. Coarser the particles smaller will be their erodibility. Similarly
greater the relative density less will be the erodibility. The clay content combines with organic matter
and forms clods of soil. The stability of the clods determines the resistance to erosion. The shear
strength parameter is more useful in the study of mass movements such as landslides. The erodibility
index of the soil designated as K is used in the Universal Soil Loss Equation USLE for agricultural lands
discussed in section 3.6. It can be determined for the known values of per cent of silt and clay, per cent
of sand (0.10 mm to 0.20 mm), percent of organic matter, soil structure and permeability. Figure 3.6
shows the monograph for determining the value of K for the known characteristics as given by
Wischmeir et al. (1971). If all the details of soil are not available one can use the following average
values given in Table 3.6.
43
Soil Erosion and Sediment Yield
Table 3.6
Average value of erodibility Factor K
Soil
Range of K
Soil loams
0.40 to 0.70
Clay loams
0.30 to 0.40
Sandy loams
0.10 to 0.30
Gravely loams
0.03 to 0.10
0.7
0
%OM = 0
10
Silt + very fine sand
30
80
60
0.5
0.4
0.3
40
40
50
60
70
80
1 Very fine granular
2 Fine granular
3 Coarse granular
4 Blocky massive
1234
Soil strucuture
0.6
20
0.2
0.7
0.1
0.6
0
Percent sand
(0.1 0.2 mm)
0
90
100
Example given 65% Silt + V.F. sand
20% Sand (0.1 = 0.2 mm)
3% Organic matter
Soil structure Fine granular
Permeability slow to moderate
Soil erodibility factor K
20
1
2
3
4
0.5
0.4
0.3
0.2
0.1
0
6
5
4
3
2
1 Permeability
6 Very slow
5 Slow
4 Slow to mod
3 Moderate
2 Mode-rapid
1 Rapid
K = 0.38
Fig. 3.6 Monograph for computing soil erodibility factor K in Universal Soil Loss Equation
(Weischmeir et al. 1971)
Slope Geometry
Erosion is found to increase with increase in slope and length of the slope; this is due to corresponding
increase in the velocity and volume of surface runoff. Erosion rate per unit area can be expressed as
Erosion
~ S m Ln
Area
...(3.1)
where the values of m and n are found to be different by different investigators. Values of m and n
obtained by various investigators as given by Morgan (1979) are listed in Table 3.7. It can be seen that m
and n are functions of process of erosion, magnitude of slope, steepness, length and vegetal cover.
Vegetation
Vegetation or plant cover reduces erosion of soil, its effectiveness depending on the height and
continuity of canopy, density of ground cover and the root density. For a given temperature, as the
precipitation increases the sediment yield in tons/km2 increases and reaches a maximum value. If the
44
River Morphology
Table 3.7 Values of m and n in Eq. 3.1(Robinson 1977)
Investigator
m
n
Zingg
Hudson and Jackson
Hovarth and Erodi
1.40
2.0
1.60 to 0.70
0.60
—
—
Quinn, Morgan and Smith
Kirkby
0.70 to 1.0
1.0 to 2.0
1.3 to 2.0
—
—
—
0.3 – 0.7
1.0 – 2.0
Conditions/Comments
From five experimental stations in U.S.A.
From experimental stations in Zimbabwe
m decreased with increase in slope in laboratory
studies
m increased as grass cover decreased
For soil creep and splash erosion
For erosion by overland flow
For erosion with rilling
canopy is near the ground it dissipates the kinetic energy of rain. Canopy on the ground also increases
roughness and reduces the velocity of surface flow. Roots play an important role in reducing erosion
rate. Roots create easy passages for water to infiltrate thereby increasing the infiltration rate and
reducing the surface runoff. Small roots also bind the soil mass thereby increasing its resistance to
erosion. Generally forests are the most effective in reducing erosion because of their canopy; dense
grass is equally effective.
Experimental evidence indicates that the erosion-cover relationship is non-linear. As vegetal cover
increases from zero there is a rapid decreases in soil loss; however beyond 60 percent cover, further
increase in vegetal cover reduces the soil loss marginally. Table 3.8 shows the erosion-cover relationship
generalised after Elwell (1980) and Elwell and Stocking (1974). It can be seen from Table 3.8 that for
adequate erosion protection at least 60–70 percent of the ground should be covered by vegetation.
Table 3.8 Relationship between percent vegetal cover and percent reduction in soil loss
20
32
400
10
60
5
70
20°C
It may be mentioned that there is an interaction between
rainfall and vegetation in controlling erosion rates. Langbein and
Schumm (1958) have found that vegetation bulk in kg/m2 varies as
the annual precipitation raised to a power greater than unity. With
increasing precipitation the vegetation changes from desert shrubs
to grassland to forest. As a result, when vegetation intensity
becomes adequate it inhibits erosion. Hence, on a regional scale
initially erosion rate increases with increase in annual
precipitation, reaches a maximum and then decreases with further
increase in precipitation. Schumm (1977) expressed the effect of
mean annual temperature and annual precipitation on sediment
yield as shown in Fig. 3.7. It can be seen that as the annual
temperature increases the peak of the sediment yield occurs at
higher value of annual precipitation. This is so because at higher
40
10
15°C
60
5
5°C
10°C
80
1.5
2
100
0.5
Mean annual sed. yield tons/km
Mean seasonal vegetal cover %
Soil loss as a % of bare plot soil loss
300
200
100
0
0
40
80
120
160
Mean annual precipitation cm
Fig. 3.7 Variation of sediment yield
with mean annual precipitation and
temperature (Schumm 1977)
45
Soil Erosion and Sediment Yield
temperature there is greater evapo-transpiration; hence less amount of precipitation is available for
causing runoff. As a result, peak rate of sediment yield shifts to the right. However, studies by Walling
and Kleo for 1296 measuring stations all over the world, by Sharma and Chatterji for small reservoirs in
Rajasthan (India), by Dunne in Kenya, by Griffiths in New Zealand, and by Duglas in Australia do not
support the universality of Fig. 3.7. (Tiwari 1993).
3.5
MECHANICS OF SHEET EROSION
As the rainfall occurs the overland flow normally occurs at shallow depth for a short distance without
forming any small depressions or furrows called rills. The pre-rill flow is many times called inter-rill
flow and associated erosion is known as inter-rill erosion. In this area the depth of flow and the
corresponding shear on the surface are very small. Here the dominating factor influencing the surface
erosion is rainfall impact. On the other hand, once the flow enters the rills and is concentrated, the depth
of flow is large. Therefore erosion in rill-flow is related to the runoff characteristics; this erosion is
sometimes called rill-erosion.
It may be mentioned that rills are not a permanent feature. Rills formed from one storm are often
obliterated before the next storm of sufficient intensity, which can cause rilling. Most rill systems are
discontinuous i.e., they have no connection with the main stream. Rills are usually initiated at a critical
distance down the slope where overland flow becomes canalised. It may also be emphasized that rill
erosion accounts for majority of erosion from the hillside. Mutchler and Young (1975) found that on a
4.5 m slope plots in U.S.A., over eight percent of material was transported in rills. Relative importance
of rill erosion depends on the rill spacing. Smaller the spacing between rills greater will be the rill
erosion.
Four processes associated with inter-rill and rill erosion can be identified as:
Soil detachment by rainfall;
Soil transport by rainfall;
Soil detachment by runoff;
Soil transport by runoff.
Mutchler and Young (1975) have summarised the mechanism of soil detachment by raindrops.
Raindrop sizes usually range from 7.0 mm to fine mist size and in any rainfall there are raindrops of
various sizes. A normal or Gaussian distribution based on the raindrop volumes is usually assumed.
Hence median raindrop diameter d is that diameter for which equal amounts of volume are contained in
larger and smaller drops than d. Laws and Parsons (1943) have found a relationship between intensity of
rainfall I in mm/hour and d in mm as
d = 1.24 I 0.182
...(3.2)
The raindrops attain a terminal fall velocity, which depends on their size, air density and
temperature. Terminal fall velocity can be obtained from CD versus Reynolds number diagram for a
sphere, given in all textbooks on Fluid Mechanics. The terminal fall velocity for 5 mm drop will be
about 9.0 m/s and it will be 1.0 m/s for 0.25 mm drop. Presence of strong wind has two effects on
terminal fall velocity. Firstly it can increase the velocity of drops striking the land surface and secondly
it causes raindrops to strike the surface at an angle to the vertical. The ability of rain to cause soil erosion
is attributed to its rate and the distribution of drop size, both of which affect the energy load of a
rainstorm. The erosivity of a rainstorm is attributed to its kinetic energy or momentum; both these
46
River Morphology
parameters can be related to rainfall intensity or total amount of rainfall. Rose (1960), Williams (1969)
and Kinnell (1973) have related the erosivity rate to momentum of rainfall. Williams and Kinnell have
given the following equations for momentum M:
log M = 0.711 log I – 1.461
M = 0.0213 I – 1.62
UV
W
...(3.3)
Here M is in dynes cm –2 s –1 and I is in mm/hour.
The kinetic energy of the rainfall is a major factor initiating soil detachment. Kinetic energy of
rainfall can be either measured or can be computed if one knows the rain drop size distribution and
corresponding terminal fall velocities. Investigators have used the following three forms of equations to
relate kinetic energy E of rainfall expended per unit quantity of rainfall to the rainfall intensity I.
E = a + b log ( I )
E = c + (b - a I
E=bI-a
-1
U|
)V
|W
...(3.4)
Where a, b, c are empirical constants. Wischmeir and Smith (1958) gave the following equation
E = 13.32 + 9.78 log I
...(3.5)
2
where E is in J/m .mm and I is the rainfall intensity in mm/hour. Hudson (1965) has given the following
equation
E = 29.8 –
127.5
I
...(3.6)
There are a large number of equations developed for E which are based on data from different
regions such as Nigeria, Zimbabwe and U.S.A. It may be mentioned that for a given choice of equation
for E, the kinetic energy for a storm having non-uniform rainfall intensity is computed by
(i) dividing the storm into small time increments in which the rainfall intensity can be assumed to
the uniform;
(ii) determining the rainfall intensity in mm/hour for each time increment;
(iii) computing Ei for each intensity Ii using the chosen relationship between E and I;
(iv) determining E = SEi.
When the raindrop hits the soil surface there is a splash of water and its shape is as shown in
Fig. 3.8. The splash shape parameters, which define its geometry, are crater width W, splash height H,
splash angle b, sheet angle a and sheet radius r. These quantities change with respect to time and their
variation with time as recorded by a high-speed camera is also shown in Fig. 3.8. The erosive action of
raindrop is effective very early after the impact and in the vicinity of the centre of impact. Evidence
indicates that the raindrop impact is most erosive where a thin layer of water about one fifth the drop
diameter is present. If the surface water depth is about three drop diameters, it protects the soil from
raindrop impact. As the splash height reduces and the crater width increases a horizontal flow velocity
away from the splash is caused. This velocity among other parameters also depends on the ratio of water
depth to drop diameter and is maximum when this ratio is 0.33, this horizontal component of velocity
greatly increases the potential of this surface flow to transport detached soil particles.
47
Soil Erosion and Sediment Yield
b
r
Sheet
radius
H
a
W
a and b in°
90
80
Sheet angle a
70
60
Splash angle b
H and W in cm
50
0
4
0.01
0.02
0.03
Crater width W
3
Splash height H
2
1
0
0
0.01
0.02
0.03
Time after Impact s
Fig. 3.8 Changes in splash parameters with time
It must also be mentioned that as the raindrop hits a thin water layer surface, a large number of
smaller water droplets are produced. Mutchler (1971) found that one drop of 5.67 mm diameter on
0.10 mm water depth on a smooth glass produced as many as 4000 droplets which would eventually hit
the soil surface, generate turbulence and throw additional material in suspension.
Raindrop impact effects are present in rills also; but because of relatively larger water depth
compared to the size of drops, the impact effect is not so pronounced.
Erosivity Indices
In developing equations for predicting sheet erosion some investigators have developed erosivity
indices, which depend on rainfall intensity, kinetic energy and other characteristics of rainfall. Some of
these indices are described below:
Wischmeier and Smith (1958) use the rainfall parameter R = EI 30 where E is the total kinetic energy
of the storm and I30 is the maximum 30 minute intensity of rainfall during the storm. They found that soil
loss correlates well with EI30. The term I30 is computed as twice the greatest amount of rain falling in
any 30 consecutive minutes; E is calculated using Eq. (3.5). The parameter R is used in Universal Soil
Loss Equation (see below).
Fournier (1960) developed an erosivity index for river basins on the basis of relationship between
suspended load in rivers and climatic data and relief characteristics. The index called climate index C is
defined as
C = p2/P
where p is the rainfall amount in wettest month and P is the annual rainfall. This index was subsequently
modified by FAO (1977) as follows:
2
C1 = S12
1 p i /P
48
River Morphology
where pi is rainfall in ith month. It is also found that the index C1 is linearly related to the index R i.e. EI30
as
R = a + b C1
...(3.7)
where a and b vary widely from region to region having different climatic conditions.
3.6
EQUATIONS FOR PREDICTING SOIL LOSS FROM AGRICULTURAL
LANDS
Since about 1940 considerable research on soil erosion from agricultural lands has been carried out in
U.S.A. and other countries. Often laboratory and field plots have been used to obtain experimental data
for predicting and evaluating soil erosion. Laboratory plots are of area about 1.0 m2 or less and many
times rainfall simulators are used on them. These are used to study basic erosion phases that are difficult
to study on larger plots, for example, surface sealing, aggregate stability, raindrop detachment, and
splash transport. In such experiments one must be careful in minimising the edge effects in such plots.
The plots used in the development of Universal Soil Loss Equation are large enough to represent the
complete process of rill and inter-rill erosion. These are of such size that their sediment delivery ratio is
very high.
There are various empirical equations, which give the rate of sheet erosion. However, because of
their empirical nature the equations would be strictly valid in the region where they are developed.
Hence only the functional relationships are mentioned to emphasize the variables to which soil erosion
has been related. According to Ellison (1945) the soil dislodged E1 in weight per unit area per unit time
can be expressed as
E1 = K wo4.33 d1.07 I0.65
...(3.8)
where wo is the terminal fall velocity, d is the raindrop diameter, I is the intensity of rainfall, and K is a
constant. Musgrave and his associates in the Soil Conservation Service in U.S.A. made observations
and analysed rates of sheet erosion. As a result an empirical equation of the form
Ei ~ F Ri So1.35 L10.35 P1.75
...(3.9)
was proposed in which Ei is the soil loss in weight per unit area per year, F is the soil factor based the
erodibility of soil and other physical factors, Ri is the factor which is related to the land use, So is the
steepness of slope in percent, L1 is the length of the slope and P is the maximum 30 minute rainfall
expected in the locality with a 2 years return period. The constant of proportionality in this equation
depends on the units used to describe these variables.
Universal Soil Loss Equation (USLE)
Soil erosion rates from cultivated lands in U.S.A. are predicted by using the Universal Soil Loss
Equation (USLE) developed by Wischmeier and Smith (1962, 1965) on the basis of statistical analysis
of a large number of plot-years of data from 47 locations in 24 states. The equation takes into account
the effect of rainfall, soil characteristics, slope and length factor for the land, and crop and management
practices on soil erosion. This equation is an improvement over the earlier methods in that the abovementioned factors have been quantified and used in the equation. The Universal Soil Loss Equation is
E =RKLSCP
...(3.10)
49
Soil Erosion and Sediment Yield
where E is the computed soil loss either in tons/acre year or tons/ha year. R is the rainfall factor in
hundred of foot-ton-inches per acre-hour-year or in MJ. mm/ha h yr. It is the combined erosivity due to
rainfall and runoff. It is the average number of erosion index units in a year of rain.
K is the soil erodibility factor in tons-acre-hours per hundreds of foot-ton-inches-acres or tons-hahour-ha-MJ-mm. (see Fig. 3.6)
L is the slope length factor
S is the slope steepness factor
C is the cropping management factor
P is the erosion control practice factor
Erosion index is a measure of erosive force of the rainfall and is computed as the product of the total
kinetic energy of the rainstorm and its maximum 30 minutes intensity. This is summed for a period of
record and divided by the number of years to get its average value. This product correlates well with the
soil erosion. Wischmeier and Smith (1965) have prepared a map of U.S.A. indicating Iso-R value lines;
R-value varies from 0 to 600 in U.S.A.
Soil erodibility factor K has been discussed earlier. It is defined as the erosion rate per unit of
erosion index on 72.6 feet long and nine percent slope of cultivated soil. K values give an integrated
effect of the characteristics of the soil which influence its permeability and ability to resist detachment
and transport by rainfall and runoff. In central and eastern U.S.A. K values range from 0.03 to 0.70.
The slope length factor L accounts for the fact that as the length of slope increases, there is
increased runoff. It is defined as the ratio of soil loss for a given slope length to the soil loss from 72.6
feet length, other factors remaining the same. If l is the slope length it is found that the soil loss
~ l1.3 to 1.6 and hence soil loss per unit length will be approximately proportional to l0.50.
Slope steepness factor S takes into account the increase in the velocity of runoff as slope increases.
Taking nine percent slope as standard, S is defined as the ratio of soil loss for a given slope to that from
a nine percent slope. If So is the slope steepness in percent, S is related to So as
S = 0.0076 + 0.0053 So + 0.000 776 So2
...(3.11)
Hence the combined effect of slope length and slope steepness in USLE is given as
LS = l0.50 (0.0076 + 0.0053 So + 0.000 776 So2 )
...(3.12)
Cropping management factor C accounts for the crop rotation, used tillage method, crop residue
treatment, productivity level and other cultural practices. Its value is the ratio of soil loss from a field
with given cropping and management practices to the soil loss from the fallow conditions used to
evaluate the K factor. The C factor for individual crops varies with the stage of crop growth and has been
evaluated. Erosion control practice factor P accounts for the effect of conservation practices such as
contouring strip cropping, and terracing on the resulting erosion (see Blakely et al. (1955) and Meyer
and Mannering (1967)). Its value is the ratio of soil loss with one of these practices to the soil loss with
straight row farming.
Earlier USLE is revised and updated by the Agricultural Research Service and some universities in
U.S.A., (see Foster (1988)). This is done
i. to incorporate recently collected data for conservation tillage and range lands into the equation;
ii. to improve the applicability of USLE to other climatic regions;
50
River Morphology
iii. to improve the performance of USLE for conditions where no data exist; and
iv. to estimate values of the factor C.
Attempts are also made to use USLE to estimate soil loss from isolated storm events. Other
improvement being attempted is to evaluate sediment yield by using USLE equation. However this
would require use of the concept of sediment delivery ratio. At present effect of topographic features on
sediment delivery ratio is not known; hence this method of estimating sediment yield is not accurate.
The Universal Soil Loss Equation is used for a number of purposes. Commonly it is used to find out
the soil loss under a given condition. If an acceptable value of soil loss E is chosen the slope length L
required to bring down the soil loss to the chosen value can be calculated. In this way appropriate terrace
spacing can be determined. Alternatively the value of C can be predicted and appropriate cropping
practice is specified. It may however be mentioned that the data on which USLE is based are from east
of Rocky Mountains in U.S.A. Hence values of C pertain to this region only. As mentioned by Morgan
(1979), Hudson and Roose have applied this equation in Zimbabwe and Ivory Coast respectively.
Morgan (1979) has pointed out that there is considerable interdependence between the variables used in
USLE and some are counted twice. For example, rainfall affects both R and C factors, and terracing the
L and P factors. It is also pointed out that one important factor to which soil loss is closely related
namely runoff has not been included in USLE. This has been overcome by Foster, Meyer, and Onstad
who have suggested replacement of rainfall factor R by R1, which depends on R, the storm runoff Q in
inches and qp the storm peak runoff in in/hr. R1 is given by
R1 = 0.50 R + 15 Q qp1/3
...(3.13)
However this needs further verification.
McCool and Rendard (1990) have reported the efforts made in U.S.A. to revise USLE to estimate
more accurately the soil loss from both crop and range land areas. The modified equation is known as
Revised Universal Soil Loss Equation (RUSLE). All the factors R, K, LS, C and P have received
attention. McCool and Rendard have discussed major changes incorporated in RUSLE. Thus R-values
are related to (El15). Further R equivalent approach is used to reflect the combined effect of drain and
snowmelt.
3.7
MEASUREMENT OF SEDIMENT YIELD
Sediment yield is the amount of sediment passing through a given section in unit time. It can be
expressed in tons/km2/yr. Two most common methods of determining sediment yield from river basins
are by measurement of suspended load, and from reservoir sedimentation surveys. These methods and
associated problems are briefly discussed below:
Suspended Sediment Measurements
Determining the average suspended sediment concentration and multiplying it by the discharge can
measure suspended sediment. Average suspended sediment concentration in a vertical can be obtained
by first taking a number of samples at different locations in the vertical and then taking the average.
However, since this is time-consuming and expensive, the following procedures are adopted.
A single sample at water surface or 0.6 times the depth below water surface is taken. Sampling at
water surface is easier and can give reasonably good results if suspended sediment is very fine. For
slightly coarser materials, an empirical coefficient can be used to get average concentration from the
51
Soil Erosion and Sediment Yield
known surface concentration. However, it may be mentioned that the coefficient would really depend on
suspended sediment size and flow conditions. Sampling at 0.60 depths has been used in India and some
parts of U.S.A. in the hope that it gives the average concentration, presumably because the mean
velocity occurs approximately at this level. Analysis of wide range of data indicates that, for reasonable
accuracy, one-point measurements should be made between 0.6 and 0.8 depths, the larger value being
suitable for coarser sediment. A better method would be to take concentrations at 0.2D and 0.8D and
obtain the average concentration as
C=
F3C
H8
0 .2 D
5
+ C0 .8 D
8
I
K
...(3.14)
as suggested by Straub. The three point method involves measurement of concentration at surface, mid
depth and bottom; the mean concentration can then be obtained either by giving equal weightage to all
the three samples or by giving a weightage of two to the mid-depth sample and one to the other two
samples.
If the stream cross-section is non-rectangular the average concentration in the vertical will be
different for different verticals; hence sampling verticals have to be chosen. The following methods are
available:
i. single vertical at the midstream;
ii. single vertical at the point of greatest depth;
iii. verticals at 1/4, 1/2, 3/4 width;
iv. verticals at 1/6, 1/2, 5/6 width;
v. four or more verticals spaced equally across the stream;
vi. verticals at middles of sections of equal discharge.
The final choice of the number of verticals depends on the availability of man power, funds, crosssectional shape and accuracy desired. The suspended load carried by the stream can then be determined
from
Qs =
å
N
1
qi Ci
...(3.15)
where N is the number of verticals, qi is discharge at the centre of each vertical and Ci is the average
concentration.
A brief comment about the frequency of sampling is in order. In reality, samples must be collected at
such a frequency which is satisfactory both from the point of view of accuracy needed and the expenses
involved. Variations of sediment load occur due to variations in storm characteristics; size, shape,
geological and topographical features of the drainage area, and characteristics of the stream. Out of
these, the size of the drainage area appears to be the single most important factor. For smaller drainage
areas water and sediment discharges are greatly dependent on local storm characteristics. For larger
drainage areas, where the runoff accrues from different storms and sub-watersheds, the variation in
water and sediment discharge with time is smaller. Therefore, as a rule, larger the drainage area smaller
can be the frequency; however during a flood when discharge and sediment concentration vary rapidly,
frequent sampling is required. For example, in the case of the Coon Creek, Wisconsin (U.S.A.), having
a drainage area of 200 km2, it was found that 90 percent of the total sediment load for 15 months was
52
River Morphology
discharged within ten days or 2.2 percent of the time, (see TCPSM (1969)). Sampling frequencies vary
widely depending on agency conducting the sampling, purpose of collection of data, nature of stream
and funds available. Sampling interval during low flows can vary from a day to a week. During the
rising stage of a flood, intervals varying from 30 minutes to 12 hours have been utilised.
After collecting such data the suspended load Qs is related to the corresponding water discharge Q;
or alternately suspended load per unit width qs is related to discharge per unit width q. Several field
engineers have reported a relationship between qs and q in the form
qs = a qb
...(3.16)
where b is found to vary between 1.9 and 2.2 and can be taken as 2.0 as an approximation. However,
Leopold and Maddock (1953) found that b varies between 2.0 and 3.0 for many American rivers. The
value of ‘a’ would depend on the units used. The usual practice is to develop such a relationship from
data for a few years and then use it to compute suspended load for other years where only water
discharge variation is known.
Certain limitations of qs vs q relation need to be discussed. The qs vs q relations do not take into
account such factors as sediment size, river slope, watershed characteristics, and pattern of discharge
variation. Experience has shown that such relationships can be different for the rising and falling stages
of the streams. In fact, these can be different for different seasons for the same stream. Significant
variations can also be obtained because the peak of sediment discharge and that of water discharge may
not coincide. For these reasons qs vs q or Qs vs Q relation can only be an approximate guide to the
amount of suspended load and should be used with caution.
To the suspended load must be added the bed-load carried by stream to get the total load. As
mentioned earlier except in the case of shallow streams flowing through relatively coarse material, it is
rather difficult to measure the bed-load. Lane and Borland (1951) cite the following classification of
Maddock, in which percentage of unmeasured load (i.e. bed-load plus unmeasured suspended load) is
related to the concentration of measured suspended load, type of bed material and the texture of
suspended material, see Table 3.9.
Table 3.9 Maddock’s classification to determine unmeasured load
Concentration of
measured suspended
sediment in ppm
Type of material
forming the channel
Texture of the suspended
sediment
Less than 1000
Less than 1000
1000 to 7500
1000 to 7500
Over 7500
Over 7500
Sand
Gravel, rock or consolidated clay
Sand
Gravel, rock or consolidated clay
Sand
Gravel, rock or consolidated clay
Similar to bed material
Small amount of sand
Similar to bed material
25 percent sand or clay
Similar to bed material
25 percent sand or less
Unmeasured load as
a percentage
25 to 150
5 to 12
10 to 35
5 to 12
10 to 15
2 to 8
The average values of qS /qT as obtained from actual measurements or otherwise are available for
some natural streams. Here qT is the total load. These are listed in Table 3.10.
Dekov and Mozzherin (1984) found the ratio of bed-load to suspended load for large streams to be
0.08 for rivers in plain and 0.23 for mountain rivers.
53
Soil Erosion and Sediment Yield
Table 3.10
River
Mississippi river at mouth
Colorado river at Yuma
Niobrara river near Cody
Niobrara river near Valentine
Snake river near Burge
Five mile creek near Riverton
Middle Loup river near Dunning
Biose river near Twin Springs
Moore Creek above Granite Creek
Typical values of qS / qT for natural streams in U.S.A.
Sediment size in mm
Average qS / qT
0.14
0.10
0.30
0.27
0.29
0.24
0.33
0.10
0.25
0.90
0.80
0.49
0.47
0.67
0.81
0.53
0.65
0.75
Tricart (1962) has highlighted the dangers in determining the average erosion rates caused by the
temporal and spatial variation in erosion. His main argument is that there are different types of
discontinuities in the time domain. We have already seen that Qs vs Q relation is not truly unique. Time
lags between flow and sediment are much greater for less mobile material such as coarse sand, gravel
and boulders than for colloids, silts and clays, because while the former move slowly and intermittently
as bed-load the latter move as suspended load and with nearly the same velocity as the flow.
Then there are seasonal discontinuities, which cease more or less for long periods but recur nearly
every year. Sporadic phenomena are caused by floods of large return periods. Catastrophic phenomena
caused by landslides and earthquakes bring in a very large amount of sediment over a short period and
only once in a while. Since the material in transport moves at different speeds, is stopped and is stored in
location dictated by geomorphic evolution, the temporal discontinuities and spatial discontinuities are
closely interlinked. On micro scale, the erosion-taking place from hill slopes caused by rainfall may not
be uniform over the whole slope because of spatial changes in vegetation, roughness and erodibility of
the material. Then as the material moves to the foot of the slope, coarse material may get deposited due
to reduction in slope. This is also assisted due to reduction in flow caused by the high permeability of the
fan. Further, material brought down by avalanches, land slides and source chutes is also discontinuous
and sporadic in variation. Lastly, in the main river sediment is trapped by vegetation, on flood plain, in
the riverbed, and at places where currents are weak. It may take years before the material is mobilised
again and deposited elsewhere. This seems to be too complex a phenomenon to utilise deterministic
model and hence Tricart thought that a statistical approach needs to be used.
Reservoir Surveys
When a large capacity dam is constructed across a stream, a backwater is caused on the upstream side of
the dam, which reduces the energy gradient, and velocity of flow. This effect is felt for several
kilometers in the upstream direction. As a result, the ability of the stream to transport sediment load is
progressively reduced from beginning of backwater curve towards the dam and the excess sediment gets
deposited. If the reservoir capacity to the annual inflow ratio is about or greater than unity, most of the
sediment gets deposited upstream of the dam and only a small percent of finer material may pass over
the dam and through the sluices. Since such deposition over a period of years reduces the valuable
capacity of the reservoir to store water, reservoirs are periodically surveyed to determine the amount of
54
River Morphology
sediment deposited in the reservoir. Hence such surveys provide valuable data on sediment load carried
by the stream.
There are two general methods of conducting reservoir surveys. These are the range-line survey,
and contour survey. The general procedure of carrying out reservoir surveys has changed little in the
past four or five decades; however significant advances have taken place in the equipment available for
carrying out the surveys. Choice of the method depends on availability and character of previous
mapping or survey records, the size of reservoir, degree of accuracy needed, and scope of study
objectives. The range-line method is more widely used for medium and large reservoirs. In this method
a number of cross sections of the reservoir are surveyed before the reservoir is first filled and then
periodically resurveyed. These cross sections are called ranges. From known data for the consecutive
surveys at each range line, one can determine area of sediment deposition, from which total volume of
sediment deposited on the upstream side of the dam can be determined.
Contour method is used for small reservoirs, which are occasionally empty, or at low stage. The
contour method uses essentially the topographic mapping procedures. To apply this method first a good
contour map of the reservoir is prepared before its filling. Similar contour map can be obtained
periodically many times by aerial survey. The contour interval is 1.5 m to 0.5 m. From such consecutive
contour maps the sediment volume deposited during certain period can be ascertained. New techniques
of reservoir surveys are being used at present and these are discussed by Bruk (1985).
Now a days reservoir surveys are carried out using Global Positioning System (GPS). GPS
(GARMIN 2000 and Chatterjee et al. 2001) is a satellite-based navigation system made up of a network
of 24 satellites placed into orbit by U.S. Department of Defence; this system is now available for civilian
use. It works in any weather condition, 24 hours a day.
These satellites circle the earth twice a day in a precise orbit and transmit signal information to the
earth. Using signal information from three or more satellites at the same time, the receivers on the earth
use triangulation techniques to calculate the exact location of the reservoir. The GPS receivers have a
number of potential errors, but if Differential Global Positioning System (DGPS), is used by having two
identical receivers, they provide an accurate means of surveying. The basic principle of DGPS is that
errors calculated by two receivers in a local area will have common errors. Here one GPS receiver at the
base station is located on the surveyed point, and the second one called the rover station is located on the
motorised boat, which collects bathymetric data for reservoirs. The reference station GPS receiver
knows the position of its antenna and can determine the errors in satellite signals. The error between
measured and calculated is the total error. The range errors for each satellite are formatted into messages
and the modular encodes these data. In an amplified form these data are radiated through antenna to
roving GPS Station for real time position correction. Hence, when the two receivers are operated
concurrently, by comparing and processing of signals of both the stations, the position of roving station
can be obtained with adequate accuracy. The depth measuring unit consists of sonic sounding
equipment, which comprises recorder, transmitting and recovering transducers and a power supply. This
equipment needs frequent calibration. With such equipment depths can be measured with an error less
than one percent.
Once the volume of sediment deposited in a given period is known, it can be converted into
corresponding weight if the average unit weight of sediment Wav over a period of T years is known.
Miller (1953) has given the following equation for Wav.
55
Soil Erosion and Sediment Yield
Wav = Wo + 0.434K
LM T ln (T - 1)OP
NT - 1
Q
...(3.17)
where Wav and Wo are the average unit weight and initial unit weight in kN/m3 of the deposited sediment
in T years and the coefficient K depends on the sediment size and method of reservoir operation. Values
of K as recommended by Lane and Koelzer are given in Table 3.11.
Table 3.11 Recommended values of K in Eq. 3.17 (U.S. Govt. and IIHR 1943)
S. No.
1.
2.
3.
4.
Reservoir operation
Deposited sediment
Boulders, gravel sand
Silt
Clays
Sediment always submerged or nearly submerged
Normally a moderate reservoir draw down
Normally considerable reservoir
Reservoir normally empty
0
0
0
0
0.90
0.42
0.16
0
2.51
1.68
0.94
0
Knowing the percentages of the individual fractions in the deposited sediment Wo can be
determined as Wo = S iN= 1 Woi pi/100. In the same way weighted K value can be determined and used in
Eq. (3.17).
To determine initial unit weight Table 3.12 can be used:
Table 3.12
Initial unit weights of sediment
Material
kN/m3
Clays
Silts
Sands
Gravel
Boulders
7.5
9.5
16
20
22
As has been already mentioned, some material flows over and through the dam; therefore sediment
deposited in the reservoir during a given time will be less than sediment flowing into the reservoir
during the same time. This ratio expressed in percent is commonly known as the trap efficiency Te of the
reservoir, which will vary between 0 and 100 percent. If the trap efficiency of the reservoir is known,
yearly quantity of sediment deposited in the reservoir can be converted into sediment yield using the
relation:
FG Annual quantity of sedimentIJ
H deposited in the reservoir K
Sediment yield =
(Trap efficiency/100)
...(3.18)
56
River Morphology
In general, the trap efficiency of a reservoir depends on the ratio of storage capacity to annual
inflow, age of the reservoir, shape of the reservoir, method of reservoir operation, sediment size and its
distribution and type and location of outlets. There is no general method available for the determination
of trap efficiency, which takes into account all these factors. What is being used at present is the trap
efficiency versus (capacity/inflow) ratio curve proposed by Brune (1953) on the basis of record of 44
normally ponded reservoirs in U.S.A., (see Fig. 3.9). On the same figure are also plotted some data from
reservoirs in China, India and South Africa. At present this curve is used in most of the countries for
normally ponded reservoirs.
Trap efficiency, To (%)
100
80
60
Envelopes
40
Reservoirs in China
Reservoirs in USA
Reservoirs in S. Africa
Reservoirs in India
20
0
0.001
0.01
0.1
1.0
10.0
Capacity/Inflow
Fig. 3.9 Trap efficiency of normally ponded reservoirs
Sediment Yield Computations
Theoretically one can use the equations for bed-load and suspended load computations given in Chapter
V and determine the bed material load carried by the stream at a given discharge, which will be the sum
of bed-load and suspended load. To this should be added an estimated quantity of wash load i.e.,
material that is washed into the stream from the drainage basin and which is usually finer than the
material found in the bed and banks of the stream. If such calculations are made for various discharges,
one can prepare the sediment discharge vs water discharge curve from which average annual sediment
discharge can be computed. However, it may be pointed out that what is obtained from such calculations
is really the sediment transport capacity; and it may be quite different from measured sediment yield
especially in the upper reaches of the river. Hence this method is inferior to the other two methods
discussed above.
3.8
SEDIMENT DELIVERY RATIO
As mentioned earlier, sediment delivery ratio is defined as the ratio between amount of sediment load
passing a given section during a certain period and the total amount of erosion from the upstream
catchment during the same period. It can be either expressed as a mere ratio or as a percentage. For plots
of area less than 1.0 km2, the sediment delivery ratio SDR is almost 100 percent, and it decreases as the
57
Soil Erosion and Sediment Yield
catchment area increases. SDR for a particular basin is influenced by a wide range of geomorphological
and environmental factors including the nature, extent and location of sediment sources, relief and slope
characteristics, drainage pattern and channel conditions, vegetation cover, land use, and soil structure.
Basin area is probably the most important variable with which SDR is related. As the catchment area
increases, the catchment slope as well as the channel gradient decreases and hence there is an increasing
opportunity for sediment deposition on flood plain and in channels. Therefore, SDR decreases as A
increases. Other variables used to study variation of SDR are basin relief, annual runoff and gully
density. Figure 3.10 shows the band of scatter of variation of SDR with A for some regions in U.S.A.
and former U.S.S.R. This figure also shows the curve proposed by Soil Conservation Service of U.S.A.
It may be mentioned that for some catchments in China, SDR is found to be 100 percent even up to
catchment area of 1000 km2. This may probably be due to very fine material such as loess that is eroded
and transported without any deposition.
SDR
100
10
1.0
Curve proposed by
SCS, U.S.A.
Central and eastern U.S.A.
Corn waste lands W. Iawa, U.S.A.
Blackland Prairle, Texsas, U.S.A.
Mule creek, Iowa, U.S.A.
South-Eastern Piedmant, U.S.A.
Missouri basin loess hills, U.S.A.
Pasture waste lands, Iowa, U.S.A.
USSR
0.01
0.10
1.0
A km
Enveloping lines
2
10
100
1000
Fig. 3.10 Relation between SDR and A
It needs to be mentioned that there are some serious difficulties in the estimation of SDR, (see
Walling (1988)). Firstly, correct estimation of gross erosion must be made. This is done by estimating
sheet erosion based on soil loss equation and correcting it to take into account the channel and gully
erosion. This procedure has a certain amount of uncertainty. Another problem in the determination of
SDR is the temporal discontinuity that may be involved in the sediment delivery as pointed out by
Tricart. Sediment eroded at one location may be temporarily stored and subsequently remobilised many
times before reaching the outlet of the basin. The third difficulty in relating sediment yield downstream
to the soil erosion upstream is from the fact that the sediment transported by a river represents the
material derived from a number of sources other than upland erosion, e.g., channel and gully erosion
and mass movement etc. Their estimation is very difficult.
A study by FAO (1979) has compared the sediment yield with estimate of contemporary soil erosion
rates from a number of African river basins having catchment areas between 150 km2 and 157 400 km2.
This comparison indicates that the soil erosion rates are about one order of magnitude greater than the
reported sediment yields.
One of the equations, which take into account three variables in estimating SDR, is that by Roehl
(1962) which is based on the data from south eastern U.S.A. It is
58
River Morphology
SDR =
a
f
231.7 Steepness
A 0 . 23 B 2 . 79
0 . 51
...(3.19)
where steepness is defined as the ratio of the maximum difference in elevation in m and basin length
along the main waterway in m, A is the catchment area in km2, and B is the bifurcation ratio. Bifurcation
ratio is the weighted mean ratio of a number of streams of given order to the number of streams in the
next higher order (see Chapter II). For the average value of B = 4.37 for Roehl’s data one gets
SDR =
a
f
3.792 Steepness
A 0 . 23
0 .51
...(3.20)
Walling (1988) lists a few more equations developed for different states in U.S.A. and China.
A more rational and probably a more rigorous approach to defining and investigating the sediment
delivery characteristics of the drainage basin is provided by the sediment budget concept, originally
advocated by Dietrich and Dunne (1978) and developed by Lehre (1982) and others. Here various
sediment sources within the basin are defined and the sediment mobilised from these sources is routed to
and through the channel system by considering various sinks. A typical representation of such a budget
for the Coon Creek in U.S.A. for the period 1938–1975 is shown in Fig. 3.11. Walling (1988) has
represented similar data for the Lone Tree Creek (California), and the Oka river in U.S.S.R. It was found
that in all the cases the proportion of the eroded sediment delivered to the basin outlet is very small.
However, it may be mentioned that presently the availability of techniques for quantifying the various
sources and sinks involved in budgeting the sediment is very limited, and as such mean SDR vs A curve
is often used to obtain erosion rate from observed sediment yield.
Sources
Sinks
76.7%
Upland sheet and till
erosion
55.7%
Colluvial deposits
11.9%
Upland gully
erosion
11.4%
Channel
erosion
Area = 360 km
Fig. 3.11
77.0%
Upland valleys
4.9%
Upper main valley
25.6%
Lower main valley
2
6.7%
Sediment budget for the Coon Creek, Wisconsin (USA) (Area 360 km 2)
Since there is always a gain or loss of sediment storage in the system, the input from slopes and
catchment rarely equals the sediment yield. The sediment storages in the catchment include slope
storage (i.e., colluvium) and stream valley storage (i.e., alluvium). Colluvium when transported by
gravity or by water may partly remain colluvium, or become alluvium, or become sediment yield i.e.
59
Soil Erosion and Sediment Yield
Sediment Sediment Sediment
loss
gain
loss
Sediment
gain
Sediment Sediment Sediment Sediment
loss
gain
loss
gain
Sediment Sediment
loss
gain
efflux. Similarly alluvium can be eroded from the channel or flood plain and redeposited as alluvium or
become sediment yield. Limiting the discussion about valley storage, the most important process in
valley storage gain is vertical accretion from overbank stream flow; other important storage zones are
alluvial fans of small tributaries and colluvial deposits from adjacent slopes. In sediment budget a steady
state would imply input equals output, and upland erosion equals sediment yield. Since steady state is a
very rare, one would like to study gain or loss of sediment from the valley as a function of time, and
relate the nature of variation to the external factors, which influence the gain, or loss of storage; Trimble
(1995) has done this and identified five conceptual models of valley storage fluxes, which are shown in
Fig. 3.12 and briefly described below.
Model-1 (Quasi-steady)
+
Vertical accretion
Steady-state
Lateral
erosion
100 yrs
Model-1 (Vertical accretion
with lateral erosion)
Vertical accretion
+
Vertical erosion
100 yrs
Lateral erosion
Model-3 (Valley trenching)
+
100 yrs
Model-4 (Urban stream)
+
Paving of channels
20 yrs
Moderate control
Uncontrolled
+
Mass movements
Flushing
Colluvium
accretion
Model-5 (High energy
instability, mountains
and arid streams)
20-100 yrs
Fig. 3.12 Conceptual models of valley storage fluxes (Trimble 1995)
Model-1 (Quasi steady state) is applicable to humid regions where adequate vegetation can develop
and stabilise the landscape. There will be very little upland erosion and hence very little sediment load.
Lateral erosion of one bank would cause lateral deposition on the opposite bank. The perturbations in
the vertical accretion of floodplain would be a few centimetres per millennium at most. This situation
existed in eastern U.S.A. before European settlement.
60
River Morphology
Model-2 (Perturbation of humid area quasi steady state) is applicable in humid area where sediment
load in excess of transport capacity is generated by strong climatic or natural forces (e.g., mining or
large construction activity). This causes vertical accretion of floodplain and the channel. When the
activity in the upland area stops, this deposited sediment is gradually eroded and transported
downstream. This removal of deposited sediment shows exponential decrease. If the sediment supply
from the upland is low, lateral erosion of channel may take place later.
Model–3 (Valley trenching and arroyo cutting) is applicable when the climate or human induced
perturbations cause an incremental increase in discharge greater than incremental increase in sediment
discharge. This can result in trenching or gullying. The example of this model is found in semi arid south
western U.S.A. In such areas the fragile grasslands were overgrazed, the vegetation was thinned
drastically and the soil compacted resulting in greater stream flows and arroyo cutting.
In Model–4 (Urban streams), a brief rapid increase in erosion occurs while urbanisation in
underway, but when it is stabilised due to increasing imperviousness of the area the runoff increases and
erosion decreases. This initiates arroyo cutting. In order to save valuable land, if arroyos are stabilised
by paving the Model-4 results, otherwise Model-3 results.
Model-5 (High energy instability, mounting and arid streams) is applicable to streams with a very
narrow floodplain and very steep valley sides. The sediment budget in this case is much more episodic
than cyclic in nature. Net storage gain can come from vertical accretion coming from fans of small
tributaries and mass movement from valley sides. Sediment loss comes from large events, which flush
sediment downstream. This model shows a period of accretion followed by flushing events, and the
process is repeated at uneven time intervals.
Identifying the sediment budget model enhances our understanding of the fluvial processes working
in the system and throws light on the magnitude and time scales of sediment storage fluxes under the
given environmental conditions and natural and man made perturbations.
3.9
PROCESS BASED MODELLING OF EROSION
Even though USLE summarises a vast body of regionally derived data and expresses it in the equation
form, the researchers are aware of its empirical nature and its limitation that it is not universally
applicable. Further, it is also recognised that USLE does not explicitly represent the processes involved
in soil erosion. As a result USLE gives only an average annual soil loss. Therefore, several attempts
have been made to develop methodology for prediction of erosion by modelling the basic processes
involved. These are discussed by Rose (1988).
Overland Flow
Consider flow on a planar land surface on a slope. Let L be the length of slope. Then the sediment flux
flowing out of a unit width is
qs = q C
...(3.21)
3
where qs is in mass of sediment/time, width, q is volume rate of water in m /s m, and C is the sediment
concentration in oven dry mass of sediment per volume of suspension. One must now obtain expression
for overland flow q. One can write
61
Soil Erosion and Sediment Yield
R =P–I
...(3.22)
where R is the excess rainfall, P is the precipitation and I is the rate of infiltration all being function of
time. If Q represents runoff per unit area
Q = q/(L)
...(3.23)
One can then see that
R =Q
...(3.24)
However, if L is large and R varies with time, it will be seen that changes in Q will lag behind those
in R. Thus in general R ¹ Q. It can be shown that
R » Q + Kp
¶Q
¶t
...(3.25)
where Kp depends on length, slope and roughness of the plane, Q, and on whether the overland flow is
laminar or turbulent. The flux q(x) at any distance is given by
q(x) = Qx
...(3.26)
Erosion and Deposition Processes
The following three processes affect the sediment concentration:
1. Rainfall detachment in which raindrops splash sediment from the soil surface into the water of
overland flow.
2. Sediment deposition, which is the result of sediment settling out under the action of gravity; and
3. Entrainment of sediment from the soil surface in which sediment is picked up from rills, interrills and in sheet flow.
Rate of raindrop detachment e is expressed as
e = a Ce P
...(3.27)
2
where e is in kg/m s, a is the measure of detachability of soil by rainfall rate P and Ce is the fraction of
soil surface exposed to the rain drops. The rate of sediment deposition di for a given size class i of fall
velocity wi is expressed as
di = wi Ci
...(3.28)
where Ci is the sediment concentration of size class i. The rate of sediment entrainment can be related to
excess stream power over its critical value. Let the rate of sediment entrainment for a given size class be
gi. Then conservation of mass principle applied to a given size class i yields
¶
¶
(qCi) + (DCi) = ei + gi – di
¶x
¶t
...(3.29)
where D is the depth of overland flow at any time. Making certain approximations, Eq. (3.29) can be
reduced to ordinary first order differential equation, which can be solved to yield
C(L, t) =
FG ac p IJ S
H QI K
e
I
i = 1 (g i)
+ r f gSKC g (1 – x*/L)
...(3.30)
62
River Morphology
FG
H
for L > xi . Here I is the number of sediment class ranges, gi = 1 +
IJ
K
wi
rf is mass density of water, S is
Q
the land slope, K = (1 + 0.2677h), where h is the efficiency of net sediment entrainment and transport, Cr
is the fraction of soil surface unprotected from entrainment by overland flow, and x* is the distance down
slope from the top of the plane beyond which sediment entrainment commences. The accumulated mass
of sediment Ms from a plane of width W is thus given by
Ms = WL
z
t
R C(L, t)QDt
...(3.31)
0
where tR is the duration of runoff. Equation (3.30) can be written as
C (L, t) = A + B
...(3.32)
where A is the net contribution to sediment concentration of rainfall detachment over deposition, and B
is the net contribution of entrainment over deposition. Assuming A to be negligible and taking time
average values of x*, Q and h, as x* , Q and h, C (L) can be expressed as
F
H
C(L) = 2700ShCr 1 -
x*
L
I
K
...(3.33)
Dynamic Simulation Models
A more elaborate model is given by Negev (1969), which is commonly known as Stanford Sediment
Model. In this model, the rainfall impinging on the land surface is divided into two parts, that falling on
the impervious surfaces and that falling on the pervious surfaces. The sediment supply from impervious
surface is determined by a power function relationship taking hourly rainfall as the independent
variable. Rain falling on the soil is assumed to loosen the material by raindrop splash. This loosened
material, called soil splash is then considered as potential sediment for the stream. If overland flow
occurs, as computed by Stanford Watershed Model, then all the soil splash material in previous storages
is transported together with the current soil splash material. Overland flow is also used to compute the
rate of rill and gully erosion using power function relationship. Rill and gully erosion is then divided
into inter load and bed material storage.
The input to this model consists of hourly and daily recorded rainfall, daily recorded flow and
sediment load, hourly overland flow, a translation histogram for routing the sediment through the stream
system, information on the sediment rating curve for use in adjusting the material assigned to inter load
and bed material load from rill and gully process, and set of parameters and exponents for use in the
various power functions by which the sediment erosion processes are estimated. These are adjusted
during the runs to calibrate the model. Use of this model to the Napa river, St. Helena, California
(U.S.A.) and the river Clyde in Scotland has given good results.
Other dynamic models developed include the one developed by Simons et al., (1975). The various
processes modelled in this program include, interception, infiltration, overland flow from rainfall
excess, sediment detachment due to raindrop impact, sheet erosion by overland flow, channel erosion
and the routing of water and sediment through the channel system. The sediment detachment is
calculated during a specific time increment as a function of rainfall intensity and provision is made for
63
Soil Erosion and Sediment Yield
Storm
characteristics
Basin
characteristics
Sizewise soil detachment by
raindrop impact with provision
for amounting
Water
routing
Overland
flow
data
Overland flow
routing
Overland flow
bed material
routing
Channel flow
data
Overland flow
bed material
routing
Bed material
load hydrograph
Antecedent
characteristics
Loose soil
storage
Soil detachment by overland
flow considering sizewise
transport capacity and supply
of loose soil
Loose soil storage
Overland flow
wash load
routing
Soil detachment by
channel erosion
Loose soil erosion
Total sediment
yield
Channel flow
wash load
routing
Wash load
hydrograph
Fig. 3.13 Flow chart for water and sediment routing model developed at Colorado State University (Simons et al. 1975)
calculating the detachment of different size fractions and for the development of surface armouring.
Sediment supply for the transport depends on the initial depth of loose soil remaining from the previous
storms, the amount of soil detachment by rain drop impact and the amount of soil detached by surface
runoff. Sediment transported by overland flow is calculated using Meyer-Peter and Müller’s formula for
bed-load transport. Similar procedure is used to route the wash load and the bed material load through
the channel system using continuity equation to determine occurrence of aggradation or degradation.
Figure 3.13 shows flow chart for this model. It may be mentioned that in recent times several such
models have been developed. Morgan et al. (1990) describe the European Soil Erosion Model
(EUROSEM) developed as a collaborative project by seven European countries.
Two more models can be briefly discussed. Kothyari et al. (1997) have developed a method for
estimation of temporal variation of sediment yield for a single storm in small catchments. The method is
based on numerical solution of kinematic wave equation for simulation of overland flow, continuity
equation for sediment and expressions for sediment detachment and transport. The model is calibrated
and verified using twelve experimental catchments ranging in size from 0.002 km2 to 92.5 km2. For
single storm events sediment yield varied from 0.003 tons to 800 tons.
Julien and Rojas (2002) have discussed a physically based model simulating hydrologic response of
a watershed to distributed rainfall field, considering time-dependent processes such as precipitation,
interception, infiltration, surface runoff and channel routing, and upland erosion, transport and
sedimentation, the model predicts, flood and sediment load variations with time. The model was applied
to 21 km2 Goodwin Creek catchment in U.S.A.
64
River Morphology
Stochastic Models
Lack of detailed long duration record of erosion rates has hampered the application of various stochastic
and time series modelling procedures to the erosion process. Yet some attempts have been made in the
application of Autoregressive Moving Average (ARMA) Models to the records of Suspended Sediment
concentration. Sharma et al. (1979) describe the use of a simple system model of this type to model the
monthly and daily sediment yield of several catchments in Ontario, Canada. The model used to describe
daily erosion rates explained 95 percent of the variation in the erosion process of the Thames river at
Ingersol, while the monthly model accounted for more than 81 percent of short-term values of sediment
concentration recorded during individual storm events.
3.10
EROSION RATES FROM INDIAN CATCHMENTS
In India the approaches used for prediction of erosion rates have been essentially empirical involving
regression method. This is primarily so because of the lack of availability of extensive data needed for
use of physically based and simulation models. Earlier Khosla (1953) analysed the then available data
from Indian reservoirs and reservoirs from abroad and found that the annual sediment yield in Mm3 is
proportional to A0.72 where A is the catchment area in km2. However, Garde and Kothyari (1987) found
large variations from this relationship when it was tested with recently collected Indian data. Dhruva
Narayan et al. (1983) used the data from seventeen catchments in India and obtained the following
relations for annual sediment yield T1 in metric tons.
T1 = 5.5 + 1.1 Q
...(3.34)
where Q is the annual runoff in M ham. This equation was further modified to
T1 = 5.3 + 12.7 QW1
...(3.35)
where W1 = T1/A, A being in M ha. Average value of W1 was found to be 1.25 M tons/M ha. Another
relationship proposed by them involved use of EI30.
T1 = (0.342 ´ 10 –6)A0.84 (EI30)1.65
...(3.36)
where EI30 is the product of average annual value of the sum of maximum 30 minute rainfall intensity in
cm/hr and kinetic energy value E given by
E = 210 + 89 log I30
...(3.37)
E being in tons/ha m. However, these equations need to be verified with additional data before these
can be used with confidence.
By far the most detailed analysis of Indian data has been carried out by Garde and Kothyari (1987,
1990). They analysed the average annual sediment yield data from 50 catchments in India having areas
varying from 43 km2 to 83 880 km2. These data were obtained from the surveys of small, medium and
large reservoirs with sedimentation period of at least ten years. Analysis of data indicated that the
average annual erosion rate Sa in cm is a function of average annual rainfall P in cm, the average
1 n
S AiSi, the drainage density D in km –1, the ratio (Pmax /P) where Pmax
A1
is the average monthly maximum rainfall in cm, and the erosion factor Fe which gives an integrated
effect of vegetation on erosion. The erosion factor Fe was defined as
catchment slope defined as S =
65
Soil Erosion and Sediment Yield
Fe =
1
[0.8 AA + 0.6 AG + 0.3 AF + 0.1 AW]
A
...(3.38)
where AA is the arable area, AG scrub and grass covered area, AF is protected forest area, and AW is the
waste land area all in km2. A map showing lines of constant Fe values was prepared from available data
and this is shown as Fig. 3.14. The range of variables used by Garde and Kothyari are given below:
– 108.3 cm
P 63.77 cm – 381.11 cm
Pmax 9.0 cm
– 1.00
S 0.001
– 0.200
Fe 0.28
2
2
–1
D 0.002 km – 0.31 km–1
A 43 km – 82 880 km
The regression analysis of the data gave the following equation for Sa
Sa = 0.02 P0.60 Fe1.70 S 0.25 Dd0.10 (Pmax/P)0.19
...(3.39)
This relationship was then used on ungauged catchments for which all other data except Sa values
were available. Sa was then computed from which sediment yield was expressed in tons/km2/year. Thus
using data from 154 catchments an iso-erosion rate map was prepared which is shown in Fig. 3.15. It can
be seen that the erosion rates in India vary from about 350 tons/km2/year to 2500 tons/km2/year. High
erosion rates in North eastern region, parts of U.P., Bihar and Punjab, and in certain areas in Andhra
Pradesh are partly due to high rainfall in these regions and partly due to geologic conditions and land
usages.
Considering that out of the variables affecting the erosion rate, only the annual rainfall changes
from year to year, the following equation was proposed by Garde and Kothyari (1987) for the estimation
of annual erosion rates.
Pa = 0.02 Pam Fe1.70 S – 0.25 Dd0.10(Pmax/P)0.19
...(3.40)
where Pa is the annual precipitation in cm. Here m is the exponent, which was found to be related to
coefficient of variation of annual precipitation. It may be seen from comparing Eqs. (3.39) and (3.40)
that
P0.6 =
1
n
å
n
i
Paim
where n is the number of years. Analysis of rainfall data from 100 rainfall stations indicated that as
coefficient of variation changed from 0.1 to 0.70, m, value of the exponent increased from 0.600 to
0.607. This variation is shown in the following table:
Cv
0.10
0.20
0.30
0.40
0.50
0.70
m in Eq. (3.40)
0.600
0.601
0.602
0.603
0.605
0.607
Thus for annual sediment yield computation Eq. 3.40 with table for m can be utilised. For future
year wise prediction of sediment yield, one must generate annual rainfall series for known P and Cv and
then compute the sediment yield. The annual series in India are found to follow normal distribution. It
may be mentioned that with the passage of time land use pattern as well as extent of forest and other
vegetation is bound to change and hence Fig. 3.11 need to be modified at regular time intervals and so
also Fig. 3.12. However Eqs. (3.39) and (3.40) will not change.
66
River Morphology
0.55
0.55
0.55
0.6
0.6
0.55
0.6
0.5
0.55
Nep
al
0.5
n
Bhuta
0.6
0.6
0.6
0.4
0.4
0.55 Bangladesh
0.6
0.4
0.5
0.5
0.5
0.55
0.55
0.45
0.54
0.54
0.45
Notations
Igneous intrusive rocks
Sedimentary unconsolidated
(Recent alluviums)
Metamorphic (Schists)
0.55
Sedimentary consolidated
Unclassified crystallines
Khondalite
0.45
Other igneous and
metamorphic rocks
0.5
Iso-erosion factor lines
Geologic boundaries
Sri
Lanka
Fig. 3.14 Lines of constant Fe superimposed on the geological map of India (Garde and Kothyari 1987)
Soil Erosion and Sediment Yield
Fig. 3.15 Iso-erosion rate lines in tons/km2 yr (Garde and Kothyari 1987)
67
68
River Morphology
References
Blakely, B.D., Coyle, J.J. and Steele, J.G. (1955) Erosion on Cultivated Land. Soil- The 1957 USDA Year Book of
Agriculture.
Brown, L.R. (1984) Conserving Soils. In State of the World 1984, (Ed. Brown L.R.) Norton, New York.
Bruk, S. (1985) Methods of Computing Sedimentation in Lakes and Reservoirs. A Contribution to the IHP-II
Project, A. 2.6.1. Panel, UNESCO, Paris, pp. 224.
Brune, G.M. (1953) Trap Efficiency of Reservoirs. Trans. AGU, Vol. 34, No. 3, July, pp. 407-418.
Chatterjee, P.K., Bathija, T.S. and Sangeet, S. (2001) Methods of Reservoir Sedimentation surveys. Proc. Of
C.B.I.P. Seminar on Reservoir Sedimentation, Ooty, Tamil Nadu, India, pp. 33-41.
Dekov, A.P. and Mozzherin, V.I. (1984) Eroziya I Stok Nanosov na Zemle. Izadatolstvo Karzanskogo Universiteta.
Dendy, F.E. (1968) Sedimentation in Nation’s Reservoirs. Jour. Soil and Water Conservation, Vol. 23, No. 4.
Dietrich, W.B. and Dunne, T. (1978) Sediment Budget for a Small Catchment in Mountain Terrain. Zeitschrift fur
Geomorphologie. Supplementband, 29, pp. 191-206.
Dhruva Narayana and Ram Babu (1983) Estimates of soil Erosion from India. JIDD, Proc. ASCE, Vol. 109, No. 4.
Ellison, W.D. (1945) Some Effects of Rainfall and Surface on Erosion and Infiltration. Trans. AGU, Vol. 26, No. 3.
El-Swaify, S.A., Dangler, E.W. and Armstrong, C.L., (1982) Soil Erosion by Water in the Tropics. University of
Hawaii Research Extension Series No. 024.
Elwell, H.A. (1980) Design of Safe Rotational Systems. Department of Conservation and Extension, Harare
(Zimbabwe).
Elwell, H.A. and Stocking M.A. (1974) Rainfall Parameter and a Cover Model to Predict Runoff and Soil Loss
from Grazing Trails in the Rhodesian Sandveld. Proc. of the Grassland Society of South Africa, Vol. 9.
FAO, U.N. (1977) Assessing Soil Degradation. Soils Bulletin 34, Rome, Italy.
FAO, U.N. (1979) A Provisional Methodology of Soil Degradation Assessment, Rome, Italy.
Foster, G.R. (1988) Modelling Soil Erosion and Sediment Yield. In Soil Erosion Research Methods (Ed. Lal R.)
Soil Water Conservation Society, Ankeny, Iowa (U.S.A.), pp. 97-118.
Fournier, F. (1949) Les Facteurs Climatiques de l ‘Erosion du Sol. Assoc. Geo’graphes Francais, Bull. Vol. 203.
Fournier, F. (1960) Climat et Erosion: la Relation entre l ‘Erosion du Sol par l ‘Eau et les Precipitations
Atmospheriques. Presses Universitaires de France, Paris.
Garde, R.J. and Dattatri, J. (1961) Investigation of the Total Sediment discharge of Alluvial Streams. Roorkee
University of Research Journal (India), Vol. No. pp. 65-78.
Garde, R.J. and Kothyari U.C. (1987) Sediment Yield Estimation. Journal of Irrigation and Power (India), CBIP,
Vol. 44, No. 3.
Garde, R.J. and Kothyari U.C. (1990) Erosion Prediction Models for Large Catchments. International Symposium
on Water Erosion, Sedimentation and Resources Conservation. CSWCRTI, Dehradun, Oct. pp 89-102
GARMIN (2000) G.P.S. Guide for Beginners. Garmin Intl. Inc. Olathe, Kansas (U.S.A.)
Heede, B.H. (1975) Stages of Development of Gullies in the West. Proc. of the Sediment Yield Workshop, USDA,
Oxford (Mississippi), ARS-S-40.
Holeman, J.N. (1968) The Sediment Yield of Major Rivers of the World. W.R. Research, Vol. 4, pp. 737-747.
Hudson, N.W. (1965) The Influence of Rainfall on Mechanics of Soil Erosion with Particular Reference to
Northern Rhodesia. M.S. Thesis, University of Cape Town, South Africa.
Janda, T. Dunne and Swanson, D.N. General Tech. Report PNW 141, Forest Service USDA Portland, Oregon,
U.S.A.
Soil Erosion and Sediment Yield
69
Julien, P. and Rojas, R. (2002) Computer Modeling of Upland Erosion. Proc. Of 12 APD Intl. Congress,
Singapore, Vol. 1, pp. 475-483.
Kinnell, P.I.A. (1973) The Problem of Assessing the Erosive Power of Rainfall from Meteorological Observations.
Proc. Soil Science Society of America, Vol. 37, pp. 617-621.
Khosla, A.N. (1953) Silting of Reservoirs. CBIP Publication No. 51, New Delhi (India).
Kothyari, U.C., Tiwari, A.K. and Singh, R. (1997) Estimation of Temporal Variation of Sediment Yield from Small
Catchments through the Kinematic Method. Jour. Of Hydrology, Vol. 203, pp. 39-57.
Kuenen, P.H. (1950) Marine Geology. John Wiley and Sons, Inc., New York.
Lane, E.W. and Borland, W.M. (1951) Estimating Bed Load. Trans. AGU, Vol. 32, No. 1, February.
Langbein, W.B. and Schumm, S.A. (1958) Yield of Sediment in Relation to Mean Annual Precipitation. Trans.
AGU, Vol. 39.
Laws, J.O. and Parsons, D.A. (1943) The Relation of Raindrop Size to Intensity. Trans. AGU., Vol. 24.
Lehre, A.K. (1982) Sediment Budget in a Small Coast Range Drainage Basin in North Central California. In
Sediment Budget and Routing in Forest Drainage Basins (Ed Swanson, R.J.)
Leopold, L.B. and Wolman, M.G. and Miller, J.P. (1964) Fluvial Processes in Geomorphology. W.H. Freeman and
Co., San Francisco, U.S.A.
Leopold, L.B. and Maddock, T. (1953) The Hydraulic Geometry of Steam Channel and Some Physiographic
Implications. USGS Professional Paper 252.
Mackenzie, F.T. and Garrel, R.M. (1966) Chemical Mass Balance Between Rivers and Oceans. Am. Jour. Sci.,
Vol. 264, pp. 507-525.
McCool, D.K. and Rendard, K.G. (1990) The Revised Universal Soil Loss Equation. Proc. of Int. Symposium on
Water Erosion Sedimentation and Resource conservation, Dehradun (India), Oct., pp. 60-70.
Meyer, L.D. and Mannering, J.V. (1967) Tillage and Land Modification for Water Erosion Control. ASAE-ASASCSA Tillage Conference Proc. pp. 58-62.
Miller, C.R. (1953) Determination of Unit Weight of Sediment for Use in Sediment Volume Computations. USBR,
Denver, U.S.A..
Milliman, J.D. and Meade, R.H. (1983) Worldwide Delivery of River Sediments to Oceans. Jour. Geology Vol. 91,
pp. 1-21.
Morgan, R.P.C. (1979) Soil Erosion. Longman Group Ltd., London.
Morgan, R.P.C., Quinton, J.N. and Rikson, R.J. (1990) Structure of Soil Erosion Prediction Model for the
European Community. International Symposium on Water Erosion, Sedimentation and Resource
Conservation - CSWCRTI, Dehradun, Oct., pp. 49-59.
Mutchler, C.K. (1971) Splash Production by Water Drop Impact. Water Resources Research, Vol. 7.
Mutchler, C.K. and Young, R.A. (1975) Soil Detachment by Raindrops. Proc. of the Sediment Yield Workshop,
USDA, Oxford (Mississippi), U.S.A., ARS-S-40, pp. 113-117.
Negev, M. (1969) A Sediment Model on Digital Computer. Stanford University, U.S.A., Civil Engg. Deptt., Tech.
Rep. No. 76.
Pechinov, D. (1959) Vodna Eroziya I To’rd Ottok. Priroda, Vol. 8, pp. 49-52.
Piest R.F., Bradford, J.M. and Spomer, R.G. (1975) Mechanism of Erosion and Sediment Movement from Gullies.
Proc. of the Sediment Yield Workshop. USDA, Oxford, Mississippi, ARS-S-40, pp. 162-176.
Robinson, A.R. (1977) Relationship Between Soil Erosion and Sediment Delivery. Symposium on Erosion and
Solid Matter Transport in Inland Waters, IASH, No. 122, July, pp. 159-167.
Roehl, J.E. (1963) Sediment Source Areas, Delivery Areas and Influencing Morphological Factors. IASH
Publication No. 59.
70
River Morphology
Rose, C.W. (1960) Soil Detachment Caused by Rainfall. Soil Science, Vol. 89, pp. 28-35.
Rose, C.W. (1988) Research Progress on Soil Erosion Processes and a Basis for Soil Conservation Practices. In
Soil Erosion Research Methods (Ed. R. Lal. ) Soil and Water Conservation Society, Ankeny, Iowa, U.S.A., pp.
119-140.
Schumm, S.A. (1963) Disparity Between Present Rates of Denudation and Orogeny. U.S. Geological Survey,
Professional Pape 454-H, pp. 13
Schumm, S.A. (1977) The Fluvial System A Wiley Interscience Publication, John Wiley and Sons Inc.
Sharma, T.C., Hines, W.G.S. and Dickinson, W.T. (1979) Input-Output Model for Runoff Sediment Yield
Processes. J. of Hydrology, Vol. 40.
Simons, D.B., Li, R.M. and Stevens, M.A. (1975) Development of Models for Predicting Water and Sediment
Routing and Sediment Yield from Storms on Small Watersheds. CSU Report No. CER-74-75, DBS-RMLMAS-24.
TCPSM (1969) Sediment Measurement Techniques: A Fluvial Sediment Task Force Committee on the
Preparation of Sediment Manual Report, JHD, Proc. ASCE. Vol. 95, No. HY-5, September.
Tiwari, A.K. (1993) Temporal variation of Sediment Yield from Small Catchments. Ph.D Thesis, University of
Roorkee.
Tricart, J. (1962) Les Discontinuities dan les Phenomenes d’ Erosion. Int. Assoc. Sci. Hydro., Vol. 59.
Trimble, S.W. (1995) Catchment Sediment Budgets and Change. In chaning River channels (Eds. Gruznell, A and
Petts, G.) John Wiley and Sons, Chicester, pp. 210-215.
U.N.E.P. (1980) Annual Review. United Nations Environmental Program, Nairobi, Kenya.
U.S. Govt. and IIHR (1943) A Study of Measurement and Analysis of Sediment Loads in Streams. Density of
Sediments Deposited in Reservoirs, Rep. No. 9.
U.S.S.R. National Committee for I.H.D. (1974) Mirovoi Vodnyi Balans I Vodnye Resursy Zemli. Gidrometerozat,
Leningrad.
Van Rijn, L.C. (1982) Sediment Transport, Part II: Suspended Load Transport. JHE, Proc. ASCE, Vol. 110, No. 11,
November, pp. 1613-1641.
Walling, D.E. (1988) Measuring Sediment Yield from River Basin In Soil Erosion Research Methods (Ed) R.Lal.
Soil and Water Conservation Society, Ankeny, Iowa, U.S.A., pp. 39-74.
Walling, D.E. and Webb, B.W. (1983) Patterns of Sediment Yield. In Background to Palaeohydrology (Ed Gregory
K.J.) John Wiley and Sons, Chichester, U.K., pp. 69-100.
Williams, M.A. (1969) Prediction of Rainfall Splash Erosion in the Seasonaly Wet Tropics. Nature, Vol. 222, pp.
763-765.
Wischmeier, W.H. and Smith, D.D. (1958) Rainfall Energy and its Relationship to Soil Loss. Trans. AGU, Vol. 39,
pp. 285-291.
Wischmeier, W.H. and Smith, D.D. (1962) Soil Loss Estimation as a Tool in Water Management Planning. Int.
Assoc. For Sci. Hydro. Pub. No.59, pp. 148-159.
Wischmeier, W.H. and Smith, D.D. (1978) Predicting Rainfall Erosion Losses: A Guide to Conservation Planning.
USDA Agricultural Handbook No. 537, pp. 58.
Wischmeier, W.H., Jhonson, C.B. and Cross, B.V. (1971) A Soil Erodibility Monograph for Farmland and
Construction Sites. Jour. Soil and Water Conservation, Vol. 26, pp. 189-192.
Young, A. (1969) Present Rate of Land Erosion. Nature, Vol. 224, pp. 851-852.
C H A P T E R
4
Fluvial Morphology
4.1
GEOMORPHOLOGY AND FLUVIAL MORPHOLOGY
The name geomorphology originates from the Greek terms geo meaning earth, morphe meaning form
and logos meaning discourse. Hence, geomorphology is the science of the origin and evolution of
topographic features caused by physical and chemical processes operating at or near the earth’s surface.
The landforms may result or may be modified by denudational processes, depositional processes or
a combination of the two. Denudational or degradational processes are sometimes called exogenous
processes while the depositional processes are known as endogenous processes. Together they are
known as geomorphic processes. Among the agents and processes which shape the configuration of
earth’s surface, the important ones are: (i) Running water, (ii) Glaciers, (iii) Ground water, (iv) Waves
and currents, (v) Wind, (vi) Weathering, (vii) Volcanism and (viii) Diastrophism.
Running water is that part of rainfall or snows melt which flows on earth’s surface after infiltration
requirement is satisfied; this is known as surface runoff. It collects in streams, which continually erode
the land and deposit the material elsewhere. Landforms produced by glaciers are markedly different
because glaciers move slowly and are capable of carrying large quantities of coarse material with them.
Groundwater, while in contact with rocks, promotes solution and other types of chemical weathering.
This leads to unique landforms, especially in the areas of rapidly soluble rocks, such as limestone.
Waves beating against the shorelines of seas and large lakes modify shorelines by their erosive
action and subsequent deposition of the eroded material elsewhere. In arid and semi-arid regions and in
regions having abundant supply of loose sand, wind is an effective agent of erosion and deposition.
Weathering action loosens the rocks and breaks them into smaller pieces, which can be transported by
different agencies. Mechanical weathering produces angular hill-slopes whereas chemical weathering
promotes smooth rounded slopes. Volcanic eruptions produce distinctive landforms such as volcanic
cones and lava flows. A sudden change in land surface or part of it due to tensile or compressive forces
is known as diastrophism. It can be seen that volcanism and diastrophism are endogenous processes.
Since the word fluvial means produced by rivers, the term fluvial morphology can be defined as a
science dealing with forms as those produced by river action. Fluvial morphology is of great interest to
72
River Morphology
hydraulic engineers, geologists, geo-morphologists, geographers and environmental engineers, since
many of the complex problems they have to deal with are due to the form of the streams created by the
erosion, transportation and deposition of sediment carried by them.
Even though several scientists have contributed to the development of the science of geomorphology, W.M. Davis in the early 20th century was primarily responsible for synthesising many of
the earlier developments and presenting them in the form of a unified system for the study of landforms.
Certain basic concepts developed by geo-morphologists are of significance to hydraulic engineers and
these are discussed here in brief.
4.2
GEOMORPHIC CYCLE (OR CYCLE OF EROSION)
The basic idea underlying the concept of geomorphic cycle or the cycle of erosion is that the topography
of a stable region evolves through a continuous sequence of landforms having distinctive characteristics
at successive stages of development. The process starts with the initial uplift of landmass through
diastrophism. This initial uplift is tacitly assumed to take place without appreciable erosion. Since in
most regions the current uplift rates are much greater than the denudation rates, the above assumption is
a reasonable one. Later the cycle of erosion proceeds under prolonged tectonic stability producing
various types of topography, which are characteristic of the various lengths of time for which the water
has acted on it; the material is continually eroded from the land surface and deposited in the sea. The
elevation of the land surface is thus gradually lowered and land surface flattened until after a very long
time the whole surface is reduced to a gently sloping plain called peneplain. This is the end of the cycle
and an upheaval will start a new cycle (Davis 1909, Lane 1955). Davis introduced the word peneplain to
describe landscapes that have undergone long continued weathering and erosion in humid climate. In
the geographical context the word plain connotes a surface of very low relief. Realising that the ultimate
base level is the limit of sub-aerial erosion, which like a mathematical limit, may be approached
asymptotically but never reached, Davis prefixed the word “plain” by the Latin word “pene” meaning
almost. This peneplain is a surface of regional extent, resulting from long continued fluvial erosion.
Another concept introduced by the geo-morphologists and which is useful in discussion of fluvial
morphology in general and the cycle of erosion in particular is that of base level first formulated by
Powell in 1875. In fact he wrote (Esterbrook 1969),
“We may consider the level of sea to be a grand base level, below which the dry lands cannot be
eroded; but we may also have, for local and temporary purposes, other base levels of erosion, which are
the levels of the beds of the principal streams which carry away the products of erosion. The base level
would in fact, be an imaginary surface inclining slightly in all parts towards the lower end of principal
stream”.
Powell’s definition of base level, thus includes three basic ideas; namely
(i) The ultimate limit of sub-aerial erosion of the continent is the base level of the sea.
(ii) Locally resistant rocks in the path of the stream, lakes in the stream path, or other obstacles can
produce temporary base level.
(iii) Tributaries may not erode below that of the main stream, and since mainstream will always
have some slope, the base level need not always be a flat surface.
Fluvial Morphology
73
Thus, sea level may be considered as a general, permanent base level which fluctuates from time to
time but which remains normally within a range of a few metres. Local base levels such as rock outcrops
and lakes are temporary; changes in base level cause changes in the mainstream, tributaries and subtributaries.
The geomorphic cycle is subdivided into parts of unequal duration, each part being characterised by
the degree and the variety of relief and by the rate of change, as well as by the amount of change that has
been accomplished since the initiation of the cycle. The various stages in the geomorphic cycle are
described in terms of age beginning with youth, which passes into maturity and then into old age. The
topographic features of the first stage are spoken of as young or youthful, later ones as mature and those
of the last stage as old, with further subdivisions when desirable such as, for example, early and late
maturity. It may also be mentioned that each of these stages need not be of the same duration. Davis
considered youth a relatively brief phase and thought old age involved a tremendously longer period of
time than either of the two stages.
It should also be noted that the blending of types of topographies is the rule rather than an exception.
Thus in a region of general youthful characteristics, some streams and valleys may be mature. Similarly
in mature plateaus there will be some youthful streams actively engaged in deepening their valleys. The
span of time involved in a complete transformation of landscape may run into millions of years.
Consequently during a period of scientific observation the changes in topography may be unnoticeable.
Youthful Topography
Youthful topography is characterised by comparatively few streams but usually they have high
gradients. Drainage may be poor with lakes and swamps on the divides between the streams. Streams
flow in deep walled canyons or V-shaped valleys; these will be shallow or deep depending on the height
of the region above sea level. Usually streams are actively engaged in cutting their valleys deeper.
Youthful topography also possesses rapids and falls. There will be general lack of development of flood
plain except along trunk streams.
Mature Topography
When the region advances from youth to maturity in the cycle of erosion, the drainage is better
developed with the number of streams increasing. The streams cut their valleys to lowermost levels,
their tributaries are well established and lakes, swamps and rapids disappear. Meanders may exist. Since
streams start eroding laterally, valleys are flat but the widths of the valley floors do not greatly exceed
the width of the meander belt. If streams flow through homogenous rocks, tree-like drainage pattern
known as dendritic pattern is developed during maturity of topography. In the regions of folded beds the
drainage pattern is rectangular i.e. tributaries meet their main streams at right angles.
Old Topography
In old topography, all main streams have very flat slope and are meandering back and forth over their
flood plains. Valleys are extremely broad and slope gently both laterally and longitudinally; valley
widths are considerably greater than the widths of meander belts. Their velocities are low and
transporting power for sediment very limited. The whole landscape is gently rolling. Occasionally
erosional remnants stand above the general land surface. Lakes, swamps and marshes may be present
but they are on flood plains and not in inter-stream tracts as in youth. The topography tends towards the
74
River Morphology
ultimate form namely peneplain which is a large land area of low relief that has been reduced to nearly
base level by the combined action of weathering and streams. As a rule, surfaces of peneplains are not
flat but gently rolling with low hills standing island-like erosion remnants in the general surface of lands
(Worcester 1948).
Geomorphic cycle discussed above is for humid region. An arid region is deficient in rainfall and
also in vegetation. The groundwater table is also low. As a result deep subsurface chemical weathering
is light, but surface chemical weathering does take place. Strong winds that blow carry dust from
wherever it is found. As a result of these differences, the landforms obtained in the youth, mature and
old ages in arid region are different from those in humid region. Worcester (1948) has discussed these in
detail.
4.3
REJUVENATION OF EROSION CYCLE
Once initiated the erosion cycle does not always proceed to completion without interruption. Worldwide
changes in sea level, tectonic uplifts of the earth’s crust and climatic changes are the three principal
causes of rejuvenation. Changes in sea level are brought about by subsidence of portions of ocean
basins. The lowering of base level will cause streams to cut into the valley and form incised channels
whereas rise of sea levels will force streams to deposit their sediment load in channels and aggrade.
Tectonic down warping or uplifting of land produces the same effects as lowering or rising of sea level.
Changes in morphology due to change in climate are discussed in detail by Schumm (1969). Climatic
changes affect the precipitation, which in turn affects the vegetation and surface runoff. The latter two,
in turn, change the discharge in the stream, erosion pattern and sediment load. Thus climatic changes
induce significant changes in drainage pattern and stream behaviour. In general, typical topography
formed due to rejuvenation includes uplifted peneplains, incised meanders, stream terraces and hanging
valleys. If rejuvenation takes place in this manner, the first erosion cycle remains incomplete and a new
one starts. It may happen that before the new cycle completes, rejuvenation may be effected. It is,
therefore, believed that partial erosion cycles may be more common than the complete ones.
4.4
CRITICISM OF GEOMORPHIC CYCLE
For the purpose of exposition, Davis made several simplifying assumptions, which have become the
target of critical comment (Rice 1977); one of the most important was the separation of uplift and
erosion into two distinct episodes. He thereby envisaged initial uplift taking place without appreciable
erosion and then erosion under prolonged tectonic stability. However, current rates of uplift so exceed
those for denudation that it is clear erosion does not normally constitute a limit of continued surface
elevation.
It is also argued, as partly discussed under rejuvenation, that stability is unlikely to stay long enough
to permit reduction of an upland area to peneplain because of persistent tectonic activity. It is thus
argued that the only stage in the Davisian cycle not represented on the earth’s surface at the present day
is the peneplain.
It is also worth recalling that periodicity of major climatic oscillations during the Pleistocene epoch
(see Sect. 4.6) seem to have been of the order of 105 years. On the basis of known denudation rates the
length of time required for an erosion cycle to run its full course cannot be less than 106 years. This
75
Fluvial Morphology
means that any area will almost certainly have experienced many climatic fluctuations in the course of a
single cycle with consequent changes in erosional processes.
Penck (Penck 1924, Bloom 1978) differed fundamentally from Davis. Even though he accepted the
idea that landscapes could be reduced to the end forms of low relief, he maintained that these end forms
never became the initial forms of new episode of dissection. According to him the uplift was not rapid
and then zero as Davis supposed, but always began slowly, reached a maximum and then waned
gradually to a stop. During the long stage of initial slow uplift, all prior forms were destroyed, and a new
surface of low relief, adjusted to a balance between uplift and degradation developed. This initial
surface of low relief was called Primärrumpf by Penck. He argued that the rate of crustal movement
varies greatly from time to time. Hence according to him, depending on whether rate of uplift is equal to,
less than or greater than down cutting, the slope profile will be straight, convex upwards or concave
upwards.
No erosional sequence of forms was allowed by Penck’s scheme, because each morphologic
assemblage was related to certain tectonic condition. Penck also denied any climatic control of
geomorphic processes other than glaciations, believing that tectonics alone determined landform
assemblages.
For many years, the ideas of Penck received little support from English speaking geomorphologists. However, these have attracted attention since then and found them thought provoking
even though at times contradictory.
King (1962) a geo-morphologist from South Africa, formulated his ideas in a predominantly semiarid region where very little geological deformation had taken place in recent times. King believes in the
supremacy of cyclic erosion in the development of continental landscapes and argues that the chief
defect of Davisian concept is the absence of parallel slope retreat. King’s concept of changes in valley
slope is that the chief means of landscape change is the migration of valley side slopes away from the
rivers without significant change of angle as shown in Fig. 4.1 (a). On the other hand, Davis concluded
that during youthful stream incision, valley sides would be steep. Once rapid valley deepening has
ceased, the slope processes almost solely influence the form leading to a gradual decline in the angle,
(see Fig. 4.1 (b)).
Stream incision
Almost parallel
slope receding
a King
Stream incision
Slope
reducing
b Davis
Fig. 4.1 Valley slope evolution according to King and Davis
Both King and Davis argue that their models of landscape evolution could be adapted to a wide
variety of climatic environment with only minor modifications. However, in 1909 Davis was convinced
76
River Morphology
of the need to formulate a separate cycle for arid region because of (i) absence of the normal base level
control in areas without perennial streams draining to the coast; (ii) increasing importance of wind
action; and (iii) belief that a unique combination of the processes might lead to slope retreat without
angular decline. Since then many writers such as Peltier have proposed variety of the original Davisian
cycle, believed to be more appropriate to specific climatic zones. It is shown that climatic zone in which
the cycle of erosion has been deemed to be significantly different from those outlined by Davis and King
is the humid tropics, where chemical weathering significantly affects the development of landforms.
Another climatic zone for which a distinctive cycle of erosion has been proposed is peri-glacial.
4.5
NON-CYCLIC CONCEPT OF LANDSCAPE EVOLUTION
Reactions against the limitations of the Davisian cycle of erosion have led to reassessments more radical
than those discussed so far. Hack (1960) views landscape as the product of competition between the
resistance of crustal materials to erosion and the forces of denudation. He argues that the orderliness of
stream organization first discerned by Horton (1945) will naturally lead to regularity in the overall
pattern of relief. Within a single climatic region where stream and slope profiles are both controlled by
the nature of bedrock, similar geologic conditions should produce similar topography. Thus Hack put
forward the concept of non-cyclic approach in the form of dynamic equilibrium. He does not probably
question the existence of a very long period of land form evolution, but argues that its details are now
lost beyond reconstruction; hence he is more concerned about the relationship between form and
processes and adopts an attitude of ignorance towards land form history. Thus, Hacks’s argument
implies that landforms adapt easily to changing environmental controls; however if this logic were
stretched too far it would preclude, for instance, the identification of formerly glaciated areas.
It may be mentioned (Craig 1982) that during the past the geo-morphologists have developed
mathematical models for slope erosion. Three models can be mentioned in this respect. The first is
¶Z
¶Z
=–b
¶t
¶x
...(4.1)
where Z is the elevation, t is the time, x is the distance from the divide and b is a positive constant called
recession coefficient. Thus the rate of denudation is proportional to the slope. Where the denudation is
proportional to convex curvature, the equation used is
¶Z
¶2 Z
=a
¶t
¶x 2
...(4.2)
where a is called debris diffusion coefficient. These two equations have been brought together by
Hirano (see Craig 1982) in a form, which describes the combined effects of weathering (Eq. 4.1) and
creep (Eq. 4.2). The equation is
¶2 Z
¶Z
¶Z
=a
+b
2
¶t
¶x
¶x
...(4.3)
There is considerable difficulty in determining which equation should be used for a particular
situation and hence only a few areas are subjected to this type of analysis.
Fluvial Morphology
77
Hence, in spite of all the limitations of Davisian erosion cycle, it is still considered as the best
because no other viable alternative meeting all the objections to Davisian cycle is available.
4.6
GEOLOGICAL TIME SCALE
Historical or stratigraphical geology is mainly concerned with the description and classification of rocks
with a view to arranging them in chronological order in which they were laid down on the surface of the
earth. Of the three groups of rocks – sedimentary, igneous and metamorphic – only the sedimentary
rocks are amenable to such an arrangement since they have been deposited layer by layer and contain the
remains of organisms which flourished while they were formed.
The time scales used by the hydraulic engineer and the geologist are quite different. The hydraulic
engineer uses seconds or days as the unit of time when dealing with transport rates of water or sediment.
When he is dealing with the morphological changes such as aggradation or degradation of the riverbed
he is concerned with bed level changes occurring in a few years or a few decades at the most. As against
this in stratigraphy the unit time used is million years. Thus Lord Kelvin (Rice 1977) assumed that earth
started as a molten body, and applying the theory of cooling to this mass he estimated that to attain the
present day temperature the earth must have taken 20 to 40 million years.
For arranging the various geologic formations in the order of increasing antiquity, the geologist uses
various means at his disposal. The first is the fundamental principle of superposition in which the upper
beds in an un-inverted succession are dated as younger than the lower ones. The second means is the
palaentological dating depending on the fossil content of the formation. Each formation encloses a
fossil assemblage, which is characteristic and different from that of the underlying or over lying
formations. The animal and vegetable organisms of each geological age bear special characters not
found in those of other ages. It needs to be emphasised that the fossils present in a series of formations
are not only a function of the period when the formation was laid down but are also a function of (i) the
geological period when rocks were formed; (ii) the zoological or botanical provinces in which the
locality was situated; and (iii) the physical conditions prevalent at the time, e.g. depth, salinity,
muddiness of water, temperature, character of sea bottom and currents. The geological formations are
named in such a manner that they indicate the stage of development of the organisms. Thus the Azoic
era is completely devoid of organisms, while Proterozoic era shows traces of the most primitive life. The
Palaeozoic era contains the remains of ancient plants and animals, and so on to the recent time. The third
means used for determining the age of formation is the lithology. Each lithology unit may comprise a
number of individual beds having more or less the same characters, when it is spoken of as a formation,
and given a local or specific name to distinguish it from a similar formation of different age or belonging
to a different area. Lithology is many times useful in the determination of chronology.
With the discovery of radioactive elements uranium and thorium at the end of 19th and beginning of
20th century a more powerful means was available for determining the chronology of rocks and other
formations. It was found that uranium and thorium emit alpha and beta radiations; alpha radiation
consists of positively charged helium nuclei with two positive charges while beta radiation consists of
negatively charged electrons. Depending on the nature of radioactive elements half the atoms of the
element will disintegrate in this manner in a period known as half-life of the element concerned. As a
result of such emission of alpha and beta radiation a new element or daughter element is formed. If the
quantity of the parent element to the daughter element is known at any time, the period during which the
78
River Morphology
radioactive decay has taken place can be calculated. Uranium and thorium, as a result of radioactive
decay are finally converted to lead Pb206, Pb207, or Pb208 isotopes. The isotopic analysis of the minerals
is carried out using the technique of mass spectroscopy. Using radioactive dating techniques, it is
estimated that the age of crustal material of the earth is about 4,500 million years while the age of lunar
rock ranges from 3,000 to 4,500 million years.
Table 4.1 gives the era, group, system or formation or rocks, and the chief fossils found in these
formations. Even though geologists are interested in all the eras from Quaternary to Azoic or Archaen,
geo-morphologists consider Quaternary and Tertiary periods as of primary significance to them; this is
so because it is believed that the majority of landforms are about a million years old, and the remaining
not more than 20 to 30 million years old. Hence, from the geo-morphologist’s point of view it becomes
crucial that the dating between Quaternary and Tertiary periods is done carefully. This aspect has been
discussed in detail by Rice (1977) and the following discussion is based on his comments. The dating of
Cenozoic era has become complicated because of various reasons. Earlier stratigraphic column was
constructed on the basis of marine sediments and faunas raised above the modern sea level. Such
continuous marine successions are rare in the late Cenozoic age, and the contemporary terrestrial beds
tend to be fragmentary, of short duration and local. The second difficulty arises because of the relatively
brief duration of Cenozoic era because of which the biological evolution during this period was not
adequate to delimit the era. Then there were at least eight or probably even more environmental changes
during this period, which have complicated building up of the chronological sequence. Lastly, as
regards methods of estimating the age of the formation, K/Ar dating is most suitable for Cenozoic era;
however because of the very small amount of Ar present in the formations the accuracy of the method is
doubtful.
Sufficient light has been thrown on the chronology of Cenozoic era by obtaining cores of materials
deposited on the beds of deep seas. These deposits contain fossils of marine organisms such as
foraminiferal, globorotalia menardii and diatoms in large numbers. Since these organisms have different
environmental requirements, their fossils give information on the changing temperature of seawater.
The change in the ratio O18/O16 of the isotopes of oxygen in the shells also indicates the temperature
changes. Shells formed in the cold climate are relatively richer in O18. Such evidences have helped in
fixing the chronology of later Cenozoic era.
Some investigators argue that the most distinctive characteristic of Pleistocene epoch is the
development of large continental ice sheets in Europe and North America. Hence the beginning of
Pleistocene should be equated with dramatic fall in temperature. However, glaciation in different parts
of the world leads to a very large variation in the onset of Pleistocene. Therefore many argue that it is
unwise to relate glaciation to Pleistocene.
Similar uncertainty prevails in fixing the Pleistocene–Holocene boundary. The term Holocene was
originally intended to designate the post glaciation period. However, the melting of ice sheets being
transgressive of time, the post glaciation period in one region could be glaciation period in another
region. Therefore, this criterion was difficult to use. Hence the boundary between Pleistocene and
Holocene is fixed arbitrarily. The most accepted boundary is that first proposed by Scandinavian
workers using pollen analysis. Using this technique the period of rapid warming indicating the onset of
Holocene has been fixed at about 10,000 years ago.
It is necessary to emphasize that during the Pleistocene era some areas were covered by ice sheets
while some were not. In glaciated areas the attention was focussed on till sheets laid down one over the
79
Fluvial Morphology
Table 4.1 Geological time scale [Adapted from Wadia (1961), and Krishnan (1982)]
Era
Period
Epoch
Duration
M years
Years before
present
Chief fossils
M years (Ma)
Cenozoic
Quaternary
Tertiary
Mesozoic
Palaezoic
Proterozoic
Azoic
Secondary
Holocene
(present)
Pleistocene
(Glacial)
Pliocene
Miocene
Oligocene
Eocene
0.01
0.01
1
1
7
17
13
27
8
25
38
65
Cretaceons
75
140
Giant reptiles and ammonites
disappear at the end. Flowering
plants become numerous
Jurassic
60
200
Triassic
Permian
Carboni-ferous
40
50
60
240
290
350
Ammonites abundant. First birds,
flowering plants and sea urchins
Ammonites, reptiles, amphibia
abundant. Arid climate
Devonian
Silurian
60
410
Ordovician
35
445
Cambrion
60
100
505
605
Primary
Precambrian
Archaen
Precambrian
Archaen
2500
3600
Living animals
Man appears; many animals dies
off during glaciation
Mamals, mollusca, and flowering
plants dominate. Divisian largely
based on proportion of living to
extinct species of mollusca and the
presence of mammal species
Trilobites disappear at the end
Many non-flowering plants, first
reptiles appear
Abundance of corals, branchiopoda,
first amphibious and lung-fishes
Graptolites disappear at the end;
first fishes; probably first land plants
Abundance of trilobites and
graptolites
Abundance of trilobites
Soft bodied animals and plants
Lifeless
other as a result of multiple glacial advances. Equal attention was given to the pollen analysis of
biogenic materials entrapped within the tills. Similarly a thorough study was made of non-marine
molluscs and beetles. However, it has been found that the record of terrestrial sediments in glaciated
regions is small and is confined to the later part of Pleistocene era. In the unglaciated regions, at a
limited number of places pollen analysis has been used. Some deep core samples have also been
obtained from the desert areas where earlier lakes existed. Another technique used to determine the
chronology of continental land surfaces in Pleistocene era is the carbon C14 dating which is very useful
for dating of Pleistocene and Holocene eras because of short half-life of 5730 years of C14.
This method depends on the fact that the atmosphere and the hydrosphere represent reservoirs of
radioactive carbon C14, which are tapped by animals and plants to build up their structures and tissues.
The source of radioactive carbon lies in the cosmic ray bombardment of nitrogen in the atmosphere,
which converts it into C14. Carbon has three isotopes C12, C13 and C14 and it is present in the atmosphere
80
River Morphology
in the form of CO2. Out of the three isotopes C14 is the only unstable isotope with half-life of 5730 years.
In historical times a balance was reached between new C14 received from cosmic radiation and that
disintegrated due to radioactive decay. Since living organisms absorb CO2, each organism absorbs a
fixed proportion of C14 of the total carbon absorbed during the lifetime. After the death of the living
organism, the replenishment of C14 ceases and C14 content declines due to radioactive decay. The ratio
of radioactive to the total carbon present at any time is, therefore, a measure of the age of the organic
materials such as bones, tusks, grains, wood, hide, peat etc. The method is suitable for dating up to
50,000 years.
4.7
GLACIATION
Glacier is a slow moving mass of ice formed by accumulation of snow in mountain valleys and other
places. Area of the continents that is covered by ice at present is close to 15 M km2, the largest part of
which is concentrated in Antarctica (12.5 M km2) and in Greenland (1.7 M km2). Glaciers today, except
at high altitudes and in high latitudes, are of minor importance in shaping landforms; but those that
existed during the Pleistocene epoch have left their imprints on many millions of square kilometres of
the earth’s surface. About 10 M km2 of the North America, 5 M km2 of Europe, 4 M km2 of Siberia and
large parts of the Himalayas were glaciated. Pleistocene epoch consisted of four major glacial ages
separated by interglacial ages of probably far greater duration than the glacial ones. The latest glaciation
has left the most obvious imprints on the topography. Glaciers are classified into ice caps, valley
glaciers, ice-streams and glacier ice.
Glaciers that are continuous sheets of snow from which ice may move in all directions are known as
ice caps. Glaciers that are confined to courses, which direct their movement, are called valley-glaciers
and ice-streams. Glacier, which spreads in cake-like sheets over level ground at the base of glaciated
areas, is known as glacier ice.
Glaciation in India (Wadia 1961, Krishnan 1982)
Majority of the present Himalayan glaciers are three to five km in lengths, however there are some giant
glaciers of forty km or more in length such as the Milam and Gangotri glaciers of Kumon and Zemu
glacier draining Kanchanjunga group of peaks in Sikkim. The latest glaciers of the Indian subcontinent
are those of Karakoram discharging into the Indus river; these are Hispar and Batura of the Hunza
valley, and Biafo and Baltora of the Shigar, a tributary of the Indus. These are about 50 km in length and
130 to 330 m in thickness. These are the latest survivors of the last Ice Age of the Himalayas. Presence
of terminal moraines covered, many times by grass, seen in Pir Panjal moraines at the snouts of existing
glaciers at low level hills of Punjab lead to the conclusion that at least this part of India experienced
glacial age in Pleistocene epoch. Parts of India lying to the south of Himalayas experienced cold pluvial
epochs during this period. The evidence leading to this conclusion is derived from the fauna and flora of
the hills and mountains in India and Sri Lanka.
According to Wadia (1961) indications of extensive glaciation in the immediate past and in the
present glaciers are: (i) presence of enormous heaps of terminal moraine covered by grass and trees; (ii)
presence of ice transported blocks; and (iii) smoothed or striated hummocky rock surfaces. According to
geologists the Kashmir area of the Himalayas underwent four distinct glaciations separated by the
interglacial warm periods; the last of the glaciations occurred about ten to twenty thousand years back.
Fluvial Morphology
81
Glacial Movement and Erosion
Glaciers move slowly showing erratic and sudden advances of their fronts. Glaciers reduce in size by the
combined action of melting and evaporation/sublimation, a process known as ablation. Glaciers may
also get nourishment and thus increase in size. Depending on whether a glacier gets nourishment or not
the glacier is called an active or inactive glacier. Active glacier will have an advancing front whereas an
inactive glacier will have a receding front. Abundant striations, polished and grooved rock surfaces give
evidence of effective glacial erosion. The bottom topography of bedrock floor may show irregularity
and over deepening which cannot possibly be explained by any other way than to assume that they are
due to local glacial scouring.
One of the simplest ways of assessing the rate of erosion due to glaciers is by the measurement of
sediment being carried by melt water issuing from glacier snout. On the basis of observations by Reid,
Thorarinson and Corbel from Muir, Hoffellsjokul and St. Sorlin glaciers respectively, Rice (1977)
suggests that the mean erosion rate by active glacier lies in the range of 1 to 5 mm/year which is seen to
be much higher than most of the figures for stream erosion. Glacial erosion includes two processes,
namely plucking and abrasion. Plucking occurs when moving ice freezes on to the bed rock and pulls
out blocks which are then carried away. Abrasion is due to grinding effect. Grooves formed on the
bottom can be 2 m deep and 100 m long, even though grooves up to 30 m deep and ten km long have also
been observed. Large blocks of un-weathered rock found in both glacial and fluvio-glacial deposits are
mainly due to plucking.
Erosional and Depositional Landforms
Ice streams flowing in high mountainous areas have modified their valleys to such a great extent that
their forms are distinctly different from the valleys caused by fluvial erosion. Some of the most
important erosional landforms produced by glacial erosion are cirques, glacial troughs and hanging
valleys.
CIRQUES: Cirque is a French word-meaning amphitheatre like basin, not completely enclosed. It is
the most distinctive, common landform caused by glacial erosion in mountain high lands. It is a steep
sided semi-circular basin found at valley heads; but it may not
Head
connect in its downstream part with a valley. The name is applied
wall
Threshold
to shallow basins which mark the steps of snow banks which
Basin
never grow into glaciers. A typical cirque consists of a steep head
wall on the upstream side, followed by a deep basin and then a
Fig. 4.2 Cirque
gradually sloping up surface known as threshold, see Fig. 4.2.
The longitudinal profile of cirques approximately follows the
equation of the form y = (1 – x) e – x and is almost independent of rock type. Conditions which favour
maximum cirque development are: (i) rather wide spacing of prelacies valleys so as to permit expansion
without intersection of adjacent cirques at an early stage; (ii) adequate snowfall which can form large
snow fields and glaciers, but not heavy enough to form ice-caps; and (iii) fairly homogenous rocks
which permit cirque extension equally well in any direction.
GLACIAL TROUGHS: Next in importance to cirques is the most distinctive topographic feature in
glaciated mountains, namely glacial trough. It is the valley, which is modified, in its cross-sectional
shape and the longitudinal profile due to glaciers. Most glacial troughs were originally stream cut
82
River Morphology
valleys. Glacial trough heads at the lower edge of the cirque threshold; however, there is a drop from
cirque threshold to the floor of glacial trough. The longitudinal profile of the glacial trough is irregular
and ungraded; the profiles are seldom smooth and concave upward type. Instead, they have a series of
glacial steps, which are more pronounced in the upper reaches than in the lower. Glacial steps have been
attributed to differential glacial abrasion in contracting and expanding sections of the valley, effect of
varying rock hardness and to preglacial irregularities. Presence of jointed rocks can also lead to glacial
steps. The cross-sectional profile of a glacial trough is significantly different from that of an unglaciated
valley in mountainous area. While many glacial troughs are U-shaped, stream formed valleys in
mountains are usually V-shaped. Davis has suggested that the cross profile of a glacial trough follows a
catenary curve. The difference in the cross profiles of glacial troughs are often related to the difference
in the thickness of glacier, valley lithology, structure of rocks in which the trough is cut, and the number
of times the valley is glaciated. Some portion of the glacial troughs may exhibit flat floors, which are
attributed to the deposition subsequent to the trough development. The material deposited may be due to
aggradation caused by deposition of outwash material by glacial recession or post-glacial alluvial
deposit.
HANGING VALLEYS: The tributaries usually join the river valley accordantly i.e., there is no
difference in bed elevation of the main river valley and that of the tributary. However, glacial troughs
often have tributary troughs or valleys joining the main trough discordantly, producing elevation drops
at the junction. This is known as the hanging valley. Some valleys in Kashmir and in Sikkim exhibit
hanging valleys of this type (see Wadia 1961, Krishnan 1982). However, it may be emphasised that
hanging valleys cannot be interpreted as evidence of past glaciation because they can be formed due to
reasons other than glaciation; for example a hanging valley can be formed if the main stream is
degrading rapidly and the tributary is intermittent.
Glacial deposits are usually heterogeneous and lack stratification. These deposits are of three types,
namely end moraine, lateral moraine, and ground moraine, depending on whether the deposition took
place at the end of, at the side of, or beneath an ice stream. Only some glaciers build end moraine; this
depends on whether the ice front maintains itself in one position for a sufficiently long time. Then if the
ice-fed stream emerging from the glacier is capable of transporting the end moraine, it wouldn’t deposit.
Lateral moraines form along the sides of an ice stream mainly from the materials, which are contributed
from the valley sides above the glacier by weathering and mass movement. Lateral moraines are usually
patchy and may or may not be found on both sides. Ground moraine is more closely associated with ice
caps than with ice streams.
The streams flowing on, within or beneath the glacier deposit the material eroded and transported
by the glaciers and ice streams. This material is known as glacio-fluviatile. The most common landforms
in this material are valley trains, eskars, kame terraces, and outwash fans or deltas. These are described
by Thornbury (1969).
4.8
FLUVIAL MORPHOLOGY
Fluvial morphology deals with streams and stream systems as produced by the action of flowing water.
The features produced on the land surface by flowing water can be aptly called fluvial landscapes. As
the erosion cycle proceeds the morphology of streams also changes and the streams pass through the
three stages of development as the earth’s surface namely youth, maturity and old age. Although the
83
Fluvial Morphology
stage reached by the stream usually corresponds to that of the surrounding topography, this is not
necessarily the case. Usually the stream is less youthful in character near its mouth than in the vicinity of
its head waters (Hack 1960).
If one considers a newly uplifted land mass as the starting point and traces the successive changes,
which occur with time, the first stage of the stream will be youth. Here streams have relatively steep
slopes and they are engaged in cutting their channels downwards. Lateral erosion and valley widening is
extremely small. The cross section of the stream will be V-shaped with no or little flood plain. A
youthful valley is shown in Fig. 4.3. Streams in youth may not have cut down enough resistant rock mass
to attain a gradual profile; hence rapids and falls may exist along its course because sufficient time has
not passed, since they were uplifted, for the stream to cut down and eliminate them. There are frequent
changes in the slope of the stream caused by the differences in hardness of the strata over which they
flow. Johnson (1932) suggests that early youth ends when lakes are eliminated and middle youth ends
when falls and rapids are eliminated.
Fig. 4.3 Youthful valley
Late youth ends and early maturity starts when the rate of down cutting decreases and the rate of
lateral erosion increases; establishment of grade also marks the passage from youth to maturity. Early
maturity ends and late maturity begins when the valley width equals the width of the belt covered by the
meanders of the stream. V-shaped valleys and rapids and waterfalls disappear which are characteristic
of youthful age of stream. Figure 4.4 shows a mature valley.
In the old stage there is pronounced meandering activity as a result of which width of flood plain
exceeds several times the width of the meander belt. Oxbow lakes and swamps are usually present as a
result of cut-offs developed naturally. Natural levees, which form banks confining stream channels, may
be built up until the channel is some metres above the general level of the flood plain. Typical old stage
is shown in Fig. 4.5.
84
River Morphology
Meander belt
= Valley – floor width
Youth
Mature
Old
Fig. 4.4 Cross-valley profiles for various stages of stream
Fig. 4.5
Old-age stream
It sometimes happens that during the cycle of erosion certain changes occur which cause streams to
incise their channels with greater vigour. This renewed down cutting is known as rejuvenation. Three
principles causes for rejuvenation are: (i) World wide changes in seal level, (ii)Tectonic changes and
(iii) Climatic changes.
Equilibrium in Natural Streams
Geo-morphologists as well as engineers have used the concept of equilibrium in streams. A stream in
equilibrium is called a graded stream or a poised stream. Mackin (1948) has given the following
definition of a graded stream:
“A graded stream is one in which, over a period of years, slope is delicately adjusted to provide,
with available discharge and with prevailing channel characteristics, just the velocity required
for the transportation of load supplied from the drainage basin. The graded stream is a system in
equilibrium; its diagnostic characteristic is that any change in any of the controlling factors will
cause a displacement of the equilibrium in a direction that will tend to absorb the effect of the
change”.
Fluvial Morphology
85
Thus, the four variables related to the concept of a graded stream are slope, discharge, channel
characteristics and sediment load. In a natural stream, the discharge is continuously changing due to
precipitation, infiltration, evaporation and withdrawals. Although stream tends to pick up sediment or
deposit it until load equals capacity, because of rapid variations in flow it cannot do so. Hence, in very
short times the stream cannot be in equilibrium. Similarly, since the tendency of the streams is to lower
the land surface to the sea level, over very long periods the stream cannot be in equilibrium. Thus,
neither in very short not very long periods can a natural stream be considered to be in true equilibrium
(Lane 1955). Yet, for all practical engineering purposes, most of the alluvial streams are in equilibrium
over periods of the order of a few decades. In such streams, the bed may go down during high flows and
fill back during low flows; yet the net amount of change is not sufficiently large to be detected by
quantitative measurements. Most of the alluvial streams which are not affected by human interferences
can be said to be graded or in equilibrium. Construction of dams, withdrawal or addition of clear water,
addition of sediment load, contraction of stream and cutting off the bends are some the ways in which
the equilibrium of the stream is disturbed by human activities.
Characteristics of Graded Streams
To get better appreciation of the stream morphology the characteristics of graded streams are briefly
enumerated here. Firstly the slope of a graded stream, in general, decreases in the downstream direction
yielding a concave profile. Secondly, partly as a consequence of decreasing slope in the downstream
direction, the stream drops the coarser material that it cannot transport, a phenomenon known as sorting;
and partly due to abrasion, the bed material of an alluvial stream becomes finer in the downstream
direction. Thirdly in humid regions as more and more tributaries join the main stream; the discharge
increases in the downstream direction. However, if the stream passes through arid region, the discharge
can actually decrease in downstream direction as in the case of the Euphrates in Iraq. This is primarily
due to seepage and evaporation.
In addition, the upper part of the drainage basin is the main source of sediment even though the
runoff from this part of the catchments may be small. The runoff from the rest of the basin is large but it
carries relatively less sediment. This leads to decrease in the average concentration of sediment in the
downstream direction necessitating a smaller slope. Lastly, because of finer material, streams usually
have relatively narrow channels i.e. larger width to depth ratio, in the downstream direction. As a result
the stream has greater hydraulic efficiency and flows with a smaller slope.
A graded stream may show aggradational tendency, albeit temporary, under the following
conditions (Cotton 1941):
1. If dissection of upland region is in progress and a vast number of smaller new valleys and
ravines come into existence in the stage of youth. To carry relatively higher load stream may
increase slope by aggradation.
2. If the river after it is graded flows in a wider channel than it has hitherto had in youth, loss of
depth in the stream may rebuilt in a reduction of velocity and transporting power that it needs
steeper slope to carry the load.
3. As a river develops increasingly large curves by lateral corrasion, its length increases and slope
decreases and hence carrying power decreases resulting in aggradation.
4. Decrease in water volume due to infiltration, evaporation or withdrawal can cause increase in
slope due to aggradation.
86
River Morphology
Variation of Sediment Size
It is important for a river morphologist to know how the sediment characteristics change along the
stream. The most important characteristic of sediment is its median size. It is found that in most of the
streams there is reduction in size of sediment due to wearing or abrasion, fragmentation, weathering,
dissolution and hydraulic sorting. Hydraulic sorting takes place in a stream because the sediment
transport ability of the stream reduces in the downstream direction. It is difficult to know the relative
importance of these processes in the reduction of sediment size. Hence, it is easier to model the
reduction in size by assuming that, as done by Sternberg in 1875 (Rohan 1967), the reduction in weight
of the particle dW is proportional to its weight W and the distance travelled dL. Hence
dW = – CW dL
...(4.4)
where C is the constant of proportionality. Integration of this equation with the initial condition W = Wo
when L = 0 yields
W = Wo e – CL
...(4.5)
3
3
Further since for spherical particle W ~ d and Wo ~ do , one gets
d3 = do3 e – CL
or
d = do e– a1L
...(4.6)
c
is known as the abrasion coefficient. Here d is the sediment size. This equation known as
3
Sternberg’s law is found to be valid on the Rhine in Germany. In Japan it is found to be valid for
sediments coarser than 4.0 mm in size. Shulits (1941) has stated that a1 ~ (particle velocity)1/4. Values of
a1 are found to vary between 0.006 km –1 and 0.11 km –1; however, it is not possible to predict its value
at present.
If dW is assumed to be proportional to surface area of the particle and dL, and one uses the initial
condition W = Wo when L = 0, the following equation is obtained from Eq. (4.4).
a1 =
F
W = GW
H
1
3
o
I
JK
c
- 1L
3
3
...(4.7)
Lastly another formula known as Schaffernak’s formula (see Rohan 1967) is also some times used
in describing the reduction in sediment size. This formula is
d
L
= 1 – C2
do
do
...(4.8)
where as C and C1 are having dimensions, C2 is dimensionless. Typical values of C2 for some reaches of
the Rhine, Danube and Mur vary from 4 ´ 10 –8 to 45 ´ 10 –8. It may be mentioned that the sediment size
varies very slowly with L and hence with proper choice of C, C1, or C2 any of the three equations can be
fitted to a given set of data.
As regards the size distribution, it may be mentioned that while sandy materials are unimodal,
gravely material is usually bimodal. Analysis of data of sandy and gravel-bed rivers by Garde (1972) has
87
Fluvial Morphology
shown that over the entire range the sample does not follow log-normal distribution; however between
d15.9 and d84.1 sizes it can be assumed to do so. The geometric standard deviation sg =
F
GH
d
1 d84.1
+ 50
d15. 9
2 d50
I
JK
is related to the median size d50 by the relation
0 .34
sg = 2.4 d50
...(4.9)
for 0.20 mm < d50 < 20 mm. Here d50 is in mm.
Classification of Streams
For systematic discussion about streams, it is advantageous to classify them; classification of streams
enables one to make generalization about a group of streams having similar attributes. As can be seen
below this classification is done using objective, qualitative or quantitative criteria. According to
Rosgen (1996) such classification often helps in (i) prediction of river behaviour from its appearance;
(ii) development of specific hydraulic and sediment transport relations for a given stream type, (iv)
extrapolating site specific data to stream reaches having similar characteristics; and (v) providing a
frame of reference for communicating about stream morphology among different disciplines.
As discussed earlier Davis (1899) divided the streams into youthful, mature and old, depending on
their stage of development in the cycle of erosion. This classification gives only qualitative attributes of
each type. Davis (1890) also distinguished between consequent streams following the natural slope of
land surface; subsequent streams flowing into consequent streams from the sides at right angles to the
dip and parallel to the strike; resequent streams as tributaries to subsequent ones more or less parallel to
consequent main streams; obsequent streams flowing against the dip of the beds; and insequent streams,
which show no apparent relation to the dip of the beds. These are shown in Fig. 4.6 and discussed in
detail by Worcester (1948). However, the classifications of Davis do not take into account the main
hydraulic variables on which stream size, shape and plan form depend.
Depending on the variation flow in the stream with time,
L
streams can be classified into three categories. Perennial or
C
B
O
permanent streams are those, which flow throughout the year.
These get their water from lakes, snow banks or glaciers, or land
C - consequent, S - subsequent,
from direct precipitation, and which maintain regular flow. Those
R - resequent, O - obsequent,
I - insequent stream
perennial streams, which have cut deep into sediment or other
L - original land surface
strata, may receive ground water flow also. Intermittent streams
Fig. 4.6 Relation of drainage to
are those whose sources of water fail intermittently. They occur
topography and geological structure
mainly in regions of seasonal rainfall or snowfall, and particularly
(Davis 1890)
common to semi-arid regions. Ephemeral streams flow only in
response to precipitation; they are not fed by springs or by slowly melting snow.
As discussed in Chapter II, Horton, Strahler and others have developed a system of ordering
channels in a drainage network; channels of the same order show similar characteristics, as shown by
Rznystin (1960).
Plan-form or channel patterns can be defined as the traces of the channel in plan as obtained from
air-photos or as presented on the map. Plan-forms of alluvial streams are of importance to hydraulic
S
88
River Morphology
engineers as well as to geo-morphologists and sedimentologists. For the hydraulic engineer not only the
plan-forms but also their spatial and temporal variation is important to decide the location of bridges,
barrages, levees and other structures. For the geo-morphologist they are an indication of modern river
behaviour; plan-forms also throw light on the past morphology of the stream. A sedimentologist studies
plan-forms and the associated sedimentary deposits in order to develop knowledge about old streams.
Lane (1957) analysed data from sand-bed rivers and rivers flowing through coarser material from USA
and other countries and broadly classified the streams according to plan-forms into straight, meandering
and braiding patterns. He further indicated that plan-forms are essentially a function of slope and
bankful discharge. Leopold and Wolman (1957) followed the same classification as that of Lane. Planforms can be classified depending on whether the stream flows in a single channel or in multi-channels.
Streams flowing in a single channel can be straight or meandering. However, in nature, streams do not
flow straight for more than 10 to 20 channel widths and even in straight channels the talweg shows a
meandering pattern. Plan-form classification is shown in Fig. 4.7.
Plan form of streams
Single channel streams
Straight
Multi channel streams
Meandering
Incised meanders
Anabranching
Reticulate
Deltaic
Braided
Meanders in flood plains
Migrating downstream
Classification according
to movement
Irregular
Inactive
Regular
Simple
Compound
Classification according
to valley width
Classification according
to shape
Irregular
Free (Lateral migration)
Regular
Simple
(sine, parabolic, circular, etc.)
Compound
Fig. 4.7 Classification of plan-forms
Underfit
Overfit
89
Fluvial Morphology
The meanders can be either incised or in plain and can take various shapes in plan. Meandering
streams can be further classified depending on whether the meanders move downstream, laterally or are
stationary. Chitale (1970) classified meanders into regular and flat, irregular and flat, regular and acute,
irregular and acute, simple, and compound meanders (see Fig. 4.8 (a) and Fig. 4.8 (c)). He also stated
that a particular stream might have a single channel in one reach and multiple channels in other reach, a
fact noticed on many streams. The multi-channel streams are classified into braided, deltaic, reticulate
and ana branching. These are schematically shown in Fig. 4.8(b).
0
Talweg
100 m
150
150 m
790 m
Straight reach of valley creek, Pa (U.S.A.)
Meander length
ML
Meander
belt
MB b
Point bar
MW
Width
Definition sketch for meandering stream
Compound meanders Buyuk meanders river (Turkey)
Incised meanders (irregular)
Fig. 4.8(a) Plan-forms of rivers
It is appropriate to describe two other forms of streams based on the relative width of meander and
the valley. A mis-fit stream (Dury 1969) is defined as one, which occupies a valley formed by a stream
of considerably larger or smaller discharge. An under-fit stream occupies the valley the valley formed by
a stream of greater discharge. Most of the streams, which are under-fit, now have had their channel
forming discharge reduced due to climatic changes. An over-fit stream occupies a valley formed by
90
River Morphology
Free meanders oxbow lakes and meander scars
Pembina river near Monola (Canada)
High land
Darling
river
High land
Braided stream
Anabranching pattern of
Darling river (Australia)
Reticulate pattern
Diamantina river (Australia)
Deltaic pattern
SS
L
L
S
L
L
R
S Valley meander scar
L Valley meander lobe
R Stream
Under-fit meandering stream
Osage-type
Fig. 4.8(b) Plan-forms of rivers
much smaller discharge; however an over-fit stream will usually remove all signs of small stream
channel and widen its valley to conform to its present flow. Therefore, over-fit stream is a transient stage
and is rarely found. Dury (1969) has discussed about another type of under-fit stream, called Osage type,
which is named after the Osage river in Missouri (USA). This type of stream lacks meanders; however,
it has pool and riffle sequence spaced at an interval of five channel widths. It behaves as if it were
straight; however it does not reflect the curves of the valley. The apparent width to depth ratio of streams
of Osage type is about forty, larger than ten as observed on meandering rivers; but actually in an underfit stream of Osage type it is the wave length of the former stream and width of the shrunken present day
stream. These types of plan-forms are shown in Fig. 4.8 (c).
91
Fluvial Morphology
Regular and flat meanders
Irregular and flat meanders
Regular and acute meanders
Irregular and acute meanders
Simple meanders
Compound meanders
Regular and flat meanders in
Mahi river (Gujrat) India
Irregular and flat meanders in
Ken river (U.P.) India
Regular and sharp meanders in
Mississippi river
Irregular and sharp meanders in
Sai River (U.P.) India
Compound meanders in Rind river (U.P.) India
Fig. 4.8(c) Meander classification according to Chitale (1970)
Schumm (1968, 1977) has classified stream channels flowing through sandy materials, based on the
mode of sediment transport (i.e., predominantly suspended load, mixed suspended load, and
predominantly bed-load), percent of silt-clay in the perimeter of the channel, and channel stability
(graded, depositing i.e. excess sediment load, and eroding i.e., with sediment load deficiency). This is
given in Table 4.2.
It may be mentioned that Blench (1955), and Simons and Albertson (1963) have also recognized the
importance of bed and bank material in shaping the geometry of stable channels. Allen (1965) has
diagrammatically represented Schumm’s ideas in terms of size and sinuosity, which is shown in Fig. 4.9.
Kellerhals et al. (1972, 1976) have given a further refinement in the classification of river channels,
which is primarily based on the interpretation of air photos and detailed survey of Canadian rivers. The
detailed data needed for classification include: (i) whether the stream is aggrading, degrading, partly
entrenched, or entrenched with no flood plains, (ii) channel plan-form description, namely straight,
sinuous (MB < 2 W), irregular or regular meanders, or tortuous meanders (q between channel axis and
valley trend greater than 90 o), (iii) presence of islands and basis; and (iv) lateral activity namely
meanders moving downstream, downstream progression and cut-offs, entrenched loop development,
avulsion etc. Figure 4.10 gives Kellerhal’s classification of lateral activity. This classification is very
exhaustive but rarely used in engineering design. Further, some of the attributes cannot be quantified.
92
River Morphology
Table 4.2 Classification of channels according to Schumm (1968, 1977)
Mode of sediment
transport
Percent of silt-clay
Suspended load
85-100 percent
100
Mixed, suspended
load 65-85% bed-load
35-15%
30
Bed-load 35-75
percent
-
Stable (graded)
W/D less than 10 Si
greater than 2 slope
relatively flat
Depositing (excess
load)
Eroding (Deficiency
of load
Major deposition on
banks, causing
narrowing of channel
Bed erosion; channel
widen-ing minor
W/D : 10 – 40
Initially major
Initial stream bed
deposition on banks
erosion; followed by
Si : 1.3 to 2
followed by stream bed
channel widening
Slope relative moderate
deposition
W/D greater than 40
Si less than 1-3
Slope relatively steep
Stream bed deposition Bed erosion minimal,
and island formation
Channel widening
predominant
Calibre of stream load
Coarse
Channel
sinuosity
High
Suspended load
Low
Low
Poor
High
Fine
Stabilisation
of meander belt
by channel fills
Good
W/D: width to depth ratio, Si: sinuosity
Fig. 4.9 Diagram relating stream channel stability to sinuosity and character of stream load (Allen 1965)
Finally, streams can also be classified depending on the type of material on their bed, character of
the sediment transported, and the slope. Boulder rivers have large size cobbles and boulders on their
bed; they are found in mountainous regions with very steep slopes and they carry much finer material
eroded from the catchments. Only in catastrophic floods do the boulders on the bed move. These rivers
are usually entrenched. Gravel- bed rivers have gravel and sand on their bed, have steep slopes and are
paved during normal flows. During the floods the pavement is destroyed. These are found in the
foothills and have large width/depth ratio. Rivers in flood-plains flow through the material deposited by
them, carry material forming the bed and banks of the river, and have relatively much flatter slope as
compared to that of gravel-bed and boulder streams. Their bank material may be slightly cohesive and
they carry varying amount of wash load.
On the basis of a study of a number of streams in USA, Rosgen (1996) has proposed a hierarchical
classification of streams. His classification provides the physical, hydrologic and geomorphic way of
linking the driving forces and response variables at different levels of inquiry. Thus as one moves from
Level I to Level IV, one progressively takes into account geomorphic characterization, morphological
classification, stream condition and validation level. To facilitate the classification Rosgen used
93
Fluvial Morphology
Entrenchment ratio ER (= width of flood prone area at an elevation twice the bankfull depth/
bankfull width)
Width to depth ratio W/D = (Bankful width/mean bankfull depth)
Sinuosity Si = (Stream length/valley length) and Slope S
Thus at Level I, based on ER, W/D ratio, sinuosity, slope and channel pattern, the streams are
classified into nine types designated as Aat, A, B, C, D, DA, E, F and G as indicated in Table 4.3.
Table 4.3
Rosgen’s stream classification at level – I (Rosgen 1996)
Stream Type
Aat
A
B
C
D
DA
E
F
G
ER
< 1.4
< 1.4
1.4 – 2.2
> 2.2
N.A.
> 2.2
> 2.2
< 1.4
< 1.4
W/D
< 12
< 12
> 12
> 12
> 40
> 12
< 12
1.0 – 1.1
1.0 – 1.2
> 1.2
> 1.4
N.A.
> 1.4
> 1.2
> 0.10
0.04 –
0.01
0.02 –
0.03
< 0.02
< 0.04
Highly
< 12
variable
Highly
> 1.5
variable
< 0.005 < 0.02
< 0.02
0.02 –
0.039
Si
Slope S
N.A.-Not applicable
The brief description of these nine types of streams is given below:
Aat: Very deep, entrenched torrent streams, mildly curved in plan, high relief, zone of deposition,
step-pool morphology
A: Steep, entrenched step-pool streams, high transport of debris; erosional or depositional
character, mildly curved in plan.
B: Moderately entrenched, moderate slope, very stable plan, longitudinal profile and stable banks,
mildly curved in plan
C: Low gradient, meandering, point bar, riffle/pool topography, alluvial channel with moderate
entrenchment and W/D ratio, broad valley.
D: Braided channel with longitudinal and transverse bars-eroding banks with very wide channel,
abundance of sediment supply, aggradational tendency.
DA: Anatomising channels, well vegetated flood plain, stable stream banks, broad valley, low bedload and high wash load.
E: Low gradient, highly meandering, low W/D ratio, broad valley flood plain with alluvial
material, high meander width ratio.
F: Entrenched meanders on low gradient, and high width/depth ratio, meanders very unstable
laterally with high bank-erosion, pool-rifle morphology
G: Entrenched gullies, step-pool morphology, narrow valleys, unstable high erosion rates.
The Level II in the classification subdivides the streams in each class into a maximum of six
categories, namely 1, 2, 3, 4, 5, 6 depending on the channel material i.e. (1) bed rock (2) boulders (3)
cobbles (4) gravel (5) sand, and (6) silt and clay. These are written as A1, A2, A3, A4 …A6 etc. Thus A5
94
River Morphology
stream will be of A type with sandy material. It also takes into account bankfull discharge and
corresponding hydraulic parameters in determining quantities such as entrenchment ratio, W/D and
Manning’s n.
Aim of Level III classification is to provide description of stream condition as related to stability of
stream, its potential, and function. This is based on additional inputs about hydrology, biology, ecology,
and human activity. It evaluates and quantifies the channel stability, bed-stability (aggrading, degrading
or stable), and bank erosion. Level IV classification is based on reach specific observations for
verification of process based assessments of stream condition, potential and stability predicted from
preceding analysis. The book by Rosgen contains valuable information for practicing river
morphologists. Since a large number of sketches are included in the book, the text connects easily with
the field conditions.
4.9
TOPOGRAPHY PRODUCED BY STREAMS
During the cycle of erosion as the streams develop they bring down a large quantity of sediment which
eventually goes into the sea. While streams perform the erosional work in the upper reaches and
deposition of sediment in the lower reaches various types
of topography are produced. According to Schumm
(1971) the fluvial system can be divided into three zones,
named Zone 1, Zone 2 and Zone 3 in the downstream
Zone 1
Zone 2
Zone 3
direction. The upper most part of the drainage basin is
(Drainage basin)
(Transfer)
(Deposition)
primarily the sediment source area (Zone 1); the water
and sediment are derived here. Zone 2 is the transfer zone
Fig. 4.11 Idealized fluvial system
where for stable channel, the input is equal to output.
Zone 3 is the sediment sink or the area of deposition. Since the sediment is stored, transported and
eroded in each zone, within each zone one process is predominant as mentioned above. The three zones
are schematically shown in Fig. 4.11 are discussed below.
Topography Resulting from Stream Erosion
VALLEYS: Usually gullies grow into ravines and ravines into valleys. Development of valley
involves three concomitant processes namely valley deepening, valley widening and valley lengthening.
Valley deepening takes place due to hydraulic action, abrasion and weathering. Valley widening takes
place by lateral erosion near the valley base which can lead to under cutting of slope, rain wash on the
valley sides, gulleying on valley sides and mass wasting. The depth of any stream-cut valley is limited to
the level of the body of water into which it flows. Valley lengthening can take place in three ways: (i)
extension by the process of head ward erosion, (ii) increase in the size of their meanders, and (iii) uplift
of land or lowering of sea level.
The valley profile near the head will be V-shaped and will gradually change to U-shaped towards
the mouth. The longitudinal profile will generally be concave upwards with longitudinal slope
decreasing in the downstream direction. The stream slope changes as S = So e– a x, where So is the slope
at x = 0 and S is the slope at a distance L from the upstream end, and a is a constant. This decrease in
slope is due to the following reasons as mentioned earlier: (i) size of the material transported by the
stream decreases in the downstream direction due to abrasion and sorting; (ii) In humid regions the
95
Fluvial Morphology
discharge in the stream increases in the downstream direction. Thus there is decrease in sediment
concentration in downstream direction thus requiring a smaller slope; (iii) Because of the finer material
streams usually have relatively narrow channels (i.e., larger depth to width ratio) in the downstream
direction, such channel is more efficient in transporting sediment at a flatter slope.
If S = – d Z/dL is substituted in the equation S = So eaL where L is measured in downstream direction
and the condition Z = Zo at L = 0 is used, one gets
–
\
dZ
= So e–aL
dL
–Z =–
So –aL
e + const
a
The value of constant can be obtained from the condition Z = Zo at L = 0. Hence –Zo +
and hence
or
–Z =
(Zo – Z) =
...(4.10)
So
= const,
a
S
- So –aL
e 1 + o – Zo
a
a
So
(1 – e–aL1 )
a
...(4.11)
The low water profiles of the Mississippi river between Fort Jackson and Cairo, of the Ohio river
from Cairo to Pittsburgh, both in U.S.A., and San Juan river in Argentina are found to follow Eq. 4.11.
The value of a was found to be between 0.0010 and 0.00183. Brush (1961) and Hack (1957) have
emphasised the importance of lithology in determining the longitudinal profile and have proposed an
equation of the form
S = a Lb
...(4.12)
For streams in the forded Appalachions in Pensilvania (U.S.A.) they found “a” to vary between
0.013 and 0.15 and “b” between – 0.47 and –1.0, for different lithological formations.
STREAM TERRACES: Stream terraces are topographic surfaces, which mark former valley floor
level. They are vestiges of former flood plains although some may have little or no alluvium on them.
Thus one can have either bedrock terraces or alluvial terraces, which may consist of gravel, sand and
silt. Terrace formation can be explained in the following way. When the stream is graded, it forms a flat
valley. Later when the stream is rejuvenated it first cuts down through valley flat to a new grade. In
doing so it develops a second valley flat inside and below the first one. Repeated rejuvenation can
develop successive terraces at lower levels. Individual terraces may be narrow or a few kilometres wide.
Height between successive terraces may be a few metres to a few hundred meters, see Fig. 4.12.
Topography Resulting from Stream Deposition
FLOOD PLAINS: As the stream becomes graded the rate of down cutting decreases as compared to
the lateral erosion; hence there is increased meandering activity. Impingement of flow during
meandering widens the valley floor thereby producing flood plain. Thus flood plain is a strip of
96
River Morphology
Flood plain
River
Alluvium
Bed Rock
River
T
T
Scarp
T2
T3
T2
T1
T1
Fig. 4.12
Development of river terraces
relatively smooth land bordering a stream and over flowed at the time of high waters. When the flood
discharge exceeds the bankful discharge it flows across the flood plain. Two processes which are
responsible for formation of most of the flood plains of the great rivers of the world are the deposition on
the inside of river curves and erosion on the outer side of meander curves. When stream is in the mature
stage the width of valley floor is approximately equal to the width of the meander belt. In the lower
reaches of mature stream the valley width is much larger because the stream meanders and wanders, see
Fig. 4.13.
Fig. 4.13 Natural levees and flood plan
MEANDERING: Earlier in this chapter reference is made to meandering as one of the plan- forms of
single channel streams. The word meandering comes from the name of the stream in south eastern
Turkey, which was at one time known as Buyuk Meanderes (Lane 1957). This stream being very
97
Fluvial Morphology
crooked in plan, a stream having a winding course and having either regular sinuous pattern or irregular
pattern is known as a meandering stream. There are some streams which follow sinuous or irregular
path, but which have cut into solid rock or hard strata in deep gorges. These are called incised or
entrenched meanders, see Fig. 4.14. Entrenched meanders can also form in the flood plain when
winding pattern is formed in a mature or old stream and rejuvenation takes place where it starts cutting
down again. The terms used to describe meandering pattern are shown in Fig. 4.8 (a). Meander length
ML is the tangential distance between corresponding points at the extreme limits of fully developed
meanders. Meander belt MB is the width between tangents drawn outside of the meanders of the stream.
Investigator such as Inglis and Central Board of Irrigation and Power, India has accepted this definition.
However, Davis (1909) and others consider meander belt as the space enclosed between the tangents. In
the present text the former definition has been used. Meander width Mw = MB – B where B is the width
of the channel. The ratio of stream length to valley length is known as the sinuosity.
Fig. 4.14 Incised meanders of the Dolores river
Because of changing conditions of flow, stream slope, sediment size, sediment load and lithology
the meandering pattern along the length can be regular or can change along its length; the latter are then
called irregular meanders. The irregularity results from variation in discharge along the length due to
tributaries, withdrawal of water, presence of lakes, rock outcrops, weirs and barrages, and nonhomogeneity of strata through which the stream flows. In most of the cases, from the point of view of
analysis, it is justified to use average values of ML, MB, Mw and sinuosity to characterise the meander
pattern in a given reach. Leopold and Wolman (1957) have set an upper limit of sinuosity of 1.5 for
differentiating straight streams from and meandering streams. For some Indian rivers sinuosity values
up to 2.5 have been reported whereas a value of about 5.5 is considered to be the upper limit. The shape
of meanders is rarely truly sinuous; it is many times arc of a circle, parabola or some other curve. One
may some times come across a case where the stream has a primary meandering pattern on which is
superposed a meander pattern of smaller meander length and belt. This happens if the stream has more
than one dominant discharge.
The meander pattern in the flood plain of a stream is normally not static but it moves in the
downstream at a small velocity; however it is likely to be influenced by the variables such as discharge
98
River Morphology
and slope which give an idea about the erosive power of stream, and the nature of strata. The Klarafvens
river in Sweden has migrated a distance of about one meander length in 2000 years (Lane 1957). There
are also certain streams in which the migration process consists of gradual lateral enlargement of
meander loop, with periodic cut-offs. Such meanders are called free meanders. The Tigris river in Iraq
has shown this characteristic (Garde 1976). There are also some streams in which the meander pattern is
stationary; these are classified as inactive meanders.
NATURAL LEVEES: Natural levees are long embankments formed by the deposition of alluvial
material by the rivers when they overflow their banks. When streams overflow their banks the velocity
is appreciably reduced and hence the carrying capacity of the flow is decreased. This causes deposition
of some of the coarser sediment load resulting in the formation low ridge along the banks of the stream;
these are called natural levees; (see Fig. 4.13). Natural levees are highest near the riverbank and slope
gradually away from it. Natural levees may be one or two kilometre in width. They cause the present
meander belt of the river to stand up above the flood plain as a low alluvial ridge. These levees may be
built up until the river channel is several meters above the general level of the flood plain. This has
occurred in the case of the Yellow river in China and the Mississippi river in U.S.A. In many cases
tributary streams have difficulty in breaching the natural levees and many flow in the same flood plain
for many kilometres before breaking through the levee to join the main stream.
DELTAS: As the stream flows into lakes, ponds, sea or in rare case in rivers, the velocity of flow is
decreased and the sediment being carried by the stream is deposited forming what is known as delta, if
the waves or currents in the body of water into which it empties are not strong enough to carry away the
sediment brought in by the stream on which delta is formed. The amount of sediment deposited and its
pattern depend on the size of sediment, changes in the water level of the body, and waves and currents.
The name delta comes from the Greek word D to which the deposition pattern resembles. However, the
shape of delta can vary depending on the local condition; the Nile river delta has a triangular shape in
plan, whereas the Mississippi river delta and some others have long extensions of tributary channels,
which are some times called bird foot deltas. Almost all the deltas are formed by splitting of the main
channel into a number of branching distributaries channels. Reduction of flow in each branch due to
branching causes reduction in flow in each branch causing further deposition. This deposition blocks
the distributaries and more distributaries are formed.
As along as the rate of supply of sediment from the stream is greater than the rate of removal by
waves and currents, the shore line of the delta continues to move downstream especially in shallow seas.
Advance rates of some of the deltas in the world are given (Pitty 1971) in Table 4.4.
Table 4.4
Rates of advance of some deltas in the world
River
Volga
Mississippi
Orinoco
Don
Po
Kilia Delta of Danube
Tigris–Euphrates
Yellow river (1870–1936)
Rate in m/yr.
170
400
200
10
20
27
25–50
300–350
99
Fluvial Morphology
While the delta growth is continuous in some case, in other cases it is spasmodic. Half of the total
annual growth may take place during a single week as in the case of Lactature delta in Northern Sweden.
Silvister and de La Cruz (1970) have analysed the data of 53 deltas from all over the world and
obtained the following relationships for the characteristics of deltas:
FQI
H 100 K
bC C g
0.30
45
Apex to sea length L in km =
0.25
s
1
F Q I Ft I
H 100 K H 10 K
0.80
46.3
Area of fan A in km2 =
Number of distributaries N = 268
e
Cs0 .40
FS I
H 1000 K
1
2.30
U|
||
||
|V
||
||
||
|W
...(4.13)
where Q is the average annual discharge in m3/s, Cs is the (slope of continental shelf ´ 104), S1 is the
river slope in percent, and Te is the average annual temperature in oF. They have also a relationship for
maximum width of delta.
Conditions favouring the deltaic accumulation are (Sparks 1972):
i) large sediment load of the stream;
ii) usually large river; otherwise action of sea might disperse the sediment;
iii) reasonably shallow water offshore; very deep water may inhibit delta building. Thus Congo
river which virtually debouches into submarine canyon has no delta;
iv) coasts on which wave energy is low; and
v) small tidal range.
The Mediterranean, Black Sea, Caspian Sea bear witness to this in the deltas of the Nile, Rhone, Po,
Danube and Volga. However, deltas can be built in areas of larger tidal range provided that the
conditions (iii) and (iv) above are met. Irrawati and Ganges deltas are in the area of 5.5 m and 4.5 m tidal
range respectively.
In general, large rivers of the world have large deltas with a large number of tributaries. The
Orinoco River in Venezuela has thirty-six tributaries. The size of the deltas of the Yellow river and the
Orinoco River is nearly same. Since deltaic regions are most fertile, these are thickly populated. A few
deltas are shown in Fig. 4.15.
The main structural features of coarse-grained deltas differ considerably from those of fine-grained
deltas. Where bed load is carried into the delta area, this material gives rise to more rapid changes in
deltaic pattern and if it reaches the delta front, it may be deposited as forest beds. In fine-grained deltas,
where accumulations are essentially deposited from suspended load, distinctive sets do not develop.
There are also contrasts in the average inclination of sub aerial parts of the delta, those on small coarsegrained deltas being rather steep up to several meters per km and overlapping with the order of gradients
100
River Morphology
Ga
Tigris
Euphrates
cca
Da
ng
a
Bhag
irath
i
Calcutta
Persian gulf
Bay of Bengal
Tigris-Euphrates
Ganges-Brahmaputra
ack
Cutt
Naraj
nadi
Maha
Mahanadi
False point
Para dip
Puri
Bay of Bengal
Gulf of Guinea
Fig. 4.15 Some large river deltas
Subaerial
deltaic plain
Upper
deltaic plain
Subaqueous
deltaic plain
Lower
deltaic plain
Delta
fringe
Prodelta marine
Carbanaceous
matter
Sea level
Gravel Sand
Silt and clay
Longitudinal section
Coastal
interdeltaic sediments
Barrier island
Delta
flank bay
Deltaic sediments
Delta fringe distributory channels
Coastal
interdeltaic sediments
Delta
Barrier island
flank bay
Carbanaceous
matter
Sea level
Cross section
Silt and clay
Fig. 4.16 Longitudinal section of delta
101
Fluvial Morphology
on bahadas. On fine-grained deltas, the inclination is much flatter, of the order of 5 cm per hundred
metres. A typical longitudinal section through the delta is shown in Fig. 4.16.
ALLUVIAL FANS: When mountain stream flows out on a gently sloping plain adjacent to the
ranges or flows into another stream of greater slope, its velocity decreases and coarse gravel, sand and
fine sediment are deposited in the form of a fan in outline. This accumulation of sediment is known as an
alluvial fan. Alluvial fans have been studied over the past eighty years or so, and an exhaustive list of
references and the present state of knowledge are given by Rachocki (1981). Figure 4.17 shows the
sketch of an alluvial fan and its internal structure. Fans can be classified into dry fans and wet fans. Dry
fans are formed under dry conditions and their streams are ephemeral. For dry fans, mudflow and debris
flow deposits frequently comprise a large part of deposits. These fans are relatively small and have been
extensively studied. Wet fans are formed by perennial stream flow. Kosi fan discussed by Gole and
Chitale (1966) is a wet fan and is discussed in Chapter 13. This fan is produced by the huge quantity of
sediment load brought down by Kosi on the Gangetic plain.
Mountain front
Canyon
Mud flow layers
Clay
Bed rock
Gravel
Sand
Silt
Fig. 4.17 Alluvial fan and its internal structure
Alluvial fans are found in the foothills of mountains irrespective of climatic conditions. They were
and are being formed at the fronts of ice-caps and glaciers, as well as in moderate semi-arid and arid
regions. However, the largest alluvial fans are formed in the foothills of mountains in drier regions of the
world. Intensive weathering together with periodic rainfall events is conducive for the production and
transportation of large amounts of sediment by the ephemeral streams. Langbein and Schumm (1958)
consider an average precipitation of 250 to 350 mm as optimum for the development of fans. Such
conditions simultaneously reduce plant cover and ensure adequate supply of water for the transportation
of sediment.
102
River Morphology
Allen, Morisawa, Thornbury and others believe the commonly accepted explanation for the
initiation of fan, to be the drastic reduction in slope between eroding valley and receiving plain.
However, according to Bull, change in the confinement of the channel is also an important factor, which
facilitates fan construction by reducing the rate of sediment transportation. Infiltration of water in the
upper portions of fan further reduces the transporting capacity; this water reappears as strings in the
middle and lower portions. Braided stream pattern is characteristic of streams flowing across alluvial
fans, and as a result of repeated channel shifting, streams at one time or other flow down in almost every
possible radius of the fan.
Most alluvial fans exhibit a semi-circular shape in plan. Alternating periods of deposition and soil
profile formation are characteristic of most alluvial fans, because the depositional area shifts from one
part of the fan to the other during the construction of cone shaped deposit. According to Bull (1962), if
sufficient time is available for weathering to occur between periods of deposition, a series of soil
profiles will result. Alluvial fan deposits are composed of two main facies, water laid deposits and mass
flow deposits. These deposits are poorly sorted even though layers can be distinguished. Mass flows that
occurred recently in the fan’s evolution show two separate deposits. The upper part near the apex
consists of large particles and lower part of mudflow. Mudflow is a type of debris flow, which consists
mainly of sand and finer sediment. The particle size in general decreases in the downstream direction.
Fan dissection is a general term used which includes both entrenchment and incision of the fan. Fan
entrenchment is down cutting into the fan surface of a channel that is contributing sediment to the fan
surface. Entrenchment usually occurs during fan construction. Fan incision is down cutting into fan
surface by channel that crosses the fan margin. Incision is usually associated with fan destruction.
According to various investigators, the two possible causes for dissection are tectonic movements and
climatic changes. According to Lobeck, fan dissection is a natural process-taking place due to reduction
of sediment load.
A few words about fan dimensions are in order. The radius of the fan may range from several
hundred metres to one hundred kilometres with the slopes averaging between 3° and 6°. Anstey (1965)
studied fans in Western U.S.A. and Baluchistan in Pakistan. From a sample of almost 2000 fans, he
found that greatest number of fans have radii between 1.6 km and 8.0 km. The largest fan in his sample
had a radius of 25 km. The upstream slope values may be as high as 10° – 15° while the lower slope can
be less than 3°. With the passage of time thickness of fan deposition increases under most climatic
conditions. Borehole data as well as the dating techniques have been used to estimate the rates accretion
from 0.50 m to 3.0 m per thousand years. Some attempts have been made to relate empirically the fan
area Af and fan slope Sf to the drainage area A. According to Bull (1962)
For basins underlain by 48-86 percent
shale and mud stone
Af = 2.4 A0.88
Sf = 0.023 A –0.16
...(4.14)
For basins underlain by 58-68 percent
sand stone
Af = 1.3 A0.88
...(4.15)
Sf = 0.022 A – 0.32
Here A and Af are in miles2. These results indicate that the fan slope decreases with increasing fan
and drainage area of the basin.
103
Fluvial Morphology
POINT BARS: When the bed of the channel bend is deformable, scour occurs on the outer side of the
bend and the sediment gets deposited on the inner side of the bend forming the bar commonly known as
point bar. In order to explain the process involved in the formation of point bar, consider flow in a rigid
boundary bend. As the flow enters such a bend, the average velocity in the vertical U varies as 1/r where
r is the radius of curvature. This free vortex flow velocity distribution gradually changes to forced
vortex flow distribution along the bend length; in forced vortex flow U ~ r. To maintain this distribution
a transverse slope towards the inside is caused to the water surface. The friction at the boundary causes
velocity variation in the vertical. This variation in velocity in the vertical along with the transverse slope
induces secondary flow in the bend which is directed towards the inside of the bend near the bottom and
towards the outside of the bend near the water surface, see Fig. 4.18. According to Rozovskii (1961), the
location from the beginning of bend at which development of secondary flow is complete is affected by
roughness coefficient and the ratio of depth to centre-line radius, see Chapter 6.
WS
a
ua
Inner
Outer
WS
ub
B
Upper layer
Lower
layer
Fig. 4.18
Flow in a rectangular bend and development of secondary flow
F
GH
The secondary circulation is dissipated at a distance of 1.77
I
JK
C
. D from the end of the bend.
g
Interaction between the main flow and secondary flow causes redistribution of shear stress on the bed.
There is higher shear stress on the outer side of the bend land smaller shear stress on the inner side. This
distribution for a typical bend in trapezoidal channel is shown in Fig. 4.19. The shear stress at the bed
has a small component towards the inside of the bend, which causes sediment to move towards the
inside of the bend.
In the case of flow around the bend in a channel with deformable bed scour occurs on the outer side
of the bend and the sediment gets deposited on the inner side of the bend, forming a bar known as point
bar. For a high constant discharge the bed topography is such that the sediment transport rate is the same
at all the sections in the bend. The bed topography and the talweg observed in the South Esk bend are
104
River Morphology
FLOW
Inside edge W S
1.2 1.4
1.0
1.5
0.8
0.6
1.6
1.8
Separation
2.0
1.8
60°
2.0
1.5
1.4
1.2
1.0
0.8
0.6
Outside edge W S
1.0
1.2
1.0
Fig. 4.19
Separation
Shear distribution in a trapezoidal bend
shown in Fig. 4.20, as given by Bridge (1983). It is found that large-scale bed topography such as point
bar changes very little with discharge. The point bar at the bend apex extends about 0.60 to 0.8 times the
distance across the bend.
4.10
VARIABLES IN RIVER MORPHOLOGY
As discussed earlier, Schumm (1971, 1977) divides the fluvial system in three zones as shown in Fig.
4.11. Zone 1 in which the uppermost is the drainage basin, watershed or sediment source area. Water and
sediment are predominantly produced in this zone. Zone 2 consists of the main river system and can be
called the transfer zone where for a stable river sediment input and output are equal. Zone 3 is the
sediment sink or area of deposition, the sediment is deposited on alluvial fans, flood plains and deltas.
Whereas Zone 1 is the primary concern of geo-morphologists, Zone 2 is of major concern to hydraulic
and river engineers, and geo-morphologists associated with river channel morphology. Zone 3 is of
main concern to geologists, coastal engineers as well as river engineers.
In connection with river morphology, three “times” are considered. In Zone 1, one considers
geologic time as an important independent variable. This refers to the time from the beginning of
erosion cycle to the present and can be millions of years. During this period, erosion occurs in Zone 1
and characteristics of fluvial system progressively change. During graded time span which is a small
part of geologic time, there may be small progressive change in landforms, but by and large the system
can be considered to be equilibrium. This is the time span considered by Mackin in defining a graded
stream, which is considered to be in equilibrium; this time span can be a few hundred years. During
steady state time a true equilibrium may exist in which landforms are time-independent. This is the time
span considered by hydraulic engineers where variables such as drainage pattern, drainage density can
105
Fluvial Morphology
5
6
7
4
3
2
1
3
10 M
Fig. 4.20 Observed bed topography of south Esk bend
be considered constant. Steady state time can be of the order of a month or less. For geo-morphologists,
the geologic time and graded time are of significance.
In geologic time, the time, initial relief, geology (i.e., the lithology and structure) and palaeoclimate
are the independent variables where as palaeohydrology, relief (i.e., volume of the system above base
level), valley dimensions (width, depth and slope) are dependent variables.
In graded time span, time is no longer an independent variable even though the drainage system as
a whole may be undergoing progressive change of small magnitude. Initial relief has also no
significance. However geology, palaeoclimate and palaeohydrology, relief, valley dimensions, climate,
vegetation and hydrology (mean water and sediment discharge) are independent variables. The only
dependent variable is channel morphology i.e. channel dimensions and slope.
During steady state time (which is a short duration of a week to a month) true steady state
equilibrium may exist. During this time span, channel morphology assumes an independent status
because it is inherited from graded time. Hence in this state geology, palaeoclimate, palaeohydrology,
relief, valley dimensions, climate (i.e., mean precipitation, temperature etc.) vegetation, hydrology
(mean discharge of water and sediment) are independent variables. On the other hand, observed water
and sediment discharge and hydraulics of flow are dependent variables. The dependent and independent
variables in different times are listed in Table 4.5.
4.11
NEOTECTONICS AND EARTHQUAKES
During the cycle of erosion the land surface is affected not only by the erosional forces but also by the
internal forces, which cause displacement of earth’s surface due to movement of earth’s plates and
resulting stress building. This displacement is usually slow and can be gradual uplift, subsidence or
lateral displacement. Neotectonics refers to these gradual and presently active aseismic crustal
deformations. If this happens in the vicinity of an alluvial stream, uplift or subsidence can cause
degradation or aggradation respectively thereby altering the gradient upstream, at the axis of movement
and in the downstream reach.
The minimum rate of uplift estimated by Zeuner (see Schumm 1977) for the Alps and the
Himalayas are a millimetre per year. In California the average mountain building rate in modern times is
0.80 mm/year. The present rate of isostatic uplift in North America is 0.50 mm/year. The subsidence in
the surrounding area caused by the storage of water and sediment in Lake Mead, U.S.A. was 1.3 mm/
year. According to Schumm et al. (1987) many streams such as the Mississippi and Rio Grande in
U.S.A. and Amazon, Niger, Tigris, Euphrates, Rhine and Indus are affected by such structural
106
River Morphology
Table 4.5 Stream variables during different times (Schumm 1977)
Variable
Geologic
Time graded
Steady
Time
I
N.R.
N.R.
Initial relief
I
N.R.
N.R.
Geology (Lithology and Structure)
I
I
I
Palaeo climate
I
I
I
Palaeo hydrology
D
I
I
Relief or volume of system above base level
D
I
I
Valley dimensions (width depth, slope)
D
I
I
Climate (mean temperature, precipitation, seasonality)
X
I
I
Hydrology (mean discharge of water and sediment)
X
I
I
Channel morphology
X
D
I
Observed Qw, Qs
X
X
D
X
D
Hydraulics of flow
I = Independent
NR = Not relevant
X
D = Dependent
X = Indeterminate
instability. In Northern Iraq (i.e., Ancient Mesopotamia) Diyala River that is the tributary of the Tigris
has incised into its alluvial deposit due to uplift during the past 1000-1200 years. As a result the
inundation canal system developed in the earlier times has had to be abandoned. Upwarping of the
Brahmaputra basin is found to be partly responsible for flood problems in Bangladesh. Similarly,
tectonic uplift is likely to be at least partly responsible for the shifting of the river Kosi through 110 km
to the west in the past 200 years. Such uplift and downwarping may look innocuous during a short
period but can cause aggradation, degradation or change in plan form in different stretches of the
stream. This aspect has been studied by Ouchi (1985) in the laboratory and his results are summarised in
the Table 4.6.
Reach A: from 2.0 to 3.5 m where no significant uplift or subsidence occurred. Reach B: from 3.5 to
4.65 m, the upstream half of the uplifted or subsided zone. Reach C: from 4.65 to 5.75 m downstream of
uplifted or subsided zone.
Reach D: from 5.75 to 7.0 m where no significant uplift or subsidence occurred.
The lateral movement along the fault may cause a lateral shift in the stream crossing the fault. Such
a shift has been observed in the case of Narmada River in India. It has also been reported that prior to
Uttarkashi earthquake of 20th October 1991 of magnitude 7.1, horizontal and vertical movements were
noticed in Garhwal, Himalayas during 1972-1978. Horizontal movements were about 30 to 150 mm
while vertical movements ranged from 10 to 90 mm.
Earthquakes in Zone 1 can cause large-scale land slides and mass movement and produce enormous
amount of sediment which eventually reaches the stream and can cause aggradation, change in plan
form, shifting of tributaries and flooding in Zones 1 and 2. This is what happened in the Brahmaputra
after 15th August 1950 earthquake of 8.6 magnitude, see Gee (1951). The effects that were observed
immediately after that earthquake and in subsequent years were
107
Fluvial Morphology
Effect of uplift and subsidence on channel morphology (Ouchi 1985)
A
B
m
2.00
3.50
Uplift
Subsidence
Uplift
Zone
Subsidence
Meandering channel
Briaded channel
Table 4.6
Axis
4.50
Aggradation
Talweg shift
Submerged bars
Degradation
Terrace formation
Single bars
Degradation
Single Talweg
Aggradation
Braided
Aggradation Flooding
Multiple channels
Degradation
C
D
5.65
7.00
Aggradation
Braided
Flooding
Degradation
Single talweg
Degradation
Aggradation
Sinuosity increase
Bank erosion
Aggradation
Sinuosity increase
Bank erosion
Local scour
Flooding, cut-off
Multiple channels
zone of uplift or subsidence
Flow Direction
i) Some tributaries got blocked by temporary dams created by the debris falling in them from land
slides;
ii) Subsequent bursting of these dams caused large floods;
iii) A large quantity of sediment was brought down in the Brahmaputra causing aggradation of the
order of two to three metres over several kilometers; and
iv) Some tributaries shifted their course.
According to Walters (1975) channel widening and meander cut-offs in the Mississippi river in the
early 19th century were due to New Madrid earthquakes of 1811 and 1812.
References
Anstey, R.K. (1965) Physical Characteristics of Alluvial Fans. U.S. Army Natick Laboratory, Tech. Rep. ES-20
Bloom, A.L. (1978) Geomorphology: A Systematic Analysis of Late Cenozoic Landforms. Prentice Hall Inc.,
Englewood Cliffs (U.S.A.), Chapter 12.
Bridge, J.S. (1983) Flow and Sedimentary Processes in River Bends: Comparison of Field Observations and
Theory. In River Meandering: Proc. of Conference Rivers 1983, ASCE, pp. 857-872.
Brush, L.M. Jr. (1961) Drainage Basins, Channels, and Flow Characteristics of Selected Streams in Central
Pennsylvania. USGS Prof. Paper 282-F
Bull, W.B. (1962) Relations of Alluvial Fan Size and Slope to Drainage Basin Size and Lithology in Western
Frenso County, California, USGS Prof. Paper 450-B.
108
River Morphology
Bull, W.B. (1964) Alluvial Fans and Near Surface Subsidence in Western Fresno County, California, USGS Prof.
Paper 237-A.
Chitale, S.V. (1970) River Channel Patterns. JHD, Proc. ASCE., Vol. 96, HY 1, Jan. pp.201-222
Cotton, C.A. (1941) Landscape: As Developed by the Processes of Normal Erosion. Cambridge University Press,
U.K.
Craig, R.C. (1982) The Ergodic Principle in Erosion Models. In Space and Time in Geomorphology (Ed. Thorne
C.E.). George Allen and Unwin Ltd., London. pp. 81-115.
Davis, W.M. (1909). Geomorphological Essays. Ginn and Co., U.S.A.
Dury, G.H. (1969) Relation of Morphology to Runoff Frequency : In Introduction to Fluvial Processes (Ed.
Chorley R.J.) Mathuen and Co. Ltd., Chapter 9.11
Esterbrook, D.J. (1969). Principles of Geomorphology. McGraw Hill Book Co., New York, U.S.A.
Garde, R.J. (1972) Bed Material Characteristics of Alluvial Streams. Sedimentary Geology. Vol.7. pp 127-135
Garde, R.J. (1978) Irrigation in Ancient Mesopotamia. ICID Bulletin, New Delhi, Vol..27, No. 2, July, pp. 11-22.
Garde, R.J. and Kothyari, U.C. (1990). Erosion Prediction Models for Large Catchments. International
Symposium on Water Erosion, Sedimentation and Resources Conservation. CSWCRTI, Dehradun, Oct, pp.
89 - 102.
Gee, E.P. (1951).The Assam Earthquake of 1950. Jour. Bombay Natural History Society, Vol. 50, pp. 629-638.
Gole, C.V. and Chitale, S.V. (1966) Inland Delta Building Activity of Kosi River. JHD, Proc. ASCE, Vol. 92, No.
HY-2, March, pp. 111-126.
Hack, J.T. (1957). Study of Longitudinal Stream Profiles in Virgina and Maryland. USGS Prof. Paper 294-B.
Hack, J.T. (1960). Interpretation of Erosional Topography in Humid Temperature Regions. Am. Jour. Sci. Vol.
285A, pp. 80-97.
Horton, R.E. (1945) Erosional Development of Streams and Their Drainage Basins: Hydrophysical Approach to
Quantitative Morphology. Geo. Soc. of Am., Bull. Vol.56.
Johnson, D. (1932). Streams and Their Significance. Jour. of Geol. Vol. 40, Aug. – Sept.
Kellerhals, R., Church M. and Bray D.I. (1976) Classification and Analysis of River Processes JHD, Proc. ASCE,
Vol. 102 No. HY 7 July pp. 813-830
King, L.C. (1962). Morphology of Earth. Oliver and Boyd., U.K.
Krishnan, M.S. (1982). Geology of India and Burma. CBS Publishers and Distributors, India. 6th Edition, Chapter
III.
Lane, E.W. (1955). The Importance of Fluvial Morphology in Hydraulic Engineering. Proc. ASCE, Paper 745,
July, pp. 1-17.
Lane, E.W. (1957). A Study of Shape of Channels Formed by Natural Streams Flowing in Erodible Material. US
Army Engineers Division, Missouri River, Corps of Engineers, Omaha, U.S.A. No. 9.
Langbein, W.B. and Schumm, S.A. (1958). Yield of Sediment in Relation to Mean Annual Precipitation. Trans.
AGU, Vol. 39. pp. 1076-1084.
Leopold, L.B. and Wolman, M.G. (1957). River Channel Patterns: Braided, Meandering and Straight. USGS Prof.
Paper 282-B, 85 p.
Leopold, L.B. and Wolman, M.G. (1960). River Meanders. Bull. Geol. Soc. of Am. Vol. 71, pp. 769-794
Mackin, J.H. (1948). Concept of Graded River - Bull. Geol. Soc. of Am. Vol. 59, pp. 463-512.
Neill, C.R. (1970). Discussion of Paper “Formation of Flood Plain Lands” JHD., Proc. ASCE, Vol. 96, HY – 1,
Jan., pp. 297- 298.
Ouchi, S. (1985). Response of Alluvial Rivers to Slow Active Tectonic Movement. Geol. Soc. of Am. Vol. 96,
April, pp. 504-515.
Fluvial Morphology
109
Penck, W. (1924) Die Morphologische Analyse. Jour. Engelhorns Nachfolger, Stuttgart.
Pitty, A.F. (1971). Introduction to Geomorphology. Mathuen and Co., London. pp. 233-236.
Rachocki, A. (1981). Alluvial Fans: An Attempt at an Empirical Approach. A Wiley – Interscience Publication,
John Wiley and Sons, New York, U.S.A., 157 p.
Rice, R.J. (1977). Fundamentals of Geomorphology. Longman Inc., New York, U.S.A. 1st Edition.
Richards, K. (1982) Rivers. Mathuen and Co., London. Chapter 8.
Rohan, K. (1967).On the Problems of Longitudinal Profile Stabilization in Streams Transporting Sediment. Proc.
12th Congress of IAHR, Fort Collins, U.S.A., Vol. 3 – C28, pp. 237-248.
Rosgen, D. (1996) Applied River Morphology. Pagoda Spring, Colorado (U.S.A.)
Rozovskii, I.L. (1961) The Flow of Water in Bends of Open Channels. Israel Program for Scientific Translations,
Jerusalem.
Schumm, S.A. (1969). Geomorphic Implications of Climatic Changes. In Introduction to Fluvial Processes (Ed.
Chorley R.J.) Mathuen and Co., London, Chapter 11.11
Schumm, S.A. (1971). Fluvial Geomorphology: The Historical Perspective. In River Mechanics (Ed. Shen H.W.)
Published by H.W. Shen, Fort Collins, U.S.A., Chapter 4.
Schumm, S.A. (1977). The Fluvial System. A Wiley – Interscience Publication. John Wiley and Sons, New York,
U.S.A.
Schumm, S.A, Mosley, N.P. and Weaver, W.E. (1987). Experimental Fluvial Geomorphology. A Wiley InterScience Publication. John Wiley and Sons, New York, U.S.A., 2nd Edition.
Simons, D.B. and Albertson, M.L. (1963) Uniform Conveyance Channels in Alluvial Material, Trans. ASCE, Vol.
128, pp. 1.
Silvester, R. and de La Cruz, C.d. R. (1970) Pattern Forming Forces in Deltas. JWHD, Proc. ASCE, Vol. 96, No.
WW-2, May, pp. 201-217.
Shulits, S. (1941) Rational Equation for river Bed Profile. Trans. AGU, Vol. 22., pp. 522-531
Sparks, B.W. (1972). Geomorphology. Longman Group Ltd., London, 2nd Edition, pp. 275-279.
Thornbury, W.D. (1969). Principles of Geomorphology. Wiley International Edition, John Wiley and Sons Inc.,
New York, U.S.A., 2nd Edition.
Wadia, D.N. (1961). Geology of India. MacMillan and co. Ltd., London. 3rd Edition (Revised)
Walters, W.H. Jr. (1975). Regime Changes of the Lower Mississippi River. M.S. Thesis, Civil Engineering
Department, Colorado State University, Fort Collins, U.S.A.
Worcester, P.G. (1948). A Text Book of Geomorphology. D. Van Nostrand Company Inc., New York, 2nd Edition.
C H A P T E R
5
Hydraulics of Alluvial Streams
5.1
INTRODUCTION
Alluvial streams are those, which flow through sandy material, carve their channels through it and carry
water and sediment. In dealing with alluvial streams the material in the bed and banks of the channel is
generally assumed to be non-cohesive, though some of the fine sediment in transport may settle on the
banks and make the bank material cohesive. In the discussion below unless otherwise stated the flow is
assumed to be steady and uniform and the channel is taken as prismatic. Gravel-bed rivers are those
flowing through very coarse material with rather steep slopes, and their characteristics are discussed in
Chapter VII. The following aspects of the alluvial streams are relevant to the theme of the book and are
discussed below.
• Beginning of motion of uniform and non-uniform material: critical shear, and critical velocity
approaches
• Modes of sediment transport
• Bed-forms
• Resistance to flow
• Sediment transport
■ Bed-load
■ Suspended load
■ Total load
5.2
INCIPIENT MOTION
Consider a channel with given slope and bed material. As the discharge (and hence the depth flow) is
gradually increased and bed condition observed, it will be seen that up to a certain depth there is no
movement of sediment on the bed. However, with further increase in depth a stage is reached when
random occasional motion starts on the bed. This is known as the incipient motion condition or the
111
Hydraulics of Alluvial Streams
condition of critical motion. In determining this condition in laboratory experiments, the criterion could
be a single particle moving, a few particles moving, general movement on the bed, or the limiting
condition when the rate of sediment transport tends to zero. Out of these the last one is considered more
rational even though, in the past investigators have used one or the other criteria, which has made
comparison of formulae for critical tractive stress difficult. Knowledge of the condition of incipient
motion is important in sediment transport studies, in the design of channels carrying clear water, and
degradation phenomenon.
In the case of steady uniform flow the average shear stress on the bed is given by to = gf RSo where
R is the hydraulic radius and So is the bed slope, which is equal to the water surface slope Sw and slope
of energy line Sf. In the case of non-uniform flow this shear stress is given as to = gf RSf . The condition
of incipient motion for given sediment can be related to the average shear stress on the bed to to, average
velocity of flow U or velocity at the level of particle ud.
Empirical Equations: Critical Shear Stress Approach
During the latter part of the 19th century and first four decades of the 20th century, a number of
investigators carried out experiments in the laboratory to determine the critical shear stress at which
sediment of given characteristics would move. Equations proposed by Kramer, USWES, Chang, Krey,
Schoklitsch, Indri, Sakai and Aki and Sato (see Garde and Ranga Raju, 2000) fall under this category.
Most of these formulae can be expressed as
Fr -r d I
GH r M JK
F r - r d I . All these formulae recognise that the t
= const G
H r M JK
s
toc = F
f
...(5.1)
f
and can take the form toc
s
f
oc
depends on,
f
F r - r I d and M; here M is Kramer’s uniformity coefficient. However, their actual forms are
GH r JK
s
f
f
different, because (i) each equation is based on a limited amount of laboratory data, and (ii) these are
based on different criteria for defining critical condition viz. isolated, appreciable or general movement
on the bed.
Some theoretical and semi-theoretical analyses have also been carried out by investigators such as
Shields, White, Kurihara, Iwagaki, and Egiazaroff (see Garde and Ranga Raju, 2000) to determine the
incipient motion condition for cohesionless sediment particles of size d. However, we will discuss only
Shields’ (1936) analysis since it is based on sound principles and even after seven decades the results are
often quoted and widely used.
Shields’ (1936) Analysis
According to Shields, at condition of incipient motion of the sediment particle of size d on the bed, the
drag force on the particle caused by fluid flow is equal to the force required to move the particle. Using
Karman-Prandtl’s equation for velocity distribution in turbulent flow, namely
112
River Morphology
F
H
ud
u d
= f1 *
u*
v
I
K
...(5.2)
one can determine ud. Here ud is the velocity at the top of the particle level, u* = shear velocity
to
,d
rf
is the particle size, and v the kinematic viscosity. The fluid force on the particle is given by F1 = CD
rf
p d2
4
ud2
u2
= CD rf d ´ a2 d2 where a2 is a constant that depends on the shape of the particle. But the drag
2
2
coefficient CD = f2
F u dI = f F u dI .
H vK HvK
d
*
3
F1 = f3 (R*) rf
Hence
u*2 2
f1 (R*) a2 d2
2
...(5.3)
u* d
v
The resisting force F is related to the submerged weight of the particle and the coefficient of
friction. Hence F can be expressed as
R* =
where
F = a1 (gs – gf) d3
...(5.4)
where a1 depends on the shape of the particle and the coefficient of friction. Equating F and F1 under
incipient motion condition and introducing the subscript c to indicate incipient motion condition, one
gets
a1 (gs – gf) d3 = f3 (R*c) rf
or
dg
t oc
s
i
-gf d
=
u*2c 2
f1 (R*c) a2 d2
2
2a 1
f (R*c)
a2
u*c d
. The coefficient a1 and a2 can be assumed to be constant for particles of given shape.
v
Hence under the condition of incipient motion
where R*c =
t oc
=f
Dgs d
F u d I or t
H v K
*c
*c
= f (R*c)
...(5.5)
Shields used closely graded sediment viz. sand, barite, granite, amber, and brown coal with relative
density varying between 1.06 and 4.25. He used the critical condition corresponding to the case where
bed-load transport is zero and produced a graph between
F
H
I
K
u d
t oc
and * c . Later the mean curve
Dgs d
v
113
Hydraulics of Alluvial Streams
through the points was drawn by Rouse (1939) who gave wide publicity to Shields’ work in Englishspeaking countries. Recently Shields’ work has been critically examined by Buffington (1999) who
pointed out certain ambiguities in Shields’ presentation; however the writer feels that this criticism does
not reduce the importance of Shields’ work. Yalin and Karahan (1979) used large volume of data on
critical shear stress of nearly uniform material and prepared a modified curve between t*c and R*c. The
two curves of Shields’ and Yalin and Karahan are shown in Fig. 5.1. It is relevant to mention the
F
H
I
K
u d
t oc
vs *c
bears similarity to the
v
Dgs d
transition function for friction factor for pipes. The straight line portion on the right has d¢ < < d and is
applicable for hydrodynamically rough surface. In the region 2.5 < R*c < 40, the laminar sub-layer and d
significance of parameters used by Shields. The graph
are of same order of magnitude and it represents the transition region. For
hydrodynamically smooth and d¢ >> d.
10
*c
0
Data from different sources
for developed turbulent flow
gf)d
toc/(gs
F u d I < 2.5 the boundary is
H v K
10
1
Shields
Yalin-Karahan
10
2
10
1
10
0
1
10
u*cd/v
10
2
10
3
Fig. 5.1 Critical tractive stress relation for developed turbulent flow according to Shields, and Yalin and Karahan
Two additional comments are warranted about Shields’ diagram. Some investigators have argued
that according to dimensional analysis the ratio of depth of flow to size of sediment would be another
relevant parameter governing critical condition. Even though such argument looks logical, it must be
realised that flow conditions including turbulence close to the wall, which are responsible for sediment
movement, depend on shear velocity and relative distance from the wall measured in terms of multiples
of particle diameter. The thickness of boundary layer that equals the depth of flow in open channels is
not important. Secondly, Gessler (1965) has emphasised that the shear stress on the bed fluctuates and
follows Gaussian law with standard deviation of 0.57. Hence in a sediment mixture there is no cut-off
particle size such that one could say all particles larger than cut-off size will stay in bed and those finer
will be moved. In other words the sediment movement is probabilistic in nature. The statistical variation
of shear stress as well as orientation of individual particles is responsible for this. By sampling the bed
surface layer, Gessler determined that size for which the probability of remaining in bed is 0.50; the
average shear stress was critical for that size. In this way he obtained critical stress values for various
sizes and obtained curve similar to Shields’ curve. In this analysis Gessler made no allowance for the
effect of sediment non-uniformity on toc. He obtained toc values somewhat smaller than those obtained
by Shields for the same
F u d I . According to Gessler (1965) this has happened primarily because
H v K
*c
114
River Morphology
Shields has considered difference between time-averaged bottom shear stress and critical shear stress in
obtaining the condition for zero bed-load transport, whereas he should have used the time average of
difference between instantaneous bottom shear stress and critical shear stress. According to Shields, and
Yalin and Karahan, limiting value of t*c for coarse material is 0.060 and 0.045 respectively.
It may be noticed that u*c occurs in both the parameters of Shields relationship; hence if one wants
to determine t*c or u*c for given Dgs, rf, d and v, a trial and error procedure has to be used. This can be
avoided by using another parameters R02* defined as
R02* = (R*c)2
and R02* can be plotted against
FG D g d IJ
H t K
s
oc
=
D g s d3
r f v2
...(5.6)
t oc
. Choosing different points on the curve in Fig. 5.1 the following
Dgs d
table is prepared which can give directly values of
t oc
and hence toc for known values of, Dgs, rf v
Dgs d
and d.
Table 5.1
Variation of
t oc
Dgs d
with Ro2* according to Fig. 5.1
Ro2*
0.01
0.05
0.926
6.40
60.0
2065
3225
11764
40000
t oc
D gs d
0.25
0.20
0.14
0.10
0.066
0.031
0.031
0.034
0.04
108900
and above
0.045
Mantz (1979, 1983) has carried out experiments on transport of sediment in the size range of 0.01
mm to 0.10 mm. According to him if soft water is used these sediments exhibit the same packing
properties as cohesionless material. His critical shear results support Yalin and Karahan’s curve for fully
developed flows.
It needs to be mentioned that in turbulent flow all flow parameters fluctuate and so does the
boundary shear stress. Therefore beginning of motion of sediment particles as well as its transport on the
bed is a stochastic phenomenon. As mentioned earlier Gessler (1965), Grass (1970), Yalin (1977) and
Mantz (1979) have used a stochastic approach in the analysis of sediment movement. Another comment
that needs to be made is the role of lift force in Shields’ analysis. When the fluid flows past a spherical
particle resting on the bed, a lift force is generated due to modification of flow pattern around the
particle (Jeffrey 1929). The magnitude of this force would depend on the same parameters as the drag or
drag coefficient, namely u*d/v. Hence lift force is implicitly taken into account in Shields’ analysis.
Critical Velocity Approach
The idea of using average velocity of flow for describing the incipient motion condition is logical since
the average shear stress on the boundary will depend on U and D or R; further U and D or R can be more
115
Hydraulics of Alluvial Streams
directly obtained than to. Earlier attempts were made by Brahms, Airy and Rubey to relate critical
velocity to size and relative density of the particle (see Garde and Ranga Raju 2000). Thus equating the
dynamic force on the sediment particle to its resistance to motion, Brahms obtained
x
u2
p d2
p d3
rf d =
(gs – gf) tanq
4
2
3
...(5.7)
Here x is the fraction indicating the part of frontal area of the particle exposed to the flow, tan q is
the friction coefficient, and ud is the velocity at the level of particle at which particle will move. This
gives
|UV
= K W |W
ud2 = k d
or
ud6
...(5.8)
1
when the particle is under the incipient motion condition. Here K and K1 are constants and W is the
weight of the particle. Some empirical or semi-theoretical equations have been proposed for ud or U
mainly for hydrodynamically rough boundary.
These are based on analysis of experimental data for nearly uniform material and are listed below.
Garde (1970)
udcr
Dgs d
= 1.51
rf
Ucr
D
Dgs d
= 1.414
rf
d
Ucr
D
Dgs d
= 0.5 log
+ 1.63
rf
d
...(5.9)
Neill (1968)
F I
H K
1/ 6
...(5.10)
Garde (1970)
F I
H K
...(5.11)
Levy (see Bogardi 1974)
F
GH
U cr
D
= 1.4 1 + ln
7d
gd
F I
H K
I ¼ if 1.0 £ D £ 60
JK
d
U cr
D
D
= 1.4 ln
¼ if
> 60
7d
d
gd
...(5.12)
...(5.13)
116
River Morphology
With certain manipulation of equation for the mean velocity in open channels and the Shields’
Dg s d 3
D
Dg s d
2
as related to
and Ro*
=
for
rf
d
r f v2
curve, it is possible to obtain expressions for Ucr
hydrodynamically smooth, transition and rough boundaries. For this, consider the equation
F
GH
I
JK
u d
R
U
x which is valid for plane surface; Here x is related to * 65 as follows:
= 5.75log10 12.27
u*
d65
v
u* d65
11.6v
0.2
0.3
0.50
0.70
1.0
2.0
4.0
6.0
10 and more
x
0.7
1.0
1.38
1.56
The above equation can be written as
1.61
1.38
1.10
1.03
1.0
LM
N
Ucr
D
1/2
5.75 log + 6.26 + 5.75 log x
= t*c
d
Dg s d
rf
OP
Q
for uniform sediment. This needs to be used along with Shields’ relationship (in Tabular form) between
t*c, Ro2 and
u*c d
u d
D
. For each value of t*c and Ro2 different values of
are chosen and knowing *c , x
d
v
v
Ucr
. Thus a set of values of
Dg s d
rf
is determined and then
D
Ucr
2
,
and Ro*
were obtained along with
Dg s d d
rf
u*c d
. On the basis of these generated values the following equations are obtained
v
Smooth boundary
F u d < 2.5I
H v
K
*c
F I
H K
D
Ucr
= 1.77
d
Dg s d
rf
F
H
Transition 2.5 <
Rough
u* c d
< 7.0
v
F u d > 7.0I
H v
K
*c
I
K
0.166
dR i
2 0.05
o
F I
H K
D
Ucr
= 1.38
d
Dg s d
rf
F I
H K
D
Ucr
= 1.656
d
Dg s d
rf
0 .18
0.18
U|
||
||
||
V|
||
||
||
W
...(5.14)
117
Hydraulics of Alluvial Streams
10
9
Eq. 5.12
8
vy
Eq. 5.14c
Le
Ucr (Dgsd/rf)
7
6
Eq. 5.10
5
ill
Ne
4
3
Eq. 5.11
Garde
2
1
0
10
100
1000
10000
D/d
Fig. 5.2 Comparison of equations for Ucr / (∆g s d / rf ) for rough boundary
Figure 5.2 shows comparison of equations for
Ucr
for rough boundaries.
Dg s d
rf
Critical Shear Stress for Non-uniform Sediments
When the channel bed consists of a mixture of different sizes of non-cohesive sediment, the critical
shear stress toci of any size di in the mixture can be determined by carrying out a series of experiments
under steady uniform flow condition with decreasing shear stress and preparing a graph of qB vs to for
each size. By setting the condition that to = toci when the dimensionless bed-load transport of size di is
negligibly small (or less than a predetermined value), toci can be determined for different sizes in the
mixture. Value of toci for any size di is affected due to sheltering effect caused by the presence of
sediments of size greater than di and relatively greater exposure to flow for larger sizes. Hence if one
t
t
takes arithmetic mean size da as the reference size, and further defines t*ci = oci and t*ca = *ca
D g s di
D g s da
118
River Morphology
where toci and toca are critical shear stress for sizes of di and da respectively, it is logical to expect that
FG IJ
H K
t*ci
d
would be a function of i .
t*ca
da
Analysis of Egiazaroff (1965), Ashida and Michiue (1971), Hayashi et al. (1980) and others
indicates that indeed
t*ci
is primarily a function of
t*ca
FG di IJ when the material is coarse and hence
H da K
viscous effects can be neglected. The equations proposed by these investigators are listed below and
plotted in Fig. 5.3.
Egiazaroff (1965)
t*ci =
0.10
FG log 19 di IJ 2
H da K
...(5.15)
Ashida and Michiue (1971)
t*ci =
0.10
FG log 19 di IJ 2
H da K
...(5.16)
FG di IJ is between 0.40 and 1.0, they found that this equation gives a larger value than
H da K
Fd I
observed when G i J is less than 0.40. Tentatively they assumed
H da K
F d I -1
t*ci
= 0.85 G i J
...(5.17)
t*ca
H da K
When
for
di
less than 0.40.
da
Hayashi et al. (1980)
t*ci
t*ci
t*ca
-1
F
d
di I
= G J for i £ 1.0
d
d
H aK
a
L log 8 OP 2 for di > 1.0
=M
MN log b8 di / da g PQ da
U|
||
V|
||
W
...(5.18)
Earlier it was found that the value of t*ca varied between 0.05 and 0.02 and an average value of 0.03
was recommended.
119
Hydraulics of Alluvial Streams
20.0
Egiazaroff (1965)
Ashida-Michlue (1971)
Hayashi et al. (1980)
10.0
t*c
t*ca
1.0
0.2
0.05
0.1
di
da
1.0
10.0
Fig. 5.3 Variation of t*ci /t*ca with di /da for mixtures
Recently Patel and Ranga Raju (1999) have collected addition data and found that t*ca depends on
the geometric standard deviation sg =
t*ca =
F
GH
d84
d16
I the relationship between the two being
JK
0.045
s 0g .60
...(5.19)
t
d
Patel and Ranga Raju (1999) have also proposed the following relationship between *ci and i
t*cs
ds
FG IJ -0.96
H K
t*ci
d
= i
ds
t*cs
in which t*cs =
...(5.20)
t oc
and ds = dg sg there is a relationship between t*cs and sg as listed below.
D g s ds
Hence for known size distribution of bed material one can determine sg, geometric mean size dg and
ds = (dg sg). Then knowing t*cs from the table below for known, sg Eq. 5.20 will give t*ci for the size di.
Their studies also indicated that if arithmetic mean size is used, Hayashi’s equation yields more accurate
results than the other equations.
Table 5.2 Relationship between s g and t *cs
sg
t*cs
1.0
0.045
1.5
0.03
2.0
0.21
3.0
0.15
6.0
0.13
120
5.3
River Morphology
MODES OF SEDIMENT TRANSPORT
Once the shear stress acting on the bed exceeds the critical shear stress for the bed material, the sediment
particles start moving in the general direction of flow and the manner in which these are transported
depends on the flow conditions, ratio of densities of sediment and fluid and the size of the particle.
These modes of transport can be classified into the following categories.
Contact load
The sediment particles that roll or slide along the bed for some time, then come to rest and again start
rolling or sliding constitute the contact load. Hence contact load is the material rolled or slid along the
bed in substantially continuous contact with the bed.
Saltation load
The sediment particles hopping or bouncing along the bed thereby losing contact with the bed for some
time constitute saltation load. Hence saltation load is the sediment bouncing along the bed, or moved
directly or indirectly by the impact of bouncing particles.
Bed-load
Since saltation load, especially in streams, is difficult to measure, it is clubbed with contact load and
sediment moved on or near the bed is called bed-load.
Suspended load
Suspended load is the material moving in suspension in the fluid, being kept in suspension by the
turbulent fluctuations.
w
According to the theory of suspended sediment distribution; if o > 5.0 there is no suspended
u* k
sediment (see section 5.7). Hence taking Karman constant k = 0.40, the material will be transported as
w
to
bed-load if o > 2.0; however material of size d will move if
is greater than that gives by
D
gs d
u*
Shields’ diagram. Hence for purely bed-load transport the conditions to be satisfied are
to
is greater
Dgs d
t oc
w
and o is greater than 2.0.
Dgs d
u*
One can also assume that when vertical turbulent fluctuation near the bed is greater than the fall
than
velocity wo, sediment will go into suspension. At the edge of laminar sub-layer
v¢2
u¢
2
u¢ 2
= 2.5 to 3.0 and
u*
0.4 to 0.50. Hence it can be assumed that near the bed v ¢ 2 » u* at incipient suspension. Several
investigators e.g. Van Rijn, Sumer, Celik and others have related
variation is fairly well represented by the empirical equation
D g s d3
wo
to
and it is found that this
r f v2
u* s
121
Hydraulics of Alluvial Streams
F
GH
wo
D g s d3
= 0.5
u* s
r f v2
up to
I
JK
0. 40
D g s d3
values of 20. Here u*s is the shear velocity at incipient suspension of sediment of size d
r f v2
and fall velocity wo.
Daniel, Durand and Condolios (1953) have presented an interesting description, albeit qualitative,
of the mechanism of saltation. They have considered four idealised positions in which a particle will be
found on the surface of the bed and the possibility of their movement by saltation is discussed. These
positions are shown in Fig. 5.4.
1
2
Fig. 5.4
3
4
Particle position and its susceptibility to saltate
Out of the four possible positions, the particle in position 2 is more likely to travel by saltation under
favourable hydraulic condition. The two forces acting on the particle are the submerged weight of the
particle acting vertically downwards and resultant hydrodynamic force, which consists of drag and lift.
Where the lift is equal to the submerged weight of the particle, the particle will be lifted up thereby
increasing the lift. The particle acquires a vertical velocity and eventually in the final stages of taking
off, the movement is accompanied by a quick rotation as shown in the second part of the figure.
The particle in position 1 will either slide or roll over the layer of other particles. Particle in position
3 can have the saltation movement only if the particles upstream of it move in such a way that the
particle in position 3 is brought in position 2, or the particle in position 3 occupies some other position
because of the impact of the particle in saltation movement. The particle in position 4 will be set in
motion mostly under the condition of direct or indirect effect of particle in saltation.
According to Kalinske (1942) the height of saltation, for the same particle size, is proportional to
the ratio of mass densities of sediment and fluid. Hence it is apparent that the height of saltation in air is
about 800 times that in water for the same particle. For this reason saltation is not very important for
122
River Morphology
sand transport in water. The phenomenon of saltation is further analysed by Hayashi and Ozaki (1980).
While Einstein assumed that the saltation height hs is twice the diameter of the particle, Hayashi and
wo d
v
where t¢*, is the dimensionless grain shear stress and the value of hs/d can vary between 0.1 and 6.0
Ozaki’s analysis indicates that hs/d i.e. the dimensionless height of saltation depends on t¢* and
ls
w d
also depends on t¢* and o (see Fig. 5.6); however when
d
v
(see Fig. 5.5); similarly the step length
wo d
greater than about 100, as assumed by Einstein (1950)
v
ls
» 100
d
10
8
6
...(5.21)
Ref = wod/v
rs/rf = 2.65
4
CL = 0.50
R ef
2
ls
d
1
8
6
Reg = 40
100
400
4
0
=1
4
Ref ³ 2000
2
10
1
10
1
2
4
6 8 10
1
2
4
6 8 1
2
t¢*
Fig. 5.5 Saltation heights (Hayashi and Ozaki 1980)
At this stage it is interesting to know about the motion of individual particles moving as bed-load.
With the advent of radio isotopes, some information has been gathered about the average rate at which
sediment particles move on the channel bed. Such measurements by Hubbell and Sayre (1964) in the
case of the Middle Loup river, and laboratory flume indicate the following.
Table 5.3 Rate of movement of individual particles
Middle Loup river in USA
Lab. flume 2.44 m wide
Lab. flume 2.44 m wide
U m/s
Dm
d mm
Bed condition
Ug m/hr
0.527
0.610
0.326
0.76
0.317
0.317
0.29
0.93
0.19
Dunes
Long low dunes
Ripples
0.9
2.0
0.02
Thus, it can be seen that the average velocity of particles moving as bed-load is much smaller than
the flow velocity. The analysis of Engelund and Fredsoe along with Luque and Van Beek indicates that
(see Garde and Ranga Raju, 2000) the average velocity of bed particle Ug is given by
123
Hydraulics of Alluvial Streams
200
ls
= 100 t¢*
d
Ref = wod/v
rs/rf = 2.65
100
80
CL = 0.50
R ef
60
40
ls
d
=
4
Reg = 40
100
10
400
³ 2000
20
10
8
6
4
2
1
10
1
2
4
6
8 10
1
2
4
6
8 1
2
t¢*
Fig. 5.6 Step lengths (Hayashi and Ozaki 1980)
Ug
u*
F
GH
= 9 1 - 0.7
t *c
t*
I
JK
...(5.22)
where t*c can be obtained from Shields’ diagram. It may be further mentioned that when the particle
goes into suspension it is carried by the flow in the forward direction at the flow velocity at that level.
It is appropriate to mention distinction between bed material load and wash load at this place. The
sediment load carried by an alluvial stream can be divided into bed material load and wash load. Bed
material load is that part of the sediment load carried by the stream that has originated from the bed and
banks of the stream; hence it consists of sediment sizes found in appreciable quantity in the bed and
banks of the stream. Bed material load correlates well with the hydraulic conditions in the stream. The
other part of the sediment load is composed of those fine sizes not available in appreciable quantities in
the bed and banks of the stream. This part, known as wash load, is washed into the stream from the
catchment and is usually finer. Hence, the amount of wash load carried by the stream is more related to
the hydrologic conditions of catchments than to the hydraulic conditions in the stream. For this reason it
is difficult to estimate the amount of wash load carried by the stream. It is usually not possible to
stipulate the size limit for wash load. For sandy streams with flat slopes, the wash load may be in the clay
and silt range. On the other hand in the case of mountain streams with steep slopes, wash load may be in
the range of coarse to fine sand. Einstein (1950) recommends that the limiting size for the wash load
may be arbitrarily taken from the mechanical analysis of the bed material, as that size of which ten
percent of the material is finer. Hence one can write
Total load of stream = (bed material load) + (wash load)
Bed material load = (bed-load + suspended load)
124
5.4
River Morphology
BED-FORMS IN UNIDIRECTIONAL FLOW
Once the critical shear stress on the bed in unidirectional flow is exceeded, the sediment particles
forming the bed are transported at a rate, which increases with increase in shear stress on the bed. The
bed in the process remains plane under some conditions, but under other conditions develops
transversely oriented bed features known as ripples, sand waves or dunes, and antidunes as observed by
Blasius, Cornish, and Gilbert and recently by Simons et al. These bed-forms travel beneath the flow,
take part in the sediment transport, and govern the relationship between flow velocity, flow depth and
slope. In other words, they affect the friction and sediment transport. They also leave back a
characteristic imprint in the enclosed deposits. The purpose of this section is to describe the
characteristics of these bed-forms and study the methods available for their prediction.
Definitions of Bed-forms
The Task Force of ASCE (1966) has given the following descriptions/definitions of various bed-forms:
Ripples are small bed-forms with wavelengths less than about 0.30 m and heights less than
approximately 30 mm. They occur only rarely in sediments coarser than approximately 0.60 mm. These
are sometimes called current ripples.
Dunes are bed-forms larger than ripples but smaller than bars (see below) and are out of phase with
water surface gravity waves that accompany them. These are some times called sand waves or sand bars.
Bars are bed-forms having lengths of the some order as the channel width or greater, and heights
comparable to the mean depth of generating flow. Point bars at the bend and alternating bars fall in this
category.
With increased shear stress, dunes tend to get washed out and especially for finer material they can
be completely washed out and a flat or a plane bed can form. At this stage Froude number U/ gD can
be high but less than unity.
Further increase in flow leads to the formation of symmetrical sinusoidal sand waves on the bed and
similar water surface waves in phase. These are known as standing waves. Further increase in flow
causes these waves to move upstream, increase in amplitude and then break. These are called antidunes.
After breaking of waves the bed becomes plane and undergoes the same sequence. These bed-forms are
shown in Fig. 5.7.
Jackson II (1975) classifies bed-forms occurring in shearing flows on the basis of bed-form size,
time span of existence, superposition, flow regime and channel process. The larger bed-forms (macroforms), such as point bars, pools and riffles respond to geo-morphological regime of the environment
and are relatively insensitive to changes in fluid dynamic regime during an individual dynamic event
such as a flood in a river. A two-zone structural model of turbulent boundary layer provides a genetic
framework for two smaller classes of bed-forms. Meso forms, such as dunes in the rivers, respond to
flow conditions in the outer zone of the turbulent boundary layer as the flow varies through the dynamic
event; their life scales correspond with the duration of that event. The smallest bed-forms (micro forms)
viz. the ripples are governed by the flow structure in the inner zone i.e. the laminar sub-layer; their lives
are much shorter than the periodicity of dynamic events. According to Jackson II, ranges of wave
lengths of the different bed-forms are:
125
Hydraulics of Alluvial Streams
(a) Typical ripple pattern
Weak boil
(b) Dunes with ripples superposed
Boil
Boil
(c) Dunes
(e) Plane bed
(f) Antidunes, standing waves
(g) Antidunes, breaking waves
Breaking antidune wave
Pool
(d) Washed out dunes or transition
Accelerating
flow
Pod
Fr < 1
(h) Chutes and pools
Fig. 5.7 Bed-forms in alluvial channels
Ripples
Dunes
Sand waves and alternate bars
Sand bars, point bars
50 mm to 2.0 mm
0.40 m to 300 m
10 m to 1000 m
500 m to 5000 m
As mentioned earlier, alternate bars and point bars are the largest in each environment and their
dimensions compare to those of the environmental flow system. They are quite insensitive to changes in
flow.
Jackson II identifies four different types of super positions of bed-forms. These are as follows:
1. Imposition of lower regime bed-form upon the bed-form moulded by higher flow regime e.g.
small ripples migrating over upstream face of dunes.
2. Under equilibrium condition such superposition of ripples and dunes can be explained from
stability considerations. According to Kennedy (1969) perturbations of bed-load transport rates
are responsible for ripple formation while perturbations of the longitudinal distribution of
suspended load cause dunes. Hence when appreciable suspended load is present, ripples and
dunes can be superposed e.g., in fine to medium sands.
3. Superposition of fluid dynamic bed-forms on much larger bed-forms that are more permanent
e.g., large scale ripples on the point bar.
4. Superposition in which neither bed configuration responds to be local fluid dynamic regime;
e.g., mid-channel islands and sand bars in braided rivers such as the Brahmaputra river as
observed by Coleman.
Jackson II also discusses about three universal time scales of unsteadiness and discusses the effect
of each upon the bed-forms. The shortest time scale is that of the turbulent boundary layer of the flow,
126
River Morphology
for which a wide spectrum of time scales exists. The shortest is the time scale of Kolmogorov and is of
the order of a second. The largest corresponds to large eddies and their scales are of the order of a minute
or a few minutes. Several investigators attribute large-scale ripples to the eddies of this time scale. The
second time scale is related to each dynamic event taking place in the stream. It is the time interval TE in
which the event occurs e.g., passage of flood. The largest time scale is the geo-morphological scale,
which encompasses many dynamic events and is much longer than TE. This time scale reflects the
imposition of geological controls on the development of bed-forms.
Bed-forms have been observed and measured on some rivers. Lane and Eden (1940) have
summarised the results of field measurements by Johnson in the Mississippi river at Helena. Sand waves
of height up to 6.7 m and length up to 305 m were observed in a depth ranging from 4 to 9 m. Carey and
Keller (1957) have also reported measurements on the Mississippi. Whetten and Fullam (1967) have
measured dune lengths, dune heights and their migration velocity in the Columbia river downstream of
Bonneville dam in USA. Measurements have also been reported by Gallay (1967) on the North
Saskatchewan river in Alberta (Canada), by Singh and Kumar (1974) in the Ganga, the Yamuna and the
Son rivers in India, by Itakura et al. (1986) on the Ishikari river Hokkaido, Japan and by Haque and
Mahmood (1983) in irrigation canals in Pakistan. Similarly a number of laboratory studies have been
conducted during 1950 to 1985 or so. These data have been utilised to study the bed-form dimensions
and criteria for their occurrence.
Distinction Between Ripples and Dunes
Studies by Garde and Albertson (1959), Yalin (1971) and Garde and Issac (1993) have indicated that
ripples form in the initial stages of sediment movement and are near-bed phenomena. Hence their length
scale is obtained from u* and v as
later he indicated that for
L
v
. Even though earlier Yalin had indicated that for ripples » 1000,
u*
d
u* d
< 3.5
v
u* L
L
= 2250 or = 2250/(u* d/v)
d
v
Garde and Albertson (1959) had also proposed that
Mantz (1992) related
...(5.23)
H
u d
to
for ripples is governed by * and
.
Dg s d
L
v
u* L
u H
u d
to
and * to * and
. Garde and Issac (1993) have concluded that
Dg s d
v
v
v
ripples will form if sediment size is less than 0.60 mm,
u* d
is less than 10 – 12 and Froude number
v
U gD less than 0.80. If Fr is greater than 0.80 ripples are changed to symmetrical sand waves.
According to them ripple length and ripple height are given by
127
Hydraulics of Alluvial Streams
F I FG t IJ
H K H Dg d K
FG t IJ
H F u dI
=
H
K
d
v
H Dg d K
L
u d
= 4115 *
d
v
-0 .316
o
s
0.828
-0.660
and
*
o
s
-0.717
U|
|
V|
||
W
...(5.24)
Stability Analysis
The approach of explaining the formation of ripples, dunes and anti-dunes from the consideration of
stability of a plane alluvial bed transporting sediment has been followed by a number of investigators
such as Matsunashi, Engelund and Hansen, Kennedy, Hayashi, Engelund, Fredsoe, Parker, Reynolds,
Hayashi and Onishi, and Richards. Most scientists today agree that the problem of sand wave formation
is a problem of instability of an original plane bed transporting sediment when it is slightly perturbed by
a small sinusoidal disturbance. As a result the flow and sediment transport are perturbed. Then there will
be the following two main possibilities:
1. The change in flow pattern and sediment transport will tend to attenuate the amplitude of
perturbation, so that the bed goes back to the original plane bed state. This means that the plane
bed is stable.
2. The second possibility is that the flow causes the perturbation on the bed to increase with time,
which corresponds to the unstable situation, ultimately leading to formation of ripples, dunes
and antidunes.
Basically the analysis starts with the equations of motion and continuity equation on which onedimensional sinusoidal disturbance is introduced. This causes fluctuation in velocity component and
sediment transport. The analysis is essentially linear so that higher order fluctuations are neglected.
The instability caused is primarily dependent on the lag distance d which is the distance by which
local sediment transport rate lags the local velocity or shear stress at the bed. The total lag effect is built
of the following possible contributions:
1. fluid friction,
2. rate of suspended sediment transport in relation to bed-load transport rate,
3. gravity forces on moving bed-load,
4. inertia of sediment particles, and
5. percolation in river bed.
Such stability analysis has indicated the importance of the following parameters in determining the
F
H
flow regime, or stable wave length KD or
I
K
D U
to
2 pD
: Froude number, , ,
; here K is called the
L
d u¢* D g s d
wave number.
Dune Dimensions
Since the outer region of turbulent boundary layer controls formation of dunes, the length and velocity
scales that are most appropriate are the depth D and average velocity of flow U. Hence it is expected that
dune length L = constant ´ D. Yalin, Hino and Van Rijn (see Garde and Issac 1993) found the constant
128
River Morphology
of proportionality to be 5.0, 7.0 and 7.3 respectively. Using a large volume of laboratory and field data
Garde and Issac (1993) found that
L = 4.737 D
...(5.25)
which has the correlation coefficient of 0.674 and for which 33.25, 57.19 and 83.38 percent of the data
fell within ± 30, ± 50, and ± 100 percent error lines. The stability analysis, on the other hand, indicates
2pD
i.e. KD depends essentially on Fr. Figure 5.8 shows this graph. The empirical equation, which
L
fits the data reasonably well, is
that
Fr =
1 + KD tanh KD
2
KD + 8 KD tanh KD
a f
...(5.26)
1.6
Flume, River and canal data
1.4
1.2
Eq. 5.26
1 + tan h KD
2
Fr =
2
(KD) + 8KD tan h KD
Fr
1
0.8
0.6
0.4
0.2
0
0
1
2
Fig. 5.8
It was also found that as
3
4
I
K
6
7
8
9
10
Variation of KD with Fr for dunes (Garde and Isaac 1993)
u* d
u d
L
increases
also increases especially when * is between 20 and
D
v
v
30. Earlier Hayashi and Onishi had found that
F
H
5
KD
D
is also an important parameter. Hence assuming that
d
L
D
= f Fr,
, Garde and Issac obtained the equation
D
d
F I
H K
L
D
= 4.58 (Fr)0.397
D
d
0 .0546
...(5.27)
129
Hydraulics of Alluvial Streams
Accuracy of prediction of L by this equation is slightly superior to that of the equation L = 4.737 D.
A number of equations have been proposed for dune height. Some of these are listed below:
FG
H
IJ
K
Yalin (1971):
H
1
t
1 - *c
=
D 6
t*
Gill (1971):
H
t
1
=
(1 – Fr2) 1 - *c
D 2na
t*
...(5.28)
FG
H
IJ
K
...(5.29)
where a is shape factor for dunes and lies between 0.50 and 0.637, and n is the exponent of shear
parameter in the bed-load equation.
Fredsøe (1975):
H
L
FG
H
f
1
0.06
1=
- 0.40 t *
2
50
t*
IJ
K
3
...(5.30)
where f is Darcy Weisbach friction factor
Allen (1978):
FG IJ – 0.004077 FG t IJ U|
H K
Ht K |
V|
F
F
t I
t I
+ 0.000239 G
||
H t JK – 0.0000045 GH t JK
W
2
H
t*
= 0.079865 + 0.0336
D
t *c
*
*c
3
where t*c = 0.045
Van Rijn (1984):
where
F I
H K
F t ¢ IJ
T= G
Ht K
H
D
= 0.11
D
d
...(5.31)
4
*
*
*c
*c
-0 .30
(1 – e–0.5T) (25 – T)
...(5.32)
*
*c
Using a large volume of data Garde and Issac (1993) concluded that most of these equations predict
dune height with 29 to 35 percent of data falling between ± 30 percent error lines. They also concluded
that by far Allen’s equation is marginally superior to the other equations mentioned above. Figure 5.9
shows verification of Yalin’s and Allen’s equations using a wide range of flume, canal and river data. It
may be mentioned that Garde and Issac used flume and field data covering a wide range as can be seen
below
Sediment size
Flow depth
Height of undulation
Length of undulations
Channel slope
0.100 mm to 2.4 mm
0.051 m to 51 m
0.011 m to 5.58 m
0.090 m to 252 m
0.015 ´ 10 –3 to 14 ´ 10-3
130
River Morphology
1
Allen
H/D
Yalin and Karahan
0.1
Flume data
River data
Canal data
0.01
0.01
Fig. 5.9
0.1
t*c/t*
Variation of H/D with
1
t *c
for dunes according to Yalin and Allen (Garde and Isaac 1993)
t*
On the basis of their analysis they found that the maximum value of
primarily a function of
d
and is given by
D
F HI
H DK
= 0.22 + 0.4
m
F dI
H DK
and then they proposed the following equations for
is
m
...(5.33)
H
.
D
2.57
*c
if 0.03 £
t *c
£ 0.103
t*
if 0.103 £
t *c
£ 0.150
t*
if 0.150 £
t *c
£ 0.80
t*
*
m
1.15
m
F HI
H DK
0.60
a H / Df = 341.8 FG t IJ
a H / Df
Ht K
a H / Df = 1
a H / Df
a H / Df = 0.12 – 0.06
a H / Df F t I
GH t JK
m
H
designated as
D
*c
U|
||
|V
||
||
W
...(5.34)
*
Ripples and dunes are found to move in the downward direction at a velocity Uw that is given by
Garde and Kondap as
Uw
= 0.021 Fr4.0
gD
...(5.35)
131
Hydraulics of Alluvial Streams
Transverse Ribs
Transverse ribs are regularly spaced rows of clustered pebbles, cobbles or boulders lying at right angles
to the flow on the bars and the channels of braided streams. Their average longitudinal spacing ranges
from 0.06 m to as large as 2.5 m, and their height ranges from one to two times the maximum size of bed
material. Their wavelength seems to be proportional to the maximum size of the bed material, and
inversely related to the stream slope. Laboratory experiments indicate that the transverse ribs are
associated with near critical to supercritical flows.
It must be emphasised that the above relations have been obtained assuming the flow to be steady
and uniform. Even though this may be true in the case of flume studies, the flows in rivers are changing
which can have effect on bed undulations. To study this effect a population of dunes or any bed-form
that occur in a given reach of the channel can be considered and its statistical properties studied. In other
words frequency distribution of dune height or length can be studied to determine if the distribution is
uni-modal or bimodal. Bimodal distribution would imply two types of undulations. Similarly time series
analysis has been carried out on a train of dunes. This type of analysis was initiated after studying
changing dune characteristics in rivers such as the Fraser in British Columbia (Canada) and in the
Gironde Estuary in France. Further discussion on this aspect can be seen in Chapter XII of Sedimentary
Structures written by Allen.
Antidunes
Antidunes are symmetrical sand and water waves that are in phase and which may move upstream,
downstream or remain stationary. These were first observed by Cornish and then studied in detail by
Gilbert, Simons, and Kennedy. These were called antidunes because they moved against the flow even
when the sediment is transported downstream. As the waves move upstream their amplitude goes on
increasing. However there is a limit to the maximum steepness of water surface waves, which depends
on velocity, depth and sediment size. When this limit is reached the waves break, form a plane bed on
which sinusoidal waves had formed and then the process is repeated. These waves break when height to
wavelength ratio reaches approximately 0.14. The wavelength of the surface waves is given by
Ls =
2 pU 2
g
...(5.36)
Antidunes have been observed on several streams in USA, e.g., the San Juan River in Utah, the
Muddy creek in Wyoming, the Mendano Creek in Colorado and on the Assiniboine river in Canada.
When the antidunes form Fr number is close to or greater than unity.
Prediction of Regimes of Flow
For several reasons engineers, geomorphologists and sedimentologists are interested in predicting the
type of bed-form that would occur for given flow conditions and fluid, sediment and channel
characteristics in a stream. This is illustrated by two practically important examples. Figure 5.10 shows
the variations of Manning’s n obtained in laboratory flume for sediment size of 0.45 mm when the
average shear stress is varied. It can be seen that Manning’s n undergoes a three-fold change as the bedforms change from plane bed without motion, to ripples, to dunes of lower flow regime to the transition
and then upper flow regime of plane bed and anti-dunes. Thus, the resistance to flow changes
appreciably with flow conditions and needs to be predicted correctly.
132
River Morphology
0.18 mm Barton-Lin
Plane bed
Ripples
Dunes
Transition
Antidunes
0.03
0.02
n
0.01
0.038
0.45 mm USGS
0.03
n
0.02
0.01
0.002
0.2
1.0
Fig. 5.10
10
to
Variation of n with to
10
10
6
6
4
4
Hydraulic radius in feet
Hydraulic radius in feet
As can be seen from the above figure the roughness coefficient undergoes a definite reduction as the
flow changes from lower flow regime into transition while dunes are washed out and the bed becomes
flat. This is reflected in the discontinuous rating curve between discharge q and depth D for the Middle
Loup and the Pigeon Roost Creek in Mississippi (USA) see Fig. 5.11 (Dawdy 1963).
2
1
Fig. 5.11
1
5
5
3
2
1
2
4
Velocity in feet per second
10
3
1
2
4
Velocity in feet per second
10
Discontinuous stage discharge curves for the Middle–Loup and Pigeon Roost Creek (USA)
133
Hydraulics of Alluvial Streams
Part of the shear stress to, designated as t¢¢o is used in overcoming the form resistance of bed-forms
and only the remaining shear stress t¢o = (to – t¢¢o ) is available for bed-load transport. It is found that bedload transport rate correlates well with t¢o and not with to. Therefore, for the same shear stress and
sediment characteristics, the bed-load transport rate will be smaller when dunes than when it is flat cover
the bed. Thus, regime of flow also plays an important role in sediment transport phenomenon.
A number of attempts have been made to develop criteria for the prediction of regimes of flow.
These are based on the valuable experimental data collected by Gilbert, U.S.W.E.S., Simons et al. at
Colorado State University and others, together with data from irrigation canals and natural streams. It is
to be cautioned that irregularity in channel cross-section, and unsteadiness and non-uniformly of flow in
natural channels can vitiate the prediction of regime in natural rivers made using criteria primarily based
on steady, uniform flows in channels with rectangular shape. In such cases the recipe for successful
prediction is perhaps the combination of laboratory and field evidence. While discussing the various
criteria proposed by different investigators, the writer feels that as far as possible average flow velocity
should not be used as an independent variable because it is not known a priori. The most commonly
used dimensionless parameters in regime predictors are Froude number
stress
d or
U
, dimensionless shear
gD
u d u
D
to
, shear velocity Reynolds number * , * , , slope S, stream power to U, sediment size
Dg s d
v wo d
FG
H
D g s d 3 t *¢ - t * c
,
t *c
r f v2
IJ and U . These criteria are listed in Table 5.4 along with some comments.
K u¢
*
In the opinion of the writer the most important parameter in the prediction of regime is
to
or
Dg s d
t ¢o
which is an index of sediment mobility. Greater its value, greater will be the rate of sediment
Dg s d
transport. However
t ¢o
to
can be computed only if average velocity U is known; for this reason
Dg s d
Dg s d
is to be preferred. Then the Froude number U
gD
which is ratio of inertial force to gravity force
should also be important when bed undulations are large and affect the water surface. Hence Garde and
Albertson (1959) proposed
to
vs Fr criterion shown in Fig. 5.12.
Dg s d
Garde and Anil Kumar (1988) further checked this with additional data. This criterion clubs ripples
and dunes together. Plotting of additional data indicated Fr » 1.0 as a reasonable line of demarcation
to
.
Dg s d
Engelund and Hansen’s U/u*¢ vs Fr number criterion (1966) is shown in Fig. 5.13. It also works well and
in addition differentiates between negative sinus bed (i.e., anti-dunes) and positive sinus bed. Positive
between transition and antidunes regimes. Its limitations arise from the use of U along with
134
River Morphology
10
Ripple and dunes ... Blank
Transitions
... Half solid
Antidunes
... Solid
Modified
line
Original line
Ripple and
dunes
Transitio
n
Antidunes
t*
1.0
0.1
0.06
0.06
0.1
Fig. 5.12
t* – U
2
1.0
U gD
4
6
regime criterion of Garde and Albertson (1959)
gD
e bed
Positive sinus
bed (Dunes)
Negative sinus bed
(Antidunes)
Plan
30
25
U/U¢*
20
15
Plane bed
10
Positive
sinus bed
5
0
0.5
Fig. 5.13 U/u*¢ - U
Ripple and dunes ... Blank
Transition ...
... Half solid
Antidunes ...
... Solid
1.0
gD
U/ gD
1.5
2.0
2.5
regime criterion of Engelund and Hansen (1966)
135
Hydraulics of Alluvial Streams
Parameters used for prediction of regime
Table 5.4
Investigator
1. Langbein (1942)
Parameters used
U
Comments
vs UR
Limited laboratory data of Gilbert of 0.50 mm size;
dimensional parameter
gR
2. Albertson, Simons,
and Richardson (1958)
3. Bogardi (1974)
4. Garde and Albertson
(1959)
u*
ud
vs *
wo
n
gd
Flume data with d varying from 0.011 to 4.94 mm. Predicts
regimes fairly well for flume data but fails for river data.
vs d
u2*
U
Same as above, use of dimensional parameter
to
∆g s d
vs
gD
5. Garde and Ranga
Raju (1963)
S
R
vs
(∆g s g f )
d
6. Tsubaki and Sato
(1974)
S
R
vs
d
( ∆g s g f )
7. Engelund and Hansen
(1966)
U
vs
u*′
8. Simons and Richardson
(1962)
9. Van Rijn (1984)
Flume and field data; does not separate ripples from dues,
works fairly well.
Lines of demarcation between dunes and transition, and
transition and anti-dunes differ slightly from Garde and
Ranga Raju (1963).
U
Has theoretical basis, works well with flume and field data,
differentiates between positive sinus and negative sinus
(anti-dunes), and uses velocity. Needs trial error solution if
velocity is not known.
gD
to U vs d
Ft
GH t
o
Uses both shear and velocity. Uses primarily flume data,
prediction of regimes unsatisfactory.
I F ∆g d I
JK GH r n JK
3 13
− 1 vs
oc
10. Brownlie (1981)
Flume and field data, works fairly well, does not separate
ripples from dunes, and uses velocity.
US1 3
∆g s d
rf
s
f
vs
d
,
d
2
Based on flume and some field data, predictive ability mixed.
Flow in upper regime if S is greater than 76 ´ 10 –3. Needs
trial-error solution if velocity is not known.
sinus bed is one where the disturbance travels in the flow direction; however such a bed is accompanied
by appreciable form drag and is converted into dune pattern. This criterion is based on stability analysis
and finds qualitative support in earlier work by Matsunashi. It suffers from the same drawback as
vs Fr criterion in the use of velocity U as well as shear stress.
to
Dg s d
136
River Morphology
2 ´ 10
2
10
2
Modified line
Original line
Tsubaki-Satio
Garde-Raju
Transition
3
10
4
S/(gs/gf)
10
Antidunes
Ripple
and dunes
No sediment motion
t0
= 0.5
(Ags)d
Transition
Half Solid
Ripple and dunes Blank
Antidunes
Solid
10
5
10
10
Fig. 5.14 R/d – S
2
R/d
10
3
4
10
10
c∆g s / g f h regime criterion of Garde and Ranga Raju (1963)
The criterion proposed by Garde and Ranga Raju (1963) which uses
fact that smaller R/d and
dDg
s
/g f
i
dDg
S
s
/g f
i and R/d as two
to
is split into two parameters this criterion recognises the
Dg s d
S
larger, and larger R/d and smaller
which may have the
Dg s / g f
parameters is shown in Fig. 5.14. Since
S
5
b
g
d
i
to
can have different regimes. It seems to work well for both flume and field data, and has
Dg s d
the advantage that it does not use velocity. Later analysis by Tsubaki and Sato supported this criterion
even though their lines of demarcation are slightly different. Lastly it may be mentioned that according
to Van Rijn (1984),
same
b
g
U|
If d < 10 and 3.0 < T < 15.0 dunes will occur
||
If d < 10 and T < 15.0
dunes will occur
If T > 15.0
transition will occur V
||
F
I
F t¢ - 1IJ and d = d Dg
Here T = G
|W
GH r v JK
Ht K
If d* < 10 and T < 3.0
ripples will occur
*
*
1/ 3
o
s
2
*
oc
f
...(5.37)
137
Hydraulics of Alluvial Streams
It may be mentioned that only Van Rijn’s and Browntie’s criteria for regime predictions involve
kinematic viscosity and hence these take into account the effect of water temperature on flow regimes.
With the change in temperature, the fall velocity of sediment particle will change and hence its effective
size will be different. This is found to have significant effect on bed-forms, resistance and suspended
load discharge. Such studies by Lane, Straub and Taylor have shown increase in suspended load with
decrease in temperature, other conditions remaining same. Colby and Scott (1965) found that on the
Middle Loup river the bed-forms were more pronounced in summer.
5.5
RESISTANCE TO FLOW IN ALLUVIAL STREAMS
As the water flows through a channel, the channel bed, sides and the interface between water and air
offer resistance to flow. The resistance at the interface is usually negligible except when antidunes are
formed and even then that part of resistance is included in the overall resistance of bed and banks. This
resistance to flow is manifested in the slope of energy gradient Sf, which is equal to bed, slope So and
water surface slope Sw in steady uniform flow. The relationship between average velocity U, hydraulic
radius R, slope Sf and a coefficient representing roughness of boundary is known as the resistance law
and three commonly resistance equations used in open channel are
1 2/3 1/2
R Sf
n
Manning’s equation
:
U=
Chezy’s equation
:
U=C
Darcy-Weisbach equation
:
U=
RSf
8g RSf
f
...(5.38)
...(5.39)
...(5.40)
Writing these equations in non-dimensional form it can be seen that
C
U
U
R1/ 6
=
=
=
=
u* n g
g
g RSf
8
f
where u* is the shear velocity. Any one of these Eqs. (5.38) - (5.40) can be used to determine the velocity
if R and Sf (= So for steady uniform flow) along with the coefficient n, C or f are known. Using sand
coated roughness of uniform size ks along with Karman-Prandtl equation, U/u* can be expressed as
FG
H
IJ
K
FG
H
IJ
K
12.27 Rx
U
= 5.75 log10
u*
ks
One can relate Manning’s n to ks as
12.27 Rx
R1/ 6
= 5.75 log10
ks
n g
...(5.41)
138
River Morphology
Here x is a function of
x with
ks
11.6 v
where d¢ is the thickness of laminar sub-layer d¢ =
. The variation of
u*
d¢
ks
is given in Table 5.5.
d¢
Table 5.5 Variation of x with
ks
δ′
x
When
0.2
0.3
0.5
0.7
1.0
2.0
4.0
6.0
0.7
1.0
1.38
1.56
1.61
1.38
1.10
1.03
10.0 and more
1.0
ks
is less than 0.25 the boundary is hydrodynamically smooth; when it is greater than 6.0 it
d¢
is rough and when 0.25 <
ks
< 6.0 it is in transition. Thus in the case of smooth and boundaries in
d¢
transition C, n or f are functions of both
on
ks
δ′
u* k s
R
and , while in the case of rough boundary they depend
ks
v
R
R1/ 6
R
only. If one were to plot
vs
for hydrodynamically rough surfaces, one gets the
ks
ks
n g
approximation
FG IJ
H K
R1/ 6
R
= 24.0
ks
n g
1/ 6
or n =
k s1/ 6
25.6
which can be compared with the empirical equation obtained by Strickler for a number of Swiss rivers
flowing through coarse material and having plane bed,
n=
1/ 6
d50
24.0
Here ks and d50 are in m. For plane bed resistance in alluvial channels, Einstein recommends ks = d65
in Eq. (5.41).
Bank Resistance
A
in the
P
hydraulic computations; in such situations one can use hydraulic radius with respect to bed Rb in
resistance and sediment transport relationships and to can be calculated as gf Rb S. This is computed by
subdividing A into area corresponding to bed Ab, and area corresponding to sides Aw, and assuming U
When the roughness coefficient of bed and banks is different, it is not correct to use R =
139
Hydraulics of Alluvial Streams
and S to remain same for main channel as well as Aw. For rectangular channel of width B, depth D,
average velocity U and Manning’s coefficient for wall nw, one can write
A = Aw + Ab
BD = 2DRw + BRb
or
UV
W
1
Rw2/3 S1/2
nw
and
U=
Hence,
Rb = D - 2
F
H
D
Rw
B
...(5.42)
I = D F1 - 2 R I
K H BK
w
...(5.43)
Knowing Rw from Eqn. (5.42), Rb can be calculated.
General Comments on Resistance to Flow with Alluvial Beds
In the case of alluvial streams with shear stress greater than the critical, the analysis of resistance
becomes more complex due to changing bed-forms with the change in flow condition. With the
undulations on the bed the resistance of the bed is made up of the resistance due sand particles on plane
surface which is called grain resistance, and the form resistance due to the presence of bed undulations.
Even though grain resistance may not change significantly with flow, the form resistance will change.
Another factor which influences the resistance is presence of sediment in suspension. In the beginning
of the 20th century Buckley and Lacey observed reduction in the resistance to flow in the Nile and Indus
rivers respectively, in the presence of fine sediment. Similar observations were made by Vanoni and
Nomicos (1959) in their laboratory studies in which they showed that decrease in resistance is more
significant when bed is plane than when it has dunes on it. This decrease is due to the damping of
turbulence near the bed. Studies at the University of Roorkee have indicated that in plane bed channels
carrying suspended sediment of fall velocity wo the friction factor decreases when
C wo
is less than
US
C wo
is greater than 1200. Here C is the
US
average suspended sediment concentration is ppm by volume.
1200 while it is greater than that for clear water flow when
Resistance of Bed Undulations
In order to estimate separately the grain resistance and form resistance of bed undulations, Einstein and
Barbarossa (1952) divided shear stress on the bed g f Rb S into shear stress corresponding to grain
roughness t¢o and that corresponding to form roughness due to bed-forms t²o.
Hence
or
or
to = t¢o + t²o
gf Rb S = gf R¢b S + g f R²b S
Rb = R¢b + R²b
U|
|V
||
W
...(5.44)
140
River Morphology
where R¢b and R²b are hydraulic radii corresponding to grain roughness and form roughness respectively.
Einstein and Barbarossa compute R¢b using Manning’s equation along with Strickler’s equation
1/ 6
d65
25.6
where ns is for plane bed and d65 is in m. This gives
ns =
FG IJ
H K
U
Rb¢
= 7.66
u¢*
d65
1/ 6
...(5.45)
or using Eq.(5.41) with x = 1 and ks = d65 one gets
F
GH
U
= 5.75 log10 12.27 Rb¢
u¢*
d65
I
JK
...(5.46)
For river data they determined t¢o using above equations and then determined t²o = (to – t¢o). Further
D g s d35
U
to depend on bed-load transport rate and hence on Y¢ =
the relationship between
assuming
uo¢¢
t ¢o
U
and Y¢ was obtained using data from American rivers with the following ranges
u¢¢
*
d65
R
U
S
0.220 mm to 7.50 mm
0.045 m to 4.09 m
0.045 m/s to 2.79 m/s
1.740 ´ 10 –4 to 1.72 ´ 10 –3
The coordinates of the relationship between
U
and Y¢ as obtained by Einstein and Barbarossa are
uo¢¢
given in Table 5.5.
Table 5.5
Y¢
U
u*′′
0.50
100.0
Relationship between
0.70
62.0
U
and Y¢ as given by Einstein and Barbarossa (1952)
u*′′
1.0
1.5
3.0
7.0
9.0
15.0
25.0
40.0
40.0
25.0
15.5
10.0
9.0
7.0
6.0
5.0
It may be mentioned that later studies to verify Einstein-Barabarossa method by Vanoni and Brooks
U
and Y¢ plot. One can
uo¢¢
compute stage-discharge curve for an alluvial channel using this method in the following manner.
(1957), and Garde and Ranga Raju (1966) have indicated large errors on
141
Hydraulics of Alluvial Streams
1. Known quantities: channel width B, slope S, d35, d65, rf and rs. Neglect bank friction; hence R¢
and R² correspond to R¢b and R²b.
2. Assume R¢ and compute U using Eq. 5.44
3. Calculate Y¢ and find u²* using Table 5.5 and then R²
4. R = R¢ + R² for this R find D and then Q = BDU
5. Repeat the procedure with higher value of R¢
Engelund (1966) has proposed the method of estimating t¢o and t²o for known value of to by dividing
S into S¢ and S². He proposed the grain resistance to be computed using the equation
F
GH
I
JK
U
= 5.75 log10 R ¢ + 6.0
u¢*
2 d65
...(5.47)
It may be noticed that while Einstein and Barbarossa use d65 as roughness length for plane bed,
Engelund uses 2d65 implying that plane bed with sediment transport has greater roughness than plane
bed without motion.
Using some laboratory data by Guy et al. he found that t¢* =
FG t¢ IJ is related to t
H Dg d K
o
s
35
*
=
to
D g s d35
and regime of flow. For ripples and dunes, and plane bed he suggested the equations
for ripples and dunes
and for plane bed
t¢* = 0.06 + 0.4 t2*
t¢* = t*
for t¢* < 0.55
for 0.55 < t*¢ < 1.0
UV
W
...(5.48)
Brownlie (1983) extended the second equation in the higher regions of upper flow regime t*¢ > 1.0
as
t¢* = (0.702 [t*]–1.8 + 0.298)–1/1.8
To obtain velocity for given depth, slope, d65, d35, and Dgs one must first assume the regime flow,
then obtain t¢* and R’ from Eq. (5.47) or (5.48) for known to. Now use Eq. (5.46) to determine U and
U
vs Fr graph in Fig. 5.13. If the assumed regime is correct the solution
u¢*
is right; otherwise assume a different regime and repeat the procedure.
Lovera and Kennedy (1969) used flume and river data and showed that the friction factor for plane
bed with motion increases with increase in Re for given R/d whereas the lowest values of f ¢ for given
R/d are those given by Karman-Prandtl’s equation for hydrodynamically smooth boundary; see
Fig. 5.15. In their analysis Alam and Kennedy (1969), instead of subdividing R into R¢ and R², split S
into S¢ and, S² the slopes corresponding to grain roughness and form roughness respectively. Since
check the regime of flow using
f=
8g RS 8g R
= 2 (S¢ + S²)
U2
U
f=
8 g R S ¢ 8 g R S ¢¢
+
or f = f ¢ + f ²
U2
U2
142
River Morphology
River and flume data
d 0.088 to 0.788 mm
D 0.03 to 3.10 m
U 0.45 to 2.34 m/s
f¢ 0.04
2
R
= 10
d
= 1
2
3
4
5
6 8 10 12 15
20 25 30
40
50
100
125
0.03
0.02
0.01
Prandtl's smooth boundary relation
4
2.5 ´ 10
6
10
4
5
Re =
6
10
4
6
6
UR
v
Fig. 5.15 Friction factor for flat beds according to Lovera and Kennedy (1969)
where f ¢ are f ² friction factors corresponding to grain roughness and form roughness respectively.
Recently Patil (1997) has obtained equation for variation of f ¢ given by Lovera and Kennedy as follows:
f ¢ = m log10 Re + C
where
m = 0.1919 ´ 10 –4
for
R
+ 0.016 if
d
R
£ 3000
d
if
R
> 3000
d
R
+ 0.016 if
d
R
£ 3000
d
if
R
> 3000
d
and = 0.076
C = 0.1396 ´ 10 –3
= 0.478
Rec = 0.7256
and
F RI
H dK
Re > Rec
1.7735
f = 0.0032 + 0.221/(Re)0.237
if Re < Rec
U|
||
||
||
||
||
V|
||
||
||
||
||
W
...(5.49)
He also found that for laboratory and field data having a wide range of variables t¢¢* is given by
t¢¢* = 0.6 t *1.27
...(5.50)
143
Hydraulics of Alluvial Streams
Here t¢¢* and t * are with respect to d 50. Thus for known to and regime, t²* can be calculated and
then R¢b. Then using Eq. (5.47), U can be calculated.
Using Lovera and Kennedy’s relationship for f ¢, Alam and Kennedy (1969) found that f ² depends
on R/d and U
or U
; when R/d is greater than 3000 approximately, f ² depends only on
g d50
gR
U
(this is true for river data) or U
, see Fig. 5.16. As shown by Alam and Kennedy (1969)
g d50
gR
determination of depth or velocity when other parameters are known is a trial and error procedure
whereas determination of slope for known velocity, depth and sediment size involves no trial.
3
2
10
U gd = 50
1
7.5
Legend
Contours of values of
FD = U gd
10
15
20
0.15
2 50
25
2
30
25
10
0.3 0.2
10
35
0.5 0.4
15
U gRb
0.6
20
0.7
25 30
2
35
10
Contours of values of
F = U gRb
3
10
2
10
3
10
4
10
5
Rb/d
Fig. 5.16
Friction factor for bed-forms according to Alam and Kennedy (1969)
Total Resistance Approach
A number of methods have been proposed to determine the velocity of flow in alluvial streams by
considering the total resistance to flow without splitting it into grain resistance and form resistance. One
of the earlier attempts in this direction is Lacey’s equation (Lacey 1932)
U = 10.8 R2/3 S1/3
...(5.51)
which was proposed for stable alluvial channels but is often used for bankful discharge in alluvial rivers.
Sugio (JSCE, 1974) has proposed the equation
U = K R0.54 S0.27
...(5.52)
where K = 6.15 for ripples, 9.64 for dunes and 11.28 for transition regime. Thus one must first determine
the regime of flow by one of the methods involving R, S and d and then use Eq. (5.52).
Garde and Ranga Raju (1966) carried out dimensional analysis and indicated that
U
=F
Dgs d
rf
F F RI
GG H d K dD g S/ g i and g
H
1/ 3
s
f
1/ 2
d 3/ 2
v
I
JJ
K
144
River Morphology
First neglecting the effect of viscosity and hence of g1/2 d3/2/v, they obtained the following equation
F I FG S IJ
H K H D g /g K
R
U
=K
d
Dgs d
rf
with
2 /3
s
1/ 2
…(5.53)
f
K = 7.66 for plane bed without motion,
= 3.2 for ripples and dunes, and
= 6.0 for transition regime.
Later they plotted
F I FG S IJ and obtained a continuous relationship for all
H K H D g /g K
1/ 3
R
U
vs
d
Dgs R
rf
s
f
the regimes. The mean curve obtained them is shown in Fig. 5.17. Ranga Raju (1970) found that the
scatter on Fig. 5.17 can be reduced if K1
U
is plotted against K2
Dgs
R
rf
F
F RI GG s
H d K GG D g
Hg
1/ 3
f
s
I
JJ where K and
JJ
K
1
K2 are functions of d or g1/2 d3/2/v .
3.0
No sediment motion
D gs
rf R
U
1.0
Antidunes R.D. = 2.65
Ripples, dunes, transition
0.1
0.05
10
4
Fig. 5.17 Relation between
10
3
FG R FG1/3 IJ s IJ
H d H KDgs / g f K
10
D gs R
rf
vs
10
1
FG R IJ FG S IJ for all regimes and materials with different relative
Hd K H Dg /g K
1/ 3
U
2
s
f
densities (Garde and Ranga Raju 1966)
145
Hydraulics of Alluvial Streams
Patil (1997) found that for a large volume of data in ripple and dune regime covering a wide range
of related variables the following equation
F I
H K
R
U
= 6.05
d
gd
0. 5
S0.4
...(5.54)
predicts velocity within ± 30% error for 92 percent of data. For plane bed without motion, and transition
regime Equation (5.53) with K = 7.66 and 6 respectively can be used. These will reduce to
Plane bed without motion
and transition
F I
H K
F RI S
= 6.0
H dK
U
R
= 7.66
d
gd
U
gd
2/3
S0.5
...(5.55)
2/3
0.5
...(5.56)
A number of other approaches to prediction of velocity are available e.g., Paris, Brownlie, and that
by Karim-Kennedy. These are discussed by Garde and Ranga Raju (2000). However, for geomorphic
analysis Eqs. (5.54), (5.55) and (5.56) may be adequate for prediction of discharge or stage-discharge
relation. It is further cautioned that in the prediction of velocity in alluvial streams, at present errors of
the order of ± 30% are likely.
5.6
BED-LOAD TRANSPORT
It was mentioned earlier that when the average shear stress on the bed is greater than the critical shear
stress for the material, the material starts moving and there is a range of u*/wo values for which the
sediment is transported as bed-load i.e. the material moves on or near the bed. The layer in which the bed
material moves can be called the bed layer. The first bed-load equation was proposed by Du Boys
(1879). Assuming that the sediment moves in layers, each having a thickness Dh, the layers move
because of the applied shear stress to = gf DS, and the velocity of layers decreases linearly downwards
from (N – 1) DV for top layer to zero at the first layer (see Fig. 5.18), one can write
qB = gs N Dh (N – 1)
DV
2
...(5.57)
where N is the number of layers and qB is rate of bed-load transport in weight/width/time. The first layer
where velocity is zero will satisfy the condition that the resisting force is equal to the shear stress. Hence
to = (gs – gf ) N D h tan f
where f is angle of repose. When N = 1, to = toc. Therefore to/toc = N and Eq. 5.57 can be written as
qB =
or
g s Dh DV
to (to – toc)
2 t 2 oc
qB = Ato (to – toc)
...(5.58)
146
River Morphology
W.S.
to
Bed
(N
Dh
1) DV
2 DV
DV
DV = 0
Fig. 5.18
Du Boys bed-load transport model
Dh DV
has the dimensions m3/N. Values of A and toc were later determined by
2 t 2oc
Straub and are given below (See Garde and Ranga Raju, 2000).
The value of A = gs
Table 5.7 Values of A/gs and toc in Eq. 5.58 according to Straub (see Rouse 1950)
d mm
A/gs x 10 –6 m6/N2s
toc N/m2
0.125
32.32
0.766
0.250
19.45
0.814
0.50
11.75
1.054
1.0
6.89
1.533
2.0
4.05
2.443
4.0
2.43
4.310
The empirical equation proposed by Meyer-Peter and Müller (1948) is based on extensive data
collected in Switzerland by Favre, Einstein and Meyer-Peter and Müller. Meyer-Peter and Mûller split
S into S¢ and S² the slopes corresponding to grain and form roughness and found that it is only the shear
corresponding to grain roughness that is responsible for bed-load transport. Since
U=
F I
H K
n
S¢
= s
n
S
2
. Here ns =
1 2/3 1/2
1 2/3 1/2
Rb S and U =
Rb S¢
ns
n
1/ 6
d90
where d90 is in m. Using data covering the following range of variables
26
Relative density
Slope
Depth
Arithmetic mean size of sediment
1.25 to 4.22
4.00 ´ 10 –4 to 2.00 ´ 10 –2
0.01 m to 1.20 m
0.40 mm to 30 mm
Meyer-Peter and Müller obtained the equation
F n I FG t IJ = 0.047 + 0.25 f
H n K H Dg d K
3/ 2
t*¢ =
s
o
s
a
2/3
B
...(5.59)
147
Hydraulics of Alluvial Streams
rf
q
fB = B
gs
where
rs - r f
FG 1 IJ
H gd K
1/ 2
3
a
where da is the arithmetic mean size. The above equation can be written in the form
fB = 8 (t*¢ – 0.047)3/2
...(5.60)
Two observations can be made here. The first is that dimensionless bed-load transport is related to
excess shear (t*¢ – 0.047), and that even though Meyer-Peter and Mûller started with the division of S
F n I FG t IJ in Eq. (5.59) really represents g R¢ S . Therefore, to fit
H n K H Dg d K
bD g g d
3/ 2
into S ¢ and S ¢¢, the term
f
o
s
s
a
b
s
a
the experimental data, in reality they have subdivided Rb into R¢b and R²b. Ning Chien (1954) has found
that Eq. (5.59) predicts bed-load transport rate as well as Einstein’s equation (see below) for uniform
sediments and also for non-uniform sediments if all sediment particles in the mixture are moving and a
single size da is used. Hansen has used this equation to compare the observed values of bed-load
transport rate on the Skive-Karup river and found the two agreed fairly well. However, generally correct
size distribution of transported bed-load is not obtained.
A number of theoretical or semi-theoretical approaches have been made to study bed-load transport,
namely by Einstein (1942), Kaliske, Bagnold, Engelund and Fredsøe, and Yalin out of which only
Einstein’s method will be discussed here briefly. Einstein (1942) started with probabilistic approach to
bed-load movement. He disagreed with the premise that a definable critical condition for bed-load
movement exists. Since turbulent shear stress and lift near the bed fluctuate, Einstein assumed that a
sediment particles moves if the instantaneous hydrodynamic lift on the particle exceeds the submerged
weight of the particle. Once the particle is in motion, the probability of the particle being re-deposited is
assumed to be equal at all points on the bed. Lastly, the average distance travelled by any particle
moving as bed-load is assumed to be constant. He thus obtained relationship between bed-load
parameter fB =
qB
gs
rf
rs - r f
FG 1 IJ
H gd K
3
1/ 2
and flow parameter Y¢ =
d g - g i d . The relationship f
d g R¢ Si
s
f
B
=
f
F (Y¢) was determined using laboratory and field data. Later Einstein (1950) presented a more
sophisticated analysis to study fraction wise transport of non-uniform bed material.
In this later version Einstein modified the bed-load function to take into account fraction wise bedload transport, by defining
q i
f*i = B B
ib g s
FG 1 IJ
dr - r i H g d K
rf
s
f
1/ 2
3
i
where qB iB is bed-load transport rate of the fraction i and ib is the fractional availability of this size di in
the bed. The parameter Y*i is defined as
148
River Morphology
Y*i
LM
log 10.6
=x Y M
MM log FH 10.6 d
D
N
OP
PI P dg g-Rg¢ Si d
K PQ
s
i
65
f
i
The parameter Y*i is made up of three parts. Part 1 namely xi is the hiding factor that depends on
where dx is the characteristic size. Variation of x i with
di
dx
di
is given below
dx
Table 5.8 Variation xi with di /dx in Einstein’s method
di /dx
xi
0.10
150
0.2
35
The fraction Y is dependent on
0.4
6.8
0.6
2.2
1.5 and above
1.0
d65
and its variation is given below in Table 5.9.
d¢
Table 5.9 Variation of Y with d65 / d¢ in Einstein’s method
d65 /d¢
Y
5.0
0.52
LM
log 10.6
The term M
MM log FH 10.6 d
D
N
3.0
0.53
65
5.0
0.60
1.6
0.80
1.10
0.82
0.9
0.80
0.70
0.65
3.5
0.44
0.30
0.22
OP
I PP arises from the fact that lift on the particle is related to the near bed velocity
K PQ
which must be measured in sediment mixture at a distance 0.35 dx above the theoretical bed. The
characteristic size dx is given by
and
dx = 0.77 D
if
D
> 1.8
d¢
dx = 0.39 d¢
if
D
< 1.8
d¢
d65
and x is given in Table 5.5. The third part Y*i is reciprocal of dimensionless shear stress
x
with respect to grain. The curve between Y*i and f*i obtained by Einstein (1950) is shown in Fig 5.19
with data by Gilbert, and Meyer-Peter and Müller plotted on it. A number of questions have been raised
where D =
149
Hydraulics of Alluvial Streams
100
y*
10
1.0
0.1
0.0001
f*
y*
Curve compared with
measured points for
uniform sediment
• d = 28.65 mm Meyer Peter
et al. (1934)
• d = 0.785 mm Gilbert (1914)
1
1
A* =
B =
0.023 * 7.0
0.001
Fig. 5.19
0.01
0.1
f*
1.0
10
Einstein’s relationship between f* and Y* (Einstein 1950)
on the assumptions made in the deviation of Einstein’s bed-load function. These can be seen in
Raudikivi (1976) and Yalin (1971). In spite of these questions, Einstein’s method is considered to be the
most logical attempt to rationalize the complex problem of bed-load transport of non-uniform sediment.
The formula of Einstein (1942) was, modified by Brown (see Rouse, 1950) using the parameters f
and Y defined as
F g L r - 1O d I
GH MMN r PPQ JK
F g - g IJ d = 1
Y=G
H t K t
q
f= B
gs F
and
f
s
f
o
and
F=
2
+
3
1/ 2
3
s
*
36 v 2
g d3
F r - 1I
GH r JK
36 v 2
–
s
g d3
f
He expressed the variation of f with Y as
f = 40 t3* =
40
where Y £ 5.5
Y3
0.465 f = e– 0.39 Y where Y > 5.5
F r - 1I
GH r JK
s
f
U|
|V
||
W
...(5.61)
The parameters F in Einstein-Brown formula appears in Rubey’s formula for fall velocity of
sediment particle and was introduced to account for the fall velocity of sediment particles. Gill (1968)
150
River Morphology
investigated Einstein-Brown relationship using data of Gilbert, and Simons-Richardson and found it
necessary to modify it to
f = 40
FG t
Ht
IJ
K
3
-1
o
oc
...(5.62)
to account for deviation in f values at low shear stresses.
It may be mentioned that at Roorkee (India) systematic investigations have been carried out to
include effect of sediment non uniformity on the rate of bed-load and total load transport. According to
Patel and Ranga Raju (1996), the fraction wise bed-load transport can be calculated as follows:
1. Divide the bed material into a number of fractions and determine the geometric mean size and
availability in the bed ib of each fraction.
2. Compute toc for size da using Shields’ curve and also t¢o
3. Determine Kramer’s uniformity coefficient M for the mixture and CM using the Equation (5.63)
CM = 1 for M ³ 0.38
CM = 0.7092 log M + 1.293 for 0.05 £ M £ 0.38
4. Compute Cs for known values of
UV
W
...(5.63)
t o¢
from Equation (5.64)
t oc
F F t ¢ I - 0.1949 F log t ¢ I I + 0.0644 Llog t ¢ O
log C = – 0.1957 – 0.9571 G log G
MN t PQ
GH t JK JK
H H t JK
2
o
o
o
oc
oc
oc
s
3
...(5.64)
5. Compute xB from Eq. (5.65)
FG
H
CM xB = 0.0713 Cs
and then compute xB
t ¢o
D g s di
IJ
K
–0.7514
...(5.65)
FG t¢ IJ
H Dg d K
o
s
i
6. Read fB from Fig. 5.20 and determine
qB iB = ib gs fB (g
di3)1/2
F Dg I
GH g JK
1/ 2
s
f
5.7
SUSPENDED LOAD TRANSPORT
As mentioned earlier at higher shear stresses the sediment particles go into suspension. Owing to the
weight of the particle, there is a tendency for the particle to settle which is counterbalanced by the
turbulent motion i.e. turbulent velocity components. Also there is a continuous exchange of sediment
151
Hydraulics of Alluvial Streams
10
1
10
1
10
0
fB
10
1
10
2
Data from different sources
10
xB =
0
t o¢
Dg s di
Curve based on uniform sediment
10
1
10
2
10
6
10
5
10
4
xB
Fig. 5.20 Variation of fB with xB
fB
10
3
10
2
10
1
F τo I for field data with non-uniform sediments (Patel and Ranga Raju 1996)
GH ∆γ s di JK
particles from suspension to the bed and bed to the suspension. Various mechanisms have been
suggested by which a sediment particle moving on the bed goes in suspension. According to the lift
concept initially proposed by Jeffreys and used by Einstein, when the instantaneous lift on the particle is
greater than its submerged weight, the particle moves up in the flow and is transported as suspended
load. According to Laursen while the particle is moving along the bed over a dune or small irregularity,
it loses contact with the bed momentarily as it is launched over the crest and is carried in suspension.
According to Sutherland (1967) the turbulent flow consists of round or oval shaped eddies; these eddies
are distorted and flattened as they approach the channel bed and the velocity within the eddy increases.
Their impingement on the laminar sub-layer disrupts it and causes spots of high shear stress at different
places on the bed and causes motion of the particles. If the turbulent velocity component at the place of
impingement is large enough and in vertically upward direction, the particle can be entrained in the flow.
In fact, all the three mechanisms discussed above work together in the process of suspension.
When sediment goes into suspension, the concentration of suspended load in the vertical decreases
with increase in distance from the bed. In general, finer the sediment, more uniform is the distribution of
suspended sediment in the vertical. The two most common ways of expressing the concentration of
suspended sediment are:
1. Absolute volume of solids per unit volume of water– sediment mixture. This can also be
expressed in parts per million by volume or in percent.
2. Dry weight of solids per unit weight of mixture. This again can be expressed in parts per million
by weight or in percent.
152
River Morphology
Suspended Sediment Distribution Equation
The suspended sediment is subjected to two actions: the first is the upward and downward turbulent
velocity fluctuation v¢ and the second is the gravitational action that causes settling of sediment which is
heavier than water. Since there is a concentration gradient
¶C
at any distance y from the bed, due to
¶y
¶C
where Îs is the
¶y
sediment transfer coefficient. The downward transfer per unit area will be woC where wo is fall velocity
of sediment and C is the concentration. Hence for steady, uniform and two dimensional flow, the
continuity equation demands that
turbulence, there is a net transfer of sediment in the upward direction equal to Îs
Îs
¶C
+ woC = 0
¶y
...(5.66)
The same equation can be obtained from general diffusion equation for sediment in open channels.
Equation (5.66) was first used by the German meteorologist Schmidt in 1925 to determine the
distribution of dust particles in the atmosphere. If Îs and wo are assumed to be independent of y, Eq. 5.66
can be integrated to obtain
C
ln
=
Ca
z
y
wo
dy
Îs
a
wo
and
C
= e Îs
Ca
( y - a)
U|
||
V|
||
W
...(5.67)
Here Ca is the concentration at a distance “a” from the bed. Schmidt obtained this equation in 1925.
Considering that momentum transfer and sediment diffusion in vertical in turbulent flow are similar, one
may assume Îs = b Îm where em is momentum transfer coefficient and b is a coefficient. If one assumes
b = 1, Îs = Îm and Îm can be determined from combining the following equations
U|
||
y
|
t = t F1 - I |
H DK V
||
t =g DS
||
u
¶u
=
¶y k y
|W
Îm =
t ¶u
rf ¶y
o
o
and
s
*
o
...(5.68)
153
Hydraulics of Alluvial Streams
where D is the depth of flow, ko is Karman constant the value of which for clear water flow in open
channel is 0.40; and the last term of Eq. (5.68) is obtained from Karman-Prandtl equation for velocity
distribution in turbulent flow. This gives
Îs = Îm = u* ko y
F D - yI
H D K
...(5.69)
Substitution of the value of Îs from Eq. (5.69) in Eq. (5.66) and subsequent integration gives
FG
H
D- y a
C
=
Ca
y D-a
where
wo
Zo =
u* k o
IJ
K
Zo
U|
|V
||
W
...(5.70)
This equation was first published by Rouse in 1937 but was independently derived by Ippen earlier.
For further discussion of Eq. (5.70) it is essential to state the assumptions made in its derivation because
any deviation from it in its verification can be attributed to one or more of the assumptions made. These
assumptions are (see Garde and Ranga Raju, 2000):
1. Derivatives with respect to t, x and z are assumed to be zero; this means the flow is steady,
uniform and two dimensional in nature.
2. Higher order derivatives of C with respect for x, y, and z are neglected. This assumption is
justified for small values of Zo but can introduce errors when Zo is large and sediment
concentration distribution near the bed is skew.
3. Intensity and scale of turbulence for upward and downward flows are the same and v’ and
mixing length l have unique values for given y.
4. While evaluating Îm it is assumed that r f is constant; yet mass density of fluid will be
maximum near the bed and will decrease upwards.
5. While integrating Eq. (5.66) it is assumed that wo is independent of y; however because of
concentration gradient and turbulence, the fall velocity of a particle near the bed will be smaller,
and increase as y increases.
6. Îs is assumed to be equal to Îm.
7. Logarithmic velocity distribution law holds well with Karman constant k = 0.40. Vanoni,
Garde, Barton and Liu and others have ascertained validity of logarithmic law for velocity
distribution law; however some investigators who have determined k from the whole velocity
distribution have found it to vary. However, if it is determined from the velocity variation near
the bed, k is found to be essentially constant by Coleman.
Two other attempts to integrate Eq. (5.66) may be mentioned. Lane and Kalinske (1941) found that
as a simplification an average value of Îm = Îs = u* D/15 can be used for wide rivers. Hence integration
of Eq. (5.66) gives
F I
H K
w o 15
( y - a)
D
C
= e u*
Ca
...(5.71)
154
River Morphology
Laursen (1980) expressed Îs as
Îs =
F
H
b Îm
y
1D
I
K
where b is introduced believing sediment may not follow the turbulent fluctuations exactly and (1 – y/D)
representing correlation coefficient, and integrated Eq. (5.66) to get
FG IJ
H K
a
C
=
Ca
y
wo
b k o u*
...(5.72)
Here value of b between 1 and 1.5 is recommended.
In addition to three sediment distributions laws (Equation 5.70, 71 and 72) a few other equations
have also been obtained by investigators such as Einstein, Hunt, Tanaka and Sugimoto, Navntoff, Willis
and others. However, the most often used equation, because of its simplicity, is Eq. (5.70). Hence, it is
desirable to consider this equation further. Equation (5.70) indicates that when y = D, C = 0 and when
y = 0, C = ¥; both these boundary conditions are unrealistic. At the boundary the concentration cannot
exceed sediment concentration of stationary bed, and at y = D there will be finite though small
concentration of suspended load, especially for finer material. However, Eq. (5.70) gives realistic
distribution in the remaining range of y.
Some studies have been carried out about variation of Îs. The sediment transfer coefficient can be
wo
. Vanoni (1946) and Ismail (1952) found that for the fine
¶ C/¶ y
sediment Îs is greater than Îm i.e. b is greater than unity while for coarse material Îs/Îm is less than
unity. Raudkivi (1967) expresses Îs/Îm as
obtained directly from Eq. (5.66) as
Îs/Îm = Rs ls/Rl
where Rs is correlation coefficient between C¢ and v¢, R is correlation coefficient between u¢ and v¢ and
ls and l are mixing lengths for sediment and fluid respectively. Hence variation of Rs, R, ls and l with y
will determine variation of b with y. Coleman (1970) analysed the Enoree river data on distribution of
suspended sediment and studied variation of Îs /u* D with y/D and found that Îs/u*D increases with
increase in y/D from 0 to about 0.25 and after which it remains essentially constant up to y/D = 1.
Further for given y/D, Îs /D increases slightly with increase in wo/u*. Thus for Enoree river data Îs /D
value for y/D = 0.90 increased from 0.06 to about 0.30 as wo/u* increased from 0.347 to 0.908.
One can also study the effect of Zo or wo /u* on the distribution of C. When Zo is small i.e. when wo
is small and/or u* is large, the concentration does not very much in the vertical. When Zo is large i.e.
when wo is large and/or u* is small, concentration distribution will show considerable variation with y. In
fact it can be seen that when Zo is less than 0.03, the concentration will be almost constant in the vertical
(this happens for silts and clays). When Zo is greater than 5.0, suspension is insignificant. Figure 5.21
shows variation of C/Ca with (y – a)/(D – a) for a/D = 0.05 various value of Zo.
155
Hydraulics of Alluvial Streams
1.0
25
0.1
0.7
0.2
0.5
0
a
a
0.5
y
D
5
0.6
0.06
25
0.8
0.0313
0.9
0.4
0
1.
0.3
0.2
4.0
a
= 0.05
D
Zo=
2.0
0.1
0
01
Bottom
02
03
wo
u * ko
04
05
06
07
08
09
10
Relative concentration C/Ca
Fig. 5.21 Distribution of suspended load in a flow according to Eq. 5.70
The general validity of Eq. 5.70 has been shown by the experimental data collected by Vanoni,
Vanoni and Namicos, Barton and Lin and others in laboratory flumes and data on rivers such as the
Missouri and the Enoree. Such verification has also indicated that even though observed and computed
distribution are similar, Z observed by the slope of C/Ca vs (D-y)/y curve is not equal to Zo computed as
wo
. This has been attributed to various reasons such as change in fall velocity due to turbulence and
u* k o
concentration, change in turbulence characteristics due to presence of bed-forms and concentration
gradient, secondary circulation and variation in Karman constant.
Integration of Sediment Distribution Equation (Eq. 5.70)
It can be seen that the distribution of suspended sediment concentration in the vertical can be obtained if
wo
, still the
u* k o
reference concentration must be known. In this connection Karman anticipated that Ca would depend on
size of sediment in suspension and shear stress to on the bed. Lane and Kalinske (1939) showed that for
some American rivers and canals Ns/Nb depends on wo/u* where Ns is the concentration of material of
fall velocity wo in suspension near the bed and Nb is the fraction of the same material found in the bed in
percent by weight. Kalinske and Hsia (1945) found that Ns/Nb depends also on u* d/n.
Einstein (1950) assumed that the bed-load transport rate qB iB of a given size range occurs in a bed
layer of thickness 2d where d is the representative size of the range. The velocity at the edge of the layer
one knows Zo and reference concentration Ca at “a”. Assuming Zo can be calculated as
is 11.6 u¢*. Hence the concentration of bed-load can be taken as C2d =
q B iB
11.6 u*¢ 2 d
a f
=
q B i B . This is
23.2 u*¢
156
River Morphology
Table 5.10 Variation of C2d with
u*2 d
according to Garde (1959)
ωo v
u2* d
ωo v
5.0
8.0
10.0
14.7
20.0
40.0
C2d in % by weight
0.01
0.02
0.06
0.40
2.0
2.0
considered as suspended load concentration at a = 2d. Garde (1959) using laboratory data of nearly
uniform materials found that C2d in percent by weight depends on
FG u
Hw
*
o
u* d
v
IJ or u d , see Table 5.10.
K wv
2
*
o
Otherwise a single measurement of suspended load concentration at known elevation can be made.
With known Ca and Zo Eq. 5.70 along with the velocity distribution law can be combined and
integrated over the depth of flow to find the total amount of suspended load carried by the stream per
unit width. As done by Einstein the logarithmic velocity distribution
F
GH
30.2 y x
u
= 5.75 log
u¢*
d65
I
JK
...(5.73)
can be used, or a simple relationship such as
F I
H K
y
u
=
um
D
n
...(5.74)
can be used with free steam velocity um and n known. The suspended sediment transport rate qs can be
obtained by integrating (Cudy) over the depth. The upper limit of integration is y = D. For lower limit of
integration one can use y = 2d as suggested by Einstein (1950) which seems reasonable for plane bed.
Brooks (1963) and, Harrison and Lidicker (1963) made the following suggestion for the lower limit of
integration. They suggest that the largest of the following three be taken as lower limit.
1. a = 2d as suggested by Einstein;
2. Value of “a” at which u = 0 according to logarithmic velocity distribution law, i.e.,
a
= e– ko um/u*
D
a
at which extrapolation of suspended sediment distribution will yield a limiting
D
concentration of 480 kg/m3. If Cmd is the concentration at mid depth.
3. Value of
FG C IJ
HC K
md
b
1/ zo
=
a
D
For details of calculation of suspended load by Einstein’s method (see Garde and Ranga Raju,
2000).
157
Hydraulics of Alluvial Streams
Relations for Sediment Discharge
In many morphological studies estimates of suspended load carried by the stream may be needed. Using
Lane and Kalinske’s method (1941) it can be shown that
qs = q Ca Pe15(wo/u*)A
...(5.75)
where A = a/D where suspended load concentration is Ca, q is the water discharge per unit width and P
depends on wo/u* and weakly on n/d1/6 where n is Manning’s n. The parameter P is given by
P = e– 8.0 wo/u*
...(5.76)
Thus if a single measurement of Ca at ‘a’ is known along with q, D and u*, qs can be determined.
Garde and Pande (1976) showed that for laboratory and field data, the following relationship holds
good:
qs
gfq
= 5.10 ´ 10 –5
FG u IJ
Hw K
4
*
...(5.77)
o
By combining Kikkawa’s relation qs a D2S for u* >> wo and Chezy’s Equation q2 a D 3S one gets qs
D a q2 which for small variation in depth of flow can be written as
qs ~ q2
...(5.78)
Data on many rivers and canals indicate that the power of q varies between 1.92 and 2.20 indicating
the validity of the above proportionality.
Van Rijn (1984) has proposed that qs be estimated using the equation
qs = gs D U Ca F
...(5.79)
in which qs is in wt/width/time, Ca is the reference concentration at y = a given by
Ca =
0.15 d50 T 1.5
a d*3
Here “a” is taken to be equal to ks or
...(5.80)
D
whichever is greater. The roughness parameter ks is
100
obtained from the equation
R
U
= 5.75 log b + 6.25
u*
ks
Lastly the correction factor F in Eq. 5.79 depends on a/D and Z¢.
where Z¢ is obtained from
w os
+f
Z¢ =
0.4 b u*
FG w IJ
Hu K
F w IJ FG C IJ
£ 1.0, j = 2.5 G
H u K HC K
2
b=1+
o
*
for
w
0.01 < os
u*
0.8
os
a
*
b
0 .40
U|
||
|V
||
||
|W
...(5.81)
...(5.81)
158
River Morphology
Here wos in Eq. 5.81 is for fall effective size ds and is given by
ds
= 1 + 0.011 (s9 – 1) (T – 25)
d50
and T =
bt ¢ - t g . Variation of F with and a/D is shown in Fig. 5.22.
o
oc
t oc
10
10
0
1
a7D
=0
.1
0.0
F
5
10
2
0.0
1
10
3
0
1.0
2.0
3.0
4.0
5.0
Z¢
Fig. 5.22 Variation of F with Z ¢ and a/D (Van Rijn 1984)
5.8
TOTAL LOAD TRANSPORT
As mentioned already, the total load carried by the stream is the sum of suspended load and bed-load
transported per unit time per unit width of channel. It does not include wash load which is not related to
flow conditions; hence it is the bed material load. Suspended load and bed-load can be calculated for
different fractions of the bed material and added to get the total load. Methods for such calculation are
already discussed earlier in this chapter. For many morphological studies such refined calculations may
not be needed. Therefore in this section only equations for computation of total are discussed which use
only one representative size such as d50 or da. If all size fractions are moving these methods can also be
used for fraction wise sediment transport; however the results are approximate because of coarser
particles are not included in these methods.
(1) Laursen’s Method (1958)
Based on flume and some field data with sediment size ranging from 0.011 mm to 4.08 mm, Laursen
proposed the relationship
159
Hydraulics of Alluvial Streams
C
F d I LM t¢ - 1OP
H DK N t Q
7/6
=F
FG u IJ
Hw K
*
...(5.82)
o
o
oc
where C is total concentration in percent by weight, toc is critical shear for median size d computed
using Shields’ method and the function F (u*/wo) is obtained experimentally as below:
u*
wo
F
FG u IJ
Hw K
*
10-2
10-1
0.6
2.0
4.0
10
30
3.95
6.0
10
27
102
103
104
40
200
103
2 ´ 104 3.8 ´ 104 5.5 ´ 104
o
(2) Relation between qs/u* gs d and to /Dgs d
Garde and Dattatri (1963) used data with size range 0.011 mm to 0.93 mm and obtained the relation
qT
= 16 t*4.0
g s u* d
...(5.83)
while Graf and Acaroglu (1968) used flume data of Gilbert, Guy et al. and obtained the relationship
qT
= 10.39 t*2.52
g s u* d
...(5.84)
Here qT is total load transport ratio in weight/width/time. It is known that exponent of t* depends on
mode of sediment transport. A lower value around 2 corresponds to bed-load transport whereas a higher
valve indicates a substantial amount of suspended load in the total load. Hence variation in the exponent
of t* in the above equations can be explained.
(3) Bagnold’s (1966) Approach
Bagnold equated rate of doing work by transport of bed-load and suspended load to the available stream
power toU and the transport efficiencies and obtained the following equation:
qT =
LM e + e b1 - e g u OP
w Q
d1 - r / r i N tan a
to U
B
s
s
s
B
...(5.85)
o
f
Here u s is the average velocity of suspended load which can be taken equal to U, eB = bed-load
transport efficiency whose value lies between 0.05 and 0.11, es = suspended load transport efficiency
which is 0.015, tan a = coefficient of intergranular solid friction of bed material whose value varies
between 0.375 and 0.75; and qT is in weight/width/time.
The above equation is simplified to the form
qT =
LM e + 0.01 U OP
w Q
/ r i N tan a
to U
d1 - r
f
B
s
o
...(5.85 a)
160
River Morphology
(4) Engelund and Hansen’s Equation (1967)
Engelund and Hansen postulated that when there are dunes on the bed, the energy required for moving
a sediment particle over a dune height H can be equated to the drag forces acting on the particle during
the same period. On the basis of this hypothesis they obtained the equation for sediment transport as
where the friction facto
UV
W
f fT = 0.40 t*5/2
f = 2 g R S/U 2
...(5.86)
The equation was obtained using flume data in the size range 0.10 mm to 0.93 mm with dunes,
transition, standing waves or anti-dunes on the bed. It needs to be emphasized that even though the
equation is derived for duned bed, it gives reasonably good results for other regime also, and subsequent
verification has given good results.
(5) Ackers and White (1973, 1980)
Using the accepted premise that whereas bed-load transport is related to shear stress with respect to
grain, total shear is responsible for sediment transport when suspended load predominates, Acker and
White have obtained the equation
Fu I
H UK
*
where
c1
gfC D
gs d
FG F - 1IJ
HC K
IF
JJ G
u
G
Dg d J G
JG
r K H
c4
= C2
1
...(5.87)
3
F1
F
GG
=
GG
H
c1
*
s
f
I
JJ
U
10 D J
32 log
J
d K
1 - c1
is the sediment mobility parameter, and the constant c1, c2, c3 and c4 are functions of dimensionless
sediment size d* as given below
For
1.0 £ d* £ 60.0
c1 = 1.0 – 0.56 log d*
c2 = 2.86 log d* – (log d*)2 – 3.53
For
c3 =
0.23
+ 0.14
d*1/ 2
c4 =
9.66
+ 1.34
d*
d* > 60.0
c1 = 0, c2 = 0.025,
c3 = 0.17,
c4 = 1.5
Here C is the total load concentration by weight. Initially this equation was developed using flume
data and limited amount of field data. However, later it was tested with lot more field data and found to
give satisfactory results.
161
Hydraulics of Alluvial Streams
(6) Yang’s Equation (1972, 1973)
Yang approached the problem of total load transport from the point of view of energy expenditure and
related rate of sediment transport to dimensionless stream power US/wo
log CT = A + B log
FG US - US IJ
Hw w K
c
o
...(5.88)
o
u* d
u
and * . Here USc is the critical stream power required to move the
wo
v
sediment. His final equation is
where A and B were related to
log CT = 5.435 – 0.286 log
U|
|
OP log FG US - U S IJ V|
Q H w w K ||W
wo d
u
– 0.457 log * +
w
v
o
LM1.799 - 0.409 log w d - 0.314 log u
w
v
N
o
*
o
...(5.89)
cr
o
o
where Ucr is the critical velocity for incipient motion and is to be calculated using the Eq. (5.90)
Ucr
=
wo
2.5
+ 0.66
u* d
- 0.06
log
v
F I
H K
Ucr
= 2.05
wo
and
for 0 <
for
u* d
< 70
v
u* d
> 70
v
U|
|
V|
||
W
...(5.90)
Yang found that the above equation gives satisfactory results for flume data as well data from the field.
(7) Shen and Hung’s Equation (1971)
Using regression analysis Shen and Hung started with the equation
log CT = ao + a1 X + a2 X2 + a3 X3
L US OP
X=M
Nw Q
0 .57
where
0.0075
0 .32
o
and is calculated in fps system of units. Their final equation is
log CT = – 10704.5 + 324214.747X – 326309.6 X 2 + 109503.872X 3
...(5.91)
Here CT is concentration of bed material in ppm by weight. This equation is based on over 500 data
points out of which 63 correspond to river data of Middle Loup and Niobrara in USA and the rest to
flume studies.
162
River Morphology
(8) Effective Shear Stress Approach of Ranga Raju et al. (1981)
Vittal et al. (1973) defined effective shear stress t t for ripple and duned bed as the shear stress required
to give the same total load transport rate of the same sized material on plane bed. The effective shear
stress is always less than the average shear stress of dune bed channel.
Ranga Raju et al. (1981) after analysis of extensive data for dune bed channels found that the
dimensionless effective shear stress
tt
is given by
Dgs d
t*t = t¢*
FG t ¢ IJ
Ht K
–m
o
...(5.92)
o
where t¢o is computed using Manning’s equation with Stickler’s ns =
and
d 1/ 6
. Here m is given as
24
m = 0 if
u*
£ 0.50 when suspended load is absent
wo
m = 0.2
u*
u
– 0.10 when * > 0.50
wo
wo
U|
|
V|
||
W
When t*t is used in the sediment transport relationship, a unique relationship is obtained between
fT =
qT
gs
FG 1 IJ
dr - r i H g d K
rf
3
s
1/ 2
and t*t for all bed-forms i.e. ripples, dunes, and plane bed. In the range
f
of 0.05 £ t*t £ 1.0, this relationship can be expressed as
fT = 60 t ¢*3
FG t ¢ IJ
Ht K
- 3m
o
...(5.93)
o
This equation is based on 900 data points out of which 235 belonged to river and canal data.
(9) Brownlie’s Equation (1981)
On the basis of analysis of laboratory and field data covering a wide range of pertinent variables,
Brownlie has proposed the following equation for concentration of bed material load C T in ppm by
weight.
CT = 7115 CF
OP
LM
MM U - U PP
MM Drg d PP
Q
N
cr
s
f
1.978
S
0.6601
F RI
H dK
- 0 .3301
...(5.94)
163
Hydraulics of Alluvial Streams
The coefficient CF for field data is 1.268 and for flume data it is unity. The critical velocity Ucr is
given by
Ucr
= 4.596 t *0c.529 S - 0 .1405 sg– 0.1606
D gs d
rf
...(5.95)
Here sg is the geometric standard deviation of the bed material.
(10) Karim-Kennedy’s Equation (1983)
Unlike many other methods, Karim and Kennedy linked the problems of prediction of resistance and
sediment transport in alluvial streams. Based on the analysis of 615 data points out of which about 100
points were for the Missouri river and rest from flume data, they obtained the following equation
qT
log
gs
LMF r - r I g d OP
MNGH r JK PQ
s
f
1/ 2
= – 2.2786 + 2.9719 V1 + 0.2989 V3 V2 + 1.06 V1 V3
3
f
where
V1
F I
G U JJ , V = log F D I
= log G
H dK
GG Drg d JJ
H K
F u -u I
= log G
H D g d / r JK
2
s
f
V3
*c
*
s
f
U|
||
||
|
V|
||
||
||
W
...(5.96)
Here d is taken as d50.
Relative Accuracies of Different Total Load Equations
Many attempts have been made to find the relative accuracy of the above methods of computing total
load transport rates in alluvial streams. However, the difficulty in the interpretation of these results is
that these investigators have used different sets of data and total number of data points are from flume
studies as well as field data. The criteria used for assessing the accuracy of these equations using the
same sets of data are usually the percent of data falling within ± 30 percent error lines, or percent of the
data for which prediction of total load is within 0.750 to 1.5, 0.5 to 2.0, or 0.33 to 3.0 times the observed
value. On the basis of such assessment the following general observations can be made. First, the
equations proposed by Ackers and White, Yang, Ranga Raju et al. and Karim and Kennedy have used a
large data base of laboratory and field data; hence these equations are likely to give more representative
results than the other equations based on limited data. Further, even though Engelund and Hansen’s
equation is based primarily on flume data, subsequent verification by other investigators have shown
that it gives very satisfactory results. Coming to specific observations, ASCE Task Force (1971) applied
164
River Morphology
various methods of total load estimation then available to sediment discharge measurements on the river
Colorado at Taylor’s Ferry, and the Niobrara river near Cody (Nebraska) and found that Engelund and
Hansens’s method gives much better accuracy than the other methods. Ackers and White (1980) used
1000 data points from flume studies and 260 points from field data and found that Ackers and White’s,
and Engelund and Hansen’s equations give more accurate prediction than the other equations. Van Rijn
(1983) used 500 data points from field data and found that consistently Engelund and Hansen’s equation
gave best results; then came Ackers and White’s equation and then Yang’s. On the other hand Yang and
Molinas (1982) reported good prediction by Yang’s equation for flume data. Hence it is felt that Yang’s
equation is not very reliable for field conditions involving large depths, fine sediment, or both. Bechteler
and Vetter (1989) used the data of six rivers on sediment transport rates; these were the Rhine, the
Mississippi, the Rio Grande, and the Rio Puerto in New Mexico, the Five Mile Creek and the Niobrara.
On these rivers the suspended load was measured and bed-load was estimated using Meyer Peter and
Mûller equation. They found that among the 15 total load equations tested, Karim-Kennedy’s equation
gave best results; then came Bagnold, Laursen and Yang’s equations. Nakato (1990) used data on the
Sacramento river at gauging stations near Butte City and Colusa in California, U.S.A. where discharge,
suspended sediment load and bed material data were available. He tested the accuracy of equations
proposed by Ackers-White, Einstein-Brown, Engelund-Fredsoe, Engelund-Hansen, Inglis-Lacey,
Karim, Meyer-Peter and Mûller, Van Rijn, Schoklitsch, Toffaleti and Yang. According to Nakato, the
predictions are not at all satisfactory by most of these formulae and predictions would have been worst
if computed depth and not measured depth were used. Considering all these observations it is prudent
for the river morphologists to use three or four equations for determining the sediment transport rate in
a given case and then make his own assessment on the basis of these results and his judgment. With the
present state of knowledge, predictions within ± 50 percent error can be acceptable.
References
Ackers, P. and White, W.R. (1973) Sediment Transport: New Approach and Analysis. JHD, Proc. ASCE, Vol. 99,
No. HY-11, pp. 2041-2060.
Ackers, P and White, W.R. (1980) Bed Material Transport: A Theory for Total Load and its Verification. Proc. 1st
Intl. Symposium on River Sedimentation, Beijing (China), March, B10–1-20.
Alam, A.M.Z. and Kennedy, J.F. (1969) Friction Factors for Flow in Sand Bed Channels, JHD, Proc. ASCE, Vol.
95, No. 6, Nov. pp. 1973-1992.
Allen, J.R.L. (1978) Computational Methods for Dune Time Lag: Calculations Using Stein’s Rule for Dune
Height. Sedimentary Geology, Vol. 20, No. 1,
ASCE Task Force on Bed-forms in Alluvial Channels: Nomenclature for Bed-forms in Alluvial Channels (1966).
JHD, Proc. ASCE, Vol. 92, No. HY-3, May, pp. 51-64,
Ashida, K. and Michiue, M. (1971) An Investigation of River Bed Degradation Downstream of a Dam. Proc. 14th
Japanese Congress of IAHR, Paris, Vol. 3, pp. C30-1 to 9.
Bagnold, R.A. (1966) An Approach to the Sediment Transport Problem from General Physics–USGS Professional
Paper 422-1.
Bechteler, W. and Vetter, M. (1989) Comparison of Existing Sediment Transport Models. 4th Intl. Symposium on
River Sedimentation, Beijing (China) Vol. 1, 466-473.
Bogardi, J.L. (1959) Sediment Transport in Alluvial Streams. Academiai Kiado, Budapest. 95p.
Hydraulics of Alluvial Streams
165
Brooks, N.H. (1963) Calculation of Suspended Load Discharge from Velocity and Concentration Parameters.
Proc. FIASC, USDA (Washington), Paper 23, pp. 229-237.
Brownlie, W.R. (1981) Prediction of Flow Depth and Sediment Discharge in Open Channels. W.M. Keck
Laboratory, Caltec (USA), Rep. No. KH-R-43A.
Brownlie, W.R. (1983) Flow Depth in Sand-Bed Channels. JHE, Proc. ASCE, Vol. 109, No. HY-7, pp.959-990.
Buffington, J.M. (1999) The Legend of A.F. Shields. JHE, Proc. ASCE, vol. 125, No.4, April, pp. 376-387.
Carey, W.C. and Keller, M.D. (1957) Systematic Changes in the Beds of Alluvial Rivers. JHD, Proc. ASCE, Vol.
83, No. HY-4, Aug. pp. 1331-1 to 24
Chien, N. (1954) Meyer-Peter Formula for Bed-load Transport and Einstein’s Bed-load Function, IER, MRD
Series No. 7.
Colby, B.R. and Scott, C.H. (1965) Effect of Water Temperature on the Discharge of Bed Material. USGS Prof.
Paper 462-G.
Coleman, N.L. (1970) Flume Studies of the Sediment Transfer Coefficient. WRS, Vol. 6, No. 3, pp. 801-809.
Daniel, P., Durand, R. and Condolios, E. (1953) Introduction a l’etude de la Saltation. La Houille Blanche, No. 2,
Special B.
David, J.K and Gangadhariah, T. (1983) The Effect of Nonuniformity in Grain Size on the Initiation of Grain
Motion. Proc. 2nd Intl. Conference on River Sedimentation, Nanjing (China), B-16, pp. 434-439.
Dawdy, D.R. (1963) Discontinuous Depth – Discharge Relationship for Sand – Channel Streams and Their Effect
on Sediment Transport. Proc. FIASC, USDA (Washington), Paper No. 35, pp. 309-324.
Du Boys, P. (1879) Le Rhone et les Rivers a Lit Affouillable Annales Des Ponts et Chaussees, Vol. 18, Series 5, pp.
141-195.
Egiazaroff, I.V. (1965) Calculation of Non-uniform Sediment Concentrations. JHD, Proc. ASCE, Vol. 9, No.4, pp.
225-247.
Einstein, H.A. and Barbarossa, N.L. (1952) River Channel Roughness. Trans. ASCE, Vol. 117, pp. 1121-1132.
Einstein, H.A. (1942) Formulas for the Transportation of Bed-load. Trans. ASCE, Vol. 107, pp. 561-573.
Einstein, H.A. (1950) Bed-load Function for Sediment Transportation in Open Channel Flows, USDA, Tech. Bull.
No.1026.
Engelund, F. (1966) Hydraulic Resistance of Alluvial Streams. JHD, Proc. ASCE, Vol. 92, No. HY-2, March pp.
315-326, and Closure of Paper in JHD, Proc. ASCE, Vol. 93, No. HY-4, July 1966.
Engelund, F. and Hansen E. (1967) A Monograph on Sediment Transport in Alluvial Streams. Tensisk Forlag,
Denmark.
Fredsøe, J. (1975) The Friction Factor and Height - Length Relations in Flow Over a Dune Covered Bed. Institute
of Hydrodynamics and Hyd. Engineering, Tech. University of Denmakr, Progress Report No. 37.
Gallay, V.J. (1967) Observed Forms of Bed Roughness in an Unstable Gravel River. Proc. Of 12th Congress of
IAHR, Fort Collins, U.S.A., Vol. 1, pp. 85-94.
Garde, R.J. (1959) Total Sediment Transport in Alluvial Channels. Ph.D. Thesis submitted to Colorado State
University, Fort Collins, USA.
Garde, R.J. (1970) Initiation of Motion on a Hydrodynamically Rough Surface; Critical Velocity Approach. Jour.
of Irrig. and Power of CBIP (India) Vol. 27, No. 3, July, pp. 271 to 282.
Garde, R.J. and Albertson, M.L. (1959) Sand Waves and Regimes of Flow in Alluvial Channels. Seminar II, Proc.
8th Congress of IAHR, Montreal (Canada), vol. 4, 28 SII-1-7.
Garde, R.J. and Anil Kumar (1988) Verification of Regime Criteria for Alluvial Streams. Indo-British Workshop
on Sediment Measurement and Control. Chandigarh (India). Paper No. 4.1, Feb. pp. 1-12,
166
River Morphology
Garde, R.J. and Dattatri, J. (1963) Investigations of the Total Sediment Discharge of Alluvial Streams, Roorkee
University Research Journal, Vol. 6, No. 2, pp. 65-78.
Garde, R.J. and Isaac, N. (1993) Bed Undulations in Unidirectional Alluvial Streams. Report Submitted to UGC,
CWPRS, Pune, Nov.
Garde, R.J. and Pande, P.K. (1976) Use of Sediment Transport Concepts in the Design of Tunnel Type Sediment
Excluders. ICID Bull. Vol. 25, No. 2, pp. 101-109.
Garde, R.J. and Ranga Raju, K.G. (1966) Resistance Relationships for Alluvial Channel Flow. JHD, Proc. ASCE,
Vol. 92, No. HY-4, July, pp. 77-100.
Garde, R.J. and Ranga Raju, K.G. (2000) Mechanics of Sediment Transportation and Alluvial Stream Problems.
New Age International (P) Ltd., New Delhi.
Gessler, J. (1965) The Beginning of Bed-load Movement of Mixtures Investigated as Natural Armouring in
Channels. Laboratory of Hydraulic Research and Soil Mechanics, Swiss Federal Institute of Technology, Rep.
No. 69.
Gill, M.A. (1968) Rationalisation of Lacey’s Regime Flow Equations, JHD, Proc. ASCE, Vol. 94, No. HY-4, July,
pp. 983-995.
Gill, M.A. (1971) Height of Sand Dunes in Open Channel Flows. JHD, Proc. ASCE, Vol. 97, No. HY-12, Dec. pp.
2067-2074.
Graf, W.H. and Acaroglu, E.R. (1968) Sediment Transport in Conveyance Systems, Pt. 1, Bull. Intl. Assoc.
Scientific Hydrology Vol.13, No. 2.
Grass, A.J. (1970) Initial Instability of Fine Sand. JHD, Proc. ASCE, vol. 96, HY-3, March, pp. 619-631.
Haque, M.I. and Mahmood, K. (1983) Analytical Determination of Form Friction Facto. JHE, Proc. ASCE, Vol.
109, No. 4. pp. 590-610
Harrison, A.S. and Lidicker, A.C. (1963) Computing Suspended Sand Loads from Field Measurements. Proc.
FIASC, USDA (Washington), Paper 56, pp. 484-492.
Hayashi, T. (1970) Formation of Dunes and Anti-dunes in Open Channels. JHD, Proc. ASCE, Vol. 96, No HY-2,
Feb. pp. 357-366.
Hayashi, T. and Ozaki, S. (1980) On the saltation Height and Step Lengths of Sediment particles in the Bed-Load
Layer. 1st International Symposium on River Sedimentation. Nanjing (China) B13-1-10.
Hayashi, T. Ozaki, S. and Ichibashi, I. (1980) Study of Bed-load Transport of Sediment Mixture. Proc. 24th
Japanese Conference on Hydraulics. pp. 35-43.
Hubbell, D.W. and Sayre, W.W. (1964) Sand Transport with Radioactive Tracers. JHD, Proc. ASCE, Vol. 90, HY3,
May, pp. 39-68.
Ismail, H.M. (1952) Turbulent Transfer Mechanism and Suspended Sediment in Closed Channels. Trans. ASCE,
Vol. 117, pp. 409-434.
Itakura, T., Yamaguchi, H. Shimuzu, Y., Kishi, T. and Kuroki, M. (1984) Observations on Bed Topography During
the 1981 Flood in the Ishikari River. Jour. Of Hydro-Science and Hydraulic Engg., Japan
Jackson II, R.G. (1975) Hierarchical Attributes and a Unifying Model of Bed-forms Composed of Cohesionless
Material and Produced by Shearing Flow. Bull. Geo. Soc. of America, Vol. 86, Nov. pp 1523-1533,
Jeffrey, H. (1929) On the Transport of Sediment in Stream . Proc. Cambridge Philosophical Society. Vol. 25, pt 3,
pp. 272-276.
JSCE (1974) Task Committee Report on Bed Configuration and Hydraulic Resistance of Alluvial Streams, Nov
Kalinske, A.A. (1942) Criteria for Determining Sand Transport by Surface Creep and Saltation. Trans. AGU, Vol.
23, pt. 2, pp. 639-643.
Kalinske, A.A. and Hsia, C.S. (1945) Study of Transportation of Fine Sediment by Flowing Water. Studies in
Engg. Bull. No. 29, Univ. of Iowa, (USA), 30 p.
Hydraulics of Alluvial Streams
167
Karim, M.F. and Kennedy, J.F. (1983) Computer – Based Predictors for Sediment Discharge and Friction Factor
for Alluvial Streams. Proc. 2nd Intl. Symposium on River Sedimentation, Nanjing (China) A-18, Oct. pp.
219-233.
Kennedy, J.F. (1969) The Formation of Sediment Ripples, Dunes and Antidunes. Annual Review of Fluid
Mechanics, Vol. 1, pp. 147-168.
Lane, E.W. and Kalinske, A.A. (1939) The Relation of Suspended to Bed material in Rivers. Trans. AGU, Vol. 20,
pp. 637-641.
Lane, E.W. and Kalinske, A.A. (1941) Engineering Calculations of Suspended Sediment. Trans. AGU, Vol. 22, pp.
603-607.
Lane, E.W. and Eden, E.W. (1940) Sand Waves in Lower Mississippi River. Jour. Of Western Society of Engineers
(USA), Vol. 45, No. 6, pp. 281-291.
Langbein, W.B. (1942 Hydraulic Criteria for Sand Waves. Trans AGU, pp. 615-618.
Laursen, E.M. (1958) The Total Sediment Load of Streams. JHD, Proc. ASCE, Vol. 84, No. HY-1, Feb., pp. 15301 to 36.
Laursen, E.M. (1980) A Sediment Concentration Distribution Based on Revised Prandtl Mixing Theory. 1st Intl.
Symposium on River Sedimentation, Beijing (China) – B-1 to 9.
Li Zenru, Chen Yuaner and Zao Yun (1983) A Remark on Shields’ Diagram. Proc. 2nd Intl. Symposium on River
Sedimentation, Nanjing (China) B-7, pp. 329-341.
Lovera, F and Kennedy, J.F. (1969) Friction Factors for Flat Bed Flows in Sand Channels. JHD, Proc. ASCE, Vol.
95, No. HY-4, July, pp. 1227-1234.
Mantz, P.A. (1992) Cohensionless, Fine Sediment Bed-forms in Shallow Flows. JHE, Proc. ASCE, Vol. 118, No.
5, May, pp. 743-764.
Mantz, P.A. (1979) Incipient Transport of Fine Grains and Flakes by fluids–An Extended Shields’ Diagram.
Closure of Discussion, JHD, Proc. ASCE, Vol. 106, HY-7, pp. 1173-1190.
Mantz, P.A. (1983) Review of Laboratory Sediment Transport Research Using Fine Sediments. Proc. 2nd
International Symposium on River Sedimentation, Nanjing (China), p. 532-557.
Meyer-Peter, E. and Müller, R. (1948) Formulas for Bed–Load Transport. Proc. of 2nd Congress of IAHR,
Stockholm, Paper No. 2, pp-39-64.
Nakato, T. (1990) Tests of Selected Sediment–Transport Formulas–JHE, Proc. ASCE, Vol. 116, No. 3, March, pp.
362-379.
Neill, C.R. (1968) Note on Initial Movement of Coarse Uniform Material. JHR, IAHR, Vol. 6, No. 2, pp-173-176.
Patel, P.L. and Ranga Raju, K.G. (1996) Fraction wise Calculation of Bed-load Transport. JHR, Vol. 34, No. 3, pp.
363-379.
Patel, P.L. and Ranga Raju, K.G. (1999) Critical Tractive Stress of Non-uniform Sediments, JHR, IAHR, Vol. 37,
No. 1, pp. 39-58.
Patil, B.M. (1997) Some Studies on Resistance to Flow in Alluvial Streams. ISH Jour. of Hyd. Engg., Vol. 3, No.
1, pp. 50-60.
Ranga Raju, K.G. (1970) Resistance Relation for Alluvial Streams. La Houille Blanche, No. 1.
Ranga Raju, K.G., Garde, R.J. and Bharadwaj, R.C. (1981) Total Load Transport in Alluvial channels, JHD, Proc.
ASCE, Vol. 107, No. HY-2, p. 179-191.
Raudkivi, A.J. (1976) Loose Boundary Hydraulics. Pergamon Press, Oxford, Civil Engg. Div. 2nd Ed. P. 144.
Rouse, H. (1939) An Analysis of Sediment Transportation in the Light of Fluid Turbulence. SCS-TP-25, USDA.
Rouse, H. (Ed.) (1950) Engineering Hydraulics. John Wiley & sons, pp. 794-795.
168
River Morphology
Shen, H.W. and Hung, C.S. (1971) An Engineering Approach to Total Bed Material Load Regression Analysis.
Proceedings of Sediments Symposium to Honour Prof. Einstein, Chapter 14.
Shields, A. (1936) Anwendung derhAhnlichkeitsmechanik und Turbulenzforschung auf die Geschiebebe wegung.
Mitteilungen der Pruesspsichen Versuchsanstalt für Wasserbau und Schiffbau, Berlin, No. 26.
Singh, I.R. and Kumar, S. (1974) Mega and Grant Ripples in the Ganga, Yamuna and Son Rivers, Uttar Pradesh,
India. Sedimentary Geology, Vol. 12.
Sutherland, A.J. (1967) Proposed Mechanisms of Sediment Entrainment by turbulent Flows. JGR, Vol. 72, No. 24,
Dec. pp. 6183-6194.
TCPSM (1971) Sediment Transportation Mechanics : H – Sedimentation Manual – JHD, Proc. ASCE, Vol. 97,
HY-4, pp. 523-567.
Van Rijn L.C. (1983) The Prediction on Bed-forms, Alluvial Roughness and Sediment Transport. DHL Rep 5487III, The Netherlands.
Van Rijn, L.C. (1984) Sediment Transport, Part III : Bed-forms and Alluvial Roughness. JHE, Proc. ASCE, Vol.
110, No. 12, Dec. pp. 1613-1641.
Van Rijn, L.C. (1983) Discussion of “Sediment Transport and Unit Stream Power function” by Yang, C.T. and
Molinas, A. (JHD, Proc. ASCE, June 1982), JHD, Proc. ASCE, Vol. 109, No. HY-8, pp. 1785-1787.
Van Rijn, L.C. (1984) Discussion Sediment Transport, Part II : Suspended Load Transport, JHE, Proc. ASCE, Vol.
110, No. 11, Nov.
Vanoni, V.A. (1946) Transportation of Suspended Sediment by Water. Trans. ASCE, Vol. III, pp. 67-102.
Vanoni, V.A. and Brooks, N.H. (1957) Laboratory Studies of the Roughness and Suspended Load of Alluvial
Streams. Caltec Rep. No. E-68, Dec.
Vanoni, V.A. and Nomicos, G.N. (1959) Resistance Properties of Sediment – Laden Streams. JHD, Proc. ASCE,
Vol. 85, No. 5, pp. 77-107.
Vittal, N., Ranga Raju, K.G. and Garde, R.J. (1973) Sediment Transport Relation Using Concept of Effective
Shear Stress. Proc. of Intl. Symposium on River Mechanics, IAHR, Bangkok, pp. 489-499.
Whetten, J.T. and Fullam, T.J. (1967) Columbia River Bed-forms. Proc. Of 12th Congress of IAHR, Fort Collins
(U.S.A.), Vol. 1, pp. 107-114.
Yalin, M.S. (1971) Mechanics of Sediment Transport. Pergamon Press, Oxford (U.K.)
Yalin, M.S. and Karahan, E. (1979) Inception of Sediment Transport. JHD, Proc. ASCE, Vol. 105, HY-11, Nov.
pp. 1433-1443.
Yang, C.T. (1972) Unit Stream Power and Sediment Transport. JHD, Proc. ASCE, Vol. 98, No. HY-10, pp. 18051826.
Yang, C.T. (1973) Incipient Motion and Sediment Transport, JHD, Proc. ASCE, Vol. 99, No. HY-10, p. 16791704.
Yang, C.T. and Molinas, A. (1982) Sediment Transport and Unit Stream Power Function. JHD, Proc. ASCE, Vol.
108, No. HY-6, June, pp. 776-796.
C H A P T E R
6
Hydraulic Geometry and Plan
Forms of Alluvial Rivers
6.1
INTRODUCTION
Chapter 5 was devoted to the discussion of the hydraulics of alluvial streams in which problems of
incipient motion of uniform and non-uniform sediments, bed-forms, their characteristics and their effect
on resistance and sediment transport, prediction of bed-forms, prediction of velocity, modes of transport
of sediment and computation of bed-load, suspended load, and total load transport were discussed. In all
these discussions the channels were assumed to be straight, the banks non-erodible, the channel shape
nearly rectangular and the discharge constant. These conditions are seldom met in natural alluvial
streams. Hence this chapter is devoted to the discussion of alluvial streams in which discharge, channel
width and plan-form are varying in time and/or space. The following aspects are discussed in this
chapter.
Stable Channels Carrying Sediment
Channels flowing through sandy material with non-cohesive bed and banks or banks with some
cohesion are used to carry water for irrigation. These channels carry nearly constant discharge and carry
known but small sediment load. Further their plan-form is imposed and does not change. British
engineers proposed the design method for such channels in the Indian subcontinent in the early
twentieth century. Further work on this was done in U.S.A. and other countries and design methods have
been proposed using resistance and transport relationships. Such analysis has made possible design of
channels carrying known discharge and sediment load.
Hydraulic Geometry of Alluvial Streams
Taking clue from stable channel relationships, attempts were made to determine relationships for width,
depth, area and slope of alluvial streams assuming a constant hypothetical flow, called bankful
170
River Morphology
discharge or dominant discharge or mean annual discharge, as being responsible for shaping the
channel. Some optimisation techniques have also been used to determine the hydraulic geometry of
channels and streams; these are discussed in brief. Lastly, relationships for hydraulic geometry obtained
by using the method of dimensional analysis are discussed.
Flow in Rigid-bed and Alluvial Channel Bends
To understand the flow in meandering stream it is desirable to know the characteristics of flow in bends
with rigid bed and sides as well as with alluvial boundaries. The aspects discussed here include velocity
distribution in the longitudinal and radial directions, growth and decay of secondary circulation, superelevation, head loss in bends, shear distribution near curved stream bed and bed topography.
Braiding and Meandering
The two most important plan-forms, namely braiding and meandering are discussed in detail. The
aspects regarding braiding that are dealt with include mechanism of braid formation, causes of braiding,
types of bars in braided streams, and braiding parameters, which quantify the extent of braiding. As
regards meandering attention is focussed on change from pool and riffle sequence in straight channel to
that of a meandering stream, meander characteristics, processes governing meander-bend migration,
and meander theories. The discussion is concluded with a discussion on the criteria for plan-forms.
6.2
STABLE CHANNELS CARRYING SEDIMENT
The efforts of British engineers working in India during late 19th and early 20th centuries were aimed at
obtaining dimensions of the channel and the velocity of flow which will yield non-silting and nondepositing sections of alluvial channels carrying a given discharge and sediment load, and flowing
through non-cohesive sandy material. Traditionally these irrigation canals taking off from the head
works are provided with elaborate arrangements for sediment removal at the head works and/or in the
canals so that they carried a limited amount of bed material load (of the order of 100 to 500 ppm by
weight). On the basis of work done by Kennedy, Lindley, Woods and Lacey himself, Lacey (1930) found
that the area, perimeter, hydraulic radius, velocity and slope of such regime channels are uniquely
determined by the design discharge Q in m3/s and size of the bed material d in mm. Specifically Lacey
obtained the following equations,
U|
||
F QI |
R = 0.47 G J |
H f K V|
U = 0.439 f Q |
0.0003 f
||
S=
Q
|
and f = 1.76 d W
P = 4.75 Q
Q5 6
A = 2.28 1 3
f1
13
1
13
1
16
13
1
16
1
...(6.1)
171
Hydraulic Geometry and Plan Forms of Alluvial Rivers
where cross sectional area A, perimeter P, hydraulic radius R and velocity U are in metric units. Here f1
is known as Lacey’s silt factor and d is the median size of bed material in mm. Out of the first four
equations only three are independent and the fourth can be obtained there from. Since 1930 several
investigators have attempted to modify or improve these relations; however Eq. (6.1) are more widely
used. Some attempts have been made to estimate the sediment load carried by Lacey channels. Ahmad
and Rahman (1962) using flume data have proposed the relation,
1000
q2 3S
=1+5 C23
w 1o 2
...(6.2)
where q is discharge per unit width in ft2/s, wo is the fall velocity of sediment in ft/s and C is bed
material concentration in ppm by weight. Similarly, Dixon and Westfall (see Garde and Ranga Raju,
2000) have used flume, canal and river data to obtain the bed material transport rate as
qT = 0.0011
U4
wo
...(6.3)
Blench (1957) argued that the effect of bed and bank materials must be taken into account
separately in determining the dimensions of stable channel and its slope. Hence, Blench introduced bed
factor Fb and side factor Fs and defined these as
Fb =
U2
D
Fs =
U3
W
...(6.4)
in which A = WD and W is mean width of the channel. The slope equation proposed by him is
U2
= 3.63 (UW/n)0.25
g DS
...(6.5)
The inclusion of Reynolds number UW/n was justified saying walls acted as smooth boundary;
however this reasoning does not seem to be tenable. Equation (6.4) can be expressed in terms of Q, Fs
and Fb as
Fb
W=
12
Fs Q
D=
FG
H
S=
Fb5 6 Fs1 2 n1 4
1.91 g Q1 6
Fs
I
F JK
b
13
Q1 3
U|
||
|V
||
||
W
(a)
(b)
(c)
...(6.6)
172
River Morphology
in SI units. The bed and side factors are given by
Fbo = 1.9 d mm
Fb = Fbo (1 + 0.012 C B)
and
Fs = 0.10 for loam of very slight cohesion
...(6.7)
= 0.20 for loam of medium cohesion
= 0.30 for loam of high cohesion
Here, Fbo is the bed factor with vanishing bed-load and C B is the bed-load transport rate in ppm by
weight. For sides made of rounded gravel embedded in fines, Blench proposed that Fs be found by the
equation
Fs = d 4
...(6.8)
where d is in mm. Finally, he has proposed an equation alternative to Eq. 6.6 (c) which includes bed-load
concentration; however, this equation is not used much.
Simons (1957), Simons and Albertson (1963) analysed data from Punjab and Sind canals along
with canals in USA and found that if the perimeter P, area A and hydraulic radius R are expressed as P,
A, R = mQn, the values of m and n depend on the nature of bed and bank material, thus supporting the
contention of Blench that nature of bed and bank material plays an important role in determining the
hydraulic geometry of stable channels. The values of m and n obtained by Simons and Albertson (1963)
are given in Table - 6.1.
Table 6.1
Category
Regime equations of Simons and Albertson, P, A, R = mQ n
Sand bed and
banks
Sand bed and
cohesive banks
Cohesive bed
and banks
Coarse non-cohesive
material
P
m
n
6.33
0.512
4.74
0.512
4.63
0.512
3.44
0.512
A
m
n
2.57
0.873
2.25
0.873
2.25
0.873
0.939
0.873
R
m
n
0.403
0.361
0.475
0.361
0.557
0.361
0.273
0.361
Thus, canals flowing through sandy bed and cohesive banks, and cohesive bed and banks will have
smaller perimeter, smaller area and greater depth (or hydraulic radius) than canals flowing through
sandy bed and banks for the same discharge. For the first three categories, they also suggested Blench
type slope equations, namely
173
Hydraulic Geometry and Plan Forms of Alluvial Rivers
Sand bed and banks
U2
= 0.324 (UW/n)0.370
gDS
Sand bed and cohesive banks
U2
= 0.525 (UW/n)0.370
gDS
Cohesive bed and banks
U2
= 0.885 (UW/n)0.370
gDS
U|
||
|V
||
||
W
...(6.9)
Gupta (1967) and Kondap (1977) used dimensional analysis and wrote
Ws A
,
d d2
F
G
and S = f G
GG d
H
12
Q
g d
, C, and
n
Dg s d
rf
2
32
I
JJ
JJ
K
where Ws is water surface width and C is total load concentration. It was further found out from analysis
Ws
A
and 2 are insensitive to variation of C. Hence, using Sind and Punjab canal data
d
d
as also the data of US canals collected by Simons, Kondap (1977) proposed the following equations:
of field data that
FG
H
F
GG
d I
J G
n K
GH d
I
JJ
Q
Dg d J
r JK
12
Ws
= 0.212 g
d
A
d2
F
GG
= 2.21
GG d
H
32
I
JJ
Q
Dg d J
r JK
0 .231
2
0 . 458
...(6.10)
s
f
0 .855
2
...(6.11)
s
f
As regards the slope he suggests the following equation
S
Dg s g f
F
= 0.0423 G
H
I FdI
JK GH y JK
1.5
U
Dg s d r f
1. 095
...(6.12)
1
where y1 = Ws . Chang (1980) realized that for designing a stable channel to carry a given discharge Q,
A
and given sediment transport rate QT and flowing through non-cohesive sediment of size d, one has the
174
River Morphology
resistance law and the sediment transport law to determine the width, depth and slope, even if one
assumes a trapezoidal channel with given side slope Z:1. Since there are three unknowns and only two
equations, Chang imposed the condition that the channel adjusts the width, depth and slope in such a
manner that the stream power per unit length of channel (Qgf S) is minimum. On this basis he has
proposed the algorithm shown in Fig. 6.1 for the computation of W, D, S, for known Q, QT, d and
trapezoidal channel of known side slope Z: 1.
Data : Q, QT, d Z:1
Assume B
Assume D
Use sediment transport law
and compute S
Use resistance law and compute
U and then Qc
No
Q=
IsIsQ
= QQc c??
Yes
minimum ? ?
Is IsSSminimum
No
Yes
Print B, D, S
Fig. 6.1
Chang’s algorithm for design of stable channel (Chang 1980)
Hydraulic Geometry and Plan Forms of Alluvial Rivers
175
White et al. (1981) have shown that optimizing (maximizing) the sediment transport rate QT for
given Q, S, d and Z yields the same results as those obtained by minimizing S for given Q, QT, d and Z.
Thus, it seems possible to use optimization technique for channel design. However, White et al. found
that for given QT, the ratio of computed slope to observed slope ratio for existing stable channels varied
between 1 and 3 whereas predicted depths and widths showed better agreement. Hence, according to
them, in general the predicted results are not accurate enough for using this method in those cases where
empirical equations of better accuracy can be used. However, this algorithm is of great value in the
design of channels which carry large quantity of sediment load and for which Lacey type equations
cannot be used. In fact Chang (1980, 1988) used the algorithm given in Fig. 6.1 with side slopes 2:1,
resistance law proposed by Lacey, viz.
U=
1.346 1/4 1/2 1/2
D R S
Na
...(6.13)
where f1 = 1.76 d , Na = 0.0225 f11/4, D is the mean depth of flow, and DuBoys bed-load equation to
prepare Q vs. S/d1/2 curves for different values of Ws and D; this is shown in Fig. 6.2. Here d expressed
is in mm and other quantities are in fps units. He also prepared a graph between S/d1/2 and Q with QT/Q
as the third variable as shown in Fig. 6.3. Here QT has been calculated using Engelund-Hansen formula.
QT
varies from 50 to about 200
Q
ppm. Chang also found that Engelund-Hansen formula produced better conformity with measured
sediment loads than DuBoys or Einstein-Brown formula. He also compared the computed and the
observed values of Ws and Ws/D for these canal data and found good agreement. Chang has mentioned
the fact, commonly used by design engineers that in sandy material for canal to be stable, Froude
number should be kept between 0.2 and 0.3 and quoted the flowing relationship between Fr and R/d
It can be seen from Fig. 6.3 that in Sind, Punjab and Simon’s canal data
Fig. 6.2
Variation of B and D with Q and S/d1/2 for stable channels (Chang 1980)
176
River Morphology
Fig. 6.3
Variation QT /Q with Q and S/d1/2 for stable channels (Chang 1980)
proposed by Athauallah and Simons
R
Fr = 4.388 F I
H dK
6.3
- 0 .31
...(6.14)
HYDRAULIC GEOMETRY OF ALLUVIAL STREAMS
Dominant Discharge
Use of a constant hypothetical discharge in the study of hydraulic geometry of streams was more or less
simultaneously done in India, Europe and USA so that simple relationships could be developed for P, A,
R or D and U, which are similar to those for stable canals. In following this approach one must bear in
mind some important differences between flow in stable canals and alluvial or gravel-bed rivers,
because of which this extension has to be done cautiously. These are:
1. Wide variation in the discharge and sediment load carried by the streams and very large
difference between their maximum and minimum values. On the other hand canals carry a
fairly constant discharge with limited variation in sediment load.
2. Large variation in the size of bed and bank material is found in streams; as a result armouring
can take place in streams having large standard deviation of bed material.
3. Whereas stable canals have more or less regular shape, river cross sections are invariably
irregular.
4. The plan-form of stable canals is fixed whereas in streams it changes along the length.
5. The slope of the river as well as the characteristic size of bed material change along the length,
whereas canal sections are designed for a constant Q, S and d.
In spite of these limitations river channel dimensions seem to be adjusted by erosion and deposition
so that the channel can contain all but the highest flows it experiences. Hence, it seems reasonable to
explore if one or more geometrical characteristics of river cross-sections can be related to a hypothetical
constant discharge.
Hydraulic Geometry and Plan Forms of Alluvial Rivers
177
Bankful and other Characteristic Discharges
This concept of a constant discharge has been used widely to describe the river regime. In order to make
stable canal formulae applicable to rivers, Inglis (1947) introduced the concept of dominant discharge;
according to him, “there is the dominant discharge and its associated charge and gradient to which the
river channel returns annually. At this discharge the equilibrium is most closely approached and
tendency to change is least. This condition may be regarded as an integrated effect of all varying
conditions over a long period of time”. Expressed differently, dominant discharge is a hypothetical
constant discharge which would produce the same result (average width or meander dimensions) as
caused by the actual varying discharge. Intuitively he assumed this discharge to be bankful discharge for
Indian rivers in plains and that it could be used in relations for width, depth, meander width etc. He
further found that for Indian rivers in the plains of North India, bankful discharge is ½ to ¾th of the flood
discharge.
While studying the hydraulic geometry of rivers in the Great Plains of USA, Leopold and Maddock
(1953) used the mean annual discharge Qma and found that this discharge had a frequency of twenty five
percent, i.e., for 91 days in a year the discharge was equal to or greater than Qma.
Nixon (1959) studied the bankful discharges of 22 non-tidal rivers in England and Wales to explore
the possibility of obtaining Lacey-type equations for rivers in U.K. Comparison of bankful discharge of
22 rivers at 29 sites led Nixon to conclude that bankful discharge is such a discharge, which is equaled
or exceeded 0.60 percent of the time. Further this percentage is not dependent on the magnitude of the
discharge. This conclusion was based on the data for two to five year period except for the river Thames
for which 72-year data were available. It may also be mentioned that percentage of time varied from
2.91 to 0.10 in individual cases.
Williams (1978) has discussed the merits and demerits of various methods of determining the
bankful stage and corresponding discharge obtained there from. Williams distinguishes between the
active flood plain where water spreads every year during the flood and sediment deposition occurs, and
the inactive flood plain or terrace which is part of the valley flat which is submerged only during the rare
floods and where sediment deposition does not occur. Among eleven methods available in literature
which are proposed by geologists and geomorphologists, he prefers the following three methods for the
determination of bankful stage.
1. Average elevation of active flood plain;
2. If elevation vs. W/D ratio is studied, the elevation at which this ratio is minimum;
3. If log-log plots of area of cross-section versus width are prepared, the elevation at which the
slope of the curve suddenly changes.
Once the bankful stage is determined, the corresponding discharge can be determined from the
rating curve at the nearby gauging station. Alternatively, knowing Q vs A, W or D graphs at a station, one
can find the bankful discharge for the known depth. The method would be to use Manning’s equation for
a reach after averaging out the hydraulic parameters at the bankful stage at two or more cross-sections
and choosing an appropriate value of n. He also studied the flow frequency duration curves at the
gauging stations and determined the frequency of bankful discharge. On the basis of analysis of data at
28 gauging sites in Western USA with 233 data points he found that determining the bankful discharge
Qb at a given site gives inaccurate results and hence this method should not be used; instead bankful
discharge in a given reach is more meaningful. Further, rating curve approach is recommended. He has
proposed the equation
178
River Morphology
Qb = 4.0 Ab1.23 S 0 .31
...(6.15)
2
3
where Ab is cross-sectional area at bankful stage in m and Qb is the bankful discharge in m /s. This
equation is based on the following ranges of Ab, S and Qb
Ab = 0.70 m2 to 8510 m2,
S = 0.000 041 to 0.081, Qb = 0.50 m3/s to 28 320 m3/s
This equation gives an average standard error of 41 percent in Qb. Similar equation was also
proposed by Riggs (1976).
Qb = 3.39 Ab1. 295 S 0 .316
...(6.16)
which was found to give larger error than Eq. (6.15). As regards frequency or return period for bankful
discharge for active flood plain stations, Williams found the average return period mode of about 1.5
years on the annual maximum series; however because of the wide range (1 to 32) years, the spread and
skewness of the distribution, the average value loses its significance. Hence, he did not recommend this
method for the determination of bankful discharge. For record it may be mentioned that the
recommended values of return periods for bankful discharge by some investigators are
Nixon (1959)
2.2 yrs
Leopold et al. (1964)
and Carlson (1965)
1.5 yrs
Dury (1973)
1.58 yrs
Hence, the only two characteristic discharges that seem to be preferred for studying bankful
geometry are the mean annual discharge Qma and the bankful discharge Qb; the relationship between the
two was graphically represented by Chang (1979) using the data of Schumm and Carlson. Garde et al.
(2002) plotted the data of Kellerhals et al. and obtained the relationship (see Fig. 6.4)
0.843
Qb = 17.253 Qma
Qb
10
7
10
6
10
5
10
4
10
3
10
2
Qb = 17.253 Qma
...(6.17)
0. 843
Carlson
Schumm
Kellerhals
Best fit line
10
10
10
2
10
3
10
4
10
5
Qma
Fig. 6.4 Relation between Qb and Qma
10
6
179
Hydraulic Geometry and Plan Forms of Alluvial Rivers
Here Qb and Qma are in m3/s. In studying river bed variation in transient flows in alluvial streams
one would prefer to use a characteristic discharge related to sediment transport or bed level variation
rather than using bankful discharge. This concept has been used by Schaffernak (1950) who introduced
the term bed-generative discharge which he defined as the discharge that transports the largest volume
of coarse material. Figure 6.5 illustrates how this discharge is computed; Fig. 6.5 (a) shows the
frequency-discharge curve while Fig. 6.5 (b) is the sediment discharge vs. water discharge relationship
for the stream. In Fig. 6.5 (c) the abscissa is obtained by multiplying the frequency DF of a particular
discharge by the corresponding sediment discharge rate Qs while the ordinate is the discharge. The
discharge that gives the maximum Qs DF is the bed generative discharge.
(a)
(b)
Q
Q
DF
(c)
Q
Qs
Fig. 6.5
Qs DF
Determination of bed generative discharge
Komura (1969) defines the dominant discharge as that constant discharge which will transport the
same quantity of sediment load as is transported by the varying discharge during the same period or year.
Hence,
Qd =
S 1N QTi Qi
S1N QTi
...(6.18)
where N is the total number of mean daily discharges, Qi and QTi are the corresponding total sediment
discharges. According to Komura in the above equation mean monthly discharges be used if flood has a
long duration, and mean daily discharge or maximum monthly discharge if flood duration is small.
Further, if one utilizes the empirical relation between discharge and sediment load in the form QT = a Qb,
the above equation reduces to
Qd =
S 1N Qi(1 + b )
S1N Qib
...(6.19)
NEDCO (1959), defines the dominant depth Dd as
z
z
T
Dd =
O
DQT dt
...(6.20)
T
O
QT dt
where D is the depth at sediment transport rate QT.
180
River Morphology
Enough information is not available about the relationship between Qb and Qd or bed generative
discharge. Gandolfo (1955) found that the bed generative discharge is greater than Qd corresponding to
average sediment transport rate and that the latter is greater than Qma. The relationship between Qb and
Qma is already given in Fig. 6.4.
6.4
EMPIRICAL RELATIONSHIPS FOR HYDRAULIC GEOMETRY
Leopold and Maddock (1953) explored the applicability of equations of the type
W = a Qb
D = c Qf
U = k Qm
Qs = p Qj
U|
|
V|
||
W
...(6.21)
at a station for variable discharge, and along the stream length for mean annual discharge Qma, by using
data from American rivers in Great Plains and South-West. Since Q = WDU it follows that for both these
types of relationships ack = 1 and b + f + m = 1. For twenty cross-sections representing a variety of rivers
Leopold and Maddock found that “at a station” the average values of b, f and m were b = 0.26, f = 0.40
and m = 0.34. Since the depth increases faster than the width, the (width/depth) ratio decreases with
increase in discharge. The relationship between suspended load discharge Qs and Q at a station showed
greater scatter, with j values ranging between two and three. Since j is greater than unity, it is obvious
that at a station Qs/Q i.e., suspended sediment concentration increases as Q increases. While relating
width, depth and velocity to discharge along the stream, they preferred to use mean annual discharge
Qma which had an average frequency of 25 percent, i.e., it is equaled or exceeded one day in every four
days over a long period. With this discharge Qma in Eq. (6.21), average values of b, f and m were b =
0.50, f = 0.40 and m = 0.30. It may be noted that values of b and f and m agree fairly well with those
obtained by Lacey. In as much as the percentage of land not contributing sediment increases in the
downstream direction and percentage of land contributing water discharge increases in downstream
direction, one would expect Qs/Q to decrease in the downstream direction, as concluded by Rubey
(1933). However, individual rivers may differ in this respect.
Experience has shown that “at a station” relationships are significantly affected by the climatic
changes, namely depending on whether the stream is perennial, ephemeral or in arid or semi-arid region.
Nixon (1959) while studying the hydraulic geometry of rivers in England and Wales found that the
bankful discharge Qb is equaled or exceeded 0.6 percent of the time i.e., on the average about two days
in a year. He further found that in the equation P = W = aQb the coefficient “a” depends on the frequency
of discharge used, see Table 6.2.
Table 6.2 Dependence of constant of proportionality in W = aQb on the frequency of
discharge (Nixon 1959)
Percentage frequency
“a” in W = aQb in SI units
30
8.87
20
7.61
10
6.16
5
5.23
3.7
4.84
0.6
3.00
181
Hydraulic Geometry and Plan Forms of Alluvial Rivers
Nixon also mentioned that if the mean annual discharge were used, the constant in the above
equation would be 7.66 which is not much different from that for 20 percent frequency. For rivers in
England and Wales, Nixon found that
W = 1.65 Qb1/ 2
D = 0.545 Qb1/ 3
U = 1.112 Qb1/ 6
Qs = 0.9 Qb3 / 4
U|
|
V|
||
W
...(6.22)
in SI units for Qb ranging from 10 m3/s to 500 m3/s. After Leopold and Maddock as well as Nixon’s
works were published, a number of investigators in U.S.A., U.K., Norway, Malaysia, Brazil and Puerto
Rico applied the same technique using either bankful discharge or discharge of certain frequency and
obtained the exponents b, f, m. Similar studies were also conducted in U.S.A., U.K. and other countries
on gravel-bed rivers (see Chapter VII).
Langbein (1964) considered streams in humid regions in which the discharge increases in the
downstream direction. He stipulated that along with the three equations of Leopold and Maddock for W,
D and U two additional equations can be considered as
S a Qz
and Manning’s n
so that
and
n a Qy
U|
V|
W
...(6.23)
b+f+m=1
m=
2
z
f+ –y
3
2
U|
V|
W
...(6.24)
since in the downstream direction stream would satisfy continuity and Manning equation. In addition,
he stipulated that (i) streams have a tendency for uniform distribution of work per unit width along the
channel, and (ii) the rate of work in the whole system is also as small as possible. On these premises he
showed that
or
S=
W
Q2
z=
b
–1
2
U|
|V
||
W
Further, to fulfill the conditions mentioned above he argued that | b2 + f 2 + m2 + z2 + (1 + z 2 )| should
be minimum. This condition is satisfied by the following values.
b = 0.53, f = 0.37, m = 0.10, z = – 0.73
These values of b. f and m agree fairly well with those obtained by Leopold and Maddock.
Some support to this approach of studying the hydraulic geometry of rivers was provided by Smith
(1974) who represented a straight stream channel as a surface
182
River Morphology
y = y (x, z, t)
...(6.25)
subjected to the following three conditions: (i) sediment mass is conserved during the transport; (ii)
channel has the form just sufficient to carry the total discharge of water given the law of water
movement; and (iii) the channel has the form just sufficient to carry its total sediment discharge given
the sediment transport law. Smith also assumed that the channel is carried in non-cohesive material and
that one has the freedom to choose a time scale for which the channel has a steady state form. He further
assumed that Q and Qs increase linearly with x, and lateral sediment transport rate is equal to
longitudinal transport rate multiplied by ¶ D . He used Manning’s equation for flow velocity and
¶z
sediment transport equation of the form
qs = const q2 S2
...(6.26)
Rather than solving the system of equations, Smith tried to find out the values of the exponents
which will satisfy all the imposed conditions. He thus obtained
W ~ Qb7 /11 , D ~ Qb3 /11 , U ~ Qb1/11 and S ~ Qb- 2 /11
...(6.27)
in the downstream direction. These values are comparable to those obtained by Leopold and Maddock,
and by Langbein.
In order to study the variation of the exponents b, f and m. Park (1977) analysed data from 139 “at
a station” sites and data from 72 “in the downstream” direction. The ranges of variation in b, f and m
obtained by Park are listed below in Table 6.3. In the analysis of data in downstream direction Q used is
the observed or estimated Qb or Q with a return period of 2.33 years.
Table 6.3 indicates that values of b, f and m vary over a wide range and hence for a given stream
these values can be very different from those given by the theory. To study further the simultaneous
variations of these exponents, Park plotted b, f and m on tri-axial diagram with one side for each
exponent. Typical tri-axial diagrams for at a station and downstream exponents in different climatic
conditions are shown in Figs. 6.6 and 6.7. The climatic factors did not seem to affect “at a station”
exponents. Hence, Park suggested that local factors such as the composition of bank material,
differences between braiding and meandering reaches, between pools and riffle sections, flow
magnitude, suspended load and channel migration might be responsible for such variations.
Table 6.3 Summary of distribution characteristics of hydraulic geometry exponents data (Park 1977)
At a station; N = 139
Exponent
In downstream direction; N = 72
B
f
m
b
f
m
Range
0.20 – 0.59
0.06 – 0.73
0.07 – 0.71
0.03 – 0.89
0.09 – 0.70
0.51 – 0.75
Modal class
0.01 – 0.10
0.30 – 0.40
0.40 – 0.45
0.40 – 0.50
0.30 – 0.40
0.10 – 0.2
0.23
0.42
0.35
0.55
0.36
0.09
0.68
0.30
0.90
*
Theory (1)
Theory (2)
**
(1)* Leopold and Langbein (2)** Smith
Hydraulic Geometry and Plan Forms of Alluvial Rivers
183
Fig. 6.6 Tri-axial graph of at-a-station hydraulic geometry exponents (Park 1977)
As regards the “downstream” data, Park found that for perennial streams in semi-arid regions the
exponents are similar to those found in humid temperate climate, whereas ephemeral streams in semiarid region tend to have lower b and high f exponents. In addition local factors such as lithology,
variation in bank erodibility, channel instability, coarser bed material, and the downstream variation in
slope are also responsible for the variation in b, f and m. On the basis of this study of tri-axial diagrams
under various environments, Park casts doubt on the use of mean values of the samples of exponents to
characterise the hydraulic geometry of streams in particular areas, and suggests that quoting mean
values gives a misleading impression. While Park concentrated on the effect of environmental factors on
b – f – m variation, Rhodes (1977, 1987) concentrated on the effect of hydraulic factors.
Some recent studies do not endorse Leopold and Maddock’s conclusion that this is a rational or
even a good way of describing cross-sectional channel adjustment. Some have also questioned whether
log-linear model of hydraulic geometry is either appropriate or meaningful. However, the greatest
184
River Morphology
Fig. 6.7 Tri-axial graph of down stream hydraulic geometry exponents
drawback seems to be the non-inclusion of sediment size, difference in specific weights of sediment and
water, and channel slope from the downstream relationships. However, in spite of these limitations
investigators continue to use this analysis as a basis, since in regional and climatically homogenous
regions they may give good approximation of hydraulic geometry.
Studies of Leopold and Maddock, and Langbein indicate that for downstream geometry m = 0.05 to
0.10 indicating that velocity at bankful stage or for mean annual discharge varies very slowly in the
downstream direction. Leopold, Wolman and Miller (1964) show constancy of U for 50 year and 5 year
floods in Yellow Stone basin, see Fig. 6.8. Some studies indicate that constant velocity along the length
of the stream is attained at a stage between mean annual discharge and modest over-bank stage of 5 year
flood (Chorley 1969). This needs further study in view of the commonly accepted view that stream
velocity decreases as it flows from mountains to the plains.
Some other efforts to include additional variables to describe the hydraulic geometry, include the
investigations of Schumm (1977) who analyzed the data on channel dimensions, mean annual discharge
185
Hydraulic Geometry and Plan Forms of Alluvial Rivers
Q50 Discharge cfs
Mean velocity in ft/s
10
5
Q5 Discharge cfs
10
5
1,000
10,000
100,000
Discharge in cfs
1,000,000
Fig. 6.8 Variation of average velocity at Q5 and Q50 in Yellow stone river basin and down stream (Leopold et al. 1984)
Qma and bed and bank sediments at 36 cross-sections from semi-arid to humid regions in the Great
Plains of U.S.A. and Plains in New South Wales in Australia in sand-bed streams. Schumm indicated
that (width/depth) ratio in these channels was related to the percentage of silt-clay M in the perimeter of
channel (see Fig. 6.9), and obtained the equations
W/D = 255 M–1.08
0.38
W = 0.38 Qma
/M0.39
Width/Depth Ratio (F)
0.29
D = 0.6 Qma
M0.342
U|
|V
||
W
Fig. 6.9 Variation of width to depth ratio with M (Schumm 1977)
...(6.28)
186
River Morphology
where Q is expressed in ft3/s and D and W in ft. Gregory and his associates (see Fergusson 1981) studied
bankful dimensions vis-à-vis the catchment area in humid areas and found that for catchment area A
between 0.1 and 4.0 km2, W ~ A0.32, D ~ A0.16 and channel capacity ~ A0.48. Hey (1982), and Hey and
Thorne (1986) while analyzing gravel-bed river data from U.K. related width and depth to bankful
discharge, d50 and the sediment transport rate Qs. These types of relationships developed in different
countries are listed by Wharton (1995).
Since in the relationships discussed above some have used bankful discharge and some mean
annual discharge, it is difficult to compare their results. Further, in studying the transient flows discharge
needs to be replaced by some hypothetical constant discharge related to sediment transport or riverbed
variation. Lastly, the relationships developed above do not contain other variables such as slope,
sediment size, Dgs and are not dimensionally homogenous. These aspects are discussed in the next two
sections.
6.5
NON-DIMENSIONAL RELATIONS FOR HYDRAULIC GEOMETRY
Some attempts have been made to obtain non-dimensional form of equations for W, D and U or A. Thus
Rybkin in 1947 (see Goncharov 1962) used the data from the upper Volga and the Oka basins and
proposed the following equations
W = a1
FG w IJ LM Q FG g S IJ OP
H g S K MN w H w K PQ
FG w IJ LM Q FG g S IJ OP
H g S K MN w H w K PQ
FG w IJ LM Q FG g S IJ OP
H g S K MN w H w K PQ
2 a1
2
o
b
2
o
o
D = a2
2 a2
2
o
b
2
o
o
U = a3
2 a3
2
o
b
2
o
o
U|
||
||
|V
||
||
||
W
...(6.29)
where wo is the fall velocity of bed material and a1 , a2 and a3 as well as a1, a2 and a3 are constants. In
1950 Velikanov proposed the following form of the equations
F
GH
F
GH d
I
JK
I
Q
gd S JK
W
Qb
= a1
2
d
d gdS
D
= a2
d
b
2
a1
a2
U|
|
V|
||
W
...(6.30)
According to his analysis a1 = 0.50 to 0.53 and a2 = 0.25 to 0.27. Ananian (1961) obtained
a1 = 2.70 and a1 = 0.42. Mukhamedov and Ismaghilov (1969) analysed the data from the middle and
lower reaches of the Amu Darya and obtained the following equations for W and D
187
Hydraulic Geometry and Plan Forms of Alluvial Rivers
LM
MN
F S I OP
GH Dg / g JK P
Q
F S I
Q
gdS GH Dg / g JK
LM
MN
g DS
= 0.095 2
Dg s d
d
and
U|
||
V|
||
W
5 / 2 0.48
Q
gs WS
= 3.8 2 b
Dg s d
d gd S
s
f
OP
PQ
5 / 2 0.28
b
s
f
which can be reduced to a simpler form as
I F S I
JK GH Dg / g JK
F Q I F S I
D
= 0.095 G
d
H d g d S JK GH Dg / g JK
F
GH
W
Qb
= 3.8
2
d
d gd S
0.20
0 .48
s
f
0 .08
- 0 .30
b
2
s
f
...(6.31)
U|
|
V|
||
W
...(6.32)
These equations have not been tested using data from other countries.
Garde et al. (2002) have analyzed a large volume of data on the hydraulic geometry of rivers from
different countries given by Leopold and Wolman (1957), Schumm (1969) Chitale (1970) and
Kellerhals et al. (1972). The ranges of basic variables used by them are
Qb = 4.24 m3/s – 52 800 m3/s
W = 5.80 m – 943 m
S = 4.1 ´ 10–5 – 6.8 ´ 10–3
U|
V|
W
They studied the possibility of relating W/d, D/d and A/d2 to Q1 =
...(6.33)
Qb
Q S
, Q2 = 2 b
and
d gd
d gd
2
Qb
Q S
. The second parameter Q2 = 2 b
represents the dimensionless stream power while
d gdS
d gd
the third parameter is that earlier used by Ananian and others. In general the results were more accurate
with Q1 and Q3 than Q2. These equations are listed below along with percent of data giving less than ±
50 percent error.
Q3 =
2
Equation
W/d = 7.5 Q10 .425
D/d = 0.14 Q10 .430
A/d2 = 1.80 Q10.855
U|
|V
||
W
% of data giving error between ± 50%
78
74
82
...(6.34)
188
River Morphology
W/d = 2.9 Q30 .402
D/d = 0.06
Q30 .405
A/d2 = 0.16 Q30.807
U|
|V
||
W
79
56
...(6.35)
74
see Fig. 6.10, 6.11 and 6.12 corresponding to Eq. (6.35).
Fig. 6.10 Variation of W/d with Q3 for River data (Garde et al. 2003)
Fig. 6.11
Variation of D/d with Q3 River data (Garde et al. 2003)
The two equations which give velocity at bankful discharge with reasonable accuracy are Lacey’s
equation
U = 10.8 D2/3 S1/3
and
F I
H K
U
D
=2
d
gd
0.60
S0.40
U|
|V
||
W
...(6.36)
189
Hydraulic Geometry and Plan Forms of Alluvial Rivers
Fig. 6.12 Variation of A/d 2 with Q3 River data (Garde et al. 2003)
6.6
FLOW AROUND BENDS WITH RIGID AND ALLUVIAL BEDS
While discussing point bars, some introductory comments were made about secondary circulation
developed in channel bends and its effect on shear distribution and formation of point bar. In this
section, flow around bends in rigid-bed and alluvial channel bends is discussed further. The aspects
discussed below include velocity distribution in radial and transverse directions, the development and
decay of secondary circulation, super-elevation and transverse bed profiles in alluvial bends.
Velocity Distribution in Rigid Bed Bends
The analysis of flow in rigid-bed bends is carried out using Reynolds’ equations of motion in
cylindrical-polar coordinate system. To obtain tangible results, the following assumptions are made:
¶
= 0;
¶t
The depth of flow is much smaller than the channel width or the radius of the bend;
Pressure distribution in the vertical is hydrostatic;
Purely viscous stresses involving m or n are neglected in relation to Reynolds stresses;
Eddy viscosity is assumed to be constant and scalar;
Except in the regions close to the walls the velocity component vy is very small compared to vq
and vr and hence can be neglected; and
1. The flow is steady so that
2.
3.
4.
5.
6.
7. Secondary flow is fully developed and hence
¶
¶
¶
= 0 and
<<
.
¶q
¶r
¶y
Hence Reynolds’ equations of motion reduce to
–
¶ 2 vr2
vq2
¶
=–
(g D) + Î
¶r
¶ y2
r
¶ 2 vq
g Ie + Î
=0
¶ y2
(a)
(b)
U|
|
V|
||
W
...(6.37)
190
River Morphology
and continuity equation
¶
(vr r) = 0
¶r
...(6.38)
Velocity Distribution vo ( y): Rozovskii (1957) has studied four types of velocity distributions vo as
a function of h = y/D namely Eqs. (6.39), (6.40), (6.41) and (6.42).
Logarithmic Law
F I
H K
1
v max - v
y
= ln
v*
D
k
which can be reduced to
LM
N
FG F I IJ OP
...(6.39)
H H KKQ
F1 + F g I I , k = Karman constant, the value of which recommended
GH GH k C JK JK
g
v
y
= 1+
1 + ln
kC
D
Vcp
Here, v* =
gDS , vmax = Vcp
by Rozovskii is 0.50, C is Chezy’s coefficient, and Vcp is average velocity in the vertical. It may be
mentioned that the subscript q is omitted here for convenience. Power law
U|
|V
||
= (1 + n) h
W
L m - m a1 - hf OP where m = 22 to 24
= M1 +
N 3C C
Q
3.3
= 1 - P a1 - hf where P = 0.37 +
C
y
v
= hn, where h =
v max
D
or
v
Vcp
v
Vcp
and
v
v max
...(6.40)
n
2
2
...(6.41)
...(6.42)
Out of these equations, Rozovskii found that Eq. (6.39) gives reliable results while Zimmerman
(1977), and Zimmerman and Kennedy (1978) used Eq. (6.40) in their analysis.
Velocity Distribution vr: The velocity distribution in radial direction for hydrodynamically smooth
and rough surfaces has been obtained by Rozovskii by using Eq. (6.39).
Hydro-dynamically smooth bend
LM a f
N
a fOP
Q
2 g
vr
D
=4
F2 h
F1 h C
Vcp
r
...(6.43)
He found that change in Chezy’s C from 60 to 30 made very little difference in distribution of nr
except near the bed and water surface.
191
Hydraulic Geometry and Plan Forms of Alluvial Rivers
Fig. 6.13 Variation of F1 (h), F2 (h) and F4 (h) with h
Hydro-dynamically rough bend
LM a f
N
a fOP
Q
2 g
vr
D
F4 h
F1 h =4
C
Vcp
r
F4 (h) = F2 (h) + 0.8 (1 + ln h)
where
...(6.44)
The functions F1 (h), F2 (h) and F4 (h) are plotted in Fig. 6.13, while experimental data are
compared with Eq. (6.43) in Fig. 6.14 which shows correctness of Eq. (6.43).
h
1.0
0.8
0.6
h
0.4
0.2
0.0
–10
–8
–6
–4
–2
vr r
Vcp D
0
2
4
Fig. 6.14 Comparison of Eq. (6.43) with experimental data (Rozovskii 1957)
6
192
River Morphology
Growth and Decay of Secondary Circulation
In a long bend, Rozovskii defines the angle qlim as the angle at which the growth of circulation is
practically complete, and qlim is given by
qlim =
2.3 C D
g rc
...(6.45)
Here, D can be taken as average depth and rc is center line radius of the bend.
Decay of vr : If vro is surface velocity at the exit of the bend, it will decay with x the distance
measured from the end of the bend according to the law
g x
Vrx
=eC D
Vro
Hence the length required to reduce vro to vrx is
...(6.46)
x
C
V
=
ln ro
Vrx
D
g
and if one assumes that when vrx /vro = 0.10, the circulation has died out, the length required is
L
C
= 2.303
D
g
...(6.47)
Distribution of Longitudinal Velocity Over Width
According to Rozovskii’s observations, the maximum velocities move nearer the convex (inner) bank
and are stronger, the sharper the bend. However, then the transformation takes place gradually and the
maximum velocity gradually moves over to the concave (outer) bank. If the bend is sufficiently gentle,
on emerging from it, the maximum velocity is already found near the concave bank. On emerging from
the bend, the velocities become sharply redistributed with their maximum coming almost in to contact
with the continuation of concave bank.
Super Elevation
Super elevation (SE) is the difference in water levels between the outer and inner banks of the bend, and
can be obtained from the equation of motion in the r direction, namely
Vcp2
¶D
= rf
gf
r
¶r
...(6.48)
where Vcp is the average velocity in the vertical at radial distance r. If it is known how Vcp varies with r,
the above equation can be integrated to obtain
SE = (Do – Di) =
1
g
z
ro
rt
Vcp2
r
dr
193
Hydraulic Geometry and Plan Forms of Alluvial Rivers
Here, Do and Di are the depths at outer and inner banks respectively.
1. If Vcp is constant across the bend, integration of the above equation gives
SE (Do – Di) =
Vcp2
g
LMln r OP
N rQ
o
...(6.49)
i
2. If Vcp varies according to free-vortex law, as assumed by Shukry (1950) i.e. Vcp = K/r, one gets
SE =
K2
2g
LM 1 - 1 OP
Nr r Q
2
i
...(6.50)
2
o
Assuming the depth of flow upstream of the bend to be the average depth in the bend, and U to
be the average velocity, Ippen and Drinker (1962) reduced the above equation to
SE =
U2 2W
2 g rc
LM
MM 1
MM1 - FG W IJ
N H 2r K
2
c
OP
PP
PP
Q
...(6.51)
3. If it is assumed that velocity variation follows forced vortex pattern i.e., higher velocities near
the outer bank and lower near the inner bank, Vcp ~ r, this assumption together with the
assumption of constant average specific energy leads to the equation
SE =
U2 2W
2 g rc
LM
MM 1
MM1 - FG W IJ
N H 2r K
2
i
OP
PP
PP
Q
...(6.52)
Apmann (1973) studied the relationship between super elevation and discharge, to predict the latter
if the former is known. On the basis of the analysis of data from rectangular and trapezoidal channels,
natural channels and ducts with included bend angle varying from 45° to 360°, Apmann expressed super
elevation as
K1 U 2
= SE
2g
...(6.53)
He found that the coefficient K1 is primarily a function of ro/ri and
K1 =
F I FG IJ
H K H K
r
5
r q
tanh c
ln o
W
4
ri
rc q
, the relation being
W
...(6.54)
194
River Morphology
As regards separation of flow on the inner side of the bend, Rozovskii has found that the possibility
of separation is greater, the deeper the stream and the gentler the bank slope, or in short the greater the
friction on the bank. With small depths and vertical walls, flow without separation is possible even when
rc /W is equal to unity. Thus, he found that in streams with small (depth/width) ratio, formation of eddy
zone at very sharp turns is possible along the convex bank, but along the convex banks which have steep
slope, it is less likely to occur.
Head-loss in Bends
Head loss in a bend is caused because of the following reasons (Rozovskii 1957):
1. Altered velocity distribution of longitudinal velocity component over the width of the stream;
2. energy required to cause secondary circulation;
3. increase in boundary friction due to circulation;
4. increase in energy loss of internal friction due to presence of secondary circulation;
5. altered velocity in the vertical; and
6. energy loss due to separation in sharp bends.
The equation proposed by Rozovskii for head loss in open channel bends is
hb =
LM 24 g + 60 g OP
N C C Q
2
2
r U
D 2g
...(6.55)
No independent check on this equation seems to have been made. By qualitative reasoning Bagnold
(1960) has postulated that the resistance in bends in pipes and open channels can be partly attributed to
force required to the creation of secondary flow and partly to overcome the boundary friction and
written
f=
r
D
+ const c
rc
D
and shown that at rc /D values between 2 and 3 the resistance is minimum. Leopold and Wolman (1960)
have also compiled field evidence to suggest that in meandering streams, bends commonly tend to have
a value of rc /W between 2 and 3. Hence, Bagnold argued that some principle of energy minimization
may be involved in meander formation.
6.7 SHEAR DIRECTION NEAR CURVED STREAM BED AND BED
TOPOGRAPHY
Because of the presence of secondary circulation, radial shear stress is caused on the bed which is
directed from outer towards inner side of the bend in radial direction. As a result, the resultant shear
stress has a small radial component, which is responsible for cross-sectional bed deformation in alluvial
channel bends. This aspect of flow in bends is studied by Engelund (1974), Kikkawa et al. (1976),
Zimmermann (1977), De Vriend (1977), Zimmermann and Kennedy (1978), Odgaard (1982) and
195
Hydraulic Geometry and Plan Forms of Alluvial Rivers
Fig. 6.15 Motion of a particle on transverse sloping plane
others. Figure 6.15 shows the directions of bed shear tq in streamwise direction, shear in radial direction
tr and the resultant shear to.
From geometry one can write,
to =
tan y =
t 2q + t r2
tr
=
tq
tr
to
Ft I
1+ G J
Ht K
2
...(6.56)
r
o
tan y »
tr
tq
since tr << to. Here y is the angle between stream wise shear stress and resultant shear. To obtain an
expression for tr, the average shear stress around the wetted perimeter in radial direction was calculated
by equating its moment about the center of cross-section to the moment produced by the interaction of
the vertical velocity gradient and the streamline curvature. Using Eq. (6.40) and expressing the
exponent n as n =
113
.
, Zimmermann obtained the following expressions for to and tr.
f
to =
113
.
f + f
1
D 2
rf
U
2
3
3
113
.
+ 2.26 f rc
a f
F DI
tan y = b(f ) G J
Hr K
F 9.04 + f I
b(f ) = G
H 3.83 f + 6.78 f JK
tr =
hence,
r f f U2
and
8
...(6.57)
c
where
...(6.58)
196
River Morphology
Fig. 6.16 Variation of b(f) with f (Zimermann 1977)
Figure 6.16 shows variation of b(f) with f according to Eq. (6.58). It can be seen that b(f ) and hence
tan y decrease rapidly as f increases; this decrease is attributed to more uniform vertical distribution of
streamwise velocities as the channel becomes rougher. For large values of f, b(f ) decreases gradually. It
may be mentioned that Engelund (1974) obtained value of b(f ) as 7.0 for smooth channels, while
Rozovskii (1957) recommends a value between 10 and 12 for rough as well as smooth beds.
The method of estimation of variation of depth along the radial direction as given by Engelund
(1974) is given below. Considering the motion of a sediment particle on a channel bed with a small
transverse bed slope a and with shear stress deviating by an angle d from the local flow direction, the
drag force on the particle in the longitudinal direction will be
FD =
LMdg
N
s
-gf
i p6d
3
- FL
OP
Q
tan f cos a
where f is the angle of repose, and FL is the lift force on the particle. In the transverse direction the
forces on the particle have the component
LMdg
N
s
-gf
i p6d
3
OP
Q
- FL sin a – FD tan y
Hence, tangent of the deviation angle d will correspond to the ratio between transverse and
longitudinal force components; or
tan d =
tan a
– tan y
tan f
...(6.59)
This result is valid only as long as the angle a is small and sediment is transported predominantly as
bed-load.
In the case of steady, uniform flow in a circular alluvial bend, there will be a small sediment
transport in the radial direction which will be balanced by the radial bed slope developed giving
increased depth at the outer wall. Thus inward sediment transport is balanced by the outward component
due to transverse bed slope. Equilibrium will be attained when y is equal to d. Engelund obtained
197
Hydraulic Geometry and Plan Forms of Alluvial Rivers
tan y = 7
D
,
r
D
1 dD
=
tan j d r
r
7
which on integration gives
D = C1 r7 tan f.
The constant of integration can be determined from the condition that at r = rc, D = Dc. Hence, the
depth D at any radial distance will be given by
D = Dc
FG r IJ
Hr K
7 tan j
...(6.60)
c
Engelund recommends the value of f = 30°
The particle size distribution in a bend is not uniform when the river bed material is graded; the
coarser sediment accumulates near the concave bank and finer near the convex bank. Odgaard (1981,
1982 and 1984) has suggested a method for prediction of the particle size distribution in a bend. As a
first approximation, he assumed that the bed profile is a straight line and further assumed that the
dimensionless critical shear stress tc is proportional to d-2/3, and obtained the particle size distribution in
the radial direction as
FG IJ F r I
H K H rK
d
D
=
dc
Dc
5/ 3
3/ 2
c
...(6.61)
He has also found that the radial distribution of average velocity in the vertical is given by
Vcp
Vcpc
F d I FG D IJ F r I
H dK HD K H rK
2/3
1/ 6
=
c
c
1/ 2
...(6.62)
c
Here Dc and Vcpc are the centre line depth and centre line average velocity in the vertical.
River bends can be either entrenched or meandering surface bends. Entrenched bends include those
bends, which follow the bends in the valley. The river on the floor of valley forms meandering surface
bends, which is erodible. In these bends the nature of bank material predominantly determines the radius
of curvature of bends. These bends are also classified into free bends, limited bends and forced bends.
The banks in free bends are composed of alluvial material, which is easily erodible. In limited bends, the
banks are composed of consolidated parent material, which limits lateral erosion, as in entrenched
bends. In forced bends, the stream impinges straight on the parent bank at an angle between 60° to 100°
rc
varies from 4.5 to 5.0 for free bends, 7.0 to 8.0 for limited bends and
W
2.5 to 3.0 for forced bends. Meandering rivers assume a natural alignment consisting of bends and
shallows in the crossings between bends. The profile of the talweg consists of successive deeps and
pools in the bends and shallows or shoals in the crossings.
approximately. For these bends
198
6.8
River Morphology
BRAIDED RIVERS
The basic mechanism of initiation and development of braiding has been studied through laboratory
experiments carried out by Leopold and Wolman (1957), Edgar (1973), Zimpfer (1975), Hong and
Davies (1974) and Ashmore (1982). Leopold and Wolman (1957) have suggested the following
sequence of events in the development of braided reach. In an originally single or undivided reach a
short submerged bar is deposited during high flows. The head of this gravel bar is composed of coarse
fraction of bed-load that is moving along the center of the channel. Most of the finer particles move over
it, some are trapped on or behind it leading to its growth in the downstream direction. Simultaneously it
grows laterally. When it becomes sufficiently wide, it starts affecting the channel along its side by
increase in velocity, which initiates widening of the channel. The bar gradually gets stabilized due to
vegetation that induces some more deposition on and around it. Later similar process starts in the
divided channels leading to island formation and division of channels. Observation by Hong and Davies
(1979), Ashmore (1982), Zimpfer (1975) and Edgar (1973) at Colorado State University indicate that
the channel division can occur either by separation around middle bar; or incision of a new channel
across the diagonal bar. Ashmore (1991) has shown that braiding can be accomplished in four ways:
accumulation of a control bar, chute cutoff of point bars, conversion of transverse unit bars to mid
channel braid bars, and dissection of multiple bars. The Brahmaputra river in Assam (India), the Kosi in
Bihar (India) and parts of the lower Mississippi are excellent examples of braided streams.
A braided river reach is characterized by a number of alluvial channels with bars and islands
between meeting and dividing, and present the intertwining effect of a braid when seen from the air.
Braided rivers may be considered as a series of channel segments that divide and rejoin in more or less
regular and repeatable manner. However, even in a braided reach a single dominant channel can be
distinguishable. Plan-form of braided rivers can change radically with the change in discharge; hence
some investigators e.g., Bristow and Best (1993) have opined that the fluctuations in discharge are a prerequisite for braiding especially in sand bed rivers, even though flume experiments in gravel carried out
by Ashmore at constant discharge discount this observation. A few rivers act as single channels at
bankful stage and have characteristic braided pattern at lower stages; however in many other rivers some
of the islands are permanent and at low stage as well as at high stage the rivers show braided pattern.
It seems that presence of wide range of sediment sizes in the bed material is conducive to bar
formation and hence braiding. Braiding has been observed and studied in laboratory flumes as well as in
rivers as large as the Brahmaputra and the Mississippi. Plans of braided rivers often reveal the gross
similarity in the appearance of braided patterns. Study of braided rivers is not only important from the
point of view of river morphology; braided alluvial deposits form substantial hydrocarbon reservoirs,
sites for deposition and accumulation of heavy minerals, and important sand gravel reserves (Schumm
1977).
Leopold and Wolman (1957) on the basis of study of the hydraulic characteristics of divided and
undivided channels indicate that for a divided stream (i) the slope is steeper, (ii) width is larger, and (iii)
depth is smaller, than that for an undivided stream. The ratio of slope of divided to undivided stream
varies for 1.3 to 2.3, while the ratio of corresponding widths ranges from 1.05 to 2.0.
Causes of Braiding
It has been observed that the important variables that affect the braiding of rivers are discharge and its
variability, the size distribution of the bed material and the rate and size distribution of sediment load,
Hydraulic Geometry and Plan Forms of Alluvial Rivers
199
width, depth, slope, climate and geologic factors. It is observed on many rivers that a given channel can
change in a short distance from a braided to meandering and vice versa; such changes are therefore
attributed to the variations in locally independent variables. It is also observed that those rivers
dominated by braided as against the meandering channels have on the average a higher flood
peakedness, higher total discharge range and higher monthly discharge variability. Braiding is
developed by sorting as the stream leaves behind those fractions of the load it is incompetent to
transport. If the stream is competent to move all sizes that it is transporting but is overloaded aggradation
may take place without braiding.
Lane (1957) studied plan-forms of a number of streams as well as their history, and concluded that
there are two primary causes of braiding; these are (i) overloading i.e., stream may be supplied with
more sediment than it can carry and hence part may be deposited; and (ii) steep slopes causing a wide
shallow stream in which bars and islands may readily form. All steep slope type braided channels have
many characteristics in common in addition to that of multiple channels; these are i) relatively straight
course of main channel; ii) steep longitudinal slopes; iii) wide channels; iv) shallow depths; v) sand or
coarse bed material; and vi) usually high bed-load. Since braided form can be due to steep slope or due
to aggradation resulting from the overloading of stream with sediment, or due to combination of the two,
braided streams can be classified into the following five subdivisions as per Lane (1957):
I Braiding due to steep slope:
II Braiding due to aggradation:
a) Braiding due to steep slope with degradation
b) Braiding due to steep slope with approximate equilibrium
c) Braiding due to steep slope with aggradation
d) Braiding due to moderate slope with aggradation
e) Braiding due to low slope with aggradation
Types of Bars in Braided Rivers
As described by Miall (1977) the bars occurring in a braided river can be classified as under (see Fig.
6.17)
Fig. 6.17 Principal types of bars (Miall 1977)
200
River Morphology
Longitudinal Bars
These are diamond or lozenge shaped in plan and are elongated parallel to flow direction. They are
bounded by active channels on both sides and may have partially eroded margins. Bars formed in gravel
are most commonly of this type. Longitudinal bars are the classical braid bars of Leopold and Wolman
(1957) and the sequence of events leading to their formation is discussed earlier. The initial bar relief
may be no greater than the size of the largest fraction of the bed material but as growth continues it may
increase to as much as metre. Bar length may reach several hundred metres. The internal structure of the
bars is massive or crude horizontal bedding.
Linguoid or Transverse Bars
Linguoid or transverse bars are most typical of sand braided rivers. They are found to occur in channels
that are deep and confined within narrow banks. The characteristic shape of linguoid bars is rhombic or
lobate, with upper surfaces that dip gently upstream towards the preceding bar and downstream facing
avalanche – slope terminations. These bars vary in width from a few metres to 150 m and length up to
300 m. Most typical heights of these bars range from 0.50 to 1.0 m. Dunes and ripples commonly cover
Linguoid bars that are exposed to view in modern rivers. Transverse bars are geometrically similar to
linguoid bars, except that they tend to have straighter crests.
Point Bars, Side Bars, Lateral Bars
Geometrically these bars are similar. They form in the areas of relatively low energy such as inside of the
meander. Point bars are usually associated with a meandering river, but they also occur in a braided
environment. Side bar is the longitudinal deposition along the side. Other large-scale structures are
observed in fairly large rivers.
Thus sand waves observed by Coleman (1969) in Brahmaputra, and dunes and bars observed in
rivers such as the Lower Red River (Alberta) fall in this category. Figure 6.17 shows longitudinal bar,
Linguoid bar, point bar and side bar. Large and sudden changes in water discharge mean the bed is
seldom if ever in equilibrium with the flow. Such reduction in flow has two effects on the bed – higher
relief structures may be eroded or dissected, and smaller scale structures may be superimposed. Bar
relief tends to be smoothened over as a result of reduction in flow and consequent sheet flow or wave
action. In the last stage of decreasing flow the deposition of this sheet of silt or mud takes place and the
channel fills in inactive areas.
After an extensive study of literature and braided stream deposits, Miall (1977) has classified these
deposits into three gravel facies Gm, Gt and Gp, five sand facies St, Sp, Sr, Sh and Ss, and two finegrained facies Fi and Fm. Their description, associated sedimentary structures, and interpretation are
given in Table 6.4.
Braiding Parameters
In recent times some thought has been given to characterise the braiding pattern, see Friend and Sinha
(1993). As a result, three parameters have been proposed (see Fig. 6.18).
Brice Index BI = 2 S Li/Lr
where S Li is the length of the islands or bars in a reach and Lr is the reach measured midway between
the banks of the channel. The factor two accounts for the total length of the bars.
201
Hydraulic Geometry and Plan Forms of Alluvial Rivers
Table 6.4 Lithofacies and sedimentary structures of modern and ancient braided-stream deposits
(Miall 1977)
Facies identifier
Gm
Lithofacies
Sedimentary structures
Gt
gravel, massive or crudely
bedded, minor sand silt
or clay lenses
gravel, stratified
Gp
gravel, stratified
broad, shallow trough cross-beds
imbrications
planar cross-beds
St
sand, medium to very
coarse, may be pebbly
sand, medium to very
coarse, may be pebbly
solitary (theta) or grouped (pi)
cross beds
solitary (alpha) or grouped
(omikron) planar cross beds
St
sand very fine to coarse
Sh
sand, very fine to very
coarse, may be pebbly
sand, fine to coarse, may
be pebbly
sand (very fine), silt, mud,
inter-bedded
ripple marks of all types,
including climbing ripples
horizontal lamination, parting or
streaming lineation
broad, shallow scours (including
eta-cross-stratification)
ripple marks, undulatory
bedding, bioturbation, plant rootlets,
caliche
rootlets, desiccation cracks
Sp
Ss
Fl
Fm
mud, silt
Interpretation
ripple marks, cross beds in sand
units, gravel imbrications
longitudinal bars, channellag deposits
minor channel fills
linguoid bars or deltaic
growths from older bar
remnants
dunes (lower flow regime)
linguoid bars, sand waves
(upper and lower flow
regime)
ripples (lower flow regime)
planar bed flow (lower and
upper flow regime)
minor channels or scour
hollows
deposits of waning floods,
overbank deposits
drape deposits formed in
pools of standing water
Fig. 6.18 Calculation of braiding indices of Brice (1964), Rust (1978) and Sinha (1993)
202
River Morphology
Braiding parameter of Rust (1968) RI = S
Lb
Lm
where S Lb is the sum, in a reach, of the braid lengths between the channel talweg divergences and
confluences, and Lm is the average of meander wave lengths in the reach. Friend and Sinha (1993) have
proposed braid–channel ratio BR which is defined as
BR = Lctot /Lcmax
where Lctot is the sum of mid-channel lengths of all the segments of primary channels in a reach, and
Lcmax is the mid-channel length of the widest channel through the reach. The ratio BR is a measure of
tendency of the channel belt to develop multiple channels in a reach. If the reach has a single channel,
BR will be unity. For the Gandak river in India BR was found to vary from 1 to 5.5.
Modeling of Braiding
In order to explain why and under what conditions alluvial streams braid, Engelund and Skovgaard
(1973), Parker (1976), Fredsøe (1978) and Kishi and Kuroki (1985) have treated braiding as a stability
problem. A double periodic disturbance with different wave lengths in the flow direction x and lateral
direction z is introduced on the bed of an alluvial channel and the resulting flow is analysed using
shallow water flow model. It is found that the deviation of sediment from the mean flow direction has an
important effect on the amplification of the disturbance leading to braiding. This analysis is usually
linear in that higher order of the disturbances and their derivatives are neglected. Such analysis has
t o , width to depth ratio W/D, Froude number Fr = U and
gD
Dg s d
slope are the important parameters that decide whether the stream will braid or meander. The criteria for
formation of braiding are discussed later in this chapter.
Another approach to explain braiding phenomenon is that of random walk model proposed by
Rachocki (1981). In this approach it is assumed that at the mouth of the valley a stream channel may
move downstream in one of three ways: to the right, to the left or it can bifurcate. The minimum distance
traveled in uni-directional flow in the model is termed as the step. Each step is graphically represented
by the diagonal of grid square. After the first step, the channel is again able to follow one of these three
options. Choosing three dice from a set of thirty, which avoids systematic error, generates the model.
The dice are changed after every three model generations. The following procedure was used by
Rachocki (1981). After the dice have been thrown, their values are added. If the total is even, the stream
deviates to the right, if it is odd it deviates to the left, and if the number is divisible by three it bifurcates.
After several steps are followed the pattern obtained is that of a braided stream, (see Fig. 6.19). It may be
seen that the approach is purely statistical and does not involve any consideration of fluvial dynamics,
bank erodibility etc. as such the approach is unlikely to satisfy river morphologists.
shown that dimensionless shear stress
6.9
MEANDERING
In Chapter IV a brief mention has been made about the classification of plan-forms of alluvial streams.
In this section additional hydrodynamic information will be presented regarding process of meandering,
theories of meandering, meander parameters and criteria for the prediction of major plan-forms.
Callander (1978) has given an excellent review about the state of knowledge on meandering.
Hydraulic Geometry and Plan Forms of Alluvial Rivers
203
Fig. 6.19 Random walk model of braiding (Rachocki 1981)
Meandering appears to begin with the establishment of pools and riffles sequence. Straight
laboratory channels with bed comprising of homogenous material deform into pools and riffles
sequence when water flows over the bed and sediment transport takes place. Kinoshita (1957, 1961)
observed that the free meanders of a stream start first with the formation alternate bars, or pools and
riffles sequence; these change the streamline curvature and velocity variation to induce bank erosion
and deposition; this starts meandering process when banks are erodible. The average pool spacing is
about five times the bed width. As the meanders form, the alternate pools migrate to alternate sides
giving approximate wave lengths of two inter-pool spacing of ten bed widths as observed in nature (see
Fig. 6.20). It is interesting to briefly mention about the studies conducted by Agarwal (1983) who
imposed a two-dimensional harmonic disturbance near the bed of sediment transporting channel. With
0.27 mm sand and disturbances having frequency of 1.8 to 3.4 Hz, he found that when bed is covered
with dunes (low Fr) the disturbance did not have any effect on the bed. On the other hand when the bed
was plane and transporting sediment (Fr = 0.8) the disturbance produced alternate bars and pools over
27 m long flume. He also carried out some runs in which alternate bars and pools were formed in the
initial length of flume due to disturbance and then the disturbance was removed. In such runs, after
sufficient time the entire flume was covered with bars and pools. His studies thus showed that two
dimensional harmonic disturbance can induce formation of alternate bars and pools, and that if such
disturbance is introduced on the upstream side it can change the bed downstream to alternate pools and
bars.
Once the talweg takes a sinusoidal course due to formation of alternate bars and pools it causes
redistribution of velocity; it also initiates development of secondary flow. If the banks are erodible they
are eroded on the convex side of the talweg and more sediment is brought into the channel, which is
transported to the other side by secondary flow thus developing the point bar. In this way, in an erodible
channel formation of alternate bars and pools leads to meandering of the channel. Field studies have
shown that riffles tend to be eroded somewhat at lower stages of flow and the eroded material deposits
in the pools. As the discharge is increased to approximately the bankful discharge, the pools are scoured
204
River Morphology
W
5W
Pool
Initial straight channel
Meandering talweg
10 W
Riffle
Meandering channel
Fig. 6.20 Formation of pools, riffles and meandering channel
and scoured sediment forms riffles. Hence, hydraulic geometry of meandering streams is related to the
channel-forming discharge. Since the channel width is related to Qb as W ~ Qb1/2, it seems logical to
relate meander parameters to W. Once a meandering pattern is developed it is likely to persist unless
some really powerful factor comes into play. Experience on the Mississippi, the Ganga and other rivers
has shown that the obstacles including the variation in the cohesiveness of alluvium distort or even
suppress the meanders. Hence meander geometry is significantly affected by the nature of strata through
which it flows.
In natural streams, alternate bars will form if the stable width for channel- forming discharge (e.g.,
Lacey width) is less than the confining width, which is fixed by rigid banks or “khadir”, and the
discharge is low. Thus they occur in channelised flows at lower stages. Alternate bar formation has been
experimentally and analytically studied by Kinoshita, Hayashi (1980), Sukegawa (1972, 1974) and
Parker (1976).
A typical meandering stream is shown in Fig. 6.21. As mentioned in Chapter-4 meandering loops
are irregular most of the time; further they change their shape and size in the downstream direction.
Hence any average values of meander characteristics for a given reach only give us an approximate idea
about their dimensions. It must also be mentioned that along the reach of the river, it may be braiding in
one reach and meandering in another, since local conditions governing the plan form may change.
Rivers cutting into bedrock have also been found to meander. In such rivers the erodibility of the
bed rock along its length would govern the meandering pattern. Further such meanders would be more
or less stationary unlike meanders in alluvial strata (see Leopold and Wolman 1960). It is interesting to
note that the relationship between width and ML for such meanders of the Gulf stream of North Atlantic
follow the same trend as that for meanders in rivers in plains. Laboratory experiments of Friedkin
(1945), Inglis (1949), Agarwal (1983) and field studies on many rivers have indicated that the meander
pattern as a whole moves downstream in many rivers; this is by far the most common situation. Hickin
and Nanson (1975) used dendro-chronological method to measure the rate of migration of bends of the
Beatton river. The average rate of migration of ten bends was 0.475 m/yr. The maximum rate occurred
when Rm/W ratio was approximately 3 implying a rapid approach to limiting value of this ratio to 2.5.
Here Rm is mean radius of the bends. However, on some streams such as the Tigris in Iraq and the
Hydraulic Geometry and Plan Forms of Alluvial Rivers
Fig. 6.21
205
Typical meandering river-the White river in Arkansas (U.S.A.)
Pembina river near Manola, Alberta (Canada) the migration consists of gradual lateral enlargement
without or with small downward movement. Such meanders are called free meanders in Russian
literature. The enlargement of loops can occasionally result in natural cutoffs. According to Neill (1970)
downstream migration seems to be usually associated with alluvial fills in narrow valleys whereas free
meandering tends to occur in broad flats. In engineering applications to river training it is essential to
study historical changes of the river under consideration while planning river improvement works.
Processes Governing Meander Bend Migration (Chang 1988)
Meander bends may migrate downstream or laterally as mentioned earlier. This process is governed by
channel curvature, flow curvature and variation of secondary circulation along the bend. As long as
there is an angle between the flow path and the channel path, the primary flow and secondary flow have
components in streamwise and cross-stream directions. As mentioned in the section on flow in bends,
secondary circulation is responsible for transporting sediment from the concave bank downstream and
towards the convex bank. Essentially the migration of a bend depends on the relative depth of flow and
sharpness of the bend, and delayed response of flow curvature to channel curvature. The longitudinal
component of shear caused by the main flow causes bank erosion wherever the flow hugs the bank; this
area is shown hatched in Fig. 6.22; deposition occurs along the banks away from the flow path. The
bank resistance, vegetation on the banks and mode of bank failure also govern the method of migration
of bends. Figure 6.22 shows four cases of different combinations of channel curvature and flow
condition. In Case–A with low flow and mild bend curvature, secondary flow develops and the flow
line is more in line with channel configuration; the maximum flow curvature is close to apex and hence
lateral migration of bend takes place. Case–B refers to mild channel curvature and high flows. In this
case flow changes its direction slowly due to inertia and hence maximum flow curvature takes place
206
River Morphology
Fig. 6.22 Common modes of meander bend deformation in relation to flow pattern (Chang 1988)
further downstream from the apex thereby causing downstream migration. In Case–C with low flow
and sharp bend, the flow is unable to follow bend curvature and attacks the outer bank downstream of
apex, thus leading to downstream migration. In Case–D corresponding to high flow and sharp bend,
there is sufficient difference in bed and flow curvature. This leads to downstream migration together
with reduction in bend curvature.
Meander Characteristics
The main characteristics of a meandering river are the shape, size and mobility of meander loops. These
characteristics play an important role in the location, design and maintenance of hydraulic structures
such as bridges, barrages, flood embankments and guide bunds.
An arc of a circle, a sine curve or a parabolic curve can describe meander shape, even though the
common practice is to fit an arc of a circle and characterise it by the average radius Rm. The other two
length dimensions that characterise meanders are meander length ML and meander belt MB. These
characteristics depends on whether meanders are incised or are in flood plain, process and stage of
development of meanders, discharge, slope and sediment size, and terrain through which the river flows.
Therefore, these parameters cannot be precisely estimated by any theory and the most commonly used
technique for their estimation is statistical correlations using laboratory and field data collected by
Friedkin, Ackers and Charlton, Ferguson, Jefferson, Inglis, Bates, Shaw, Leopold et al, Carlson,
Schumm, Chitale and others. Most of these relationships are of the form ML, MB = const. Q1/2, where Q
is mean annual discharge or bankful discharge. However since channel width W ~ Q1/2 one can expect
ML, MB and Rm to be related channel width. Those relationships, which are based on use of dimensional
analysis or some form of stability or theoretical analysis, take the form
ML S
= f (Fr) where Fr =
D
used by the investigators.
F
GH
ML
M
Q2
or B = f
2
d
d
d gd
I or
JK
U
. Some of these relation-ships are listed in Table 6.5 along with the data
gD
207
Hydraulic Geometry and Plan Forms of Alluvial Rivers
Table 6.5 Relations for meander geometry
Investigator
Relations proposed
Data used
Furguson (1863)
ML = 6.0 W
Ganga data
Jefferson (1902)
MB = 17.6 W
Remarks
American and European rivers
1/2
ML = 6.06 W = 29.6 Q
MB = 17.6 W = 84.7 Q1/2
Rm = 20.64 Q1/2
ML= 11.45W = 25.4 Q1/2
MB = 27.3 W = 56.4 Q1/2
Rm = 14.0 Q1/2
Jefferson’s data
For rivers in flood
plains
Jefferson’s data
Incised streams
Inglis (1939)
Leopold et al. (1964)
ML= 27.4 Q1/2
ML = 10.9 W1. 01
MB = 2.7 W1.1
ML = 4.7 Rm 0.98
Shaw’s data for 16 rivers in Orissa
Fifty rivers ranging from models
to large rivers
Rivers in flood plains
Dury (1958)
American river data. Relation
used in Europe as design criterion
Prus-Chinsky
ML = 32.9 Q 0.55
ML = (10 to 14) W
ML = 15 W
Ackers and
Charlton (1970)
ML = 38 Q0.467
MB = 18.5 Q0.505
Laboratory data with
d = 0.15 mm
Schumm
ML = 1890 Q0.34/M0.74
Thirty eight sites on Australian
M = % of silt and clay
and Western USA rivers
in banks
Lewin (1961)
ML = 20 W1. 04
ML ~ Ai 0.3 to 0.4
English and Scottish river data
A1is catchment area
in km2
Chitale (1970)
Si = 1.429 (d/D)–0.077
S*0.052 (W/D)–0.065
42 river data
Si = S ´ 104 Si is
sinuosity
Inglis (1938)
Ackers and
Charlton (1970)
Anderson (1967)
F
GG
H
ML
= 123 Q / d 2
d
ML
Ac
Dgs d
rf
I
JJ
K
0. 378
River and flume data
= 72 Fr1/2
Ac = cross sectional
area
Hansen (1967)
56 D
ML =
f
f Darcy–Weiscbach
coefficient
Altunin (see
Kondratev 1950)
ML = (12 to 15) W
Rivers of Central Asia
Kudryashov (195458) (see Kondratev
1950)
ML = 449 Q0.5 S0.50
MB = 142 Q0.74
Laboratory data
Contd.
208
River Morphology
Contd.
Hayashi and Ozaki
(see Hayashi 1980)
ML = K W
Hansen (1967)
ML S/D = const Fr 2
Agarwal (1983)
ML = Nonlinear function of Q1/2
ML = 2.1 MB
F
GG
H
Data from Japanese rivers,
Leopold and Wolman,
Schumm & Chitale
Si = 0.97 Q / d 2
D gs d
rf
I
JJ
K
K is a function of Fr
Based on field and flume data
with Q up to 104 m3/s
0. 033
S0.04
It may be seen from the above table that many of the equations proposed for ML and MB are not
dimensionally homogenous. Dimensional homogeneity requires that ML = K1 MB = K2W and Rm = K3W.
According to Hayashi and Ozaki (see Hayashi 1980), in the relation ML = KW, K depends on Froude
number
U
and decreases with increase in Fr as indicated below
gD
Fr
0.10
0.20
0.40
1.0
K
40
20
10
7
Agarwal’s relation (1983) between ML and Q is shown in Fig. 6.23. Any one of the relations given
in Table 6.5 or Fig. 6.23 can be used to estimate ML. On the other hand, for rivers in flood plains
MB = 3 ML, ML/W = 10 to 14 and minimum value of Rm/W = 2 to 3 seem to be good thumb rules.
Fig. 6.23 Variation of ML with Q (Agarwal 1983)
Hydraulic Geometry and Plan Forms of Alluvial Rivers
209
Relations such as those mentioned above overlook the random character of meandering. Wallis
(1973) repeated the same experiment 60 times in a small flume using crushed polythene of median
diameter 2.6 mm and relative density 1.46 and measured meander characteristics at 30 s interval using
photographic technique. His measurements indicated the stochastic nature of meander properties. The
wave-lengths followed uni-modal distribution with a coefficient of variation of 0.22. Both mean and
standard deviation increased with time but the ratio of the two remained nearly the same. Spectral
analysis approach has been used by Toebes and Chang (1967), Speight (1965) and Fergusson (1975).
Theories of Meandering
Engineers and geomorphologists have given a number of reasons as to why streams meander. These are
briefly discussed below.
Excess energy concept
Schoklitsch (1937) and Inglis (1947, 1949) have argued that meandering is the natural way of reducing
excess energy (and hence excess slope) of the stream by increasing its length. On the basis of Bagnold’s
findings that for a large number of natural bends the ratio of radius of bend to channel width lies
between 2 and 3 at which the bend loss is minimum, Leopold and Wolman (1960) believe that some
principle related to minimization of energy is associated with meander formation. A somewhat similar
principle is used by Ramette (1980). On the other hand, Joglekar argues that the primary cause of
meandering is excess sediment load. According to Indian engineers, the excess sediment load during
floods tends to deposit on the bed and increase the slope. This deposition creates shoals on the bed
causing deviation in the flow. If the banks are erodible this deviation in flow direction can initiate
meandering. However, this hypothesis cannot explain the formation meanders in glacial streams,
observed by Leopold and Wolman (1960). Yang (1971) also has questioned the validity of the
hypothesis that streams meanders in order to dissipate excess energy. Hence, he has introduced a law of
least time rate of energy expenditure according to which, during the evolution towards its equilibrium
condition, a natural stream chooses its course of flow in such a manner that the time rate of potential
energy expenditure per unit mass of water along its course is minimum. Or
DH
= f (discharge, valley slope, sediment concentration, geological constraints)
Dt
However, this concept is not further developed linking flow parameters to meander characteristics.
Earth’s rotation theory
Gilbert (1884), Eaking (1910) and Neu (1967) have given earth’s rotation as a cause of meandering.
Due to rotation of earth, a body on the earth’s surface experiences a Coriolis force which represents
inertia of the body to partake in the rotational motion. Due to this force a body moving in the north-south
direction in the northern hemisphere will experience a force towards the east which can deflect the body
in that direction. The tendency of the Mississippi river and some other rivers in Alaska to deflect to the
right is often quoted in support of this theory. Neu (1967) has shown that the secondary circulation
developed due to earth’s rotation is proportional to D/U of the stream and the latitude of the place. The
deviations caused by this circulation can be of the order of 10° to 20°. However it is argued that if earth’s
rotation alone were responsible for meandering, all the streams at or near the equator should be straight,
210
River Morphology
whereas meandering streams are found on the equator as well as elsewhere on the earth’s surface.
Further, it has been shown by Quaraishy (1944) that the tendency of the stream to deflect either to the
right or to the left is just a chance, and force due to earth’s rotation is relatively small. Lastly the
erodibility of banks plays a major role in meandering, which is not taken into consideration in such a
theory. Hence it is felt that even though earth’s rotation may play a small part in the meandering process,
it cannot be the sole reason.
Disturbance theory
Proponents of disturbance theory argue that any disturbance caused on the bed or in the flow at the
upstream end causes changes in the flow pattern in the downstream direction leading to meandering.
This disturbance can be differential deposition across the channel width in an overloaded stream, or
transverse oscillations in the flow, or an inclined entry into the channel. Earlier Griggs (1906), Werner
(1951) and Hjulstrom (1957) have suggested this mechanism. Friedkin (1945) was able to initiate
meandering in a laboratory channel with mobile boundary by allowing flow at an angle. Agarwal (1983)
was able to obtain alternate bars in a laboratory flume by imposing a two-dimensional harmonic
disturbance near the bed. Lewin’s (1976) observation on the Ystwyth river where a straight channel
changed to a meandering one without apparent changes in geological or hydro-geological conditions
supports this theory. The change in Ystwyth river began with the formation of lobate transverse bar.
Since the disturbance imposed on the flow can be decomposed into harmonics and for a given flow
condition, one of the harmonics can cause instability to form meanders, disturbance theory can be linked
to instability theory discussed later where the investigators have assumed that meanders occur as a result
of unstable response of the bed to a small perturbation.
Helicoidal motion theory
Some investigators argue that helical motion or secondary circulation is somehow responsible for
occurrence of meandering. Since secondary flow is present in all the channels, it is believed that
secondary circulation has to become unsymmetrical so as to cause meandering. This is probably caused
by unsymmetrical cross-section of the channel and/or by the changing resistance characteristics of bank
and bed along the channel length, see Leliavsky (1955), Prus-Chacinsky (1954), Onishi et al. (1976),
Jain and Kennedy (1976), and Shen (1983). Prus-Chacinsky has shown that by introducing an artificial
secondary flow at the entry of the first bend, it is possible to produce various patterns of secondary flow
at the entry of the first bend, and various kinds of secondary flows in the next successive bends. This in
turn, affects the circulation in the next bend, and so on. Prus-Chacinski ascribes meandering to any
disturbance which produces the initial circulation. Onishi et al. (1976) have concluded that the most
important cause of meandering is secondary flow, which produces point bars, modifies the distribution
of velocity across the channels, modifies the shape of ripples and dunes on the bed and affects the
entrainment and transport of sand on the bed. This concept is loosely linked to disturbance theory.
Conceptual model of Leopold and Langbein
Leopold and Langbein (1978) have proposed a model according to which the meander form is the same
as the most favourable itinerary of a rod of fixed length and defined by a random walk process between
two points. They obtained a curve analogues to the rod buckling in with some real meanders. The
concept is true provided that the constraints (discharge variation, erodibility, and human interference
etc.) can be included in the random walk process. However, it is felt that inclusion of such constraints
would result in a different shape.
211
Hydraulic Geometry and Plan Forms of Alluvial Rivers
Ramette’s approach
According to Ramette (1980) the five characteristics of river geometry, namely width W, depth D, free
surface slope S, meander wave length ML and meander amplitude MB are functions of discharge Q, d50,
d90 and valley slope Sv which vary along x direction. His model computes the first five when the last four
are specified. According to Ramette the river characteristics adjust in such a manner that its efficiency of
bed erosion is maximum under two constraints: the discharge Q is the bankful discharge and flow is
saturated with sediment i.e., it is carrying the maximum possible sediment load. Hence he uses the
following relationships
1. Sediment discharge formula of Meyer-Peter and Müller QB = K W (to – toc)3/2
2. Manning-Stricker equation Q = K1 (WD)5/3 (W + 2D)–2/3 (S)1/2
3. Reduction in sediment size according to Sternberg’s law
4. Maximum value of channel slope equal to valley slope: Sv £ S
5. Saturation of flow
¶ QB
=0
¶x
The potential energy of erosion from sand surface to the depth D of liquid mass is QgD/2, while
kinetic energy recovered after erosion is
d
Q U 2 - Uo2
i where U is velocity at depth D and width W, and
2
Uo is initial velocity. The energic efficiency of erosion of bed is maximum when
d
Q U 2 - Uo2
2
i
d
i
U 2 - Uo2
2
i.e.,
is maximum, or
QgD
gD
d
dx
R| dU - U i U|
S| g D V| = 0
T
W
2
2
o
From the above equations, Ramette has shown that the efficiency is maximum and the flow is
saturated when b = W/D lies between 15 and 21. According to Ramette, in the upstream reach of the
river where Sv = S, W, D, Q and da are such that the saturation condition is satisfied but not the maximum
efficiency condition, W/D is less than 15 and river is straight and tending to equilibrium (b and da
decreasing). Here da is arithmetic mean size of bed sediment. When 15 < b < 21 the river is near
equilibrium. If da is less than da1 then S is less than Sv and river meanders. The limiting diameter da1 is a
function of discharge, valley slope and initial value of da /d90. When b is greater than 21, the river is of
braided type. Thus if variation of da along the river axis is known, it is possible to find the distance x1
upstream of which S is equal to Sv, and downstream of which meanders will appear. As a result of his
analysis, Ramette has given a criterion for plan form determination in terms of da, Q0.465 with W/D as the
third variable on which regions of straight, meandering and braided reaches are indicated, see Fig. 6.24.
Further assuming that Rm /W = 2.5 for meanders as indicated by Leopold and Wolman, he has shown that
ML/MB = 2.5 and ML/W = 7 to 11. Ramette’s criterion has been checked by Agarwal (1983), but the
results are not encouraging.
212
River Morphology
Fig. 6.24
6.10
Ramette’s criterion for plan-forms
STABILITY ANALYSIS AND CRITERIA FOR PLAN-FORMS
As mentioned earlier bank erosion constitutes the necessary requirement for the occurrence of
meandering in alluvial rivers. According to the experiments of Kinoshita (1957) meandering is caused
first by the erosion of bed leading to the formation of alternate bars in channels with non-erodible
vertical walls, which then leads to meandering if the walls are erodible. Hence the theory of alternate bar
formation in non-erodible walled channel can provide an insight into the formation of meanders and
braids. This theory is based on a stability analysis in which small perturbations that are double harmonic
functions of x and z coordinates are introduced on the sediment transporting bed in rigid walls channel
and the conditions under which these are attenuated or amplified are studied. For such an analysis the
equations of continuity for flow and sediment, and sediment transport and resistance laws are used.
Depending on whether the analysis is two or three dimensional, the investigators have used two or three
equations of motion. Most of the investigators use linearisation so that higher order terms involving
perturbations are omitted. Reynolds (1965) and Hayashi (1967), Callander (1969), Sukegawa (1971,
1972), Hayashi and Ozaki (1978) and Parker (1978) have used shallow water flow models, while
Engleund and Skovgaard (1973) have used turbulent shear flow model. In these theories the factor
causing the instability of the erodible bed is the phase difference existing between shear stress gradient
and bed form gradient in the flow direction. However, these theories lead to the unjustifiable conclusion
that larger the mode of the braids m is in Eq. (6.63), larger is the growth of braid unless some additional
characteristic of sediment transport is taken into account. Here m is the braiding mode in the equation
for double sinusoidal migrating disturbance on the bed
h = ho cos
2p x
pmz
sin
L
W
...(6.63)
In Eq. (6.63) h is the disturbance imposed on the otherwise flat bed, m is the mode of sinusoidal
disturbance in z direction, W is the channel width, L is the wave length of disturbance in the flow
213
Hydraulic Geometry and Plan Forms of Alluvial Rivers
Fig. 6.25
Meandering and braiding
direction x, and z is the lateral direction. When m = 1 the pattern is meandering while m = 2 or 3 will
represent braiding modes as shown in Fig. 6.25.
According to Hayashi and Ozaki (1978) it is the spatial lag distance d between the local bed-load
transport rate and local shear stress that plays an important role in the formation of braids of mode m = 1
i.e. meandering. This lag-distance that was originally estimated by Einstein as 100 d has been modified
to
U|
||
|V
||
||
W
...(6.64)
where S is average channel slope, f is average friction factor of the bed, Fr =
U
, U and Do are
g Do
LM
R| D S U| OP
d = l d 1+ 4a S
V
MM
r / r - 1i d | P
d
|
T
W PQ
N
L
R| f D U| OP
d = l d M1 + 5 a S
VFP
MM
r / r - 1i d |
d
|
T
W PQ
N
3
o
1
*
s
f
3
or
o
1
*
s
f
6
r
average velocity and depth of flow in the undisturbed flow, l1 = 100 and a* = 4.35 as proposed by
Einstein. Since d is greater than l1 d, spatial lag distance is greater than the step length l1 d. For nonequilibrium flow Einstein and Brown formula for bed-load transport is modified as
214
River Morphology
fx (x, z) =
a f
F r - 1I g d
GH r JK
q a x, z f
F r - 1I g d
GH r JK
q Bx x , z
s
U|
||
|V
||
||
W
× F = 40 á t* (x – d), z ñ 3
3
f
fz (x, z) =
× F = fx (x, z) ×
Bz
s
3
a f
a f
w x, z
u x, z
f
where
F=
t* =
2
36 v 2
+
3 g d 3 rs / r f - 1
d
36 v 2
i
d
...(6.65)
i
g d 3 rs / r f - 1
t*
(r s - r f )g d
Here qBx and qBz are the x and z components of volumetric bed-load transport rate, d is the
characteristic size of sediment, u and w are the components of average velocity in x and z directions
respectively, fx and fz are dimensionless transport rates, and F is dimensionless fall velocity of sediment
particle. The two dimensional equations of motion, continuity equations for flow and sediment, and
resistance law are
R|u ¶ u + w ¶ u + g F ¶ D + ¶ hI + t - g S = 0
GH ¶ x ¶ x JK r D
¶x
¶z
|
Dynamic Equations S
||u ¶ w + w ¶ w + g FG ¶ D + ¶ hIJ + t = 0
T ¶x ¶z H ¶z ¶zK r D
x
f
z
f
Continuity Eq. for flow
Continuity Eq. for Sediment
Resistance law
¶
¶
(u D) +
(w D) = 0
¶x
¶z
¶ h ¶ q Bx
¶ q Bz
+
+
=0
¶t
¶x
¶z
F I
H K
F I
H K
r f u2
u
w
× tz = tx
and f = 2 *
tx = f
2
u
U
2
=2
S
Fr2
U|
||
||
||
|V
||
||
||
||
W
...(6.66)
When the disturbance of the form of Eq. (6.63) is imposed on the bed, small perturbations in various
quantities with respect to steady flow condition will be (see Fig. 6.26)
215
Hydraulic Geometry and Plan Forms of Alluvial Rivers
Fig. 6.26
Definition sketch
U|
||
V|
||
W
h=h
x=x
u = u + u¢, w = w¢
D = Do + x – h
tx = to + t¢x
tz = t¢z
qBx = qBo + q¢Bx
qBz = q¢Bz
Here uo, Do and qBo are steady state average velocity, depth of flow and sediment transport rate
respectively, h and x are displacements imposed on the bed and displacement of free surface
respectively, to is average bed shear stress in steady flow and primed quantities represent the
perturbations. These are then substituted in the equations of motion Eq. (6.66), and linearisation is done
with respect to perturbed quantities. The resulting equations are then non-dimensionalised after
eliminating t¢x, t¢z, q¢Bx and q¢Bz and solution postulated in the form
hr = ho cos lzr exp [i k (xr – Ctr)]
ur = uo cos lzr exp [i k (xr – Ctr)] + i y1
wr = wo cos lzr exp [i k (xr – Ctr)] + i y2
xr = xo cos lzr exp [i k (xr – Ctr)] + i y3
U|
||
V|
||
W
...(6.67)
Here ho, uo, wo and xo are the normalized values of h, u, w and x at t = 0, k and l are the
dimensionless wave numbers of sinusoidal disturbances in x and z directions respectively, namely
k=
2 p Do
and
L
l=
m p Do
W
and y1, y2 and y3 are phases of ur, wr and xr with respect to hr respectively. Also complex velocity
C = Cr + i Ci where Cr is dimensionless velocity of disturbance and Ci is the amplification factor. For
m = 1, the dominant wavelengths are expected to be those for which the initial rate of growth of hr are
216
River Morphology
positive and maximum. Solution of this system of equations constitutes the Eigen value problem and
Hayashi and Ozaki have done this. They have arrived at the following conclusions
1. When
FG SW IJ
H pmD K
2
<< 1 the rate of growth of hr is largest for waves of mode m = 1 i.e., for sand
o
waves associated with meandering, and the ratio L/W is given by
L/W = f1 (Fr)
2
where f1 (Fr) =
m
LM
MN - d5 + 8 Fr
2
i
d10 + 19 Fr
2
+ 7 Fr 2
i
+ 5 Fr 4 + 25 + 110 Fr 2 + 141 Fr 4 + 44 Fr 6 + 4 Fr 8
» 3.66
F 1 + FrI
H Fr K
OP
PQ
1/ 2
...(6.68)
and the effect of lag distance on formation of meandering is crucial.
2. When
FG SW IJ
H mp D K
2
>> 1, the dominant wave length is given by
o
L
=
W
6
1
2p m 3 / 2
FG W S IJ
HD K
1/ 2
...(6.69)
o
and the rate of growth has a maximum for certain value of mode m. Hence the braid of such a
mode is theoretically possible.
3. When
FG W S IJ
H pmD K
2
» 1, the dominant wave length is given by
o
L
1
=
f2 (Fr)
W
m
RS18 - 10 Fr + 7 Fr UV
T 9 + Fr
W
2
and
f2 (Fr) = 2 2
4
...(6.70)
1/ 2
2
and the rate of growth is largest when m = 1.
Analysis of laboratory data indicated that alternate bars are formed when WS/Do < 0.31 which
agrees with the above conclusions. Hence Hayashi and Ozaki have related L with W and Fr as third
variable, see Fig. 6 27. It may be noted that L corresponds to meander length ML.
Criteria for Prediction of Plan-forms
The earlier predictors for plan forms were based on the relation between discharge and slope. Thus Lane
(1957) analyzed data from models and rivers in USA with average discharge varying from 2.8 ´ 10 –3 to
25,000 m3/s and slope S varying from 1.59 ´ 10-5 to 5.49 ´ 10 –3 and found that
Hydraulic Geometry and Plan Forms of Alluvial Rivers
Fig. 6.27
217
Comparison of predicted and observed meander length (Hayashi and Ozaki 1978)
when
S ³ 4.1 ´ 10 – 3 Q –0.25 the channel is braided
and when
S £ 7.0 ´ 10 –4 Q –0.25 it is straight
When the slope lies between these two limits the channels are meandering. It may be mentioned that
Lane did not propose a quantitative criterion to distinguish between straight and meandering channels.
Leopold and Wolman (1957) analysed the data from American and some Indian rivers with mean annual
discharge varying from 8.4 to 28 000 m3/s and slope varying from 8.9 ´ 10 –5 to 3.6 ´ 10 – 2 and found
that
if
S ³ 0.0125 Q –0.44 streams are braided
and if
S £ 0.0125 Q –0.44 streams are meandering
while relatively straight channels with sinuosity less than 1.5 were scattered on both sides at this line.
Leopold and Wolman have also observed that the channel patterns braided, meandering or straight, each
occurs in nature throughout the whole range of possible discharge and slope. Some of the largest rivers
in the world are braided e.g. the Lower Ganges, the Amazon, the Brahmaputra and parts of the
Mississippi. Leopold and Wolman’s principal point of discussion is that there is continuum of stream
channels having different characteristics that are reflected in the combination of hydraulic factors—
each pattern is associated with certain of these combinations.
Henderson (1963) has included the effect of sediment size in Q–S criterion and modified the
equation demarcating braided streams from meandering ones to
S = 0.517 d 1.14 Q –0.44
where d is in m and Q in m3/s.
218
River Morphology
Fig. 6.28 Regime channel geometry for sand bed rivers (Chang 1980)
Chang (1980) used the condition of minimization of stream power and proposed a criterion between
S
and Q for identifying the plan-forms, see Fig. 6.28. Region below line 1 represents the condition of
d
no transport of bed-load. Region between lines 1 and 2, called region I, represents stable channels with
flat slopes, low velocity and low bed-load transport rate and width to depth ratio of 4 to 20; natural
channels in this region have a meandering pattern and occasionally straight channel for which valley
slope is equal to channel slope.
According to Chang, rivers falling in region II have smaller of the two slope minima and are less
stable. The channel geometry is sensitive to slope and slight increase in slope tends to increase the
channel width and decrease the depth of flow. Rivers falling in this region are often braided. For rivers
in region III width and depth are sensitive to slope and those rivers are braided, the extent of braiding
being directly related to slope. Rivers in region IV are highly braided and have width to depth ratio
greater than 100. On Fig. 6.28 Chang also gives contours of equal depth and width. The equations of
three lines in fps units are
Line 1
S
= 0.00238 Qb- 0.51
d
Line 2
S
= 0.05 Qb- 0.55
d
Line 3
S
= 0.047 Qb- 0.51
d
U|
|
V|
||
W
...(6.71)
Precise location of line L is not known. Here Q is expressed in cfs and d in mm. When Q is
expressed in m3/s and d in mm, the constants in the above equations are 0.000 386, 0.007 04 and 0.007
63 respectively.
219
Hydraulic Geometry and Plan Forms of Alluvial Rivers
Hayashi and Ozaki (1978) have proposed the criterion for prediction of plan-forms, using the
method of stability analysis. According to them the plan-form depends on
FG W S IJ
HD K
F W S IJ
³ Fr ³ 2 G
HD K
F W S IJ
³ Fr ³ G
HD K
WS
and Fr =
Do
U
.
g Do
1/ 2
Fr ³ 3.16
Straight
o
F W S IJ
3.16 G
HD K
F W S IJ
2G
HD K
FG W S IJ
HD K
1/ 2
o
1/ 2
Transition from straight to meandering
o
1/ 2
o
1/ 2
Coexistence of meandering and braiding
o
1/ 2
³ Fr
Braiding
o
see Fig. 6.29. Using regime type relationships, Hayashi and Ozaki expressed Do, W and U as a function
of Q namely Do ~ Q0.36, W ~ Q0.55 and U ~ Q0.05 and converted Fr –
WS
criteria into S – Q criteria,
Do
namely
Fig. 6.29 WS/Do – Fr criterion for channel patterns (Hayashi 1980)
220
River Morphology
S ³ 7.0 ´ 10 –3 Q – 0.37 braiding
S £ 7.0 ´ 10 – 3 Q – 0.37 meandering
Agarwal (1983) has verified S vs. Q criterion using available flume and field data, and concluded
that this criterion does not predict the plan-form correctly. This may partly be due to the fact that some
data especially laboratory data have constant discharge while field data have either bankful discharge or
mean annual discharge.
On the basis of the stability theory, Parker (1976) has concluded that in rivers transporting sediment,
when Do /W < 1.0 at the formative discharge (both these conditions are almost universally satisfied), the
tendency towards either meandering or braiding exists. Further meandering occurs when S/Fr << Do /W,
braiding occurs when S/Fr >> Do /W and transition between meandering and braiding occurs when S/Fr
lies between these two limits see Fig. 6.30. This criterion is based on the laboratory data of SAF,
Wolman and Brush, Schuum and Khan, Ashida and Narai, Ackers and Charlton and Qurashy, and field
observations of Simons and some rivers.
Fig. 6.30 S/Fr – Do/W criterion of Parker (1976)
Ramette (1980) has proposed d vs Q0.45 S criterion as shown in Fig. 6.24 for prediction of plan
forms, and verified it with a few experimental data of Henderson. Agarwal has used data from a number
of laboratory studies and field data and found that most of the points for straight channels fall in the
correct region while the data for meandering and braiding channels are scattered widely and hence he
found the criterion to be unsatisfactory.
Many Japanese investigators have proposed criteria for alternate bars and braids. Sukegawa (1971,
F I
GH JK
u
WS
1973) has developed a criterion using * vs
u* c
Do
FG W S IJ
HD K
o
1/ 3
plot. Kishi and Kuroki (1975) have used
1/ 4
graph, whereas Ikeda (1973) uses
FG IJ
H K
u*
WS
vs
u* c
Do
u*
vs
u* c
1/ 2
plot and Tamai et al. (1978) have
221
Hydraulic Geometry and Plan Forms of Alluvial Rivers
used
FG IJ
H K
WS
u*
vs
plot. It may be mentioned that Muramoto and Fujita (1977) have developed planu* c
Do
form criterion using
F I
H K
Do
W
vs
graph.
Do
d
It may be pointed out that stability analysis and other approaches have revealed that the parameters
D
W
u
t
, Fr, S, f, * , o , o and lag distance d. These are related by six
Do
u* c t c d
equations (see Hayashi 1980, and Hayashi and Ozaki (1978)) and hence one can choose only three as
governing plan forms are
independent parameters. Three possibilities are (i)
W
W
u
W
t
, S, Fr, (ii)
, S, o or * and (iii)
, S,
Do
Do
u* c
Do
tc
u*
W
WS
. The analysis indicates that
and S occur as
.
u* c
Do
Do
Agarwal (1983) has analysed a large volume of laboratory and field data from various countries to
verify the plan form criteria proposed by Lane, Leopold and Wolman, Parker, Ramette and those
proposed Hayashi and Ozaki, and other Japanese investigators and found that these criteria do not
predict the plan-forms correctly. Therefore he has proposed two criteria, first between t* and Fr, and
other between t* and
WS
which seem to demarcate plan forms reasonably well, see Fig. 6.31 and 6.32.
Do
Fig. 6.31 Criterion for river channel patterns (Agarwal 1983)
222
River Morphology
Fig. 6.32
WS /Do – t* criterion for plan-forms (Agarwal 1983)
Lastly Kuroki and Kishi (1985) have used stability analysis and developed a criterion for prediction
W S 0 .2
and S. On this diagram
Do
(see Fig. 6.33) three regions where no bars occur, bars and braiding occur are indicated. Figure 6.33 also
of plan-forms. Their analysis indicated that plan-forms depend on t*,
Fig. 6.33 Criterion for meso scale bed-forms (Kuroki and Kishi 1985)
223
Hydraulic Geometry and Plan Forms of Alluvial Rivers
shows that for large values of t*, no bars occur if
W S 0 .2
W S 0 .2
is less than 4 to 5, bars occur if 5 <
< 20
Do
Do
W S 0 .2
values greater than 50.They also found that the dimensionless
Do
length of bars L/W primarily depends on t*, decreasing with increase in t* for small values of t* and
gradually increasing with increasing in t* for larger t* values. For t* between 0.1 and 6, L/W varies
between 2 and 6 with an average value of 4.
to 30 and braiding occurs for
References
Agarwal, V.C. (1983) Studies on the Characteristics of Meandering Streams. Ph.D Thesis, I.I.T. (formerly
University of Roorkee), Roorkee.
Ahmad, M. and Rahman, A. (1962) Appraisal and Analysis of New Data from Alluvial Canals of West Pakistan in
Relation to Regime Concepts and Formulae. Proc. of West Pakistan Engg. Congress, Lahore, Vol. 46, Paper
351.
Allen, J.R.L. (1965) A Review of the Origin and Characteristics of Recent Alluvial Sediments, Sedimentology,
Vol. 5, pp. 89-191.
Ananian, A.K. (1961) Determination de la Formation du Lit des Riveres, Cree Par Suite de L’Abaissement de la
Cote des Leurs Bases d’Erosion. Proc. of 9th Congress of IAHR, Dubrovnik, pp. 1102-1113.
Apmann, R.P. (1973) Estimating Discharge from Super-elevation in Bends. JHD, Proc. ASCE, Vol. 99, No. HY1,
Jan, pp. 69-79.
Ashmore, P.E. (1982) Laboratory Modeling of Gravel Bedded Stream Morphology. Earth Science Processes, Vol.
7, pp. 201-225.
Ashmore, P.E. (1991) How Do Gravel – Bed Rivers Braid? Canadian Jour. of Earth Sciences, Vol. 28, pp. 326-341.
Bagnold, R.A. (1960) Some Aspects of the Shape of River meanders. USGS Prof. Paper No. 282-E.
Blench, T. (1957) Regime Behaviour of Canals and Rivers. Butterworth Scientific Publications, London.
Bristow, C.S. and Best, J.L.(1993) Braided Rivers : Perspectives and Problems. In Braided Rivers (Eds. Best J.L.
and Bristow C.S.), Geo. Soc. Special Publication No.75, pp.1-11.
Callander, R.A. (1969) Instability and River Channels. JFM, Vol. 36, Pt. 3, pp. 465-480.
Callander, R.A. (1978) River Meandering – Annual Review of Fluid Mechanics, Vol. 8, pp. 129-158.
Carlson, C.W. (1965) The Relation of Free Meander Geometry to Stream Discharge and its Geomorphic
Implications. Am. J. Sci. Vol. 263, pp. 864-885.
CBIP (1989) River Behaviour, Management and Training. Central Board of Irrigation and Power, New Delhi, Vol.
1, pp. 36-37.
Chang, H.H. (1979) Minimum Stream Power and River Channel Patterns. Journal of Hydrology, Elsevier
Scientific Publishing Co., Amsterdam, Vol. 45, pp. 303-327.
Chang, H.H. (1980) Stable Alluvial Canal Design. JHD, Proc. ASCE, Vol. 106, No. HY5, May, pp. 873-891.
Chang, H.H. (1988) Fluvial Processes in River Engineering. John Wiley and Sons, New York. A Wiley
Interscience Publication, pp. 271-284.
Chitale, S.V. (1970) River Channel Patterns. JHD, Proc. ASCE, Vol. 96, No. HY1, Jan. pp. 201-221.
Chitale, S.V. (1976) Shape and Size of Alluvial Channels. JHD, Proc. ASCE, Vol. 102, No. HY7, July, pp. 10031011.
224
River Morphology
Chorley, R.J.(Ed.) (1969) Introduction to Fluvial Processes. Mathuen and Co. Ltd., London, Chapter 7.II by Dury,
G.H..
Coleman, J.M. (1969) Brahmaputra River Channel Processes and Sedimentation. Sedimentary Geology, Vol. 3,
pp. 129-239.
De Vriend, H.J. (1977) A Mathematical Model for Steady Flow in Curved Shallow Channels. JHR, IAHR, Vol.
15, pp. 37-54.
Dury, G.H. (1973) Magnitude – Frequency Analysis and Channel Morphology. In Fluvial Geomorphology (Ed.
Morisawa, M.), State University of New York, Binghamton, pp. 91-121.
Eaking, H.M. (1910) The Influence of the Earth’s Rotation upon the Lateral Erosion of Streams. Jour. Geol. Vol.
18, pp. 435-447.
Edgar, D.E. (1973) Geomorphic and Hydraulic Properties of Laboratory Rivers. M.S. Thesis, Colorado State
University, USA, 156 p.
Engelund, F. (1974) Flow and Bed Topography in channel Bends. JHD, Proc. ASCE, Vol. 100, No. HY11, No. pp.
1631-1648.
Engelund, F. and Skovgaard, O. (1973) On the Origin of Meandering and Braiding in Alluvial Streams. JFM, Vol.
57, pp. 289-302.
Fergusson, R.I. (1975) Meandering Irregularity and Wave Length Estimation. Jour. of Hydrology, Vol. 26, pp. 315333.
Fergusson, R.I. (1981) Channel Form and Channel Changes. In British Rivers (Ed. Lewin, J.). Gorge Allen and
Unwin, London, pp. 90-125.
Fredsøe, J. (1978) Meandering and Braiding of Rivers. JFM, Vol. 84, Pt. 4, pp. 609-624.
Friedkin, J.F. (1945) Laboratory Study of the Meandering of Alluvial Rivers. USWES, Vicksburg, Mississippi,
USA, 40p.
Friend, P.F. and Sinha, R. (1993) Braiding and Meandering Parameters. In Braided Rivers (Eds. Best, J.L. and
Bristow, C.S.) Geographical Society Special Publication No. 75, pp. 105-111.
Gandolfo, J.S. (1955) Discussion of Design of Stable Channels by Lane E.W., Trans. ASCE, Vol. 120, pp 12711279.
Garde, R.J., Kumar, A. and Singh, A.K. (2002) Hydraulic Geometry of Straight and Meandering Channels. Proc.
of HYDRO-2002 Conference of ISH on Hydraulic Structures, Water Resources and Ocean Engineering, IIT,
Bombay, pp.15-19.
Garde, R.J. and Ranga Raju, K.G. (2000) Mechanics of Sediment Transportation and Alluvial Stream Problems,
New Age International (P) Ltd., New Delhi.
Gilbert, G.K. (1884) The Sufficiency of Terrestrial Rotation for the Deflection of Streams. Nat. Ac. of Sci. (USA),
Vol. 3.
Gill, M.A. (1968) Discussion of Dominant Discharge of Platte-Missouri Confluence. JWWHD, Proc. ASCE, Vol.
94, No. WW4, pp. 527-529.
Goncharov, G.N. (1962) Dynamics of Channel Flow (Translated from Russian), Israel Program for Scientific
Research and Published by USDI and NSF, USA.
Griggs, R.F. (1906) The Buffalo River : An Interesting Meandering Stream. Bull. Geol. Soc. Am. Vol. 38, No. 3.
Gupta R.D. (1967) Total Sediment Load as a Parameter in the Design of Stable Channels. M.E. Thesis, I.I.T.
Roorkee.
Hayashi, T. (1980) Plan Forms of Alluvial Rivers. Proc. of 1st intl. Workshop on Alluvial River Problems,
Roorkee, pp. 4-1 to 19.
Hydraulic Geometry and Plan Forms of Alluvial Rivers
225
Hayashi, T. and Ozaki, S. (1978) Alluvial Bed Form Analysis I, Formation of Alternating Bars and Braids. Proc. of
US-Japan Bi-national Seminar on Erosion and Sedimentation, Hawaii, Chap. 7-1 to 39.
Hey, R.D. (1982) Design Equations for Mobile Gravel – Bed Rivers. In Gravel-bed Rivers (Eds. Hey, R.D. and
Thorne, C.R) John Wiley and Sons, Chichester, pp. 553-574.
Hey, R.D. and Thorne, C.R. (1986) Stable Channels with Mobile Gravel Beds. JHE, Proc. ASCE, Vol. 112, No. 8,
Aug. pp. 671-689.
Hjulstorm, F.A. (1957) A Study of the Meander Problem. Institute of Hydraulics, Royal Institute of Technology,
Stockholm, Bull. No. 51.
Hong, L.B. and Davies, T.R.H. (1974) A Study of Stream Braiding: A Summary
Inglis, C.C. (1947) Meanders and Their Bearing on River Training. ICE (London), Maritime Paper No. 7, pp. 3-54.
Inglis, C.C. (1949) The Behaviour and Control of Rivers and Canals (With the Aid of Models). Pt. 1, CWINRS,
Research Publication No. 13.
Ippen, A.T. and Drinker, P.A. (1962) Boundary Shear Stresses in Curved Trapezoidal Channels. JHD, Proc.
ASCE, Vol. 88, No. HY5, pp.143-179.
Kellerhals, R., Church, M. and Bray, D.I. (1976) Classification and Analysis of River Processes. JHD, Proc.
ASCE, Vol. 102, No. HY7, July, pp. 813-829.
Kellerhals, R., Neill, C.R. and Bray, D.I. (1972) Hydraulic and Geomorphic Characteristics of Rivers in Canada.
River Engineering and Surface Hydrology. Rep. 72-1, Res. Council of Alberta, Edmonton (Canada).
Kikkawa, H., Ikeda, S. and Kitagawa, A. (1976) Flow and Bed Topography in Curved Open Cannels. JHD, Proc.
ASCE, Vol. 102, No. HY9, September, pp. 1327-1342.
Kinoshita, R. (1957) Formation of Dunes on River Bed – An Observation on the Condition of River Meandering
(In Japanese). Proc. JSCE, No. 42.
Kinoshita, R. (1961) Investigation of Channel Migration of the Ishikari River (In Japanese) Science and
Technology Agency, Bureau of Resources, No. 31, 138 p.
Kishi, T. and Kuroki, M. (1985) Hydraulic Characteristics of Alternating Bars (In Japanese), Hokkaido University,
Hydraulic Laboratory Report.
Komura, S. (1969) Computation of Dominant Discharge. Proc. of 13th Congress of IAHR, Kyoto (Japan), Vol. 5.1,
pp. 265-268.
Kondratev, N.E. (Ed.) River Flow and River Channel Formation (Translated from Russian), Israel Program of
Scientific Translation, Published by USDI and NSF, USA.
Kondap, D.M. (1977) Some Aspects of Flow in Stable Channels. Ph.D. Thesis, University of Roorkee (now I.I.T.
Roorkee)
Kuroki, M. and Kishi, T. (1985) Regime Criteria on Bars and Braids. Hydraulics Papers, Civil and Environmental
Engineering Research Laboratory, Hokkaido University, Sapporo (Japan).
Lacey, G. (1930) Stable Channels in Alluvium. Paper No. 4736, Min. Proc. ICE. (London), Vol. 229, pp. 259-384.
Lane, E.W. (1957) A Study of the Shape of Channels Formed by Natural Streams Flowing in Erodible Material.
US Army Engineer Div., Missouri River, Corps of Engineers, Omaha (Nebraska) USA, MRD Series No. 4,
106 p.
Langbein, W.B. (1964) Geometry of River Channels. JHD, Proc. ASCE, Vol. 90, No. HY2, March, pp. 301-347.
Leliavsky, S. (1955) An Introduction to Fluvial Hydraulics. Constable and Co. Ltd., London, pp. 115-120.
Leopold, L.B. and Langbein, W.B. (1978) Les Meanders des Rivieres. La Bibliotheque “Pour La Science” Les
Phenomenes Naturrels.
Leopold, L.B. and Maddock, T. (1953) The Hydraulic Geometry of Stream Channels and Some Physiographic
Implications. US G.S. Professional Paper 252, 58 p.
226
River Morphology
Leopold, L.B. and Wolman, M.G. (1959) River Channel Patterns : Processes in Geomorphology. W.H. Freeman
and Co., San Francisco (USA).
Leopold, L.B. and Wolman, M.G. (1960) River Meanders, Bull. of Geo. Soc. of America, Vol. 71, pp. 769-794.
Leopold, L.B., Wolman, M.G. and Miller, J.P. (1964) Fluvial Processes in Geomorphology. W.H. Freeman and
Co., San Francisco, (USA).
Lewin, J. (1976) Initiation of Bed Forms and Meanders in Coarse Grained Sediment. Geo. Soc. of America, Bull.
Vol. 87, pp. 281-285.
Miall, A.D. (1977) A Review of the Braided-River Depositional Environment. Earth Science Reviews, Vol. 13,
pp. 1-62.
Mukhamedov, A.M. and Ismaghilov, H.A. (1969) Some Morphological Relationships in the Middle and Lower
Reaches of the Amu Darya. Proc. of 13th Congress of IAHR, Kyoto (Japan), Vol. 5.1, pp. 191-193.
Muramoto, Y. and Fujita, Y. (1977) Study on Meso-Scale River Bed Configuration (In Japanese). Annuals, DPRI,
Kyoto (Japan), No. 20, B-2, pp.243-258.
NEDCO (1959) River Studies in Niger and Benue. North Holland Publication, Holland.
Neill, C.R. (1970) Discussion of formation of Flood Plain Lands by Carrey, W.C., JHD, Proc. ASCE, Vol. 96, No.
HY1, Jan. pp. 297-298.
Neu, H.A. (1967) Transverse Flow of a River Due to Earth’s Rotation. JHD, Proc. ASCE, Vol. 93, No. HY5, Sept.
pp. 149-165.
Nixon, M.A. (1959) A Study of Bankful Discharge of Rivers in England and Wales. Proc. ICE. (London), Paper
No. 6322, Dec., pp. 157-173.
Odgaard, A.J. (1981) Transverse Bed Slope in Alluvial Channel Bends. JHD, Proc. ASCE, Vol. 107, No. HY12,
December, pp.1677-1694.
Odgaard, A.J. (1982) Bed Characteristics in Alluvial Channel Bends. JHD, Proc. ASCE, Vol. 108, No. HY11,
November, pp.1268-1281.
Odgaard, A.J. (1984) Grain Size Distribution of River Bed Armor Layers. JHE, Proc. ASCE, Vol. 110, No. HY9,
September, pp.1267-1272.
Onishi, Y., Jain , S.C. and Kennedy, J.F. (1976) Effects of Meandering in Alluvial Streams. JHD, Proc. ASCE, Vol.
112, No. HY7, September, pp.899-917.
Park, C.C. (1977) World-Wide Variations in Hydraulic Geometry Exponents of Stream Channels: An Analysis and
Some Observations. Jour. of Hydrology, Vol.33, pp.133-146.
Parker, G. (1976) Cause and Characteristic Scales of Meandering, and Braiding in Rivers. JFM Vol. 76, Pt. 3.
Prus-Chacinski, T.M. (1954) Patterns of Motions in Open Channel Bends. Assoc. Intl. d’Hydrologie, Publ. 38,
Vol. 3, pp.311-318.
Quaraishy, M.S. (1944) River Meandering and Earth’s Rotation. Current Science, Vol. 13, October, pp.36-39.
Rachocki, A. (1981) Alluvial Fans: An Attempt at an Empirical Approach. Wiley Interscience Publication, John
Wiley and Sons Inc., (USA).
Ramette, M. (1980) A Theoretical Approach on Fluvial Processes. 1st Intl. Symposium on River Sedimentation,
Beijing (China), C16- 1 to 18.
Reynolds, A.J. (1965) Waves on the Erodible Bed of an Open Channel. JFM, Vol. 22, Pt. 1, pp. 113-133.
Rhodes, C.C. (1977) The b-f-m Diagram: Graphical Representation and Interpretation of at a Station Hydraulic
Geometry. Am. Jour. Sci. Vol. 277, pp. 73-96.
Rhodes, C.C. (1987) The b-f-m Diagram for Downstream Hydraulic Geometry. Geografisca Annaler, Series A,
69A (1), pp. 147-161.
Hydraulic Geometry and Plan Forms of Alluvial Rivers
227
Riggs, H.C. (1976) A Simplified Slope-Area Method for Estimating Flood Discharges in Natural Channels.
USGS, J. Res., Vol. 4, pp. 285-291.
Rozovskii, J.L. (1957) Flow of Water in Bends of Open Channels. Academy of Sciences of the Ukrainian SSR,
Kiev, 233 p. (Translated from Russian by NSF, Washington D.C.), 233 p.
Rundquist, L.A. (1975) A Classification and Analysis of Natural Rivers. Ph.D. Thesis, Colorado State University,
Fort Collins, USA, 377 p.
Rubey, W.W. (1933) Equilibrium Conditions in Debris Laden Streams. Trans. AGU, pp. 497-505.
Schaffernak, F. (1950) Flussmorphologie und Flussbau. Springer Verlag, Vienna.
Schoklitsch, A. (1937) Hydraulic Structures, Vol. 1, Am. Soc. Mech. Engineers, 504 p.
Schumm, S.A. (1969) River Metamorphosis. JHD, Proc. ASCE, Vol. 45, No. HY1, January, pp. 255-273.
Schumm, S.A. (1977) The Fluvial System. John Wiley and Sons. A Wiley Interscience Publication, New York,
Chapter V, pp. 106-111.
Shen, H.W. (1983) Keynote Examination of Present Knowledge of River Meandering. River Meandering – Proc.
of the Conference Rivers-83, ASCE, New York, USA, pp. 1008-1013.
Shukry, A. (1950) Flow Around Bends in an Open Flume. Trans. ASCE, Vol. 115, paper No. 2411, pp. 751-779.
Simons, D.B. (1957) Theory and Design of Stable Channels in Alluvial Material. Ph.D. Thesis. Colorado State
University, Fort Collins, USA.
Simons, D.B. and Albertson, M.L. (1963) Uniform Water Conveyance Channels in Alluvial Material. Trans.
ASCE, Vol. 128, Pt. 1, pp. 65-107.
Smith, T.R. (1974) A Derivation of Hydraulic Geometry of Steady State Channels form Conservations Principles
and Sediment Transport Laws. Jour. of Geology, Geological Notes, Univ. of Chicago, Vol. 82, pp. 98-104
Speight, J.G. (1965) Meander Spectra of the Anabunga River. Jour. of Hydrology, Vol. 3, pp. 1-15.
Sukegawa, N. (1970) On the Formation of Alternate Bars in Straight – Alluvial Channels. Trans. JSCE, Vol. 2, pp.
259-261.
Sukegawa, N. (1971) Conditions for Occurrence of River Meanders (In Japanese), Proc. JSCE, Vol. 2, Pt. 2.
Sukegawa, N. (1972) Criterion for Alternate Bars Formation. Memoirs of the School of Science and Engineering,
No. 36, Waseda University (Japan), pp.77-84.
Tamai, N., Nagao, T. and Mikuni, N. (1978) On Large Scale Bar Patterns in a Straight Channel (In Japanese), Proc.
22nd Japanese Conference on Hydraulics. .
Tobes, G.H. and Chang, T.P. (1967) Plan-Form Analysis of Meandering Rivers. Proc. of 12th Congress of IAHR,
Vol. 1, pp. 362-369.
Wallis, I.G. (1973) On the Development of River Meanders. Part I: Laboratory Experiments, Monash University,
Geophysical Fluid Dynamics Lab. Paper No. 57, 28 p.
Werner, P.W. (1951) On the Origin of River Meanders. Trans. AGU, Vol. 32, pp.898-902.
Wharton, G. (1995) Information from Channel Geometry – Discharge Relations. In Changing Rivers (Eds.
Grunnell, A. and Petts G.), John Wiley and Sons, Chicester, pp. 325-346.
White, W.R., Paris, W.E. and Bettess, R. (1981) River Regime Based on Sediment Transport Concept. Rep. No. JJ
201, Hydraulic Research Station, Wallingford, U.K.
Williams, G.P. (1978) Bankful Discharge of Rivers. W.R. Research, Vol. 14, No. 6, December, pp. 1141-1154.
Wolamn, M.G. and Leopold, L.B. (1957) River Flood Plains : Some Observations on Their Formation. USGS
Professional Paper, 282-C.
Woodyer, K.D. and Flemming, P.M. (1968) Reconnaissance Estimation of Stream Discharge Frequency
Relationships. In Land Evaluation (Ed. Stewart, G.A.) Macmillan of Australia, pp. 287-298.
228
River Morphology
Yang, C.T. (1971) On River Meanders. Jour. of Hydrology, Vol. 13, pp. 231-253.
Yang, C.T. (1976) Minimum Unit Stream Power and Fluvial Hydraulics, JHD, Proc. ASCE, Vol. 102, No. HY7,
July, pp. 919-934.
Zimmermann, C. (1977) Roughness Effects on Flow Direction Near Curved Stream Beds. JHR, IAHR, vol. 15,
No. 1, pp. 73-85.
Zimmermann, C. and Kennedy, J.F. (1978) Transverse Bed Slope in Curved Alluvial Streams. JHD, Proc. ASCE,
Vol. 104, No. HY1, Jan.. pp. 33-48.
Zimpfer, G.L. (1975) Development of Laboratory River Channels. M.S. Thesis, Colorado State University, Fort
Collins, USA, 111 p.
C H A P T E R
7
Gravel-Bed Rivers
7.1
INTRODUCTION
Gravel and boulder-bed rivers are those rivers that flow through predominantly gravelly and bouldery
materials respectively. Bathurst characterizes boulder rivers as those rivers in which the width is an
order of the magnitude greater than the median size of the bed material, the depth is of the order of
magnitude of the bed material size, and the slope is unlikely to exceed 0.05. Not much is known about
boulder rivers, even though some studies have been conducted about their resistance characteristics.
However, the last three decades have seen significant research activity on gravel-bed rivers.
Gravel-bed rivers differ from the commonly encountered sand bed rivers in many respects. Gravelbed rivers flow through much coarser material having a much wider spectrum of sediment sizes–from
cobbles to fine sand–than sand bed rivers. Their slopes are much steeper (0.001 to 0.05 or even larger)
than those of sand bed rivers. In sand bed rivers all the fractions of bed material move for most of the
discharges except the very small ones; however in gravel-bed rivers all the fractions of bed material
move only at a few flows in a year. During the rest of the time sediment transport takes place over the
pavement (see below). The other difference pertains to the bed forms. Unlike in sand-bed rivers, ripples
and dunes do not form in gravel-bed rivers; instead large bed features known as bars, transverse and
diagonal bars, riffles and pools, and transverse ribs of coarse material are common features in gravelbed rivers. These bed features not only offer resistance to flow but also act as sediment storage spaces.
Further, since the slope of gravel-bed rivers varies over a wide range, the Froude number U/ gD for the
gravel-bed rivers can be less than unity to greater than unity.
As regards the plan form, sand-bed rivers are either meandering, transitional or braiding and they
may change from one plan-form to another dramatically as the discharge changes. Gravel-bed rivers
have a much greater tendency to be transitional or braided. For cobble and boulder rivers it is rare to find
reaches that meander significantly. In other words, it is rather easy to define talweg for sand bed streams;
yet for cobble and boulder rivers it is impossible to define its location.
230
River Morphology
Since upland areas supply sediment to the river systems, gravel-bed rivers are closer to the sediment
source. Because the sediment supply events, such as landslides are discontinuous, the sediment
transport in gravel-bed rivers shows greater variability than the sediment transport in sand-bed rivers. In
fact, sediment transport in gravel-bed rivers can be unsteady and non-uniform even for steady water
discharge. Depending on the supply of sediment to the channel, there may be two orders of magnitude of
variation in sediment transport rate for a given discharge. This does not happen in sand-bed rivers.
Lastly, it is found that gravel-bed rivers are more stable than sand-bed rivers. Hence rapid and large bed
level variations that often occur in sand-bed rivers do not occur in gravel-bed rivers.
The study of gravel-bed rivers poses some complexities that should be mentioned. The first relates
to the size distribution of the bed material. Since the bed material size varies from cobbles to fine sand,
different methods should be used to analyse different size fractions. Also, with such wide variation in
the bed material size, difficulty is experienced in choosing the characteristic size of the bed material for
studies related to resistance, sediment transport and hydraulic geometry. Further complexities are
caused by the formation of the pavement and its destruction that affect the size distribution of the
transported material which also causes a sudden increase in the transport rate once the pavement is
destroyed.
7.2
DATA FOR GRAVEL-BED RIVERS
Several studies have been conducted on gravel-bed rivers in U.S.A., U.K., New Zealand, Canada, Italy
and other European countries and these data are available in literature. These data pertain to the
hydraulic geometry and resistance to flow either at bankful discharge or other discharges. In many cases
the size distribution of bed material and information on whether the bed was mobile or paved has been
given. Data collected by Leopold and Wolman (1957) for many American rivers, Kellerhals (1967) for
some rivers in British Columbia, and Bray (1979) for rivers in Alberta (Canada), are useful for the study
of hydraulic geometry of rivers at bankful discharge. Data useful for resistance analysis of mobile and
paved bed at variable discharge are given by Samide (1971) for the north Saskatchewan and Elbow
rivers in Canada, Milhaus (1973) for the Oak Creek in U.S.A., Griffiths (1981) for the rivers in New
Zealand, Thorne and Zevenbergen (1985) on the Boulder Creek in Colorado, U.S.A., Michalik (1989)
on the Wisloka and the Dunajee rivers in Poland, Colosimo, Copertino and Veltri (1988) for gravel
rivers in Italy, and by Gladky (1979), Church and Rook (1983) and Hey and Thorne (1986, 1988). These
data have been tabulated by Garde et al. (1998).
Field data on bed-load transport in gravel-bed rivers have been mentioned by Bathurst (1987).
These are for the rivers Pitzbach in Austria, Elbow in Alberta (Canada), Clearwater in Idaho, Snake in
Idaho, Oak Creek in Oregon, Slate in Idaho and Tanana in Alaska, all in the U.S.A. and Aare in
Switzerland. The median size of the surface material for these rivers varied from 12 mm to 260 mm
while the water discharge varied from 3.0 m3/s to 1680.0 m3/s.
7.3
BED MATERIAL
The sampling of the surface of gravel-bed rivers is usually carried out by one of the following methods:
1. Grid or Transect Sampling: Wolman (1954) has proposed grid sampling. In this method a grid
is established over the surface and particles immediately below the grid points are sampled. In
transect sampling all the particles lying along the predetermined line are collected and
analysed.
231
Gravel-Bed Rivers
2. Areal Sampling: All the particles exposed within a predetermined area are sampled. This
method was used by Lane and Carlson (1953).
3. Volumetric Sampling of the Surface Area: In this method the sample is acquired either by the
photographic method proposed by Adams (1979), or by removing particles from this area by
using adhesive or grease.
In order to see if d50 of the gravel-bed rivers can be predicted, it was plotted against slope S. In spite
of the scatter it was found that (see Garde et al. 1998) an equation of the form
d50 = 882.5 S 0.492
...(7.1)
can be fitted through the data; here d50 is in mm. The large scatter is attributed to the fact that the data
used are from diverse lithological environments and also there is a large variation in the dominant
discharge.
It has been reported that gravel-bed materials exhibit bimodality. There usually is a lack of particles
in the range 1 mm to 8 mm. The reasons advanced to explain these characteristics include catchment
geology, mixing of sediments transported in two different modes viz. traction and suspension,
restriction in sediment sizes supplied by the source area and abrasion and sorting during the transport.
Odgaard (1984a) found that the size distribution of surface layer particles follows normal distribution.
Analysis of size distribution data for bed materials of gravel-bed rivers has indicated that the size
distribution neither follows normal nor long normal distribution over the entire range of sizes in the
sample.
Fig. 7.1 Variation of d /d50 with percent finer for gravel-bed river materials
Figure 7.1 shows the size distribution plotted as d/d50 versus percent finer on normal probability
paper. It can be seen that the average curve passes through d50/d16 = 2.88 and d84/d50 = 2.121. Further,
even though there is considerable scatter in the magnitude of d99.9/d50, (from 6 to over 10), its average
magnitude can be taken as 8.2. The mean curve passing through these points on the normal probability
paper can be represented by the straight line using the transformation:
232
River Morphology
dt /d 50 = {(d/d50) l – 1}/l
...(7.2)
where l is the parameter to be determined by trial and error, such that the transformed distribution is
gaussian. The value of l was found to be 0.40. This value along with the known median size will give
the size distribution when the above equation is used.
It is also interesting to know how the geometric standard deviation for bed material of gravel-bed
rivers varies with d50. Earlier studies of bed materials of sand-bed rivers by Garde (1972) and Kothyari
(1994) indicate that the geometric standard deviation sg increases as d50 increases and follows the
equation
sg = 1.4 d 500.34
...(7.3)
where d50 is in mm and sg = 1/2 ( d84/d50 + d50/d16 ). This is based on data for d50 varying from 0.14 mm
to 17 mm. Kothyari also analysed the data with d50 varying from 0.15 mm to 37 mm. Figure 7.2 shows
the variation of sg with d50 for sandy and gravelly bed materials. It can be seen that for gravelly-bed
materials, sg decreases with increase in d50. Since in general d50/d16 and d84/d50 have different values,
variation of d50 /d16 and d84 /d50 with d50 was studied by Garde et al. (1998). It was found that for gravelbed materials d84/d50 is nearly constant; however d50/d16 decreases with increase in d50. As a result
sg =
1
2
FG d
Hd
50
16
+
d84
d50
IJ decreases as d
K
50
increases.
Fig. 7.2 Variation of sg with d50 for sandy and gravelly bed materials
As regard the size distribution of river bed sediments it may be mentioned that Moss (1962, 1963)
has shown that the river bed sediments are deposited as composites and are made up of three
populations, each of which is related to a specific sediment process. Vischer (1969) found each of these
three sub-populations to follow log-normal distribution. Since these three populations would be mixed
in different proportions, it is very unlikely that the river bed material samples as a whole would follow
log-normal distribution.
233
Gravel-Bed Rivers
7.4
PAVEMENT
River beds composed of heterogeneous mixtures of gravel and smaller particles form a surface layer
with thickness of the size of coarse particles. Bray and Church (1980), and Andrews and Parker (1987)
have explained the distinction between armouring and paving. If there is no sediment supply from the
upstream as in the case of downstream of large capacity dams, the bed surface will get progressively
coarser and eventually become immobile for all discharges less than the maximum sustained flow. If
higher flow occurs, the bed particles will be entrained, the bed will degrade further and the bed surface
will become somewhat coarser. Such conditions occur downstream of dam and the immobile bed is
considered to be armored.
The coarse surface layer in gravel-bed rivers, known as the pavement, is maintained by successive
periods of bed-load transport during which essentially all sizes move. This sediment is supplied from the
upstream side and hence the channel remains in equilibrium. The particles on the bed are transported
frequently within a span of several years. In this process, even if occasionally a few coarse particles on
the bed move, it does not affect the stability of the pavement and hence there are no general motions.
Thus pavement is present in gravel-bed rivers even while most available sizes are transported. Studies
by Harrison (1950) and Andrews and Parker (1987) have indicated equal mobility of all particle sizes
present in the sub-pavement material; that is the ratio of transport rate of a given size fraction to its
percentage abundance in the sub-pavement material is approximately constant for all sizes. This has
been confirmed by the data on the East Fork, the Snake and the Clear Water rivers all in USA. If equal
mobility is to be achieved with respect to the subsurface material, the surface layer must be considerably
coarser than either the subsurface material or the bed-load. The bed-load and the subsurface size
distributions are approximately equal because the lesser mobility of coarser size fractions is
counterbalanced by their abundance in surface. Field experience has indicated that for gravel-bed rivers,
the ratio of median size of the pavement to that of the sub-pavement material ranges from 2.0 to 6.0 with
an average value of 2.71. Neill (1968) has suggested the value of toc/D gs d50 = 0.03 constitutes the
criterion for braking of the pavement; here d50 is the median size of the pavement. If d50 of the subpavement is used, the corresponding criterion will be toc/D gs d50 = 0.081 since d50 of the pavement is
equal to 2.71 times d50 of the pavement.
7.5
HYDRAULIC GEOMETRY
The average width or perimeter, depth of flow or the hydraulic radius, flow area at the bankful
discharge, and the slope, describe the hydraulic geometry of the rivers. The knowledge of hydraulic
geometry is needed for the study of problems related to river training, location of bridges and barrages
and for navigation. The hydraulic geometry of alluvial rivers and channels has been studied by Lacey
(1930), Inglis (1947), Leopold and Maddock (1953) and others. They have related the perimeter P or
width W, depth D or hydraulic radius R and the area A to the dominant discharge Q and in some case d50
or silt factor f1. It is found that
P or W ~ Q0.50
D or R ~ Q0.33
A ~ Q0.8
U|
V|
W
...(7.4)
234
River Morphology
approximately. Langbein (1964) has applied the principle of minimum expenditure of power per unit of
the bed area, and minimum work rate in the whole river system to obtain the parameters of hydraulic
geometry and found that W ~ Q0.53, D ~ Q0.37, U ~ Q0.10 and S ~ Q – 0.73. Considering the channel to be in
an unstable state, Knighton (1977) studied whether development of the channel to a new state
represented an attempt by the system to approach some form of dynamic equilibrium. His analysis led to
the condition that
b2 + f 2 + m2 ® minimum
W ~ Q b, D ~ Q f and U ~ Q m
where
The hydraulic geometry of gravel-bed rivers has been studied by Kellerhals (1967), Bhowmik
(1968), Charlton (1977), Parker (1979), Bray (1982) and Hey (1982). While Kellerhals, Bhowmik,
Charlton and Bray have related W, D and U to the bankful discharge Q and median sediment size, Parker
has used the functional relationship:
W/d, D/d, S, U
F
GH
Dgs d
= F Q/ d 2
rf
Dgs d
rf
I
JK
thus taking the slope as independent variable. If Q1 = Q/d2
equations:
W/d = 4.400 Q10.50
D/d = 0.253 Q10.415
S = 0.223
Q1–0.41
U
= 0.898 Q10.616
Dgs d
rf
U|
||
V|
||
W
...(7.5)
Dgs d
, he obtained the following
rf
...( 7.6)
In general, these studies have shown that the geometric parameters strongly depend on Q whereas d
occurs to a very small power. Recently Garde et al. (1998) have analyzed the available gravel-bed river
data with paved as well as mobile bed conditions and studied the hydraulic geometry at bankful
discharge. The first question that they wanted to answer was whether the slope can be taken as
dependent or independent variable. On any given river the slope decreases in the downstream direction
as Q increases and d decreases in the downstream direction. When all the available data were plotted as
S vs Q, even though S decreased as Q increased, there was considerable scatter which is believed to be
due to the difference in terrain, length of river, lithology and bankful discharge, see Fig. 7.3.
Interpreting the scatter on Fig. 7.3 as implying that S should be taken as an independent variable
along with Q and d, Garde et al. (1998) used the functional relationship:
235
Gravel-Bed Rivers
Fig. 7.3 Variation of slope with bankful discharge for gravel-bed rivers
W, D, A = F (Q, d, D gs, rf and S)
...(7.7)
The viscosity was not considered since we are dealing with very coarse material. As a first
approximation the geometric standard deviation sg of bed material was also not considered. Using
dimensional analysis the following alternative functional relations were obtained for the study of
geometry of gravel-bed rivers.
W, D, A, = f (Q)
(a)
F
GH
F QS / d
GH
F Q/ d
GH
2
W/d, D/d, A/d = F2
W/d, D/d, A/d 2 = F3
2
I
JK
Dg d I
, J = F (Q )
r
K
I
Dg
d S J = F (Q )
r
K
Dgs d
, S = F1 (Q1, S)
rf
W/d, D/d, A/d 2 = F1 Q / d 2
2
(b)
s
2
(c)
2
f
s
3
(d)
3
f
U|
||
||
V|
||
||
W
...(7.8)
Hence
Q1 = Q/d 2
Dgs
d, Q2 = QS
rf
F D g I d and Q = Q/d F D g I dS
GH r JK
GH r JK
2
s
s
3
f
f
236
River Morphology
Using 140 data points for both paved and mobile bed at the bankful discharge, the following
equations were obtained. It may be mentioned that the data for paved and mobile bed intermingled and
hence the relationships valid for both the cases were developed using Eq. (7.8). It was found that
relationships involving Eq. (7.8 (a)) and (7.8 (b)) gave the same accuracy and were more accurate than
Eq. (7.8 (c)). Further relationships involving Eq. (7.8 (d)) were most accurate. Below are given
equations corresponding to Eq. (7.8 (b)) and (7.8 (d)) and are recommended for use since they are
dimensionally homogeneous.
W/d = 7.675Q10.448
D/d = 0.504Q10.373
A/d2 = 3.872Q10.821
W/d = 3.872Q30.396
D/d = 0.308Q30.330
A/d2 = 1.108Q30.726
U|
|V
||
W
U|
|V
||
W
...(7.8 b)
...(7.8 d)
It may be mentioned that Q2 = QS/ D g s d / r f can be interpreted as the dimensionless stream
power. The parameter Q3 where slope occurs in the denominator has been used in Russia to study the
hydraulic geometry. Further, equations involving Q3 viz. Eq. (7.8 (d)) give smaller errors than the
equations involving Q alone or Q1, and in addition the former are dimensionless while the latter
involving Q are in dimensional form. Hence, it is recommended that Eq. (7.8 (d)) be used for predicting
W, D and A for gravel-bed rivers. For the data used, these equations predicted W, D and A within ±, 30
percent error for 58%, 85% and 71% of the data respectively. Variation of W/d, D/d and A/d2 with Q3 are
shown in Figs. 7.4, 7.5 and 7.6 respectively.
Fig. 7.4 Variation of W/d with Q3
237
Gravel-Bed Rivers
Fig. 7.5 Variation of D/d with Q3
Fig. 7.6 Variation of A/d 2 with Q3
7.6
BED FEATURES IN GRAVEL-BED RIVERS
As mentioned in the introduction to this chapter ripples and dunes commonly observed in sand bed
rivers, do not form in gravel-bed rivers. Instead large scale sedimentary accumulations called bars are
present in gravel-bed streams. They represent major storage spaces for bed-load sediment that is moved
once in a while and also offer resistance to flow. Taking clue from Jackson II (1975) bed features can be
classified in the following manner.
238
River Morphology
The micro and meso forms in the form of ripples and dunes are rather rare in gravel-bed rivers.
Antidunes have been found to occur at steep slopes. Hence as regards the gravel-bed rivers, one is
interested in sedimentary accumulations whose scale is channel width or greater. These are loosely
called bars. Their height is comparable with the depth of flow. Bars persist for a long time and are
radically modified only during high floods. Bars fall in the category of macro and mega forms.
Table 7.1 Classification of bed features (Jackson 1975, Church and Jones 1987)
Class
System scale
Typical wave length
–2
0
Time scale
Features
Remarks
Microforms
d
10
to 10 m
<< tc
Ripples, lineation
Absent in gravelbed rivers
Mesoforms
D
100 to 102 m
~ tc
Dunes
Rare in gravel-bed
rivers. Probably
absent if d > 0.1 D
Macroforms
W
101 to 103 m
> = tc
Antidunes, unit
bars, channel bars
Uncommon, of
gravel-ribs
Megaforms
³=l
> 103 m
Regime time
Bar assemblages
A large variety of
sedimentation
zones.
tc = time for the flood wave to pass through the reach
l = wavelength of bed-forms
When in a portion of the channel carrying sediment the shear stress is reduced, the bed-load being
transported deposits and forms a bar. Hence bars occur at the apex of the channel bends along the
convex bank, places where the channel widens, at the junctions and at flow divergence. According to
Church and Jones (1987), if D is less than 3d bars will not occur. Further if t* is to be greater than 0.05
g f DS
D g f d90
= 0.05 and if D gs /gf = 1.65, S @ 0.08
d90
D
Substituting d90 /D = 0.30 one gets S = 0.025.
Hence the upper limit of the slope for the bar formation is about S = 0.05 after which the sediment
would be washed off. Smith (1978) has identified five unit bar features, these are:
1. Longitudinal or spool bars: These are formed in the centre of the channel at a relatively wider
section. These are convex and elongated and they grow by upstream deposition of coarse
material and downward deposition of finer material. Crescent bar is its early form.
2. Transverse bars: These tend to form at an abrupt channel expansion. They have lobate front
and an upstream ramp.
3. Point bar: Point bars occur near the convex bank of a curved channel. In gravel-bed rivers point
bars often possess a steep outer face and a chute or secondary channel between it and the shore.
4. Diagonal bars: These are oriented obliquely across the channel and are attached to both the
banks. The upstream side is usually anchored at the concave bank. There is an upstream ramp
and there may be an avalanche face on the downstream front. Bars that are attached to the banks
tend to be more stable than those that are detached.
239
Gravel-Bed Rivers
5. Alternate bars: These bars form on alternate sides of the channel and talweg meanders between
them. Pools form opposite the bars while riffles form at the cross over point between bars.
Alternate bars are a feature of straight channels. Since alternate bars are a three dimensional
phenomenon, their formation is related in part to the channel width.
Twice the pool to pool spacing l = aW where the constant a is found to vary between 4 and 17 with
an average of 10. According to Chang et al.
lS
= 3 Fr2
D
...( 7.9)
According to Ikeda (1984)
l
0.55
W = 22.6 f (W/D)
H
= 0.189 f (W/D)1.455
...(7.10)
D
where H = bar height and f is Darcy-Weisbach friction factor. Different bars are shown in Fig. 7.7.
and
Point bar
Longitudinal bar
Transverse bar
Point bar
Meandering talweg
Diagonal bar
Alternate bar
Fig. 7.7
Different bars
Another bed feature occurring in gravel-bed rivers and which is important from the point of view of
resistance is riffle-pool sequence. Riffle primarily represents a hydraulic resistance element and may
store little or no transient material. Riffles seem to develop by selective scour and deposition along the
240
River Morphology
Fig. 7.8 Riffle-pool sequence
channel and are formed in gravel-bed rivers when their slope is less than 0.05. These are diagonal riffles.
Material eroded from the convergence of flow towards one bank is deposited in the “cross-over zone”,
where the flow diverges and the main current moves from one bank to another. Such erosion and
deposition cause riffle and pool sequence shown in Fig. 7.8.
The sediment texture strongly affects the character and relative stability of pool-riffle sequences.
When the river bed material is widely graded, the largest sizes are moved more rarely than the remaining
material; this is deposited on the riffle. This material on the riffle which induces deposition of more
material, which increases the stability of riffle for long periods between the floods. When the bed
sediments are narrowly graded, all the material is moved relatively frequently and riffles as such do not
form. Riffles are then merely leading edge of sediment storage bar. Analysis of data has indicated that:
pool to pool distance = (5 to 7) times channel width. Keller and Melhorn (1973) found that
Pool to pool distance l = 5.42 W1.01 in SI units.
The channel width is also found to vary between pools and riffles. Generally riffles are wider than
the neighbouring pools as a result of flow divergence causing bank erosion. Pool and riffle sequences
are generally very stable and in some cases found to be stationary and moving downstream at a speed of
only 150–500 m/yr. Parker has given a stability analysis leading to the development of pool-riffle
sequences. Theories of pool–riffle sequences are summarized by Richards (1982) and Langbein and
Leopold (1968). The latter have proposed a kinematic wave model in which sediment particles move in
groups along the channel. Richards suggests that the generation of turbulent eddies cause alternate
acceleration and deceleration of the flow which is responsible for their formation.
Transverse ribs: Transverse ribs are a set of regularly spaced cobble or gravel ridges oriented
transverse to the flow and are found on riffles and steep slopes. Ribs comprise the coarsest sediment
particles in the channel while finer material is exposed between the ribs. Maximum flow depth in the
ribbed reaches is about twice the size of largest median axis of the sediment. The bed material size and
channel slope are the two primary factors which determine the rib spacing. Most studies indicated that
ribs are upper flow regime bed forms.
According to Koster (1978):
241
Gravel-Bed Rivers
Mean rib width
W = 0.47 l
dmax = m l
UV
W
...(7.11)
where l is the mean rib wave length and m = 0.075 to 0.165.
7.7
RESISTANCE TO FLOW IN GRAVEL-BED RIVERS
The resistance relationship is the relationship between average velocity U in the channel, depth D or
hydraulic radius R, channel slope S and the coefficient dependent on the resistance offered by the
channel boundary. If the flow is steady and uniform S is the channel slope; however for unsteady, nonuniform flow S should be the slope of the energy line. Three most often used equations for U are those
of Manning, Chezy, and Darcy-Weisbach.
Equating the relationships for U, the following relationships obtained between n, C and f.
U
C
1 R1 / 6
=
=
=
gRS
g
n g
8
f
...(7.12)
where gRS = u* the shear velocity. The objective of this discussion is to obtain predictors for n, f and
C. For gravel-bed rivers n is found to vary from 0.02 to 0.2, and f from 0.01 to 0.5. For boulder rivers
these values will be still higher.
When considered in the above form n, f and C will include the frictional resistance of the bed and
sides, form roughness due to bed deformation, changes in cross sectional shapes, wave resistance due to
surface waves and form resistance due to changes in channel profile in plan. Since the flow in gravelbed rivers takes place over very coarse surface material, the boundary would act as hydrodynamically
rough; as a result Reynolds number in the form of UR/v or u* d/v will not affect resistance. Further, most
of the data available for gravel-bed rivers have width/depth ratio between 10 and 100. Hence, bank
resistance can be safely neglected and depth D used in place of R in the resistance relationships. It has
already been pointed out that conventional ripples and dunes whose character changes with the flow do
not form in gravel-bed rivers; various bars or bed features that occur in gravel-bed rivers have been
discussed earlier. Bars have a close relation with channel shape in plan and these are fairly stable being
radically modified only during high floods. Therefore, it seems more logical not to consider their effect
on resistance separately and include it in the overall resistance coefficient. However, it may be
mentioned that some investigators e.g., Hey (1988) have studied the bar resistance separately.
As regards the characteristic size of bed material Ks to be used, there is considerable discussion in
the literature; various sizes such as d35, d50, d65 and d90 have been used and then the effect of nonuniformity is neglected. The recommendations of some of the investigators are listed below (see Van
Rijn 1982)
Ackers and White
Einstein
Engeland and Hansen
Hey
Mahmood
Kamphus
Ks = 1.35 d35
Ks = 1.00 d65
Ks = 2.00 d65
Ks = 3.50 d84
Ks = 5.10 d84
Ks = 2.50 d90
242
River Morphology
Van Rijn (1982) after analyzing 120 data points from flume and field studies for the plane bed
condition and with width/depth ratio greater than five, found that Ks/d90 varied from a very small value
to almost 12 as (to – tc)/Dgs d50 varied over a wide range, but there was no correlation between the two.
The average value of Ks/d90 was three. Since in many data sets the size distribution is not given and only
median size is known it is preferable to use d50 in the expression for Ks which is done here.
Lastly some investigators such as Colosimo et al. (1988) have recognized that when Froude number
U/ g D is greater than 1.65 the flow in the open channel becomes unstable and hence resistance
coefficient f should be related Fr, in addition to the relative roughness. Further if t*/t*c is greater than
unity, f should also depend on this parameter. Thus according to them
FG IJ
H K
1
bD
= a log
+ f1 (Fr) + f2 (t*/t*c)
ks
f
Here t* = to /Dgs d50 and t*c = toc /Dgs d50 Alternatively the expression for velocity can be written in
most general dimensional form as
FG IJ
H K
U
U
= const
d50
gD
x
Sy or U/ gd50 S = const (D/d50)x }
...(7.13)
and the constants x and y are determined from the analysis of field data.
Results of The Analysis
As mentioned earlier Garde et al. (1998) have analyzed a large volume of data in gravel-bed rivers for
the prediction of resistance to flow. Their results are briefly discussed below.
Resistance at bankful discharge
Since the shear stress acting on the bed depends on the stream slope, some investigators e.g. Golubstov
(1969) and Bray (1979) have related Manning’s n to S. In general n increases with increase in S. For
paved as well as mobile bed data at bankful discharge the equation obtained is:
n = 0.168 S0.245
...(7.14)
However, the mobile bed data scattered more than the paved bed data. The exponent of S obtained
by Bray was 0.177 while Golubstov obtained the value of 0.33. Because of large scatter around the mean
line, the above equation is not recommended for use.
Since according to Strickler (n/d)1/6 = constant, one can plot (n/d) 1/6 vs D/d. When this was done
the following relation was obtained.
n/d1/6 = 0.092
F DI
H dK
- 0.135
...(7.15)
Here d is d50. However the variation of (n/d)1/6 with D/d being weak one can approximate the above
equation by
243
Gravel-Bed Rivers
Fig. 7.9 Variation of D1/6/n with D/d50
(n/d)1/6 = 0.073 for D/d values between 2 and 200. Equation (7.15) shows that
FG d IJ = 0.092F DI
H dK
HD K
16
(n d 1 6 )
- 0 .135
16
F DI
HdK
- 0 .166
or
F I
H K
D1 6
D
=F
n
d
This type of relationship in the form of log-law was suggested by Limerinos (1970). The data gave
the equation (see Fig. 7.9)
FG IJ + 12
H K
D
D1 / 6
= 14.05 log
d50
n
whereas using d84 in place of d50 the values of coefficient of log
...(7.16)
F D I and constant obtained by
H dK
Limerinos were 10.27 and 17.7 while Bray (1979) obtained the values 9.66 and 19.50 respectively. This
equation gives reasonably good predictions of n at the bankful discharge. Among the equations using
Darcy-Weisbach friction factor f, the following equation:
F I
GH JK
1
D
= 1.229
d50
f
0 .302
...(7.17)
D
d50
can be obtained. Alam’s analysis has suggested this type of relationship. This relationship obtained for
the data is (see Fig. 7.10)
was found to be satisfactory. Lastly at bankful discharge the relationship between U
FG IJ
H K
U
D
= 3.475
d50
gd50 S
gd50 S and
0 .802
...(7.18)
244
River Morphology
Fig. 7.10 Variation of U
gd 50S with
D
for bankful discharge
d 50
Resistance at varying discharge
Here also preliminary analysis indicated that for any resistance analysis, mobile bed and paved bed data
intermingle and hence all data are treated together including those at bankful discharge. The variation of
FG n IJ
Hd K
1/ 6
with
50
D
gave the equation:
d50
FG n IJ
Hd K
1/ 6
50
= 0.0702
FG D IJ
Hd K
- 0.011
...(7.19)
50
However considering the very small value of the exponent of
F D I and the relatively large scatter,
GH d JK
50
it is recommended that
FnI
GH d JK
1/ 6
= 0.08 is a good approximation. Limerinos type equations obtained for
50
all the data is:
F I + 15.41
GH JK
D
D1 / 6
= 9.132 log
d50
n
...(7.20)
245
Gravel-Bed Rivers
Other best fit results for f are:
FG IJ
H K
F D I + 1.74
= 1.031 log G
H d JK
1
D
= 1.557
d50
f
1
f
and
0 .183
...(7.21)
...(7.22)
50
The other two equations for U which are obtained by optimizing the values of exponents of
F DI
GH d JK
50
and S so that the error in the prediction of U is minimum are
FG IJ
H K
F D IJ
= 2.586 G
Hd K
U
D
= 4.403
d
gd50 S
50
and
U
g d50
0.639
...(7.23)
0.631
S0.372
...(7.24)
50
see Fig. 7.11. It is recommended that if the conditions at the bankful stage are to be predicted, one should
use the equations specifically obtained from bankful discharge data.
Fig. 7.11
Variation of
U
g d 50 S
with
F DI
GH d JK
50
for variable discharge
246
River Morphology
Universal stage discharge relation
While discussing about resistance to flow, on which the stage discharge relation depends, it is
worthwhile to mention about Grishanin’s (1967) work. Through dimensional reasoning he has shown
that, as an approximation
a f
D gW
Q
0 .25
remains constant. For 25 sites on 21 rivers in plains, he selected
three discharges on each site namely smallest, largest and close to the mean discharge. It was found that
for these data:
a f
D gW
0 .25
= 0.904
Q
...(7.25)
with the standard deviation of 0.158. For gravel-bed river data it is found that
of
FG D IJ and the relationship between the two is:
Hd K
F D IJ
D ag W f
= 0.459 G
Q
Hd K
a f
D gW
Q
0.25
is a function
50
0.117
0 .25
...(7.26)
50
so that one gets the relationship of depth D as
D = 0.459 (g W)0.25 Q
FG D IJ
Hd K
0 .117
...(7.27)
50
or
Q = 14.863 W0.50 D1.766 d500.234
...(7.28)
It should be noted that the above equation does not involve slope. Hence at best it will be an
approximate relationship.
7.8
SEDIMENT TRANSPORT IN GRAVEL-BED RIVERS
In sand bed rivers relatively large amount of sediment is transported as suspended load. However, in
gravel-bed rivers the reverse is usually the case; they carry 10 to 50 percent of total load as bed-load. The
other characteristic of sediment transport in gravel-bed rivers is that the transport of coarser material
does not take place on continuous basis as in sand bed rivers but is episodic. In such rivers a large
fraction of bed material is immobile even at bankful discharge and moves only during floods. When the
transport takes place it is unsteady and nonuniform because external sediment supply to the stream is
from overland and gully flows and by landslides and bank collapses. The overland flow supplies finer
material that is transported as suspended load. However, the material produced by landslides, and cliff
collapse is usually coarser. This material once it enters the channel may be temporarily stored in the
Gravel-Bed Rivers
247
channel in the form of bars and will be released during floods. Short term variations in bed-load can also
occur due to disruption of pavement layer and scour or fill. All these effects cause unsteadiness and nonuniformity in bed-load transport.
The non-uniformity of the bed sediment plays an important role in sediment transport. A pavement
is formed on the bed and at low flows finer material may move over the pavement layer. In such case, the
characteristic size of transported material may be smaller than that of the parent material as well as that
of pavement. Once the pavement is broken the material is exposed and the size distribution of the
transported material is significantly changed. Under such conditions all sizes of the particle have equal
mobility.
Another factor that affects the rate of sediment transport in gravel-bed rivers is the availability of
sediment, which is important in the case of flows over a paved bed. In this case if the transport rate is
calculated for a given case assuming it to be uniform, then the actual rate of transport for that size over
paved bed may be much different because the bed may be unable to satisfy the capacity of flow to
transport that sized material. As shown by Misri et al. (1984) and others the bed-load transport of non
uniform sediments can be correctly predicted if exposure and hiding corrections are applied. Once the
pavement is broken all sizes can be transported and the effect of non-uniform size distribution is
minimum.
Bed-load sampling in gravel-bed rivers
To study the applicability of available bed load equations and develop new equations one needs to
carefully collect laboratory and field data on bed-load transport and its size distribution. In the last three
decades bed-load transport in gravel-bed rivers has been measured in New Zealand and U.S.A. on
streams such as the Snake, Clear-Water, Willamete and in the rivers in U.K., Canada, Austria,
Switzerland and Poland with the bed material varying from 1 mm to 100 mm or even more. Yet not
enough data are available for sediment transport in gravel-bed rivers when the bed is paved and when
the pavement is destroyed. Further not in all the above cases the size distribution of the transported
material is given. In fact establishments of sediment transport equation for the gravel-bed rivers has met
with limited success because of the difficulties associated with (i) sampling of bed material and bed-load
in streams; (ii) extreme non-uniformity of bed material; and (iii) non-equilibrium bed-load transport
associated with transient runoff events and episodic events associated with storage and release of bedload.
Three methods have been used to measure the bed-load in gravel-bed rivers. In 1971 Helley and
Smith developed a pressure difference type sampler specifically for use in rivers with bed material from
coarse sand to medium gravel range. This is described by Garde and Ranga Raju (1985); this sampler
was used by Klingeman and Emmett to measure bed-load in East Fork river and had an efficiency of 100
percent for particles ranging from 0.5 mm to 16 mm. The conveyor belt system was developed for
measuring bed-load in East Fork river. Material falling into 0.4 m wide and 0.6 m deep tough on the bed
of the river through 0.25 m wide and 14.6 m long slot is carried from the trough to the bank and then into
the hopper standing over the weighing machine. Thus the sediment falling per minute was recorded.
Vortex bed-load sampler has been used on the Oak Creek and has been discussed by Klingeman and
Emmett. The sampler develops a vortex flow to move bed-load through a flume embedded in the floor of
the weir structure and across the width. The bed-load and portion of the stream flow are removed to an
off-channel where the bed-load sample is collected. The water returns to the creek. The trap efficiency
of vortex tube was found to be 100% for coarse sand and higher fractions. The general design of vortex
tube is discussed by Garde and Ranga Raju (1985).
248
River Morphology
Bed-load equations
White and Day (1982) and Bathrust, Graf and Cao (1987) have studied the applicability of some bedload equations using laboratory data , and laboratory and field data respectively. White and Day, using
flume data found that if Ackers and White’s method is used for the analysis of data, one can use the
mobility parameter
OP L
OP
M
u
PP M u
P
M
Dg
10 D I P
F
d P M 32 log
H d K PQ
r
PQ N
F D g I d > 60 and
n = 0 for G
H r v JK
F D g I d for F D g I
n = 1 – 0.56 G
GH r v JK
H r v JK
LM
A = MM
MM
N
1- n
n
*
n
*
...(7.29)
s
f
1/ 3
s
2
where
f
1/ 3
s
2
s
2
f
1/ 3
d < 60
f
If for uniform material A is the value of the mobility parameter (to which transport rate is related)
and A¢ is its value for the size di in the mixture, it was found that
FG
H
Fd
= 1.6 G
Hd
di
A¢
= 0.6
dA
A
and
dA is given by
dA
d50
IJ
K
IJ
K
- 0 .5
+ 0.6
...(7.30)
- 0 .28
84
16
...(7.31)
White and Day proposed use of Ackers and White’s relationship for the computation of fraction
wise bed-load transport. Assuming uniform size and using the above relations for computing the
mobility parameter, the transport rate is calculated and multiplied by the fraction of this size available in
the bed to get the bed-load transport rate of this size. The calculations are repeated for all size fractions
and the quantities added to get the total bed-load transport rate.
The critical condition for the movement of bed-material is normally expressed for gravel-bed rivers
using the dimensionless critical discharge q*c =
qc
3
gd50
where qc is the critical discharge at which bed
material moves. Bettess (1984) has obtained the equation:
q*c =
F
H
0.134
1.221
log
S
S
I
K
...(7.32)
for constant toc and rs/rf = 2.65. The plot of q*c versus S for the flume data indicated that the best fit line
has the equation
249
Gravel-Bed Rivers
q*c = 0.15 S–1.2
...(7.33)
and that Bettess equation gives equally good results. The equation proposed by Schoklitsch namely
qc
F r - 1I
= 0.26 G
H r JK
5/3
3/ 2
d40
S7/ 6
s
f
...(7.34)
when d40 is replaced by d50 gives about 10% higher value of qc. Bathurst, Graf and Cao (1987) used
laboratory data with bed material size varying from 2.9 mm to 260 mm and assessed the accuracy of
bed-load equation proposed by Ackers and White (1973), Meyer-Peter and Müller (1948), Smart
(1984), Bagnold (1980) and Schoklitsch (1962). These equations are: Ackers and White
qTV = 0.025
where
Fgr =
LMgd
MN
LM F - 1OP
N 0.17 Q
LM
OP
1
U
MM
PP
F
I
F r - 1I OP M 5.657 log G 10 D J P
GH r JK PQ MN
H d K PQ
1.5
qd35
D
gr
...(7.35)
0 .5
s
35
35
f
where qTV = volumetric sediment transport rate per unit width. This equation is to be used only for few
flows with Fr less than 0.80.
Meyer and Peter and Müller’s equation:
q*BV =
QBV
F r - 1I d
gG
H r JK
s
=8
3
a
LMF n I
NH n K
s
3/ 2
t * - 0.047
OP
Q
...(7.36)
f
Here da is the arithmetic mean size of bed material, ns is Strickler’s value of Manning’s roughness
g f DS
coefficient, while n is the Manning’s coefficient for flow, and t* =
D g s da
Smart’s Equation: This equation is based on flume experiments using sediment sizes up to 29 mm
and slopes up to 20 percent. The equation is
LF d
= 4.0 MG
MNH d
F r - 1I d
gG
H r JK
QBV
s
f
90
3
a
30
IJ OP
K PQ
0. 2
S0.6
U 0. 5
t * (t* – t*c)
u*
...(7.37)
250
River Morphology
Mizuyama’s (1977) equation
q*BV
LM12 - 24 S
=
MM cos q
N
1/ 2
d
t * m 1.5 - S
1/ 2
i FGH1 - a
2
t *cm
t*m
IJ
K
LM1 - a F t I OP OP
MN GH t JK PQ PPQ
1/ 2
* cm
...(7.38)
*m
Here, a = f (S) and t*m and t*cm are for d = d50.
Bagnold’s equations:
LM w - w OP F D I F d I
MN bw - w g¢ PQ H D¢ K H d ¢ K
3/ 2
q BV
==
q BV
¢
-2 / 3
c
-1/ 2
...(7.39)
c
Here, w = stream power q rf S per unit width, wc is the critical value of w and the prime refers to
standard measured values from a reliable experimental plot.
Schoklitsch’s equation:
qBV =
d
2.5
rs / r f
i
S3/2 (q – qc)
...(7.40)
I
- 1J
K
...(7.41)
and qc in SI units is given by:
qc
Fg
GH g
= 0.26
s
f
5/ 3
S7/ 6
3/ 2
d 40
Verification of the equations using flume data indicated that Schoklitsch’s equation gave better
performance than the rest of the equations. Further its performance is improved if qc value obtained
q BV
,
S3/ 2
data for small and large rivers behave differently, see Fig. 7.12. Large rivers with S £ 1.0 percent and
relatively narrow range of sediment sizes (1 to 100 mm) as well as ready supply sediment within
channel, show relatively closer agreement with Schoklitsch’s Equation than data for small rivers with
S ³ 1 percent and relatively wider range of sediment size (1 to 1000 mm). While in the former case the
data fall within one order of magnitude of the line of Schoklitsch’s equation, in the latter case sediment
transport is over predicted by two orders of magnitude. Hence Bathurst et al. (1987) concluded that
while Schoklitsch’s equation can be applied with caution to large rivers, it should be applied to small
rivers for extreme flows when the whole bed is moving.
from qc* = 0.21 S –1.2 are used. In the case of field data it was found that when (q – qc) is plotted
Parker, Klingeman and Mclean’s equation
After examining the data of the Oak Creek (U.S.A.) Parker et al. (1982) found that when the shear stress
acting on the bed is greater than the critical shear stress for the pavement and thus the pavement is
251
Gravel-Bed Rivers
Cache
la
Poudre,
Colorado
Fig. 7.12 Variation of qBv/S3/2 with (q – qc), river data compared with Schoklitsch equation
broken, as a first order of approximation the size distribution of the bed-load is nearly the same as that of
the sub-pavement. Under this condition the rate of bed-load transport is governed by the hydraulic
conditions rather than the availability of material. This information is used to develop an empirical
equation for bed-load transport rate as a function of shear stress and d50 of the sub-pavemnent in paved
bed channels. Careful analysis of the Oak Creek data indicated the validity of similarity approach.
However small systematic change in size distribution with the shear stress was observed especially near
the critical condition.
Using the similarity approach proposed by Ashida and Michiue, Parker et al. (1982) used two
dimensionless parameters
Wi*
F r - 1I gq
= G
H r JK
f
R| F t I U|
S| f GH r JK V| and t
T
W
3/ 2
s
0
BVi
i
f
*
i
tc
=
D g s di
U|
V|
W
where qBVi is the volumetric bed load transport rate of size di per unit width of the channel and fi is the
fraction of size available in the sub-pavement. Plotting Wi* vs ti* for each size range, the value of ti*
252
River Morphology
designated as t*ri at which Wi* has the pre-chosen value of 0.002. Further denoting t*r50 as the value of
t*i when di = d50 it was found that
FG IJ
H K
d1
t *ri
=
d50
t *r 50
- 1.0
...(7.42)
and t*r50 = 0.0876. Defining fi = t*i /t*ri and taking W*r = 0.002, they found that when
Wi*
is plotted
Wr*
against fi the data tend to plot around a single curve whose coordinates are
Table 7.2
Coordinates of fi Vs W*i
fI
0.90
1.0
1.1
1.2
1.3
1.4
Wi*
10 – 4.5
2.3 ´ 10 –3
1.15 ´ 10 –2
3.7 ´ 10 –2
8.0 ´ 10 –2
1.9 ´ 10 –1
Wr*
This is based on ten size ranges for the Oak Creek in the range of 0.60 to 102 mm. However a
systematic deviation was apparent, viz. as fi increase, the value of Wi* for the finer material tends to fall
below the mean curve. Parker et al. showed that the above relationship can be integrated to obtain the
total bed-load transport rate in the form
W*
= G (f50)
Wr*
...(7.43)
where W* is the dimensionless bed-load transport for poorly sorted gravel-bed when the pavement is
broken, W*r = 0.002 and f50 =
t*50
with t*r50 = 0.0876. The above functional relation takes the form:
*
t r 50
W* = 0.0025 e[14.2 (f50 – 1) – 9.28 (f50 – 1)2]
...(7.44)
= 0.002 G (fi )
for 0.95 < f50 < 1.165. It is interesting to note that the coordinates of the two curves
and W*r = 0.0025 exp. [14.2 (f50 – 1) – 9.28 (f50 – 1)2] match. Parker et al. showed that data for the rivers
Elbow, Snake and Vedder reasonably conform to the above equation for W*. For data with f50 > 1.65 the
following equation gives the variation of W* and f50
W*i
W*r
F 0.822 IJ
= 11.2 G 1 H j K
4 .50
...(7.45)
50
Parker et al. also obtained three empirical equations for three size ranges of the bed material for f50
greater than 0.95. However these equations need further verification using data from other streams.
253
Gravel-Bed Rivers
References
Adams, J. (1979) Gravel Size Analysis from Photographs. JHD, Proc. ASCE, Vol. 105, No. HY-10, October, pp.
1247-1285.
Ackers, P. And White, W.R. (1973) Sediment Transport: New Approach and Analysis. JHD, Proc. ASCE, Vol. 99,
No. HY-11, November, pp. 2041-2060.
Bagnold, R.A. (1980) An Empirical Correlation of Bed-load Transport Rates in Flumes and Natural River, Proc.
RSL, A372, pp. 453-473..
Bathurst, J.C. (1978) Flow Resistance of Large Scale Roughness. JHD, Proc. ASCE, Vol. 104, No. HY-12,
December, pp. 1587-1603.
Bathurst, J.C. (1985) Flow Resistance Estimation in Mountain Rivers. JHE, Proc. ASCE, Vol. 111, No. 4, April,
pp. 625-643.
Bathurst, J.C. 1986. Some Aspects of Gravel-Bed Rivers (Lecture Notes for the British Council Visit), February.
Bathurst, J.C. Graf, W.H. and Cao, H.H. (1987) Bed-load Discharge Equations for Steep Mountain Rivers,
Chapter 15 in Gravel-Bed Rivers. (Eds. Thorne, C.R., Bathurst, J.C. and Hey, R.D.) John Wiley and Sons Ltd.,
pp. 453-492.
Bettess, R. (1984) Initiation of Sediment Transport in Gravel Stream. Proc. Inst. of Civil Engineers (London), Vol.
77, Pt. 2, Technical Note 407, pp. 79-88.
Bhowmik, N.G. (1968) “The Mechanics of Flow and Stability of Alluvial Channels Formed in Coarse Materials”,
Ph.D. Thesis, Colorado State University, Fort Collins (U.S.A.).
Bray, D.I. (1979) Estimating Average Velocity in Gravel-Bed Rivers. JHD, Proc. ASCE, Vol. 105, No. HY-9,
September, pp. 1103-1122.
Bray, D.I. (1982) Regime Equations for Gravel-Bed Rivers, Chapter 19 in Gravel-Bed Rivers. (Eds. Thorne, C.R.,
Bathurst, J.C. and Hey, R.D.) John Wiley and Sons Ltd., pp. 517-552.
Charlton, F.G. (1977) An Appraisal of Available Data on Gravel Rivers, HRS Wallingford (U.K.), Rep. No. INT –
151, p. 67.
Church, M and Jones, D. (1987) Channel Bars in Gravel-Bed Rivers, Chapter 11 in Gravel-Bed Rivers. (Eds.
Thorne, C.R., Bathurst, J.C. and Hey, R.D.) John Wiley and Sons Ltd., pp. 291-338.
Church, M and Rook, R. (1983) Catalogue of Alluvial River Channel Regime Data. University of British
Columbia, Canada.
Colosimo, C., Copertino, V.A. and Vetri, M. (1988) Friction Factor Evaluation in Gravel-Bed Rivers. JHE, Proc.
ASCE, Vol. 114, No. 8, August, pp. 861-876.
Garde, R.J. (1972) Bed Material Characteristics of Alluvial Streams. Jour. of Sedimentary Geology, Vol. 7, No. 2.,
pp. 127-135.
Garde, R.J., Prakash, H. and Arora, M. (1985) Hydraulics of Gravel-Bed Rivers. Report Prepared for I.N.S.A.,
CWPRS, Pune, 164 p.
Garde, R.J. and Ranga Raju, K.G. (1985). Mechanics of Sediment Transportation and Alluvial Stream Problems.
Wiley Eastern Publishers Ltd., New Delhi, p. 618.
Gladky, H. (1979) Resistance to Flow in Alluvial Channels with Coarse Bed Materials. JHR, IAHR, Vol. 17, No.
2, pp. 121-128.
Golubstov, V.V. (1969) Hydraulic Resistance and Formula for Computing the Average Flow Velocity of Mountain
Rivers. Soviet Hydrology, No. 5, pp. 500-511.
Griffiths, G.A. (1981) Flow Resistance in Coarse Gravel-Bed Rivers. JHD, Proc. ASCE, Vol. 107, No. HY-7,
July., pp. 899-980.
254
River Morphology
Grishanin, K.V. (1967) The Similarity in Flow at Straight Reaches of Rivers. Proc. 12th Congress of IAHR, Fort
Collins, U.S.A., Vol. 1, A-28, pp. 226-236.
Harrison, A.S. (1950) Report on Special Investigation of Bed Sediment Seggregation in a Degrading Bed. Rep.
Series 33, Issue No. 1, University of California, Berkeley, U.S.A., September.
Hey, R.D. (1982) Design Equations for Mobile Gravel-Bed Rivers, Chapter 20 in Gravel-Bed Rivers. (Eds. Hey,
R.D., Bathurst, J.C. and Thorne, C.R.) John Wiley and Sons Ltd., pp. 553-580.
Hey, R.D. and Thorne, C.R. (1986) Stable Channels with Mobile Gravel-beds. JHE, Proc. ASCE, Vol. 112, No. 8,
August, pp. 671-689.
Ikeda, S. (1984) Prediction of Alternate Bars Wave Length and Height. JHE, Proc. ASCE, Vol. 110, No. 4, April,
pp. 371-386.
Inglis, C.C. (1947) Meanders and Their Bearing on River Training. Proc. Inst. Of Civil Engineers (London),
Maritime Paper No. 7, January, pp. 3-54.
Jackson, R.G. II. (1975) Hierachical Attributes and a Unifying Model of Bed Forms Composed of Cohesionless
Material and Produced by Shearing Flow. Geol. Society Am. Bull., Vol. 86, pp. 1523-1533.
Keller, E.A. and Melhorn, W.N. (1973) Bed Forms and Alluvial Processes in Alluvial Stream Channels : Selected
Observations, In Fluvial Geomorphology (Ed. Morisawa, M.) Intl. Series No. 4, (Bingham Symposium in
Geomorphology), Alley and Unwin Ltd., London, pp. 253-284.
Kellerhals, R. (1967) Stable Channels with Gravel Paved Beds. JWHD, Proc. ASCE, Vol. 93, No. WW-1,
February, pp. 63-84.
Knighton, A.D. (1977) Short Term Changes in Hydraulic Geometry, Chapter 7 in River Channel Changes. Ed.
Gregory, K.G., Wiley Interscience Publications, U.S.A., pp. 101-119.
Koster, E.H. (1978) Transverse Ribs, their Characteristics, Origin and Palaeohydraulic Significance in Fluvial
Geomorphology. E.D. Miall, Memoir 5 of Canadian Society of Petroleum Geologists.
Kothyari, U.C. (1994) Frequency Distribution of River Bed Materials. Jour. Of Sedimentary, Vol. 42, No. 1, pp.
283-291..
Lacey, G. (1930) Stable Channels in Alluvium. Minutes of Proc. Inst. Of Civil Engineers (London), Vol. 229,
Paper No. 4736, pp. 258-292.
Lane, E.W. and Carlson, E.J. (1953) Some Aspects Affecting the Stability of Canals Constructed in Coarse
Granular Materials. Proc. 5th Congress of IAHR, Minneapolis, U.S.A., September, pp. 37-48.
Langbein, W.B. (1964) Geometry of River Channels. JHD, Proc. ASCE, Vol. 90, No. HY-2, March, pp. 301-347.
Langbein, W.B. and Leopold, L.B. (1968) River Channel Bars and Dunes - Theory of Kinematic Waves. USGS
Professional Paper 422-L, p. 20.
Leopold, L.B. and Maddock, T. (1953) Hydraulic Geometry of Stream Channels and Some Physiographic
Implications. USGS Professional Paper 252, Washington D.C., 57 p.
Leopold, L.B. and Wolman, M.G. (1957) River Channel Patterns: Braided, Meandering and Straight. USGS
Professional Paper 252, Washington D.C., pp. 39-85.
Limerinos, J.T. (1970) Determination of the Manning’s Coefficient from Measured Bed Roughness in Natural
Channels. W.S. Paper USGS, 1898-B, Washington D.C., p. 47.
Meyer-Peter, E. And Müller, R. (1948) Formulas for Bed-Load Transport. Proc. 2nd Congress of IAHR,
Stockholm., pp. 39-64.
Michalik, A.S. (1989) Some Aspects of the Bed-Load Transport in Mountain Rivers. Proc. 4th International
Symposium on River Sedimentation, Beijing, China, pp. 579-586.
Milhaus, R.T. (1973) Sediment Transport in a Gravel-Bottomed Stream. Ph.D. Thesis, Oregon State University,
U.S.A., p. 232.
Gravel-Bed Rivers
255
Misri, R.L., Garde, R.J. and Ranga Raju, K.G. (1984) Bed-Load Transport of Coarse Non-uniform Sediment. JHE,
Proc. ASCE, Vol. 110, No. 3, March., pp. 312-328.
Mizuyama, T. (1977) Bed - Load Transport in Steep Channels. Ph.D. Thesis, Kyoto University, Japan, p. 118.
Moss, A.J. (1962) The Physical Nature of Common Sandy and Pebby Deposits I. Jour. Am. Science, Vol. 260.
Moss, A.J. (1963) The Physical Nature of Common Sandy and Pebbly Deposits II. Jour. Am. Science, Vol. 261.
Neill, C.R. (1968) Note on Initial Movement of Coarse Uniform Bed Material. JHR, IAHR, Vol. 6, No. 2, pp. 173176.
Odgaard, A.J. (1984) Grain Size Distribution of River Bed Armor Layer. JHE, Proc. ASCE, Vol. 110, No. 10,
October, pp. 1479-1485.
Parker, G. (1979) Hydraulic Geometry of Active Gravel Rivers. JHD, Proc. ASCE, Vol. 105, No. HY-9,
September, pp. 1185-1201.
Parker, G., Klingeman, P.C. and McLean, D.G. (1982) Bed-load and Size Distribution in Paved Gravel-Bed
Stream. JHD, Proc.ASCE, Vol. 108, No. HY-4, April, pp. 544-571.
Richards, K.S. (1982) Forms and Processes in Alluvial Channels. Methuen, London.
Schoklitsch, A. (1962) Handbuch des Wasserbau. 3rd Edition Springer-Verlag, Vienna.
Shulits, S. (1944) Rational Equation for River Bed Profile. Trans AGU, Vol. 22. pp. 522-531
Silvester R. and del a Cruz C.D.R. (1970) Pattern Forming Forces in Delta. JWHD, Proc. ASCE, Vol. 96, No.
WW-2, May, pp. 201-217.
Smart, G.M. (1984) Sediment Transport Formula for Steep Channels. JHE, Proc. ASCE, Vol. 110, No. 3, March,
pp. 267-276.
Smith, N.D. (1978) Some Comments on Terminology. Ed. Miall, A.D., Memoir 5 of Canadian Society of
Petroleum Geologists, Ottawa, pp. 85-88.
Thompson, S.M. and Campbell, P.L. (1979) Hydraulics of Large Channel Paved with Boulders. JHR, IAHR, Vol.
17, No. 4, pp. 341-354.
Thornbury W.D. (1964) Principles of Geomorphology. Wiley International Edition, John Wiley and Sons Inc.,
New York, U.S.A., 2nd Edition.
Thorne, C.R. and Zevenbergen, L.W. (1985) Estimating Mean Velocity in Mountain Rivers. JHE, Proc. ASCE,
Vol. III, No. 4, April, pp. 612-624.
Van Rijn, U.C. (1982) Equivalent Roughness of Alluvial Bed. JHD, Proc. ASCE, Vol. 108, No. HY-10, October,
pp. 1215-1217.
Vischer, G.S. (1969) Grain Size Distribution of Depositional Processes. Jour. Sedimentary Petrology, Vol. 39.
Wadia D.N. (1961).Geology of India. MacMillan and Co. Ltd., London. 3rd Edition (Revised)
Walters W.H. Jr. (1975) Regime Changes of the Lower Mississippi River. M.S. Thesis. Civil Engineering
Department, Colorado State University, Fort Collins (U.S.A.)
White, W.R. and Day, T.J. (1982) Transport of Graded Gravel-bed Material, Chapter 8 in Gravel-Bed Rivers. Eds.
Hey, R.D., Bathurst, J.C. and Thorne, C.R., John Wiley and sons Ltd., pp. 181-223.
Wolman, M.G. (1954) A Method of Sampling Coarse River Bed Material. Trans. A.G.U., Vol. 35, No. 6, Pt. 1,
December, pp. 951-956.
Worcester P.G. (1948). A Text Book of Geomorphology. D.Van Nostrand Company Inc., New York, 2nd Edition.
C H A P T E R
8
Fluvial Palaeo Hydrology
8.1
INTRODUCTION
The word palaeo hydrology was probably first used by Leopold and Miller (1954) in the study of
postglacial chronology of alluvial valleys in Wyoming (USA). In this case they were concerned about
the interaction of climate, vegetation, stream regime and runoff, which were obtained under several
climatic conditions, each different from the present one; this led to the use of the word palaeo hydrology.
Since then several investigators such as Schumm (1965, 1977) and Cheetham (1976), have given
different definitions of palaeo hydrology. In connection with Quaternary palaeo hydrology Schumm
(1965, 1977) stated that palaeo hydrology treats the phenomenon of occurrence of water in the
atmosphere, its distribution and composition on the surface of the ground and underground, but has
reference to the past. The term is restricted to that portion of hydrologic cycle that involves the
movement of water over the surface of the earth, because runoff and the accompanying sediment load
are of major importance in determining the non-glacial erosional and depositional features of the
Quaternary. Since the composition of water on surface would naturally involve sediment, and its
movement, palaeo hydrology also involves consideration of quality and quantity of the sediment moved
through the palaeo channels. According to Cheetham (1976) palaeo hydrology is the study of fluvial
processes operated in the past and their hydraulic implications. Fluvial palaeo hydrology is that branch
of palaeo hydrology which deals with erosion, deposition and the characteristics of former channels.
Since the study of palaeo hydrology involves the use of new techniques, conceptual advances and
more interdisciplinary research, International Geological Correlation Programme (IGCP) was
formulated and initiated in 1973 as IUGS/UNESCO activity. In palaeo hydrology progress has been
made through developments in climatology, hydraulics, geomorphology and sedimentology. The fields
related to palaeo hydrology are:
Palaeo climatology:
Study of paleao climates which are climates in periods of geologic
past.
Palaeo geomorphology:
The geomorphology of ancient landscapes, especially as represented
today by features that are buried or newly exhumed.
Fluvial Palaeo Hydrology
257
Palaeo hydraulics:
Study of quantitative relationships between hydraulic parameters of
rivers (e.g., depth, width, slope, discharge, sediment type)
Palaeo pedology:
Study of palaeo soils i.e., soils that formed by the landscape of the
past.
In palaeo hydrology the interest in hydrologic and fluvial processes goes back to the times when
systematic hydrologic data were not collected, say 10 000 to 15 000 years before present (B.P.), i.e.,
during Quaternary period and Holocene and Pleistocene epochs. Evidence available for palaeo
hydrology of the temperate zone in the past 15 000 years is primarily sedimentological, morphological
and historical. Sedimentological evidence includes information deduced from the physical properties of
sediments and from organic deposits; this information is useful in the reconstruction of environment
during the past and assessing the discharges and the changing rates of erosion. Morphological
information can be obtained from the analysis of palaeo channels. Additional historical information is
obtained from old maps, records, other historical sources and the dating techniques. As indicated by
Gregory et al. (1987), in palaeo hydrology as well as historical geomorphology, a retrorespective
approach is preferred because it is desirable to reconstruct palaeo hydrology against the basic definition
of hydrology of contemporary environment. An understanding of the present day processes is therefore
a must for the interpretation of past hydrological processes. It is also necessary to attempt to extract a
considerable amount of information of recent human impact before analysing the prehistoric palaeo
hydrology. In this endeavour a better understanding of the relation of sedimentary deposits and river
morphology to hydrology is necessary so as to construct palaeo environmental models of terraces,
palaeochannels, and other deposits e.g., deltaic deposits. Hence information and discussion in chapters
five, six and seven and in earlier chapters is useful in palaeo hydrologic studies.
Since climatic changes have occurred during the post-glacial period, it is necessary to know or infer
what these climatic changes were and how these changes affected the flood and channel forming
discharge which, in turn, would affect the palaeo channels: their dimensions, plan-form and its
variation, and such other characteristics. It is presumed that the hydraulic data such as flood discharge
were not measured and hence have to be inferred indirectly from whatever measures of palaeo channels
that are available.
The dating of changes has to be done separately using study of ancient soils, tree rings, pollens and
spores, ancient cultural evidence e.g., archaeology, written or oral records, sediments (sedimentology
and stratigraphy), land forms (geomorphology and Quaternary geology), ancient floral and faunal
distribution, and isotope chemistry of ancient waters and elements such as oxygen and carbon.
8.2
OBJECTIVES OF PALAEO HYDROLOGIC STUDIES
The broad objectives of palaeo hydrologic study are to reconstruct components of hydrologic cycle, of
the water balance and of sediment budgets for the time before continuous hydrologic data were
collected. Continuous hydrologic and hydraulic data including meteorological data, stream gauges,
evaporation etc. are available for a little over 100 to 150 years, while some hydrologic records date back
to more than 2000 years. Hence, palaeo hydrologic studies can be visualised prior to this period up to
glacial age.
The study of fluvial palaeo hydrology would deal with climatic changes in the past and their
influence on vegetation, erosion and deposition, palaeo channel geometry, plan-forms, channel forming
discharges, palaeo velocities and probable changes in river courses. Such studies are also useful in
258
River Morphology
predicting future changes in fluvial channels and erosion or deposition caused by probable climatic
changes and man-made interferences.
The knowledge of palaeo hydrology and fluvial palaeo hydrology is useful in interpreting the
behaviour of alluvial streams, location of hydraulic structures, choosing sites for storing hazardous
wastes, and for exploring valuable deposits in ancient fluvial sediments (Schumm 1977).Hence for
studying fluvial palaeo hydrology one should enquire into how and why climatic changes took place in
the past and what was their effect on vegetation, runoff and erosion rates in arid, semiarid and humid
regions. How can one estimate palaeo velocity and palaeo discharge from observed dimensions of
palaeochannels? How would such climatic changes affect the plan-form characteristics?
The information presented in this chapter is based on the excellent texts and papers written on
palaeo hydrology and related topics by Schumm (1977), Gregory (1983), Berglund (1986), Gregory et
al. (1987), Dury (1976) and others.
8.3
BASIS OF ANALYSIS
It is reasonable to assume that climate and climatic changes would affect the erosional and depositional
processes and hence the landscape and rivers. Even though climate influences the weathering and soil
formation, from the point of view of palaeo studies, the effects of climate on vegetation, runoff and
sediment yield from mountainous areas are more relevant. Studies by Langbein et al. (1949), Langbein
and Schumm (1958) and Noble (1965) indicate how mean annual precipitation, average temperature
and vegetal cover affect mean annual runoff and sediment yield. Using data from gauging stations at
which the discharge was not materially affected by diversions or regulation, Langbein et al. (1949)
showed the effect of mean annual temperature on the mean annual runoff, see Fig. 8.1
Fig. 8.1
Variation of mean annual runoff with mean annual precipitation and average temperature (Langbein et al. 1949)
For a given mean annual precipitation, as the temperature increases the mean annual runoff
decreases. Also, Langbein and Schumm (1958) obtained a relation between annual sediment yield and
effective precipitation for drainage basins of approximately 3800 km2 for temperature at 10°C, see Fig.
8.2. The definition of 10°C curve is based on known values of runoff for each drainage basin from
259
Fluvial Palaeo Hydrology
Fig. 8.2 Variation of sediment yield with climate (Langbein and Schumm 1958)
which sediment yield data were obtained. These observed values were converted to an effective
precipitation, which is the annual precipitation required to produce the known runoff at 10°C using Fig.
8.1. On Fig. 8.2 are also shown the range of vegetation as effective precipitation increases. According to
Langbein and Schumm the precipitations as well as the temperature influence the sediment yield from
the catchment. This is so because as the temperature increases, higher precipitation is required to
produce a given amount of runoff. The variation in sediment yield with precipitation is explained by the
interaction of precipitation and vegetation on runoff and erosion. As precipitation increases so does the
vegetation that tends to reduce the erosion. On the other hand, as precipitation increases erosion tends to
increase. Langbein and Schumm found that when precipitation exceeds 30 cm, sediment yield decreases
with increasing precipitation due to more effective grass cover. According to Fournier (1949), in
monsoonal climate the sediment yield may increase again after rainfall exceeds 125 cm under the
influence of highly seasonal climate.
The role played by vegetation in controlling the rate of erosion is indicated by the studies by Noble
(1965) on an experimental watershed in Utah (USA). He found that the erosion rate decreased from
2935 kg/ha/storm to a negligible value as the percentage of ground cover changed from 20 to 90. The
effect of temperature and vegetation on mean annual runoff and erosion rate has also been studied by
Kothyari and Garde (1991), and Garde and Kothyari (1986). Using such type of information it is
possible to predict what may have been the effect of change in mean temperature, mean annual
precipitation and vegetal cover on the changes in runoff and sediment yield during inter-glaciation and
post-glaciation periods.
While studying palaeo hydrology it is generally assumed that in relatively recent geologic times,
during the later part of the Tertiary and the entire Quaternary period, there has been no significant
change in vegetation. Hence the relations between mean annual temperature and precipitation can be
used to show how both sediment yield and runoff changed with climatic changes in the geologic past.
The second tool available to study fluvial palaeo hydrology is Lane’s balance analogy according to
which
Qs d ~ QS
...(8.1)
where Qs and Q are sediment and water discharge in the stream, d is the sediment size and S is the stream
slope. This analogy would qualitatively predict what would happen to stream slope if Qs or Q are
260
River Morphology
changed or there is change in the base level due to sea level changes. Here one can use either mean
annual discharge or mean flood discharge. The above proportionality is helpful in interpreting channel
changes due to climatic changes resulting in change in Q and Qs in palaeo conditions. However, this
relationship does not throw light on the changes in the plan-form of the stream.
Another important relationship is the qualitative relationship for sediment discharge Qs
Qs ~
W ML S
DSi
...(8.2)
Here W is the average channel width, Si is the sinuosity, and ML meander length. Hence from
relationships 8.1 and 8.2 one can express what happens to W, D, ML, S, Si if either the water discharge Q
or sediment discharge Qs is increased (+) or decreased (–).
Thus one can write
Q + , » W + , D + , M L+ , S - , Si-
Q »
QS+ »
QS- »
-
-
W , D , M L- , S - ,
W + , M L+ , S + , D - ,
W - , M L- , S - , D + ,
Si+
Si+
Si+
U|
|V
||
W
…(8.3)
Another important tool that can be used in palaeo hydrology is the resistance relationship relating
flow velocity U to the depth D or hydraulic radius, slope S, and roughness coefficient e.g., Manning’s n
or Chezy’s C, or friction factor f defined in Chapters five and seven. This can be used if palaeo stage is
known along with slope S. The slope that has to be used is the terrain slope or palaeochannel slope
assuming the flow to be uniform. The roughness coefficient can be estimated knowing the size of the
bed material and Strickler type equation discussed in Chapters five and seven. Alternatively, one can use
other equations such as Eqs. (8.21) or (8.22). Another method would be to estimate Q knowing the
contemporary relation between Q and meander length ML.
Analysis of transverse sections of the valley floor enables one to explain the changes caused by
lateral erosion, aggradation and avulsion of channels. Examination of longitudinal profile of flood plain
allows one to evaluate the influence of eustatic and tectonic factors in fluvial history. For this reason one
needs to consider carefully the history of tectonic and neo-tectonic activity in the region and its effect on
channel change.
Sedimentological methods are used to distinguish various facies of fluvial deposits. The facial
setting is different in braiding and meandering systems and hence facial study of fluvial deposit assumes
importance. Stratigraphic analysis of undisturbed deposits of palaeo channels is also important. Size
distribution of facial units, presence of fills of different ages and recognition of rates of deposition can
assist in the reconstruction of many parameters of the past environment.
8.4 CLIMATIC CHANGES: PAST AND FUTURE
(SCHNEIDER AND ROOT 2000)
Earth’s climate is very different now from what it was 100 million years ago. It is different from what it
was 20 000 years ago when ice sheets covered much of the Northern Hemisphere. These climatic
Fluvial Palaeo Hydrology
261
changes in the past were driven by natural causes such as variations in the earth’s orbit or CO2 content of
the atmosphere. However, climatic changes in future will probably have another source namely human
activity because human actions can indirectly alter the natural flow of energy enough to create
significant climatic changes. One example is enhancing the natural capacity of the atmosphere to trap
radiant energy near earth’s surface – known as green house effect. Burning of fossil fuel that releases
CO2 and using land for agriculture or urbanisation leading to large-scale deforestation will cause global
warming of 1° to 5°C in the next century. Computer simulation models based on basic laws of
thermodynamics and Newton’s laws of motion can be used to predict future changes in climate.
The last major glacial ice age occurred about 20 000 years ago and the current 10 000 years long
interglacial period (Holocene) began. This has been determined from the ratio two oxygen molecules
O16 and O18 isotopes having different molecular weights entrapped in the ice. Ice cores taken from holes
drilled into some 2000 m of ice in Greenland and Antarctica also provide information on the presence of
CO2, important in studying greenhouse effect. Carbon dioxide concentrations during cold periods were
much less than in interglacial periods. The temperature during the past 10 000 years (before 1700 A.D.)
was remarkably constant. During the transition of Ice Age to Holocene, which took 5000 to 10 000
years, the average global temperature increased by 5°C and sea level rose by 100 m. Thus, average rate
of natural temperature rise was 0.5° to 1.0°C per thousand years. Thus, climate change was responsible
for the well known extinctions of woolly mammoths, sabertooth cats, etc. The climatic change was also
responsible for change in vegetation. During the last Ice Age most of Canada was under ice; study of
pollen cores indicate that as the ice receded, boreal trees moved northward chasing the ice cap. It
suggests that the biological communities move intact with a changing climate. It was further noticed that
even though during the transition from last Ice Age to the present inter-glaciation nearly all the species
moved northward, they moved individually and not as a group. Since due to increased human activity on
the globe the temperature changes on the earth will be more severe than during inter-glaciation period,
such changes are bound to affect vegetation patterns.
Causes for Climatic Changes
The causes for climatic changes can be external or internal. Stating which components are external or
internal to climatic system depends on the time period and spatial scale being examined, as well as on
the phenomena being considered. External causes can be:
a. Fluctuations in heat radiated by the sun – perhaps related to sun spots – are external to climatic
system.
b. Influences of gravitational tugs of other planets on the earth’s orbit are also external to climate
system. According to some scientists such tugs gave rise to 40 000 year ice cycle in the past 2.5
million years, 100 000 year ice age and inter-glacial cycles.
c. Changes in volcanic dust or CO2 in the atmosphere. On short time scale these factors are
external.
d. Effects of green house gases on temperature, on 20 year scale are also external.
e. Effect of changes in character of land surface caused by human activity is an external cause.
Some of the internal causes for climate changes are:
a. Dust generation caused by change in plant cover due to changes in climate;
b. CO2 and methane levels may rise or fall with ice age cycles; these are internal on a 10 000 years
time scale.
262
River Morphology
c. If vegetation cover changes because of climatic change, the land surface change becomes
internal; change in plant cover can influence the climate by changing albedo (i.e., reflectivity to
sun light), evapo transpiration, surface roughness and humidity.
d. Unusual patterns of ocean surface temperature – such as the El Nino - are an internal cause.
Climate Change Forecasts
To predict the significant ways the climate might change, one must specify what people do that modifies
how energy is exchanged among the atmosphere, land surface, and space because such energy flows are
the driving forces behind climate. Estimating societal impetus involves forecasting the plausible set of
human (or societal) activities affecting pollution over the next century. The next step is to estimate the
response of the various components of the earth system to such societal forcings. The earth system itself
consists of the following interacting sub-components, atmosphere, oceans, cryosphere (snow, seasonal
ice and glaciers) and land surface systems. Since knowledge about societal impetus that will actually
occur and the scientific knowledge of each sub-system are still incomplete, such models are not yet full
developed.
Global Warming Forecasts
Global warming forecasts for 21st century will depend on the projections of population, consumption,
land use and technology. The forecast of amount of CO2 emitted per unit energy will depend on the
projections of population and affluence that are increasing and the amount of energy used to produce a
unit of economic product. Hence, it is estimated that CO2 emissions will rise several fold over the next
100 years (of course this will depend on what kind of energy system is used). Roughly 50 percent of CO2
emitted will remain in the atmosphere every year i.e., about 3 billion tons of carbon as CO2. This is half
of fossil fuel injected CO2. Then one needs to estimate CO2 concentration in the atmosphere using
carbon cycle model and this should be fed in computerised climatic models to estimate its effect on
climate. The simplest model will give the global average temperature while complex atmospheric
models predict time evolution of temperature plus humidity, wind, soil moisture, sea ice and other
variables in the three dimensions in space. Such a model is known as general circulation model.
Ecologists use these inputs to produce forecasts of regional climatic changes in the future. Further,
global heating or warming is not uniform but different for centres of continents, oceans and oceans
closer to poles. These temperature differences can cause droughts, high rainfalls, hurricanes and similar
other effects. According to Inter-governmental Panel on Climate Change there is likely to be 1.5° to 4.5°
C average global rise in temperature in the 21st century.
8.5
PALAEO HYDROLOGIC ESTIMATES OF DISCHARGE AND VELOCITY
In palaeo hydrology considerable attention has been given to prediction of palaeo flood velocity or
palaeo flood discharge from observed channel dimensions or meander characteristics. Prediction of
former river discharges is the primary purpose of palaeo hydrology. Ability to calculate former river
discharge makes it possible to determine the quantitative water balance of the drainage basin, the
hydrologic regime of the river, and some elements of climate, as well as to detect and specify
quantitative changes of some hydrologic and climatic parameters in a given period of the Quaternary
and, possibly for older geologic periods too.
Fluvial Palaeo Hydrology
263
Theoretically there are two ways in which one can determine the past river discharge on the basis of
its effects, firstly through the analysis of preserved morphological effects caused by a given discharge.
Unfortunately, the connections between the deposit, its structure, and statistical parameters of grain size
distribution and the discharge are so complicated and obscure that they cannot be expressed in any
quantitative models. Grain size distribution and its parameters enable one to specify at most the local
velocity at which the deposition of given sediment took place. The top level of deposition gives an
indication of lowest palaeo flood level. The other method used is known as slack water deposit (SWD)
method which gives an idea of the stage of palaeo flood and is described later.
The second method is to use relation between characteristic discharge, such as mean annual
discharge, Qma bankful discharge Qb or mean annual flood Qmaf and the morphological parameters
which can be cross-sectional parameters at bankful discharge such as maximum depth Dmax, hydraulic
radius R, channel slope S, width to depth ratio and cross-sectional area A, and channel pattern
parameters such as meander length ML, meander belt MB and meander curvature radius Rm. It must be
emphasised that these relations are valid only for some types of rivers. The relations between discharge
and channel cross-section parameters apply to meandering and straight rivers, while the relations
between discharge and channel pattern parameters concern only meandering rivers. No such
relationships are available at present for braided rivers. Such analysis assumes that these geometric
(cross-sectional and channel pattern) parameters are only a function of characteristic discharge, even
though it is known that other parameters such as slope, sediment size and sediment discharge can
influence the relationship.
Several investigators have worked on developing such empirical relationships between geometric
parameters and discharge; a few among them are Jefferson, Carlson, Inglis, Leopold and Maddock,
Dury and Williams. They have shown and confirmed that simple power type relationships can be
obtained between geometric parameters and discharge viz. D, R, ML, MB ~ Qm. All these relationships
have been developed to predict the geometrical parameters for known discharge. On the other hand, in
palaeo hydrology, these relations are used to predict characteristic discharge for observed characteristics
of palaeo channel. Hence, the accuracy of these equations can be much different than that given by
authors when discharge predictions are made from these equations. The palaeo channels commonly
appear in the form of (1) exposed cross-sections, (2) abandoned channels on the earth’s surface and (3)
rarely as exhumed (or buried) channels. Based on such exposures palaeo fluvial estimates i.e. stream
flow of the former channels and channel characteristics can be made from (a) palaeo channel bed
sediments (particle size, dune height, etc.), (b) palaeo channel plan-form properties (ML, sinuosity etc.)
(c) palaeo channel cross-sectional features e.g., bankful width and (d) palaeo drainage features e.g.
stream length, basin area etc. A large number of investigators (see Williams 1986) have dealt with use of
(b) and (c) for palaeo fluvial estimates.
One question that needs to be discussed is out of the mean annual discharge Qma, bankful discharge
Qb and mean annual flood Qmaf , which one should be used in finding the relationship between discharge
and channel characteristics ? The use of bankful discharge Qb seems to be justified because many
authors believe it to be the channel-forming discharge, and further it value lies between mean annual
discharge Qma and mean annual flood Qmaf i.e. Qma < Qb < Qmaf. Also, the bankful stage is the only
characteristic stage that can be determined on the basis of well-preserved channel or meandering
channel. It must further be emphasised that these equations being empirical and based on limited data,
the accuracy of prediction would depend on the size of the sample and the climatic zone from which the
sample is taken.
264
River Morphology
Palaeo Velocity Determination
One of the simplest method of determination of mean flow velocity U for specified depth D or hydraulic
radius R is Lacey’s equation
U = 11 D0.67 S0.33
...(8.4)
where S is the water surface or channel slope. This is based on 188 observations on canals and rivers
with sandy beds. Bray (1979) applied it to 67 gravel and cobble bed rivers for a discharge of 2 year
return period and found it to give velocity estimates with a standard deviation of 30 percent. This
equation has the advantage that it does not require estimation of resistance coefficient as in the case of
equations of Manning, Chezy or Darcy-Weisbach, namely
1 2 / 3 1/ 2
R S
n
Manning
U=
Chezy
U = C RS
...(8.6)
Darcy-Weisbach
U = (8g RS/ f )1/ 2
...(8.7)
...(8.5)
The main difficulty in using the above three equations is regarding correct estimation of Manning’s
n, Chezy’s C or Darcy-Weisbach friction factor f. Chow (1959) and Benson and Dalrymple (1967) have
discussed about estimation of Manning’s n based on a base value of n and further increments in it to
account for vegetation, channel alignment etc. However, such refinement in case of palaeo studies may
not be warranted and estimation of n, C or f by simples equation would suffice.
On the basis of analysis of 1352 measurements for the Odra river basin in Poland, Rotnicki (1983)
proposed the equation
U=
F 0.791I R
H n K
2/3
S1/ 2 +0.141
...(8.8)
with a standard error of 12 percent. Here slope was obtained from topographic maps.
Palaeo Discharge Determination
Rotnicki (1983) has proposed a modified version of the above equation to predict discharge at a
particular instant of time as
Q=
F 0.921I AR
H n K
2/3
S1/ 2 + 2.362
...(8.9)
with a standard error varying from 7 to 26 percent depending on the discharge.
Williams (1988) used 233 river cross sections from a variety of environments and developed the
empirical equation for bankful discharge Qb.
Qb = 4.0 Ab1. 21 S 0 . 28
...(8.10)
265
Fluvial Palaeo Hydrology
where Ab is flow area at bankful stage and S is the slope. This is applicable for 0.5 £ Q £ 28 320 m3/s, 0.7
£ Ab £ 8510 m2 and 0.000 041 £ S £ 0.081. For braided channels Cheetham (1980) has analysed Leopold
and Wolman’s data and proposed the equation
Qb = 0.000 585 S –2.01
...(8.11)
for 0.0000 66 £ S £ 0.003
In the case of palaeo fluvial studies Williams (1988) prefers to use average daily flow for a number
of years Q in m3/s. He quotes the equation of Osterkamp and Hedman for 252 sites of various
environments in West Central USA,
Q = 0.027 Wb1. 71
...(8.12)
where Wb is the bankful width in m. This is applicable in the range 0.8 £ Wb £ 430 m. It may be
mentioned that Osterkamp and Hedman realised that the size of bed and bank material would affect the
coefficient in the above equation and have given their values in a tabular form (see Williams 1988).
Schumm (1972) analysed data of 33 sites in the Great Plains of USA and three sites on the
Murrumbidgee River in Australia. His data yields the equation
1.10
Q = 0.029 Wb1. 28 Dmax
...(8.13)
Cariston (1965) used data for 31 rivers in Central United States and related meander wavelength ML
to Q as
Q = 0.000017 M L2 .15
...(8.14)
which is applicable to meandering rivers with 145 £ ML £ 15,500 m.
Some investigators have used flood data at a gauging station and related flood discharge of a given
return period to the bed width B, meander wave length ML, cross sectional area, A and river sinuosity Si.
Thus according to Dury (1976, 1977) analysis of 135 data points of un-braided under-fit streams gave
the following equation
FG B IJ U|
H 2.99 K |
||
F
M I V
=G
H 32.857 JK ||
= 0.83 A S |
|W
1.81
Q1.58 =
1.81
Q1.58
Q1. 58
...(8.15)
L
1. 09
i
When the values of B. ML, A and Si are known, Q1.58 can be determined from
LMF B I
GH 2.99 JK
M
N
Q=
1.81
+
FG M IJ
H 32.857 K
L
3
1.81
+ ( 0.83 A1.09 Si )
OP
PQ
...(8.16)
266
River Morphology
Palaeo Velocity and Palaeo Discharge in Gravel-bed Rivers
Maizels (1983) has stated that in the case of gravel-bed rivers it is preferable to assume that critical
conditions prevail at bankful stage. If d is the characteristic size of bed material, for coarse sediment
critical shear stress will be given by Shields’ function
t 0c
= 0.056
( Dg s ) d
or for
Dgs = (1.65 ´ 9787), toc = 0.092d
...(8.17)
while for streams with 10 percent suspended sediment concentration
toc = 0.078d
...(8.18)
Knowing the palaeo channel slope S, critical depth Dc is obtained as
Dc = 0.092d S –1 or 0.078dS –1
...(8.19)
The flow depth can also be determined from geomorphic evidence of high water levels, bankful
depth from the thickness of sedimentary deposits or from field measurements of exposed palaeo
channels. Maizels found that for a series of 69 palaeo channels on the abandoned West Greenland
computed critical depth Dc was greater than the observed depth D and the ratio D/Dc was highly
variable, its mean value and standard deviation for clear water, and sediment laden flows being (0.5 and
0.44) and (0.83 and 0.49).
Once Dc and S are known, Manning’s n can be found using either Strickler’s equation
1/ 6
n = 0.039 d50
...(8.20)
or Limerinos equation
n=
1/ 6
0.113d50
FG116
DI
. + 2 log
J
d K
H
...(8.21)
84
or Darcy-Weisbach friction factor f using
f = 0.113
FD I
Hd K
c
50
1/ 3
..(8.22)
and velocity Uc determined. Some other equations discussed in Chapter VII can also be used.
Maizels has discussed the following four methods of palaeo discharge determination.
(1) Empirical discharge equations relating mean annual flood discharge, mean annual discharge or
bankful discharge to the channel dimensions or channel form parameters
(2) Empirical drainage area-discharge relations such
Q = aAb
...(8.23)
267
Fluvial Palaeo Hydrology
(3) Relations of the type Q as a function of S as proposed by Cheetham (1976) for Leopold and
Wolman’s braided river data
Qb = 0.000 585 S –2.01
...(8.24)
(4) Regime type relations in which bankful discharge is related to width or depth
Maizels has opined that none of these methods is very useful for coarse-bed palaeo channels; hence
he recommends those methods based on palaeo velocity determination. Further, he made palaeo
discharge computations from palaeo velocity determined by five methods namely
(1) using Chezy’s equation with C = (8g/f )1/2
1/ 6
(2) using Manning’s equation with n = 0.039 d50
(3) Manning’s equation with n obtained from Limerinos equation
(4) Darcy-Weisbach equation with f = 0.113
FD I
HdK
1/ 3
c
(5) Darcy-Weisbach equation with f obtained from White-Colebrook equation and then discharge
obtained as Qc = Uc DW.
The discharges Qc obtained by these methods for 69 palaeochannels were compared. On the basis of
this comparison Maizels recommended that for palaeo channels with coarse gravel-bed, ManningLimerinos approach is better if channel widths are uncertain, whereas Darcy-Weisbach approach is
better for well defined channels.
8.6
PALAEO HYDROLOGIC STUDIES IN INDIA
The palaeo hydrologic studies in India are primarily related to establishing palaeo flood records of some
rivers in Central and Western India. The method used for these studies is the analysis of slack water
deposits. Slack water deposits (SWD) are fine-grained sand and silt deposit that falls rapidly out of
suspension during large floods in protected areas, where the fall velocity is markedly reduced. Such
deposits take place in stable bed rock canyons expansion and contractions, back flooded tributaries,
meander bends, caves, and abrupt channel. The upper layers of SWD closely approximate the actual
stage of flood peak. These depths provide a lot of information on palaeo floods. The age of the deposits
are determined by radiometric dating of associated organic or archaeological material. It is shown that
the thickness and grain size of SWD is directly proportional to the flood magnitude. The tops of SWD
generally provide a minimum estimate of flood peak stage and hence it is possible to estimate minimum
peak discharge with each deposit. In the last two decades some studies have been conducted on five
rivers in Central and Western India with the following objectives in mind : (i) to identify temporal
patterns of large floods during late Holocene; (ii) to identify periods of high and low floods; and (iii) to
examine the relationship between flood regime and palaeo climate.
The rivers studied (see Kale 1999) have been the Narmada at Punasa, the Godavari at Papikonda,
the Krishna at Srisailam, the Tapi at Ghuttigarh Khapa and the Luni river at Bhuka. The maximum
thickness of SWD ranged from 2.5 m to 10.5 m and 11 to 37 floods are documented in these deposits.
Tributary mouths are the most common geomorphic sites for SWD. The slack water deposits at three
places on the Luni river near Bhuka in the Tahr desert in North Western India as reported by Kale et al.
(2000) are shown in Fig. 8.3. These deposits were dated using luminescence technology. The textural
268
River Morphology
Fig. 8.3
Slack water deposits on the Luni river (Kale et al. 2000)
and stratigraphical analysis of SWD indicated that near the tributary channel there is higher variability
in sediment size and predominance of finer sediment units. With increasing distance and elevation the
percentage of sand increases and the sorting improves. Change in sedimentological and stratigraphical
characteristics distinguish the individual units. These characteristics imply sediment deposition by flood
waters and also suggest that the sediments deposited at higher level were emplaced by higher magnitude
floods and some of the sediments closer to tributary channel were also deposited by moderate magnitude
floods. The deposits and their dating suggest that the river has experienced at least 17 extreme floods in
the last millennium. Evidence at this site also suggests that no floods comparable in magnitude to July
1979 mega flood have occurred during this period. This observation is in conformity with palaeo flood
record of central India. Comparison of long-term monsoon rainfall series for the Luni basin and the
region reveals a clear link between the two and indicates that the clustering of large floods in the last few
decades and during the medieval warming period is a regional phenomenon associated with wetter
conditions. Long-term fluctuations in Indian monsoon rainfall in the past have been explained in terms
of large climatic changes in the Asian monsoon region. For completeness of information it may be
mentioned that the river Luni at Gandhar has a catchment area of 35 000 km2, width 120-150 m and
depth 4 to 10 m. Maximum one-day rainfall of 100 years return period is 200 to 257 mm. The 1979 mega
flood had a discharge of about 4300 m3/s. The flood of 1990 was of similar magnitude.
Kale et al. (1993) have examined the SWD on the Choral river near Barjar in Central Narmada
Basin, India. At several locations, sequences of fine-grained sandy flood deposits have been preserved
269
Fluvial Palaeo Hydrology
on the channel margins. The stratigraphic studies of the deposits using radio carbon dating revealed that
510 + 135 B.P. record of floods is preserved in SWD. It was found that during this period discharges
greater than 4500 m3/s must have occurred. At least 7 flood units separated by scree deposits, slope
wash and charcoal were obtained; see Fig. 8.4. Geomorphic investigations revealed the presence of
boulders with intermediate axis between 23 and 42 cm. Such studies have been carried out on the
Narmada near Punasa, the Godavari at Papikonda, the Krishna at Srisailam, and the Tapi at Ghuttigarh
Khapa and the Luni at Bhuka (see above). The maximum thickness of SWD ranged from 2.5 m to 10.5
m and 11 to 37 floods are documented in these deposits.
Lithosection
SWD- Choral
Flood cm
Units 150
C0
Rubble
74 0¢N
Location map
1
KA
MA
C1
2
100
C3
Rubble
22
15¢
N
4
Rubble
50
6
0
Slope wash
4
8 kms
C4
C6
0
Fig. 8.4
CH
O
R
BARJAR AL
C2
3
R
Rubble
Shells
Rubble
Rubble
5170 ± 135 Yrs BP
Sand
Charcoat
Slack water deposits on the Choral river near Barjar (Kale et al. 1993)
Figure 8.5 given by Kale et al. (2000) summarises the palaeo flood chronology for Central and
Western India during the late Holocene climatic changes. The top scale indicates C-14 years before
present (B.P.). The second scale shows the global temperature changes (RW – Roman Warm, DAC –
Dark Ages Cold, EMC – Early Medieval Cool, MW–Medieval Warm, LIA – Little Ice Age, MOW –
Modern Warm). Below these are given the chronology of palaeo floods in the Narmada, the Luni and the
Godavari. This study shows distinct century scale variations in flood frequency and a noteworthy
clustering of large floods during the late Holocene period. The study further indicates a period of
significantly reduced frequency of large floods during late Medieval and Little Ice Age periods (i.e.
1500 A.D. to 1800 A.D.), and an enhancement in the magnitude and frequency of large floods in the
post 1950 period. The last one thousand years of relatively better resolutions of palaeo flood records
demonstrates a good association between palaeo floods and late Holocene climatic changes recognised
in wide spread area of the world. Hence the authors concluded that the century scale variations in flood
frequency and magnitude are linked to long term variations in the monsoon precipitation which are in
270
River Morphology
Fig. 8.5
Palaeo floods chronology for Central and Western India (Kale et al. 2000)
turn connected with large scale shift in global circulation patterns and ENSO (El Nino Southern
Oscillations) activity.
Similar studies about obtaining monsoonal activity have been carried out by analysing the deposits
in the lakes, studying ice cores in glaciers, and deposits in Arabian Sea. Kumar Sagar (1995) studied the
lake deposits in Jammu and Kumaon regions. The rates of deposition of sediment were assumed to be
proportional to yearly rainfall. This deposition rate varied from 0.55 mm to 1.05 mm/year in the three
lakes in Kumaon region while in Naukuchital it was between 0.16 mm to 3.08 mm/year. Kashmir lakes
showed the deposition rate of 5.5 mm for the top 30 cm. A multidisciplinary proxy palaeo climatic
investigation in Mansar Lake, Jammu indicated periods of enhanced rainfall between 580 B.C. and 300
A.D. This period is indicative of wet humid phase. From 300 A.D. to 1400 A.D. the area experienced a
relatively dry and arid phase with Medieval warming.
Thompson et al. (2000) recovered three ice-cores from the Desuopu glacier, Tibet using an
electromechanical drill. Their lengths varied from 149.2 m to 167.7 m at about 7000 m above mean sea
level. These cores were analysed over the entire length for their oxygen isotope ratio, chemical
composition, and dust concentration. In addition they were analysed for hydrogen isotope, chloride
(Cl–), sulphate (SO 4–) and nitrate (NO 3–). The bulk of annual precipitation in the Himalayas arrives
during the summer monsoon season and at Desuopu it is net 1000 mm water. The high annual
accumulation allows preservation of distinct seasonal cycles. These studies revealed that the site is
sensitive to the fluctuations in the intensity of South Asian monsoon, reduction in monsoonal intensity
are recorded by dust and chloride concentration. Deeper and older sections of Desuopu cores suggests
many periods of drought in the region, but none have been of greater intensity than the greatest recorded
drought during 1790-1796 A.D. of last millennium. 20th Century increase in anthropogenic activity in
India and Nepal, upwind from this site, is recorded by doubling of chloride concentrations and four fold
increase in dust. Like other ice cores from Tibetian Plateau, Desuopu suggests large scale plateau-wide
20th century warming trend that appears to be amplified at higher elevations.
Fluvial Palaeo Hydrology
271
Sarkar et al. (2000) collected sediment cores from Arabian sea in water depths ranging from 280 m
to 1680 m and analysed O18 and C13 composition of foraminifera. It appears that excess of evaporation
over precipitation steadily appears to have decreased during the last 10,000 to 2,000 years, most
probably due to increasing trend in summer monsoon rainfall, contrary to land-based palaeo climatic
data from the region, which indicates onset of aridity around 4000 years ago. This result is consistent
with the hypothesis that significant spatial variability in the monsoon rainfall observed today was
persistent during most of Holocene. The analysis of data also indicated significant periodicities of 700
and 1450 years. Similar periodicities have also been reported from North Atlantic and Arabian sea
sediment cores.
8.7
FLUVIAL PALAEO HYDROLOGIC STUDIES IN INDIA
As regards fluvial palaeo hydrologic studies in India, mention may be made of the efforts to trace the
course of the river Saraswati about which reference is found in ancient Indian literature. About one
hundred years back the British engineer C.F. Oldham sparked the modern quest for the river Saraswati
by questioning why the seasonal river Ghaggar should have a width of about three kilometres in places
unless it earlier occupied the bed of a wider river. Since then wind blown sand dune area of Gantiyalji
near Longewal has been studied extensively by the specialists in remote sensing, hydro geologists,
archaeologists and the historians by taking undisturbed cores of sediment plus water from a depth of 70
m below the ground surface to trace the course of lost river Saraswati, along which prehistoric culture
flourished in the historic past. The river course has been studied not only from the historic point of view
but also with the hope that it may ultimately lead to providing sweet water for drinking and irrigation
purposes in otherwise saline area. The records indicate that the river disappeared around 1500 B.C.
while the decline started about 3700 years ago. Two logical questions that need to be answered in this
regard are: What courses did the river follow? and Why did it dry up ?
In order to trace the river course water samples collected from underneath were tested using carbon
dating technique and it was estimated to be 3000-4000 B.P. (Before present) old, i.e., of the Rig Vedic
era. Rough course of some buried channels has been traced and sediment samples collected to determine
their age; the river course has also been confirmed from satellite imageries. Along the river the drilling
has been done to provide sweet drinking water, which is obtained at a depth of 30 m below the surface.
The river course can be clearly seen from marks of palaeo channels as wide as 12 km. One hundred
and seventy five archaeological sites have been found along the alluvial plain of the Ghaggar river.
Since ancient times the civilisations flourished along the river providing water for drinking and
irrigation, it is argued that the Ghaggar must have been the mighty Saraswati of the Vedic period. The
Saraswati was originally fed by two show-fed sources namely Bunderpunch massif in the Garhwal and
Kapalshikar near Manasarovar in Shivaliks. At Pipli in Haryana the Saraswati probably crossed the
Grand Trunk Road of the present and the Saraswati statue is erected there. There is reference in
Mahabharat that Kurukshetra was to the south of the Saraswati and to the north of the Drashadvati. The
river is traced from West Garhwal in the Himalayas to the Gulf of Khambat in Gujarat.
Various shifting courses of the Saraswati, as constructed by Ghosh et al. (1983) from all the
available evidence, are shown in Fig. 8.6. The oldest course obtained by joining abandoned, buried
channels passed through the present cities of Nohar, Surjansar, Samrau and Panchpadra (course 1). With
the onset of aridity during Pleistocene and advancement of sand from south-west, the river started
272
River Morphology
Fig. 8.6
Old and new courses of the Sarswati river
shifting and eventually followed the course 2 towards west. At that time the present cities of Sirsa,
Lunkaransar, Bikaner, Samrau and Panchpadra were on its right bank. Probably during the early
Holocene period, there was another shifting of the Saraswati towards west between 10,000 and 3800
B.C. The two courses followed are shown as course 3. It turned towards west near Nohar and flowed
though Rangamahal, Suratgarh, Anupgarh and Sakhi; hence it severed its confluence with Luni at
Panchpadra and discharged into Rann of Kutchh through a river course called Hakra or Nara (Pakistan).
Due to increased Aeolian sand that the river had to carry during this period the river aggraded and
ultimately took another course through Jakhal, Sirsa, Hanumangarh, Pilibangan, Suratgarh, Anupgarh
and Sakhi (course 4). Further around 3800 B.C. the Saraswati further made a westward shift at
Anupgarh and joined Indus drainage system in Pakistan (see course 5).
What caused the disappearance of the Saraswati? Because of tectonic effects the old Arawali hills
cut off the head waters of the Saraswati. The branch of river the Chambal cut deep into the strata
273
Fluvial Palaeo Hydrology
northwards and gradually diverted water of the Saraswati first by the Yamuna and then by the Sutlej.
The new channel migrated eastward became the Yamuna; similarly the Sutlej migrated westward and
joined Indus. This diversion caused a drastic reduction in the flow of Saraswati. When the Saraswati
flowed in south-westerly direction, it was flowing against north easterly moving sand advance in Thar
desert. Therefore, the Saraswati river could not overcome such sand advance and hence started drifting
towards the north with rotational migration in clockwise direction until it became buried in the
Anupgarh plains.
References
Baker V.R. (1983) Large Scale Palaeo Hydrology. In Background to Palaeo hydrology (Ed. Gregory, K.J.). A
Wiley Interscience Publication, John Wiley and Sons, New York, Chapter 20, pp. 453-478.
Benson M.A. and Dalrymple T. (1967) General Field and Office Procedures for Indirect Discharge
Measurements. Technical W.R. Investigation (USGS) Book 3, Chapter A1, pp. 1-30.
Berglund B.E. (Ed.) (1986) The Handbook of Holocene Palaeo ecology and Palaeo hydrology. John Wiley and
Sons, Chicester.
Bray, D.I. (1979) Estimating Average Velocity in Gravel-Bed Rivers. JHD, Proc. ASCE, Vol. 105, HY-9, Sept. pp.
1109-1122.
Cheetham G.H. (1976) Palaeo Hydrological Investigations of River Terrace Gravels. In Geo-archaeology (Eds.
Davidson, D.A. and Shakley, M.L.), Duckworth, London, pp. 335-344.
Chow V.T. (1959) Open Channel Hydraulics. McGraw Hill Book Co., New York.
Dury G.H. (1976) Discharge Prediction, Present and Former, From Channel Dimensions. Jour. of Hydrology, Vol.
30, pp. 219-245.
Dury G.H. (1977) Underfit Streams: Retrospect, Perspect and Prospect. In River channel Changes (Ed. Gregory,
K.J.). A Wiley Interscience Publication, John Wiley and Sons Ltd., Chicester, Chapter 18, pp. 281-289.
Garde R.J. and Kothyari U.C. (1986) Erosion in Indian Catchments. Proc. 3rd International Symposium on River
Sedimentation. The University of Mississippi (USA), pp. 1249-1258.
Ghosh B., Kar A. and Husain Z. (1983) Comparative Role of the Aravalli and Himalayan River Systems in the
Fluvial Sedimentation of the Rajasthan Desert. In Geomorphology (Ed. Dixit K.R.) Heritage Publishers, New
Delhi, pp. 209-213.
Gregory K.J. (Ed) (1983) Background to Palaeo hydrology. A Wiley Interscience Publication, John Wiley and
Sons, Chicester.
Gregory K.J., Lewin J. and Thornes J.B. (Eds) (1987) Palaeo hydrology in Practice: River Basin Analysis. A
Wiley Interscience Publication, John Wiley and Sons, Chapter 1.
Kale V.S. (1999) Late Holocene Temporal Patterns of Palaeo floods in Central and Western India. Man and
Environment, Vol. 24, No. 1, pp. 109-115.
Kale V.S., Mishra S., Baker V.R., Rajguru S.N. Enzel Y and Ely L. (1993) Prehistoric Flood Deposits on the Coral
River, Central Narmada Basin, India. Current Science, Vol. 65, No. 11, pp. 877-878, Dec. 10.
Kale V.S., Singhvi A.K., Mishra P.K. and Banerjee D. (2000) Sedimentary Records and Luminescene Chronology
of Late Holocene Palaeo floods in the Luni River. Catena, Elsevier Publishers, Vol. 40, pp. 337-358.
Kothyari U.C. and Garde R.J. (1991) Annual Runoff Estimation for Catchment in India. JWRPM, Proc. ASCE,
vol. 117, No. 1, Jan/Feb., pp. 1-10.
274
River Morphology
Kumar Sagar M.G. (1995) A Comparative Study of Monsoonal and Non-Monsoonal Himalayan Lakes, India.
Proc. 15th International C14 Conference (Eds. Cook G.T., Harkness D.D., Miller B.F., and Scott E.M.) Vol.
37, No. 2, pp. 191-195.
Lacey G. (1934). Uniform Flow in Alluvial Rivers and Canals. Min. of the Proc. Inst. C.E. (London), Vol. 237, Pt.
1, pp. 421-453.
Langbein W.B. et al. (1949) Annual Runoff in the United States. USGS, Circular-54. 14 p.
Langbein W.B. and Schumm S.A. (1958) Yield of Sediment in Relation to Mean Annual Precipitation. Trans.
A.G.U., Vol. 39, pp. 1076-1084.
Leeder M.R. (1973) Fluviatile Fining – Upward Cycles and the Magnitude of Palaeochannels. Geol. Magazine,
Vol. 110, No. 3, pp. 265-276.
Leopold L.B. and Miller J.P. (1954) Post Glacial Chronology for Alluvial Valleys in Wyoming. USGS Water
Supply Paper 1261, pp. 61-85.
Maizels J.K. (1983) Palaeo velocity and Palaeo discharge Determination of Coarse Gravel Deposits. In
Background to Palaeo hydrology (Ed. Gregory K.J.) A Wiley Interscience Publication, John Wiley and Sons
Inc., New York, Chapter 5, pp. 101-139.
Noble E.L. (1965) Sediment Reduction Through Watershed Rehabilitation, USDA, Misc. Publ. 970, pp. 114-123.
Rotnicki K. (1983) Modelling Past Discharges of Meandering Rivers. In Background to Palaeo hydrology (Ed.
Gregory K.J.) John Wiley and Sons Inc., New York, Chapter 14, pp. 321-346.
Sarkar A., Ramesh R., Somayajulu B.L., Agnihotri R., Jull A.J.T. and Burr G.S. (2000) High Resolution Holocene
Monsoon Record from Eastern Arabian Sea.. Earth and Planetary Science, Letters, Vol.117, pp 209-218.
Schneider S.H. and Root T.L. (2000) Climate Change. Available on Internet.
Schumm S.A. (1965) Quaternary Palaeo hydrology. In the Quaternary of the United States (Eds. Wright H.E. and
Frey D.G.) Princeton University Press, Princeton. pp. 783-794.
Schumm S.A. (1977) The Fluvial System. A Wiley Interscience Publication, John Wiley and Sons , Chicester.
Thompson L.G., Yao T., Mosley-Thompson E., Davis M.E., Henderson K.A. and Lin P.N. (2000) A High
Resolution Millennium Record of the South Asian Monsoon from Himalayan Ice Cores. Science Magazine,
Vol. 289, No. 5486, pp. 8.
Williams G.P. (1978) Bankful Discharge of Rivers. W.R. Res. Vol. 14, No. 6, pp. 1141-1154.
Williams G.P. (1988) Bankful Palaeo fluvial Estimates from Dimensions of Former Channels and Meanders. In
Flood Geomorphology (Eds. Baker V.R. Kochel R.C. and Patton P.C.) A Wiley Interscience Publication, John
Wiley and Sons, New York, Chapter 19, pp. 321-334.
C H A P T E R
9
Bed Level Variation in Streams
9.1
INTRODUCTION
The concept of a graded stream or stream in equilibrium has been introduced in Chapter 4. The balance
between yearly water discharge Q, yearly bed material discharge Qs, channel slope S, and the bed
material size d for such streams is expressed qualitatively by Lane’s balance analogy (Lane 1955)
QS ~ Qs d
...(9.1)
This qualitative statement is illustrated in Fig. 9.1 and is valid when channel plan-form and channel
width remain the same. This equilibrium can be disturbed by natural causes or man-made changes, and
then the channel adjusts to the new conditions by either increasing the slope over a reach (known as
aggradation), or by decreasing the slope over a reach (known as degradation). Thus, if Qs increased
keeping Q and d the same, the slope will increase by sediment deposition so that with the increased
slope and unaltered Q and d, the stream can carry the increased sediment load. In a similar manner, if Q
is increased keeping Qs and d the same, a smaller slope will be required to carry this sediment load; this
is achieved by lowering of the bed levels resulting in reduction in slope and thus degradation results.
Since a stream in equilibrium must satisfy continuity equations for flow and sediment, and
resistance and sediment transport relationships, one can get the exact form of Eq. (9.1) if choice is made
of resistance and sediment transport relationships. Assuming Q and d to remain unchanged along the
length of the stream and using Manning’s and Du Boys equations, one can write
Q = BDU
1
2 / 3 1/ 2
Q = n ( BD) D S
constant BD 2 S 2
Qs = Bqs =
d 3/ 4
U|
||
V|
||
W
...(9.2)
276
River Morphology
Q
S
Ag
gra
dat
ion
on
ati
rad
g
De
Qs
d
Fig. 9.1 Lane’s balance analogy
Eliminating D from these equations, one gets (Garde and Ranga Raju 2000)
Q 6 / 7 S 7 / 5 ~ Qs d 3 / 4 B1/ 5 n - 6 / 7
or Q
6/7
S
7/ 5
~ Qs d
3/ 4
UV
W
...(9.3)
if channel width B and Manning’s n are assumed to be constant. Similar analysis has been presented by
Jensen et al. (1979) and Klaassen (1995). If some other equations were used for resistance and rate of
sediment transport, the exponents of Q, S and d would have been slightly different; however Lane’s
balance analogy would still be valid qualitatively.
If the rate at which sediment entering a given reach of the stream is less than that at which it is going
out, the excess sediment will be picked up from the bed and banks, and there will be lowering of bed
level unless the bed is non-erodible; this is known as degradation or retrogression. Thus for degradation
¶ Qs
must be positive. On the other hand, if the rate at which sediment enters a given reach of
¶x
a stream is greater than the rate at which it goes out, the channel bed experiences deposition of sediment;
to occur
¶ Qs
must be negative. Aggradation or
¶x
degradation occurs over large lengths and both are slow processes. Degradation particularly may
proceed for years before it becomes evident. Aggradation and degradation taking place upstream and
downstream of large dams respectively are well studied and documented.
When alluvial streams are partially obstructed by hydraulic structures such as bridge piers, guide
bunds, spurs or abutments, the local flow pattern around the structure is drastically changed causing
high velocities and shear stresses in the vicinity of the structure causing local lowering of the bed level.
This is known as local scour. Local scour occurring around structures such as bridge piers can endanger
this is known as aggradation. For aggradation to occur
277
Bed Level Variation in Streams
their foundations causing bridge collapse. This chapter is devoted to the discussion of degradation, local
scour around bridge piers, aggradation, and aggradation upstream of dams.
DEGRADATION
9.2
TYPES OF DEGRADATION
Mention of the phenomenon of degradation is found in Irrigation Manual by Mullins published in 1889,
in his book on Irrigation works in India by Buckley in 1905, and in U.S.A. by Gilbert (1917) when he
clearly differentiated between scouring and degradation. Degradation occurring in a stream can proceed
either in the downstream or in the upstream direction depending on the basic cause of degradation
(Galay 1980, 1983).
If the reduction in the slope is caused by reduction in Qs, reduction of d or increase in Q at the
upstream end, downstream-progressing degradation will occur. On the other hand, if an increase in
slope is imposed at the downstream end, upstream Q, Qs and d remaining the same, upstreamprogressing degradation will result. Upstream-progressing degradation occurs if the level of the lake in
which the river discharges drops suddenly. It is found that, in general, upstream-progressing degradation
takes place at a much faster rate than the downstream-progressing degradation, because in the former
case, increase in slope results in substantial increase in the bed material discharge. In the case of
downstream-progressing degradation, the slope is progressively reduced and the bed material discharge
is asymptotically reduced to zero; hence, it takes much longer time. Occurrences of downstream and
upstream-progressing degradation are shown in Fig. 9.2.
Degradation
Progress
D/s
U/s
D/s
D/s
D/s
D/s
s
s
U/s
U/
s
Tributary with D/s
D/s
U/
U/
U/s
U/s
D/s
River Situation
Tributary
No Tributaries
D/
s
U/
s
D/
s
U/
s
U/s
U/s
D/
s
U/s
U/
s
Note: D/s = downstream progressing degradation
U/s = upstream progressing degradation
Fig. 9.2 Upstream and downstream progressing degradation (Galay 1980)
U/s
278
River Morphology
The composition of bed material of the degrading stream plays an important role in the process of
degradation. Consider degradation taking place downstream of a large capacity reservoir which traps
most of the sediment load carried by the stream. If the bed material is uniform and the stream slope is
relatively large, the flow deficient of sediment load picks up more sediment from upstream reaches and
relatively less from the downstream reach. As a result, stream slope reduces by rotation of stream bed
about some downstream control where the water level is held constant. When the slope has reduced to
the extent that shear stress on the bed is critical for that size, degradation will stop; see Fig. 9.3. This is
known as rotational degradation.
Fig. 9.3
Definition sketch for rotational degradation
However, if the bed material of the degrading stream is non-uniform and the shear stress exerted by
the flow is such that all the particles on the bed are moving, initially rotational degradation will take
place thereby reducing the shear stress acting on the bed. When the reduced shear stress t o2 is equal to
the critical shear stress for the d80 or d90 of the bed material, the coarsest fractions of the bed material
which could not move start accumulating on the surface. Fifty to sixty percent areal coverage by such
material on the surface forms an effective protective armour coat which stops further reduction in slope
and hence rotation of the bed. Now degradation takes place by the removal of finer particles at
essentially a constant slope. This is known as parallel degradation. For given parent material, any shear
stress smaller than t o2 will give one size distribution of armour coat and increasing shear stress will
coarsen the armour coat. The armour coat is coarsest at t o2 for a given non uniform bed material.
Harrison (1950) has studied the armour coat formation. He found that
i) Progressive coarsening of surface layer in armour coat development causes an increase in the
effective roughness
ii) A layer of non-moving particles of one particle size thickness is effective in preventing erosion.
iii) The non-moving particles in the pavement arrange themselves in a characteristic shingling
formation.
iv) As per Einstein’s bed-load theory
movement.
Dg s di
= 27 gives the limiting size beyond which there is no
t0
279
Bed Level Variation in Streams
Fig. 9.4 Gessler’s criterion for incipient motion
The concept of parallel degradation was first introduced by Gessler (1965). Gessler conducted
experiments on degradation using non-uniform sediment at a constant slope and the experiments were
stopped when the bed was armoured resulting in practically no movement. The surface layer was
sampled and the ratio of fraction of sediment of a given size range di in the top layer of armour coat to its
fraction in the parent material was determined. This ratio pi was taken as the probability of the size
remaining stationary for the applied shear stress t 0. This value was also interpreted as the probability
that instantaneous shear stress on the bed was smaller than the critical shear stress for that size. The
average shear stress was considered critical for that size fraction for which pi was 0.50. In this way the
critical shear stress curve similar to Shields’ curve was prepared. This curve is shown in Fig. 9.4. When
t0
obtained in this manner was plotted against pi on normal – probability scale, it yielded a straight
t 0c
line as shown in Fig. 9.5 with a standard deviation of 0.57, thereby indirectly indicting that shear
fluctuations on the bed follow normal distribution. Later studies by Little and Mayer (1972) and Davies
(1974) have given slightly smaller values of the standard deviation viz. 0.43 and lower value of critical
shear stress for coarser material. Use of Figs. 9.4 and 9.5 enables one to compute size distribution of
armour coat for parallel degradation for known parent bed material. Gessler found that for grain size
having
Dg s di
greater than 50, pi can be taken as 100 percent.
t0
Figure 9.6 shows qualitatively the regions of no motion, parallel degradation and rotation
degradation in relation to size distribution of bed material and initial shear stress. Here da is the average
size of the bed material size. According to Egiazaroff (1965) if applied shear stress is less than the
critical shear stress for di = 0.4 da, there will be no movement; if the shear stress is greater than the
critical shear stress for di = 0.4 da and less than the critical shear for di = 3.0 da parallel degradation
280
River Morphology
Fig. 9.5 Relation between probability of movement Pi and dimensionless bed shear stress
Fig. 9.6
t0
(Gessler 1995)
t 0c
Regions of no motion, and parallel and rotational degradation
would result. If applied shear is greater than critical shear for di = 3.0 da, rotational degradation results.
The demarcating value of shear stress between parallel and rotational degradation has been obtained by
Mittal (1985) by using Gessler’s method for some hypothetical mixtures. The mean curve between
281
Bed Level Variation in Streams
t0 i
D g s d501
å
and Kramer’s uniformly coefficient M defined as M =
å
50
d
0 i
100
d
50 i
D pi
D pi
along with available data
plotted on it is shown in Fig. 9.7. The coordinates of the mean curve in Fig. 9.7 are given in Table 9.1.
Fig. 9.7
Variation of
Table 9.1 Variation of
toi
with M (Mittal 1985)
D g s d 50i
toi
with M (Mittal 1985)
D g s d 50i
M
0.20
0.30
0.40
0.80
toi
D g s d 50i
0.19
0.10
0.06
0.04
Little and Mayer (1972) have proposed the equations
d50 a
= 0.908
d50 i s gi
s ga
s gi
F u
I
GG
JJ
H dr / r - 1i g K
3
*
s
f
= 1.317 – 0.2458 sgi
0.353
...(9.2)
282
River Morphology
Here u* =
t oi
and sgi and sga are geometric standard deviations of parent material and armour
rf
coat respectively.
Using limited data Shen and Lu (1983) proposed the following equation for d50a
FG IJ s
H K
t ¢o
d50 a
= 0.853.
t oc
d50 i
0.885
gi
...(9.3)
in which t¢o is the shear stress with respect to grain roughness and sgi is geometric standard deviation of
parent material of median size d50i.
Using Little and Mayer’s data and the data from San Luis Valley canals, Odgaard (1984) found that
the size distribution of armour coat follows normal distribution. Recently Garde et al. (2004) have
plotted size distribution data for armour coat from a number of studies in the form of
di
vs percent
d50 a
di
.
d50 a
Here d50a is median size of the armour coat. The distribution has a standard deviation of 0.57. Hence, if
d50a can be determined for known size distribution of the parent material and known to, armour coat size
distribution is known. Garde et al. (2004) have proposed the following equation for d50a
finer and found Odgaard’s conclusion to be true except for very small and very large values of
d50 a
d50 i
R|
U|
| - 1.648 |V
M = 0.3 + 1.361 exp. S
|| t FG D IJ ||
T Hd K W
1.241
...(9.4)
*i
50 i
t 0i
and D is depth of flow.
D g s d50 i
This equation is based on a large volume of data and is found to be more accurate than Eqs. (9.2) or
(9.3).
Here M is Kramer’s uniformity coefficient of initial mixture, t*i =
9.3
DOWNSTREAM-PROGRESSING DEGRADATION
As mentioned earlier, downstream-progressing degradation is related to the changes in Q, Qs or d at the
upstream end. The situations under which downstream-progressing degradation takes place are
discussed below.
Degradation Downstream of High Dams and Barrages
When a high dam is constructed on a movable bed river, it traps a very large percent of the incoming bed
material load; this percentage can be as high as 95 percent. As a result, water released from the dam is
283
Bed Level Variation in Streams
deficient in sediment load as compared to its sediment transport capacity. Hence the flow picks up
sediment from the bed (and from the banks if bed is non-erodible) and the bed level goes down thereby
decreasing the slope. The rate and extent of degradation depends on many factors such as flow releases
from the dam, downstream slope, size distribution of the bed material and its variation with depth,
downstream control. Extensive observations have been made in U.S.A. and other western countries on
degradation occurring downstream of dams on several streams. In this connection papers by Stevens
(1938), Hathaway (1948), Bondurant (1950), Vetter (1953) and Galay (1983) may be seen. Table 9.2
gives the information on the extent and length of degradation, duration and bed material description for
few dams, Galay (1988) has observed that degradation across the stream may not always be uniform. He
mentions the case of degradation below the Gardiner dam on the South Saskatchewan river in Canada,
where at a section 1.6 km downstream of the dam about 200 m of the 1000 m width had experienced 2–3
m lowering while it was much less in the rest of the channel width. This is likely to be due to nonuniform releases of flow from the dam as well as the non-uniformities in bed material across the width.
A brief discussion is necessary about the changes in bed level downstream of barrages in IndoGangetic plain of the Indian subcontinent, where thick alluvial strata exist. Barrage is a low–height
gated weir used to raise the water level so that canals can take off from the upstream of the barrage. The
Islam Weir on the Sutlej River failed due to excessive degradation. Two metres of degradation caused
the failure of part of the weir. It has been found that downstream of such weirs the bed degrades for a few
years which is followed by aggradation. This occurs probably because of the manner in which the gates
are operated. The data on barrages in India, Pakistan and Egypt indicate that degradation of the order of
0.8 m to 2.0 m has occurred in the past.
Table 9.2
Data on degradation downstream of high dams (Adapted from Garde 1955 and Galay 1983)
River
Dam
Degradationm
Strata
Saalach (Germany)
Reichenhall
3.0
-
Missouri (U.S.A.)
Fort Peck
1.5
Wisconsin (U.S.A.)
Praire Du Sac
2.3
South Canadian
(U.S.A.)
Conchas
3.1
Sand and
gravel
Length of
degradation km
Period of
observation years
9.0 km up to confluence
with Saalach River
21
Alluvial
About 80 km
11.5
Sandy
-
18
32 km
10
Rio Grande (U.S.A.)
Elephant Butte
2.1 to 2.4
-do-
About 150 km
2
Wolf Creek (U.S.A.)
Fort Supply
2.4
Sand
-
4.5
Colorado (U.S.A.)
Hoover
7.1
Sand and
gravel
111 km
14
Colorado (U.S.A.)
Imperial
3.1
-do-
-
18
-
4 to 5.5
Yuba (U.S.A.)
Yellow (China)
Sanmexia
Mainstee (Canada)
Junction
4
3.7
Gravel
Fine sand
Sand and clay
-
2
68
4
-
12
284
River Morphology
Data on four weirs Khanki, Rupar, Rasul and Marala on the rivers the Chenab, the Sutlej, the
Jhelum and the Chenab respectively during the period 1891-1927 indicated (see Garde 1955) that the
rate of degradation varied from 3 cm/year to 24 cm/year while the rate of recovery ranged from 6 cm/
year to 13 cm/year.
It may be mentioned that the degradation that has occurred on the Ratmau torrent in North India
over a period of 100 years has been well documented and discussed briefly in Chapter 11.
Increase in Water Discharge
An alluvial river will experience degradation if water discharge in the stream is increased by flow
diversion. Since increased flow with the same slope and sediment size has higher sediment transport
capacity, the flow picks up sediment from the bed and banks of the river, and degradation occurs; see
Fig. 9.13(b). Such degradation has been observed by Kellerhals et al. (1977) on the Mattagami river
flood way (Adam Creek) in Ontario, Canada, and also on the Five Mile Creek in Wyoming (U.S.A.)
where clear water flow was added to the creek from waste water of the irrigation project (Lane 1955).
Change of land use, such as deforestation, can also increase flood discharge and cause degradation,
however the extent of degradation would depend on the supply of sediment from the upper part of the
catchment. In a similar manner, an exceptionally high flood can cause lowering of stream bed in the
downstream direction. However, degradation occurring during high flood seems to depend on the nature
of flood and sediment concentration hydrographs. Degradation will occur during the rising limb of
hydrograph if river is carrying relatively less sediment load compared to its capacity. Such lowering of
the order of five metres occurred during 1933 on the Yellow river reach of about 50 km around Lungmen
(Todd and Eliassen 1940).
Gravel Mining
When sediment is removed from the channel bed for construction activity, the sediment transported by
the stream will get deposited in the depression created by removal of material, and hence the flow
downstream will have less sediment load compared to its capacity. As a result, degradation occurs in the
downstream reach. Such degradation of a few metres was observed on the Cherry Creek near Denver
(U.S.A.) (Lane 1947). Similarly, extensive degradation along with local scour has been observed at a
major bridge in Canada by Cullen and Humes (see Galay 1983).
Storage of Bed Material
Downstream-progressing degradation has also been found to occur below alluvial fans. As the river
emerges from a single steep channel from the mountainto the plain, it deposits most of its coarse bed
material on the alluvial fan and the river flows in multiple channels. When such channels join into a
single channel at the base of the fan, it is deficient in bed material load; hence, degradation can take
place. Such degradation has been observed by Galay (1983) in Iran.
Degradation at Channel Bifurcations
Downstream-progressing degradation also occurs at channel bifurcations. Consider a channel taking off
from the main stream and further assume fifty percent of the flow is diverted. If the stream is carrying
appreciable quantity of bed load, the diversion channel will carry a very large percent of bed load due to
formation of secondary circulation at the bend. As a result the main branch will carry less bed load and
will experience degradation, while the branch may experience aggradation.
Bed Level Variation in Streams
9.4
285
UPSTREAM-PROGRESSING DEGRADATION
If the water level of the lake or the sea into which the river discharges falls, an increased water surface
slope is imposed on the river. Hence, the river picks up material from the bed to fulfill its increased
transport capacity and degradation occurs. Such degradation has been observed in rivers in Iran and
Russia due to lowering of Caspian sea level (Ananian 1961). Such degradation progresses upstream and
if upstream flow and sediment load conditions remain the same, final degradation profile would be
parallel to the original bed. If a tributary is joining such a degrading stream, the tributary also
experiences upstream-progressing degradation. Such degradation has occurred on the Big Sioux river in
U.S.A. and on the Peace river in Canada (Galay 1983).
Execution of cut-off in a meandering river causes increase in the bed slope in the cut-off leading to
degradation upstream of the cut-off and aggradation downstream as shown in Fig. 9.13(d). Yearke
(1971) has reported 4.5 m of lowering of bed level following the development of cut-off on the Peabody
river. Similarly, removal or shift in the control section along the river channel can also cause degradation
or aggradation. If the main river, to which a tributary joins, shifts towards the tributary due to channel
shifting, the tributary will experience upstream-progressing degradation. The tributary will experience
aggradation if the main river shifts away from the tributary; see Fig. 9.13(c). This is due to lowering or
rises in temporary base level of the tributary.
Under special conditions, a combination of downstream-progressing and upstream-progressing
degradation can occur simultaneously in a given stream. Such occurrence on the Brenta River in Italy is
reported by Galay (1980). Upstream and downstream-progressing degradation is shown in Fig. 9.2.
9.5
EFFECTS OF DEGRADATION
Lowering of riverbed due to degradation has beneficial as well as harmful effects. Some of the important
effects are discussed below (Garde and Ranga Raju 2000).
i) Lowering of bed level downstream of a dam can affect the functioning of the hydraulic jump
based energy dissipator. Lowering of tail water can move the hydraulic jump downstream and
in the extreme case the jump may form outside the stilling basin.
ii) Degradation downstream of dams and weirs on permeable foundation will increase the
effective head and hence the uplift.
iii) Lowering of bed level downstream of the dam lowers the water level at irrigation outlets and
may make them ineffective. Similarly in the case of navigable rivers, considerable lowering of
water level may make the navigation locks ineffective.
iv) Lowering of bed levels in the main river can initiate degradation in the tributaries and subtributaries, and cause additional scour at bridges and abutments.
v) Degradation in a stream causes lowering of ground water levels in adjacent areas.
vi) Increase in effective head (i.e. difference between head and tail water levels) at the dam means
that additional power can be generated. This can be anticipated and provision can be made in
the design. Such provision for increased power generation was made at Uppenborn
powerhouse on the Saalach River in Germany and Praire Du Sac dam on the Wisconsin River
in U.S.A.
vii) Degradation causes increase in the capacity of the channel and hence helps in lowering high
flood levels.
286
9.6
River Morphology
PREDICTION OF DEPTH OF DEGRADATION
Prediction of the depth of degradation needs to be discussed separately for in rotational degradation and
for parallel degradation. Let us assume that Q, S, Qs and d are known as well as the location of the
control section, and that the sediment supply is completely cut-off. Hence first rotational degradation
will occur and shear stress to on the bed will reduce to to2. Hence one has two equations
t02 = gf D2 S2
and
Q=
1
B D25 / 3 S21/ 2
nf
U|
V|
W
...(9.5)
If nf is known, these equations can be solved to determine D2 and S2.
Using Stricker type equation for known d50a, d, nf can be calculated; thus depth D2 and S2 can be
known. Then depth of degradation at the dam will be L (S – S2) where L is distance of control section
from the dam. Subsequently parallel degradation will take place at constant slope. Gessler (1965) has
found that the lowering of bed level in parallel degradation is about 2 d90 of the original mixture.
Transient degradation profiles can be obtained using any one of the mathematical models available,
see Chapter 12. However, in using these models one has to use some conceptual model for coarsening of
the bed material with time. These are summarized by Murthy et al. (1998).
9.7
CONTROL OF DEGRADATION
In recent times, three methods have been tried to control degradation. These are artificial feeding of
sediment, artificial armouring of the bed and construction of weirs (Scheuerlein 1989).
Artificial Sediment Feeding
When the stream is degrading due to deficiency in sediment load, the degradation can be reduced or
arrested if properly estimated sediment load of known sizes is fed every year on regular basis. This
method was first applied at the Upper Rhine River downstream of Iffezheim barrage. The sediment
feeding began in 1978 and has been continued without interruption. Since the original river bed is in the
gravel range, sand mixed with gravel and having an average size of 20 mm is being fed at 10,000 m3/
year to 21 000 m3/yr. The conditions favourable for using this method are that there is no barrage on the
Rhine downstream of the Iffezheim barrage, and that the feeding material is available close at site. The
feeding material is transported and dropped by means of barges over a length of 760 m. The annual cost
in 1986 was seven million D.M.
Artificial Armouring
Artificial armouring means formation of a complete cover on the bed with a layer of coarse material
which is capable of resisting the shear exerted by the flow. To stop washing away of fine material
underneath, a filter of graded material or geotextile can be used. The armour thickness should be 0.8 to
1.0 m. The size distribution of the armour coat can be obtained using Gessler’s analysis combined with
estimation of design flood of 100-year return period. Scheuerlein (1989) quotes one case where this
method is applied, namely in one of the two Danube branches in Vienna, called Neue Donau. The area
covered is 3 Mm2. The armour coat can be constructed on dry bed, or at low velocity.
287
Bed Level Variation in Streams
Construction of Weirs or Dams
If a weir or dam is constructed in a reach which is degrading because of an upstream dam, it creates
backwater and reduces velocity, thereby reducing degradation. It can also cause aggradation which can
offset the degradation due to the dam upstream. Construction of a series of dams also moderates the
flood, thereby reducing the transport capacity. This has been actually observed on the Colorado River in
U.S.A. where a series of dams – Hoover, Parker and Imperial – is constructed. In the case of Naga
Hemadi barrage on the Nile River, degradation of the order of 0.8 m occurred after eight years of
operation. A subsidiary weir had to be constructed to control the degradation.
It must however be mentioned that all these methods usually protect a certain reach of the river from
further degradation. Degradation would occur downstream of that reach if the flow is still capable of
transporting sediment and there is no supply from the upstream.
Progress of degradation is also sometimes arrested by the presence of non-erodible material such as
rock reef or lenses of heavy gravel.
LOCAL SCOUR AROUND BRIDGE PIERS
Scour is the local lowering of the stream bed around a hydraulic structure. Scour takes place around
bridge piers, abutments, spurs and breakwaters due to modification of flow pattern causing increase in
local shear stress which, in turn, leads to removal of material and hence scour. Huber (1991) has
reported that since 1950 over 500 bridges have failed in U.S.A. and majority of failures were due to
scour of foundation material. Such failure is primarily due to three causes:
i) Inadequate knowledge about scour phenomenon when the bridge was constructed
ii) Inadequate data and knowledge about design flood; and
iii) Increase in the loading on bridges due to increase in the size of trucks and wagons and
frequency of loading.
The total lowering of stream bed at any site can take place due to four reasons (see Garde and
Kothyari 1995).
1. Degradation taking place at bridge site due to dam upstream. In extreme cases, the bed can go
down by as much as 4 to 6 m.
2. In the case of bridges on rivers in Indo-Gangetic plain, the river width in the vicinity of the
bridge is reduced by providing embankments and guide bunds. If the approach flow width and
depth are B1 and D1, and B2 and D2 represent width at bridge site and depth of flow, these are
related as
FG IJ
H K
D2
B
= 1
D1
B2
0.60 to 0. 79
...(9.6)
Hence, reduction in width can lead to lowering of bed level.
3. Lowering of bed level that takes place due to modification of flow pattern; this is known as
local scour.
4. Additional lowering of bed level can take place due to concentration or non-uniform flow
distribution across the river width at the bridge.
288
River Morphology
Fig. 9.8 Vortex system and definition for scour
In this section, attention is focused on local scour that takes place due to modification of flow
pattern. Earlier studies have indicated that depending on the type of pier and free stream conditions, an
eddy structure comprising all or anyone or none of the vortex systems can form. These include
horseshoe vortex system, the wake vortex system, and/or the trailing-vortex system. Figure 9.8 shows
the formation of a horseshoe vortex at the pier. This increases the local shear and causes scour.
Measurement of shear stress around bridge pier has shown that the average shear stress around the pier
can be about four times the shear stress in main channel, while the instantaneous shear stress is about 10
to 12 times the average shear stress in the main channel.
9.8
FACTORS AFFECTING SCOUR
A number of experimental investigations on scour around bridge piers have been carried out since 1940.
Two excellent reviews published in 1975 and 1977 summarise the state of art on scour at that time. The
first was prepared by U.P. Irrigation Research Institute and published by CBIP (1975), and the second is
by Breusers, Nicollet and Shen (1977) published in the Journal of Hydraulic Research of IAHR. On the
basis of these reviews and work published since then, factors affecting scour depth can be summarized
as follows.
1. Whether the incoming flow is clear water flow or sediment transporting flow: when
u*
is less
u* c
than unity, clear water flow occurs; when it is greater than unity sediment transporting flow
289
Bed Level Variation in Streams
occurs. Here u* =
d
i
g D S is average shear velocity in the channel and u*c is its value when the
bed material just starts moving. Other conditions remaining the same clear water scour is about
ten percent more than scour in sediment transporting flow; further clear water scour depth dsc
increases asymptotically while equilibrium scour depth dsc in sediment transporting flow is
attained in finite time.
2. Depth of flow: Melville and Sutherland (1988) have shown that when depth of flow to pier
width ratio D/b is greater than 2.6, the scour depth does not depend on the depth of flow;
however for smaller depth, depth of flow affects the scour depth.
3. Effect of Shape of Pier Nose: The shape of the pier nose affects the strength of horse-shoe
vortex as well as the separation around the bridge pier; hence it affects the scour depth. This
effect is quantified by the coefficient Ks, which is defined as the ratio of the scour around the
pier of given shape to that around a cylindrical pier under identical conditions. The values of Ks
have been determined on the basis of works of Tison, Laursen and Toch, Chabert and
Engeldinger, Larras, Garde and Paintal, and Garde (Garde and Kothyari 1995), and are
tabulated below.
Table 9.3
Average values of shape coefficient Ks
Shape
Cylindrical
Rectangular (d/b = 2 to 6)
Lenticular (2 : 1, 3 : 1, 4 : 1)
Elliptical (2 : 1, 3 : 1)
Triangular with apex angle 15o , 30o , 60o, 90o,
120o , 150o
Ks
1.0
1.1 to 1.25
0.93, 0.79, 0.70
1.0, 0.86
0.45, 0.61, 0.75, 0.88, 0.94, 1.00
4. Angle of Inclination of Pier with Flow: When the pier axis makes an angle with the general
direction of flow, two major changes take place in the flow field. First is that the separation
pattern is drastically changed except in the case of cylindrical pier. Secondly the open width
between piers, perpendicular to the flow direction is reduced as the angle of inclination is
increased. This effect is incorporated by introducing a coefficient Kq for non-circular piers,
which is defined as the ratio of scour around the bridge pier at a given angle of inclination to
that at 0° angle of inclination under identical conditions. On the basis of works by Laursen, and
Varzeliotis, the following values are recommended (Garde and Kothyari 1995).
Table 9.4 Effect of angle of inclination q on scour for rectangular pier (–/b = 60)
q°
Kq
0
1.0
7.5°
1.17
15°
1.37
5. Opening Ratio: The opening ratio a is defined as a =
30°
2.37
45°
3.77
a B - bf where B is centre to centre
B
spacing of piers and b is pier diameter, or width. Analysis of extensive data by Garde et al.
290
River Morphology
bD
sc
or Dse
g ~a
–0.3
. Here Dsc or Dse are scour depths measured below
D
water surface for clear water and sediment transporting conditions respectively.
6. Bed Material Characteristics: Scour depth is affected by relative density of sediment, its median
size and geometric standard deviation. For all field problems, relative density of sediment can
be taken as 2.65. According to Lacey’s approach Dse ~ d–1/6 where d is the sediment size.
Kothyari (1989) has experimentally found that in clear water scour dsc ~ d–0.31 while in
sediment transporting flow dse ~ d– 0.07. Here dsc and dse are scour depths below average bed
level in clear water and sediment transporting flows. The effect of sediment non-uniformly is
studied by Ettema (1980) and Kothyari (1989). If Ks is defined as
(1987) has shown that
Ks =
Equilibrium scour depth for non - uniform sediment of given d50
Equilibrium scour depth for uniform sediment of size d50
then the variation of Ks with geometric standard deviation sg of the bed material is as follows.
Table 9.5 Variation of Ks with s
sg
Ks
£ 1.5
1.0
2.0
0.75
2.5
0.40
3.0
0.30
2.5
0.24
4.0
0.19
4.5
0.13
Kothyari (1989) has further suggested that to take into account the effect of sediment nonuniformity, one can alternatively use effective sediment size deu defined as follows:
deu = d50
if
sg £ 1.124
deu = 0.925 d50 sg0.67 if sg £ 1.124
UV
W
...(9.7)
7. Effect of Stratification and Unsteadiness of Flow: Effect of the stratification on scour has been
studied by Ettema and Kothyari in the case of clear water scour. It is concluded that
stratification in which a relatively thin coarse top layer covers a thick fine bottom layer is the
critical condition which should be considered for design.
Similarly, unsteadiness of the flow also affects the scour depth. This aspect has been studied by
Kothyari (1989) and a method has been developed to estimate scour under unsteadiness of the
flow.
8. Flow Parameters: Most of the equations developed using experimental or field data can be
classified into the following groups:
Group – I
Here
F I
H K
d se
b
is related to
in the form
D
D
F I
H K
d se
b
=f
D
D
...(9.8)
291
Bed Level Variation in Streams
Thus, Breusers and Ettema have proposed the equation
F I
H K
d se
b
=K
D
D
...(9.9)
Where K = 1.4 according to Breusers and 3.0 according to Ettema. According to Laursen and
Toch
F I
H K
d se
b
= 1.35
D
D
0. 70
...(9.10)
Group – II
Here
Dse
D
or se is related to Fr =
D
b
F I
H K
Dse
b
= 2.1
D
b
U
b
and . Thus according to U.S. Corps of Engineers
D
gD
0.65
Fr0.20
...(9.11)
While according to Coleman
F I
H K
Dse
b
= 1.39
D
D
0.90
Fr0.20
...(9.12)
Group – III
Here
Dse
D
or se is related to or Fr, Ns =
b
D
Ub
U
or Re =
. Two typical equations in this
v
Dg s
d
rf
category are those of Shen et al. (1969) and Carsten (1975).
Shen et al. (1969)
dsc = 0.000223 Re0.619
Here dsc is in ft and Re =
...(9.13)
Ub
.
v
Carsten (1975)
LM
N
d sc
N s2 - 1.64
= 0.546
N s2 - 5.02
B
9.9
OP
Q
0.83
...(9.14)
EQUATIONS FOR PREDICTING SCOUR DEPTH
Even though a number of equations have been proposed for estimation of depth of scour around bridge
piers, only four methods are discussed here and verified with field data.
292
River Morphology
Lacey-Inglis Equation
According to Lacey the depth of flow DLQ at the dominant discharge Q is given by
DLQ
F QI
= 0.47 G J
HfK
1/ 3
...(9.15)
l
in which f1 is Lacey’s silt factor given by fl = 1.76 dmm . Inglis found that on the basis of data on 14
bridges in North India, equilibrium scour depth below W.S. Dse is given by
Dse = K DLQ
...(9.16)
where K varied from 1.76 to 2.59 with an average value of 2.09. When this equation is used for design
purposes, discharge that is to be used is the one with return period of 50 or 100 years. In the light of
discussion above regarding factors affecting scour, it stands to reason that K in Eq.(9.16) should depend
on factors such as sediment size, pier shape and obliquity of flow. Further, since Lacey’s equation is
valid for sandy non-cohesive material and data on scour by Inglis are also from bridges in alluvial rivers,
Lacey-Inglis method should not be used for clayey or gravelly beds.
Another method developed on the basis of extensive data using uniform and non-uniform sediments
is the one proposed by Kothyari et al. (1989). According to this method, the scour in clear water flow is
given by
F I F DI
H K H dK
d sc
b
= 0.66
d
d
0. 75
0.16
LM U - U
MN D g d / r
2
2
c
s
f
OP
PQ
0. 40
a–0.30
...(9.17)
where the average critical velocity is given by
F I
H K
Uc2
b
= 1.2
d
D g s d /r f
– 0 .11
F DI
H dK
0.16
...(9.18)
Similarly, scour under sediment transporting flow is given by
F I F DI
H K H dK
d sc
b
= 0.88
d
d
0.67
0. 40
a–0.30
...(9.19)
These equations are for uniform sediment. When sediment is non-uniform, effective size deu is
used in place of d in the above equations. Alternatively, one can compute dsc or dse for uniform sediment
and multiply it by Ks which depends on sg.
It may be mentioned that Melville and Sutherland have proposed an equation for maximum possible
scour depth as
dsem = 2.5b
...(9.20)
This scour depth below the general bed level is reduced by multiplying factors which depend on
whether the scour is clear water scour, depth is shallow and sediment is non-uniform. These coefficients
are determined using experimental data.
293
Bed Level Variation in Streams
9.10
VERIFICATION OF EQUATIONS FOR SCOUR DEPTH
The equation proposed by Lacey-Inglis, Laursen-Toch, Melville-Sutherland, and Kothyari et al. were
verified (see Garde and Kothyari 1995) using scour data for 17 bridges in India, 55 bridges in U.S.A., 6
bridges in New Zealand, and 5 bridges in Canada. The result of this verification is summarized in Table
9.6. and comparison of observed versus computed depth of scour by Lacey-Inglis and Kothyari et al.
methods are shown in Fig. 9.9 and 9.10 respectively.
10
2
Line of perfect agreement
1
(ds)c in m
10
10
10
Fig. 9.9
Legend :
U.S. data
Newzealand data
U.G. canal data
ganga at Mokameh
Other data of RDSO
Ravi river data
Inglis data
Canadian data
0
–1
10
–1
10
0
1
10
(ds)o in m
10
2
Comparison of (Ds)c vs (Ds)o using Lacey-Inglis method (Garde and Kothyari 1995)
10
2
Line of perfect agreement
1
(ds)c in m
10
10
10
Legend :
U.S. data
Newzealand data
U.G. canal data
ganga at Mokameh
Other data of RDSO
Ravi river data
Inglis data
Canadian data
0
–1
10
–1
10
0
10
(ds)c in m
1
10
2
Fig. 9.10 Comparison of (ds)c vs (ds)o using Kothyari et al. method (Garde and Kothyari 1995)
294
River Morphology
Table 9.6 Relative accuracy of prediction of scour depth by different equations
Percent of data falling within given error band
Method
± 30%
± 50%
± 90%
Lacey-Inglis
59
85
100
Laursen-Toch
38
65
98
Melville-Sutherland
79
95
100
Kothyari et al.
86
96
100
From this study it was concluded that among the four methods studied, methods given by Kothyari
et al. and Melville-Sutherland yield nearly the same accuracy and are better than Lacey-Inglis or
Laursen-Toch method. Their added superiority lies in the fact that they take into account all factors
which affect the scour depth.
The time variation of scour has been studied by Islam et al. (1986) who found that scour depth ds at
any time t is given by
LM
N
ds
pt
= sin
2 t max
d se
OP
Q
1/ m
...(9.21)
where m and tmax are given by
F DI
HdK
m = 0.135
F DI
H bK
0 .087
0.25
...(9.22)
Equations (9.21) and (9.22) are based on the following ranges of related variables:
Sediment size d
0.20 mm–7.8 mm
Fall velocity w
0.026 m/s–0.41 m/s
Flow depth D
0.02 m–0.70 m
Pier diameter b
28.5 mm–240 mm
Velocity U
0.10 m/s–1.30 m/s
It must be mentioned that to use Eq. (9.21), one must estimate dse by one of the method discussed
earlier.
The time variation of scour as well as scour depth for clear water scour can be determined using the
algorithm proposed by Kothyari (1989); this algorithm is shown in Fig. 9.11. First the diameter of the
horse-shoe vortex is computed. Then it is assumed that the average shear stress at the pier nose is four
times the average shear stress in the channel, and when the former reaches the critical value, scour stops.
As the scour develops, the horse-shoe vortex sinks into the bed and its area increases by
ds2
where
2 tan j
295
Bed Level Variation in Streams
Start
Red b,d,D,S,B,U,gs, ds and rf
Calculate horse-shoe vortex diameter Dv
Dv /d = 0.28 (b/D)0.85
ds is the scour depth and f is the angle of repose of bed
material. Due to increase in the area, the shear stress in
the vortex decreases, and its is assumed that shear at
any time t, tpt it is given by
tpt = 4 t0
2
Ao = PD v / 4
to = gf RS
2
tpt = 4(A/At)
...(9.23)
where Ao and At are the original and new areas of
vortex and c1 is a constant. The time required to move a
single particle is assumed to be t* =
ds
2 tan f
0.57
cl
0
t
R = BD/(B + 2D)
At = A0 +
FG A IJ
HAK
d c2
and the
p0 t u * t
probability pot is given by
to
p0t
F t IJ
= 0.45 G
H Dg dK
pt
3.45
= 0.45 t *3.pt45
...(9.24)
s
3.45
.
Pot = 0.45 t *pt
to = 0.05d/potU * t
No
Is
t £ t*c
*pt
t1 = tl–1t*
I=I+1
Yes
ds = Id
Print
tI and dsI
End
Fig. 9.11
9.11
Algorithm for computing time varying
scour (Kothyari 1989)
where t*pt =
t opt
Dgs d
.
When a single particle is removed, the time
elapsed is t*. By repeating the process one can
calculate S t* i.e. the time required to cause scour depth
of a, 2d, 3d … etc. When the shear stress in the scour
hole reaches critical value for size d, no further scour
will take place. By calibrating the model with known
data of scour depth variation with time, the constants c1
and c2 in the above equations were found to be 0.57
and 0.05. This model can also be used to study scour
depth variation with time when discharge is varying
with time.
SCOUR IN GRAVELLY MATERIAL
As discussed in detail in Chapter – 7 gravel-bed rivers are basically different from alluvial rivers. The
bed material in gravel-bed rivers is very coarse and has a large standard deviation. Further, these rivers
transport sediments on the surface and ultimately form the pavement or armour layer. As mentioned
earlier the standard deviation of the pavement is around two.
Not enough is known about scour in gravel-bed rivers and the data are very few. In the absence of
adequate data, the IRC-78-2000 code recommends that scour depth in gravel-bed rivers be estimated
using Lacey-Inglis approach and estimating depth of flow by the formula
296
River Morphology
Fq I
= 1.13 G J
HfK
2
DLq
1/ 3
...(9.25)
l
where q is discharge in m3/s, and sill factor of fl = 24 is recommended. However, this method has not
been supported by field data. Further, since relationship between depth and discharge for gravel-bed
rivers is different than Lacey’s (see Chapter 7) it is not logical to base estimation of scour depth in
gravel-bed rivers on Lacey’s equations. On the other hand, since the methods of Kothyari et al. and
Melville and Sutherland take into account the size of bed material its gradation and stratification, these
are likely to give more reliable results as shown by Garde and Kothyari (1995).
9.12
SCOUR IN COHESIVE SOILS
The process of scour in non cohesive materials is discussed above. However when the river bed consists
of gravel, sand, silt and clay the scour phenomenon becomes more complex, and very little is known
about variation of scour depth with time, maximum depth of scour and extent of scour. A few
measurements of scour in clayey soils are available (Kand 1993, Namjoshi 1992). Laboratory
experiments have been carried out by Ansari (1999) and Ansari et al. (2002). These references along
with that of Briaud et al. (1999) may be seen in this regard.
9.13
PROTECTION OF SCOUR AROUND BRIDGE PIERS
A number of devices have been tried to reduce scour depth around bridge piers. These devices either
modify the flow pattern created by horseshoe vortex or provide a hard surface which prevents horseshoe vortex from sinking or protects the surface from erosion. These include piles, collar plates, deltawing-like passive device and slot in the pier or vanes. Their relative effectiveness has been studied
among others by Gangadharaiah et al. (2003). Except piles and vanes, the other devices have not been
tested on prototype bridges. In the laboratory these devices are found to reduce scour by 40 to 70
percent. Another method which has greater potential of using in the field, is the use of rip-rap of proper
size around the pier which will resist scour. This has been studied by Wõrman (1989), and Bhalerao and
Garde (2003) and used in the field by Wörman. As mentioned earlier the instantaneous shear stress
around the pier can be 10 to 12 times the average shear stress in the channel. If the median size of the
armour layer is so chosen that it is stable at this shear stress, and if riprap has a standard deviation of
about two, one or two layers of rip-rap adequately protect the bed from scouring.
AGGRADATION
In general, aggradation in a stream takes place when the stream is carrying more sediment than its
transport capacity. If the sediment load coming into a reach in a given time is greater than the sediment
load going out in the same time, i.e. when
bed and the bed level rises i.e.
are discussed below.
¶ Qs
is negative, the excess sediment gets deposited on the
¶S
¶Z
is positive. Aggradation occurs under a variety of conditions; these
¶t
297
Bed Level Variation in Streams
9.14
OCCURRENCE OF AGGRADATION
Increase in Sediment Load
The increase in sediment load can take place for different reasons. Thus, during the gold rush period
(1850-1905), large quantities of mining waste were dumped in the Yuba river in California as a result of
which the general bed levels increased gradually. This was reflected in the rise in low water level at
Marysville, see Table 9.7. When the mining was stopped because it became uneconomical, the bed
levels were lowered gradually. Similarly, large quantities of gravel have come down in gravel-bed rivers
in the Doon Valley (Uttaranchal, India) partly due to mining activity and partly due to erosion due to
deforestation; as a result in some rivers bed levels have risen by as much as 3 to 4 m; see Fig. 9.12 and
Fig. 9.13(a).
Table 9.7 Rise in low water level at Marysville on the Yuba (Bolt et al. 1975)
Year
Water level elevation (m)
Year
Water level elevation (m)
1850
12.10
1905
17.90
1860
13.40
1910
17.00
1870
14.70
1920
16.10
1880
16.90
1930
14.60
1890
16.80
1940
14.40
Fig. 9.12
Aggradation in the Doon valley stream
Excess sediment can be brought into the stream as a result of landslides and heavy rainfall. Thus, in
the Mu-Kwa river in Taiwan (see Lane 1955) the bed level rose by as much as 12 metres in three years
and the powerhouse was completely buried in sediment. Sometimes the landslides and destruction of
hills result from high intensity earthquake followed by floods, as occurred in the Brahmaputra after
1950 earthquake. As a result, the bed levels rose by 2-3 m in long stretches of the river (see Chapter 14).
298
River Morphology
The increase in the sediment load in the tributaries and the main stream can also occur due to
reduction in vegetal cover as a result of overgrazing, deforestation, climatic changes or man’s activities
such as road building etc. As a result, the tributaries and main stream can experience aggradation.
Lastly, irrigation channels may aggrade if excess sediment enters into it when sediment excluders
and ejectors are either not provided or are not functioning properly. This has happened in the case of
Eastern Kosi main canal in which bed levels have risen by 2 to 3 m in a reach of 4 km during nine years.
The canal was designed according to Lacey’s method and had a bed material size of 0.20 mm (Sahay
et al. 1980).
Aggradation of 11.5 km reach of the Ganga Canal from its head works at Mayapur up to Pathari
powerhouse in Uttaranchal (India) needs special mention (Mohan and Agarwal, 1980). This canal takes
off from the river Ganga at Mayapur near Haridwar (India). The canal is about 150 years old and carries
a maximum discharge of 311.5 m3/s. It has a slope of 0.000725 in the first 1.6 km and 0.000230 up to
Pathari powerhouse 11.6 km downstream. Because of landslides and heavy rainfall in the Alakananda,
a major tributary of the Ganga, sediment concentration in the Ganga ranged from 36 000 to 13 500 ppm
during 21st July to 27th July 1970. In the feeder channel at Bhadrabad near Pathri the suspended
sediment concentration ranged from 16 286 to 15 584 ppm. During this period the canal discharge
gradually reduced to 71 m3/s while the water level at Pathri was held constant. It was found that the
canal had silted to the extent of 2 to 3 m in this reach. This resulted in the closure of the canal for a few
months leading to disruption of supply of water to irrigation and considerable expenditure on removal of
sediment. Later for proper functioning, of the canal a limit on maximum permissible concentration to be
allowed in the canal was fixed.
Withdrawal of Clear Water
If relatively sediment free water is diverted from a stream, otherwise in equilibrium, downstream of the
point of withdrawal the river cannot carry the sediment load with reduced discharge; hence it will
experience aggradation. This withdrawal can be for irrigation or water supply purposes. Such
aggradation has occurred on the Rio Grande, and the Arkansas rivers in U.S.A. (see Lane 1955). When
aggradation occurs either due to increase in sediment load or reduction in water discharge, the transient
and equilibrium bed profiles obtained are shown in Fig. 9.13(a). Such a reduction in peak flows and
discharge can also be caused by stream piracy in which part of the water is diverted to the pirated stream.
Profiles obtained due to withdrawal of sediment load or increases in discharge are shown in Fig.
9.13 (b).
Aggradation Due to Reduction in Water Slope (or Increase in Water
Level)
The aggradation occurring upstream of the section of increase in sediment load or decrease in discharge
is due to rise in water level at section 0-0. Aggradation occurring upstream of dam falls in this category.
When a dam is constructed on a stream to store water for irrigation, water supply, power generation or
for flood control, a backwater is caused as a result of which velocity of flow reduces as one approaches
the dam. Hence, reduction in sediment transport capacity leads to deposition of coarser sediment
upstream where backwater starts while finer sediment gets deposited closer to the dam; see Fig. 9.13 (b).
Sedimentation of reservoirs reduces their capacity to store water, raise water levels in the upstream
reaches of the river, and increase evaporation due to increase in water surface area. In literature one
299
Bed Level Variation in Streams
O
DQs
DQ
Final bed
Transient bed levels
O
Original bed
(a) Aggradation due to increase in Qs or decrease in Q
O
DQ
DQs
Original bed
Transient bed levels
O
Final bed
(b) Degradation due to increase in Q or decrease in Qs
Aggraded profile
finds several cases of reservoirs getting filled in
a few years. The 14 m high dam on the NanShik-Chi river in Taiwan was filled completely
in 8 years. Whereas the river slope was 1 in 120,
the final slope of bed was 1 in 250. Similarly, 53
m high Ichari diversion dam on the Yamuna
River has silted up to the crest in five years from
1972 to 1979. Reservoir sedimentation is
discussed in detail later in this Chapter.
Aggradation at Channel
Bifurcation
If a channel takes off from the main stream, the
off taking channel will carry relatively more bed
load compared to the main stream because of
the development of secondary flow. Hence, if
the main stream is carrying appreciable bed
load, the off taking channel is likely to aggrade.
Other Cases of Aggradation
Tributary
A stream which discharges into a lake or the sea
builds its delta. With the passage of time, the
(c) Aggradation of tributary due to shifting of main stream
delta grows into the lake or sea thereby causing
increase in the length of the river and reduction
in slope inducing aggradation. This aggradation
fills the river channel and the river spills over
the banks forming new channels. Similar
A
increase in length leads to aggradation of the
B
cut-off
C
tributary if the main stream to which it joins
a
D
b
shifts away from it due to migration. This is
New bed
shown in Fig. 9.13 (c).
c
Similar situation also occurs on alluvial
d
Original bed
fans. In many cases fan can start as delta
(d) Aggradation and degradation at cut-off
formation in a lake and after enough time has
Fig. 9.13 Bed profiles in aggrading and degrading stream
elapsed, the lake will be completely filled. Then
the river just keeps building the fan higher and
higher (Gessler 1971).
Change of hydrograph can also lead to aggradation. In many rivers, most of the bed changing
actions take place during peak flows. If by building one or more dams in series, the flood peak is
moderated, the total annual sediment transport capacity of the stream is significantly reduced. And yet
the sediment supply from the tributaries on the downstream side of dam will be unaltered and so the
stream will not be able to carry this load; hence bed level can rise or part of the degradation can be offset.
Old position
New position
300
River Morphology
Degradation, Aggradation and Planned Removal of Dams
It is reported that 85 percent of dams in U.S.A. will be at the end of their operational design lives by
2020 (Evans et al. 2000). Hence, planned removal of dams as a viable river management alternative is
being considered seriously in U.S.A., and some case studies in this regard have been conducted in order
to gain information on physical, chemical and biological impacts of removing dams. In the context of
the theme of this chapter, important issues that need to be addressed include rates and mechanics of
sediment removal from reservoirs; how watershed geomorphology and hydrology affect these rates and
mechanisms; how far and quickly the sediment will be transported downstream, and how downstream
sedimentation will affect channel morphology and biotic communities.
Doyle et al. (2003) have reported the channel adjustments that have taken place following two dam
removals in Wisconsin (U.S.A.). When the dam is removed upstream reach will experience degradation
while downstream reach will experiences aggradation. The details of two small dams removed are as
follows:
River
Dam
Catchment
River slope u/s of dam
River slope d/s of dam
Sediment
Dam height
Koshkonong
Rockdale
360 km2
0.0007
0.004
Silt to coarse gravel
3.3 m
Baraboo
Lavalle
575 km2
0.0005
0.0002
Mixture of fine sand and silt
2.0 m
The changes that took place after removal of dam can be the summarized as follows: Immediately
following the dam removal water surface elevation decreased dramatically but the reservoir sediment
surface remained undisturbed. Channel flow during this period was wide and shallow with low velocity.
Next, the channel bed incised and the flow concentrated into a narrow, deep channel with steep bank and
high flow velocity. Head cut formed at the upstream boundary. Large amount of fine and then coarse
sediment was mobilized and transported downstream. As the incision continued beyond critical bank
height, the channel started widening and large quantities of the material were transported downstream.
With this, the downstream channel started aggrading initially coarser sediment was deposited and then
the finer one as water surface slope decreased adequately.
Effects of Floods
According to Bull (1985), the following factors tend to promote net aggradation during floods:
i) Abundance of stored sediment on hill slopes as a result of either abundant soft rock types and/
or rates of rock weathering that exceed denudation rates.
ii) Climatic changes that greatly decrease vegetative cover on hill slopes, or increase rainfall
intensity.
iii) Fires that remove the vegetative cover or expose the hill slopes to accelerated erosion.
iv) Unstable slopes subject to landslides that introduce large volumes of sediment directly into
stream channels.
v) Lack of relative vertical uplift.
301
Bed Level Variation in Streams
Streams that aggrade during floods include watersheds with abundant landslides. Climatically
induced decreases in vegetal cover and concurrent increases of hill slope sediment yield have favoured
aggradation of valley floors in extremely arid to extremely humid climatic settings. Aggradation can be
estimated by determining the new equilibrium slope for changed conditions. The transient bed profiles
can be computed using methods described in Chapters 11 and 12.
RESERVOIR SEDIMENTATION
Dams are constructed on rivers so that they form reservoirs which impound water that is later used for
irrigation, water supply and industrial purposes, power generation, recreational purposes and flood
control. They also help in controlling the variations in flow in the downstream channel. Most reservoirs
serve multiple purposes. When water is impounded in the reservoir, the flow velocity is smallest near the
dam and it gradually reaches the velocity in the stream at the end of the backwater. As a result, the
sediment transport capacity of flow progressively reduces towards the dam and coarse material gets
deposited in the upstream reach while medium and finer material gets deposited near the dam. Very fine
material which remains in suspension at the dam will travel downstream over the spillway and through
outlets. This deposition progressively reduces the storage capacity of the reservoir. Even though a
predetermined dead storage is provided assuming that sediment would deposit there, yet significant
amount of sediment may start depositing in the upstream reaches right from the beginning and cause
depletion of the reservoir capacity.
Depletion of reservoir capacity with the passage of time is a serious problem because ultimately the
usable capacity of reservoir will be completely lost and a new reservoir may have to be built. Dams are
very expensive and alternate reservoir sites are not easily available. Some idea can be given about rates
of reservoir sedimentation. Yasuoka reservoir on the river Tenrya in Japan which had a capacity of 51
Mm3 lost 80 percent of the capacity in 13 years. The Ichari reservoir on the river Yamuna in India lost
almost 100 percent capacities in five years of operation. Zuni reservoir on the river Zuni in New Mexico,
U.S.A. lost 58 percent capacity in the first two years. On the basis of survey of 132 reservoirs all over
U.S.A., spanning over a period of 20-30 years, the average annual loss of capacity is found to be 0.70
percent. Sedimentation rates in China are much higher. Twenty large reservoirs in China were losing
their capacity at an average rate of 2.3 percent per year during 1960-1978; the maximum rate was 7.1
percent for Quintgonxia reservoir on the Yellow river, see IRTCES (1985). For eleven large reservoirs in
India, the sedimentation rate varied between 0.08 and 1.78 percent per year, while average loss was 0.65
percent.
There are many direct and indirect effects of sedimentation in reservoirs. These are discussed in
detail in the UNESCO (1985) publication and are briefly enumerated below.
Upstream Effects
1. Raising of bed level and water level in the upstream reach; rise in the water table which results
in the appearance of marshes.
2. Increase in water surface area causes increased evaporation loss and weed growth.
3. Accumulated sediment upstream of dam may choke the bottom outlets.
4. Since a very large percent of sediment is trapped in the reservoir, the flow in the downstream
channel is deficient in sediment load; this causes degradation in the channel and/or channel
widening. Effects of the degradation have been discussed earlier in this chapter.
302
River Morphology
5. Construction of dam and impoundment of water reduces low and medium floods in the
downstream channel. This may stop the erosion of cones of sediment deposits at the confluence
of steep gradient tributaries joining the main stream.
6. The water released from the dam is free of sediment and contains mainly dissolved solids. This
leads to impoverishment of biomass in downstream channel, which leads to decrease of
productivity of fish and breeding.
7. There are a number of economic consequences of reduction in the storage capacity of reservoir,
which include reduction in energy production, agricultural production, and non-availability of
water for domestic and industrial use.
Discussion of Reservoir Sedimentation needs consideration of the following aspects:
• Sediment inflow and trap efficiency
• Movement of sediment in reservoirs and sediment deposition
• Modelling of sediment deposition
• Methods of preserving or restoring reservoir capacity
9.15
SEDIMENT INFLOW AND TRAP EFFICIENCY
Annual sediment inflow can be assessed in different ways. If any reservoirs are in operation in the region
and their surveys are available, the same rate in tons/km 2/yr can be used for the reservoir under
consideration. For a better accuracy erosion rate can be calculated using the equations proposed in
Chapter 3 where it is related to annual rainfall, catchment slope, drainage density, catchment area and
vegetal cover factor. If suspended sediment measurements are available for few years and discharge
inflows for longer duration, a certain percent of suspended load can be taken as bed load and, flow and
sediment duration curves can be prepared to determine average annual sediment inflow rate (see
Chapter 3). If no sediment load (suspended or bed load) measurements are available, one has to use one
of the total sediment transport equations described in Chapter 5 to prepare Q vs QT curve and then assess
average sediment transport rate. For future predictions flows can be generated using available
techniques in hydrology and then determine QT determined from QT vs Q curve. Ideally, sediment
transport data are required for a period, at least equal to half the life of the project (Mahmood 1987).
Since this is seldom available, engineers and planners have to work with inadequate data, and effort is
made to extend it using statistical techniques. It may also be emphasized that hydrologic series show
greater variability in arid or semi arid climates than in humid climates.
In assessing the sediment inflow, the impact of natural events such as high magnitude earthquakes,
eruption of volcanoes, landslides, and catastrophic flood play an important role, even though
quantification of their contribution may be difficult or impossible. A few examples can be cited here in
support of this statement. New Madrid earthquakes between December 1811 and February 1812, the
greatest earthquakes in U.S.A. in Southern Missouri, were felt over 100 000 km2 area. These brought in
large quantities of sediment in the Mississippi river and changed its channel morphology (Mahmood
1987). The 1950 earthquake in the Brahmaputra Valley brought into the stream very large quantity of
sediment, which affected the morphology of the Brahmaputra. Had there been a reservoir on the river in
the downstream, it would have shown very rapid sedimentation. Similarly, the 1971 heavy monsoon and
landslides in the Alakananda valley brought down huge quantities of sediment in the Ganga River and
303
Bed Level Variation in Streams
caused sedimentation problem in the Ganga canal. Lastly, volcano eruption of Mt. St. Helens (U.S.A.)
in May 1980 brought in 50 million tons of debris and mud flows in the Cowlitz river channel. It is
estimated that in the four months after eruption, about 140 million tons of suspended sediment were
deposited by the Cowlitz river into Columbia River in U.S.A. As a result, of Mt. St. Helen’s eruption,
sediment yield of the Columbia River had increased to 40 million tons/yr from the pre-eruption value of
10 million tons/yr (Mahmood 1987).
Trap efficiency has been defined in Chapter 3 as the percentage of incoming sediment load that is
retained in the reservoir. It depends on a number of factors such as the size of sediment, variation in the
flow coming into the reservoir, characteristics of the reservoir, method of reservoir operation and time.
A method, which takes into account all these factors on the determination of trap efficiency, is not
available at present. However, Brune’s (1953) curve which is based on data obtained from 44 normally
ponded reservoirs covering drainage areas of 4-480 000 km2, and which relates trap efficiency Te to the
ratio of reservoir capacity to annual inflow is often used to determine Te. This has been later verified
using data from reservoirs in India, China and South Africa; this is given in Fig. 3.9. The mean curve can
be represented by the equation
LM
OP
1
Te = 100 M1 F
MM H1 + 50 C IK PPP
I Q
N
...(9.26)
where C is the reservoir capacity upto mean operating level and I is the average annual inflow both
expressed in the same units. The period of computation for Brune’s method should not be less than ten
years. Heinemann’s (1981) data show that Brune’s curve overestimates trap efficiency for small
reservoirs.
Swamee and Garde (1977) have analysed laboratory and field data on sedimentation of reservoirs
and found that the reservoir capacity Ct after sediment deposition, at any time t is given by
Ct
C
FG t IJ
Ht K
=
LM1 + F t I
MN GH t JK
e
m
OP
PQ
4 m 0.25
e
...(9.27)
Here C is the original capacity of reservoir and te is the period required to fill the reservoir up to
height of dam. This can be estimated by dividing C by average annual rate of sediment inflow. The
Ct
vs t on log-log
C
scale for few years and fitting a straight line in the initial period of silting. The exponent m is the slope
of the straight line and t = te when Ct = C.
exponent m varies between 0.75 and 1.0, and m and te can be determined by plotting
304
9.16
River Morphology
MOVEMENT AND SEDIMENT DEPOSITION IN RESERVOIRS
Three agencies which control the movement and deposition of sediment in reservoirs are river flows,
wind effects and solar inputs. When wind blows over the water surface in the lake formed by a dam, it
exerts a shear stress on the water surface and causes water surface to move in the direction of wind. This
leads to formation of waves, water surface currents and the associated counter currents underneath.
These counter currents carry the near-bed settling suspension. The solar heating is also responsible for
developing currents and transporting sediment in the reservoir. The difference in temperature between
deep layers and surface layers causes thermal currents. Lastly, when river flows into the reservoir, it
carries with it bed material which moves as bed load or in suspension, wash load and dissolved solids.
As a result of interaction between river flows, and wind and solar effects there can be three types of
flows of sediment-laden water, which are shown in Fig. 9.14. Inflows which are of high density because
of heavy suspended load or which are colder than water in the reservoir will cause underflow. If the
inflowing water is warmer than the surface water in the reservoir, it may flow over the surface as
overflow. When the inflowing water is slightly colder than the surface water, it flows as interflow. The
coarsest sediment may get deposited as deltaic deposits.
Fig. 9.14 Overflow, interflow and underflow in reservoir
Lane (1953) has classified the deposits in the reservoir into bottom-set beds, fore-set beds, top-set
beds and density currents, see Fig. 9.15. Bottom-set beds are formed of fine sediments brought into the
reservoir and which move farther near the dam before they settle. The fore-set bed is formed of the
coarser sediment carried by the stream on or near the bed, and is deposited where the current is retarded
as it flows into the lake. This happens when horizontal water surface in the reservoir intersects the
current. These beds are more inclined downwards in the direction of flow. Top-set beds are mainly
composed of coarser sediment (sand and gravel) and are usually sloped upstream at a low gradient from
the edge of fore-set beds. They extend as far back as the backwater curve extends upstream of reservoir.
The top-set bed deposits do not reduce the reservoir capacity, but they cause flooding problems in
upstream reach due to rise in bed and water levels. Zhou Zhide (1991) has analyzed the slopes of top-set
beds of a number of reservoirs in China and found that, on the average their slope is about 0.5 So where
So is river slope.
Bed Level Variation in Streams
Fig. 9.15
305
Longitudinal section through a reservoir showing various types of the deposits
When the water entering the reservoir carries large concentration of fine material, because of low
velocities in the reservoir the sediment settles near the bed and forms a thick layer of high density which
moves slowly towards the dam. These are known as the density currents. By provision of very low level
outlets the density currents can be vented out of the reservoir. Conditions favourable for the formation of
density current are (i) high sediment concentrations (ii) fine sediment (iii) steep stream slope, and (iv)
large depth of flow. Density currents have been found to occur in both Lake Mead and Elephant Butte
reservoirs on the Colorado River in U.S.A., and Naodehai reservoir on the Liuhe River in China.
Experience has shown that under most favourable conditions only 5 to 20 percent of sediment in the
reservoir can be vented out in the form of density currents. Basic mathematical description of the
appearance, propagation, modification and outflow of density currents is briefly described in UNESCO
(1985) Report.
Shape and Deposition Profiles
The shape of deposition profile in the reservoir depends on a number of factors such as river slope,
normal pond level and its variation, size distribution of sediment, shape of the reservoir, and ratio of
incoming sediment load to the reservoir capacity. These profiles are classified into three categories
namely deltaic deposits, wedge-type deposits and narrow band type deposits, and are shown in Fig.
9.16. Deltaic deposits are by far the most common where the material is not very fine and water level is
kept relatively high for a considerable length at time. Such deposition has occurred in the Gobindsagar
reservoir on the Sutlej River in India, and in Guanting reservoir on the Yongting River in China.
Wedge type deposition occurs in gorge-type reservoirs in which the storage capacity is small
compared to the incoming load. Hence the sediment soon reaches upto the dam resulting in a wedge
shaped profile. Such deposition has occurred in Bajiazui reservoir on the Pu river in China, the Matatila
reservoir in India and in Heisonglin reservoir on the Yeyu River in China.
In some gorge-type reservoirs where the incoming load is small and fine in size, the sediment
deposits more or less uniformly in the form of a thin band if water level in the reservoir fluctuates to a
great extent. Such narrow-thin band type of deposition has occurred in Mayurakshi reservoir in India
and in Fengman on the Mudan River in China. Based on the experience on the Chinese reservoirs,
IRTCES (1985) has given the following criteria for formation of deltaic and wedge-type deposits.
306
River Morphology
F.R.L. 515.11
Average reservoir capacity in m 3
>
Average annual sediment inflow in tons
1975
Average reservoir capacity in m 3
<
Average annual sediment inflow in tons
440
1962
410
Original bed - 1958
Years
380
80.16
10.41
75.28
55.82
63.09
50.90
44.80
32.41
37.49
26.51
DH
< 0.15 : Wedge type
H
Here DH and H are average yearly
fluctuation and head at dam respectively.
21.64
10.67
350
Distance in km u/s of dam
2.0 and
Gobindsagar reservoir
311
Top of dam 310.9 m
Full reservoir level 308.46 m
Wedge-type
305
1971
Spillway crest 301.45 m
Elevation in m
9.17 MODELING OF SEDIMENT
DEPOSITION
1966
1970
15.54
DH
< 0.15 : Deltaic deposits
H
Deltaic deposit
470
Elevation in m
2.0 and
500
299
1964
Min. drawdown level 295.66 m
293
287
Original bed (1957)
281
Modeling of sediment deposition can be done
either by using empirical methods or by using
mathematical modeling. Here two empirical
methods are described while the mathematical
modeling is discussed in Chapter 12.
275
Wedge-type deposit
5
0
10
15
20
Distance in km u/s of dam
Matatila reservoir
122
Narrow-band
(1963-63)
Live storage
110
Elevation in m
Empirical Area Reduction
Method
116
104
The empirical area reduction method proposed
by Borland and Miller (1958) is developed on
the basis of the analysis of data from 30
reservoirs in U.S.A. having capacities ranging
from 4.9 ´ 106 to 7.6 ´ 108 m3 and is based on
the premise that the sediment load in narrow
Mayurakshi reservoir
reservoir will travel farther, because the
average velocity of flow will be higher in
Fig. 9.16 Deltaic, wedge-type and narrow band deposits in
narrower reservoirs than in wide reservoirs.
reservoirs
Further, a steep narrow reservoir has a better
chance of developing density currents than the one that is wide and flat. On the basic of this, reasoning
Borland and Miller have classified the reservoirs in four categories depending on the exponent q in the
equation
Dead storage
98
=
Sx
Original bed (1955)
15
01
0.0
92
Narrow band deposit
86
0
4
8
12
14
16
18
20
Distance in km u/s of dam
C (h) = a hq
...(9.28)
where h is the height depth measured above the river bed at dam axis C (h) is the storage capacity at
depth h; see Table 9.8.
307
Bed Level Variation in Streams
Table 9.8 Reservoir classification and distribution parameters (Borland and Miller 1958)
Type
Description
Q in Eq. 9.28
Position of deposition
C1
m
n
I
Lake
3.5 – 4.5
Top
3.42
1.50
0.20
II
Flood Plain–Foot hill
2.5 – 3.5
Upper middle
2.32
0.50
0.40
III
Hill
1.5 – 2.5
Lower middle
15.88
1.10
2.30
IV
Gorge
1.0 – 1.5
Bottom
4.23
0.10
2.50
Analysis of sediment volume deposited versus fraction of reservoir depth curves obtained for these
reservoirs were converted into relative depth p versus dimensionless relative areas Ap see Eq. (9.29).
Ap = C1 pm (1 – p)n
...(9.29)
z
1
As
where K1 = As dp and As is area of sediment deposit at relative elevation p. the
0
K1
values of m and n were computed by trial and error procedure using least square technique, and then
with m and n known, C1 is fixed by the consideration that the total areas under the curve must be unity.
The computations can be carried out in Tabular form given below.
Here and As =
Table 9.9 Computations using empirical area reduction method
Elevation m
Original
2
area m
Original
capacity m
Relative depth p
3
Ap
1st Trial
Sediment
area m2
Sediment
volume m3
Procedure
1.
2.
3.
4.
5.
6.
7.
Determine q from reservoir capacity vs. depth curve
Determine the type of reservoir
Fill in columns 1, 2, 3 from known data at regular intervals of h
Find in m3 the apparent volume of sediment to be deposited at the end of T years
Determine the value of p for elevations in Col. 1 and enter Col. 4
Determine Ap values for p values in Col. 4 using Eq. (9.29) and enter in col. 5
Assume zero elevation at the dam up to which sedimentation has reached and carry trial No. 1.
Areas at and below approximated zero elevation at each increment will be those in col. 2.
New areas for each contour elevation above assumed zero elevation are obtained by dividing
the original areas at zero elevation in Col. 2 by corresponding Ap values in Col. 5 and
multiplying this by the ratio K1 values at each succeeding increment.
Thus, if assumed elevation is 4190 where surface area is 3000 and Ap at elevation 4190 is 1.125,
K1 = 3000/1.125 = 2667.
308
River Morphology
The new area at each succeeding elevation is the Ap at that elevation times 2667. This is entered
in Col. 6.
8. Increment sediment volume between two elevations h1 and h2 is
DV =
A1 + A2
´ (h2 – h1)
2
and is entered in Col. 7.
9. If the assumed elevation is correct, summation of terms in Col. 7 will be equal to sediment
volume to be distributed.
10. If they are not equal, assume a different elevation and repeat the procedure.
A solved example is given by Borland and Miller (1958) which can be seen.
Some comments on this method are necessary. This method does not account for temporary or
prolonged reservoir draw down brought about as an operational necessity or as deliberate sediment
sluicing operation. It also does not consider the sediment size distribution as a factor in the problem. In
practice these conditions can be accounted for by shifting the computed reservoir type in Table. 9.8
upwards or downwards. Thus, if fine material forms a large part of the sediment load, or if the reservoir
experiences considerable draw down, its type can be shifted downward (Mahmood 1987). Further, it
needs to be emphasized that the empirical area reduction method is to be applied for sediment
accumulated over long periods, such as few decades and not for year-to-year accumulation. Also, many
times a reservoir may not have a unique value of q for its entire depth. In such cases, the reservoir type
is selected on the basis of q value in the segment where most of sedimentation will occur.
Figure 9.17 shows percent of depth plotted against percent of deposition for the four types of
reservoirs along with data for Panchet Hill, Nizamsagar, Gobindsagar, Maithon, Mayurakshi, Matatila,
Fig. 9.17
Depth-wise sediment distribution in Indian reservoirs (Murthy 1971)
309
Bed Level Variation in Streams
and Margomahally reservoirs as given by Murthy (1971). It may be noted that except for very deep
Gobindsagar reservoir formed by Bhakra dam and Margomahally, deposition occurs mostly in the upper
part of reservoir i.e. almost half of the sediment is deposited where the depth ranges from 20 to 30
percent of the maximum depth.
Miraki’s Method
On the basis of analysis of deposition profiles in nine reservoirs in India where delta type triangular
deposition profiles were obtained, Miraki (1983) has suggested the following method for computing
deposition profile at any time t. The annual sediment volume entering the reservoir can be computed
using Garde and Kothyari’s Eq. (3.39) and using Brune’s trap efficiency curve, the volume of sediment
depositing in the reservoir can be calculated and converted into apparent volume depositing in the
reservoir at the end of T years. The triangular profile is characterized by upstream slope Su, downstream
slope Sd and maximum depth of deposition Zp (see Fig. 9.18). These are given by
Fig. 9.18
Zp
H
Su
So
Sd
So
Definition sketch for deposition in reservoir
FTI
= 0.717 G J
Ht K
FTI
= 0.34 0 G J
Ht K
FTI
= 3.850 G J
Ht K
0 .285
e
- 0 .08
e
0.20
e
U|
||
V|
||
W
...(9.30)
Here H is average depth at the reservoir and So is average channel slope. The term te is the number
of years required to fill the reservoir completely. Hence
te =
Volume of reservoir at FRL
RSAnnual vol. of sediment ´ trap efficiency in flow ´
T
2650
average unit wt. of sediment
UV
W
310
River Morphology
The volume of sediment deposited under a given profile requires average width of deposition over
the reach of deposition. Once this is determined from the reservoir characteristics, the two volumes can
be compared and made equal by changing Su or Sd slightly. The first peak occurs a distance of 0.42 Lr
from the reservoir where Lr is length of the reservoir defined as shown in Fig. 9.18; at this place, flow
depth is 0.51 H. The peak was found to move in the downstream direction at a speed of 300 m/yr
approximately. This method was used for the Almatti reservoir on the river Krishna in India and the
results were compared with those obtained by HEC-6 model. The two results were comparable.
9.18 METHODS FOR PRESERVING AND RESTORING RESERVOIR
CAPACITY (UNESCO 1985, IRTCES 1985)
Various methods are adopted by engineers and planners to decrease the quantity of sediment entering
into reservoir, to reduce the quantity of sediment depositing in the reservoir, and to recover part or whole
of the capacity lost for storage. These are briefly discussed below.
Methods to Reduce Sediment Deposition in Reservoirs
1. Soil Conservation: Sediment entering the reservoir can be reduced by following soil
conservation methods such as watershed land-treatment measures which reduce sheet erosion;
these methods are soil improvement, proper tillage methods, strip-cropping, terracing and crop
rotation. Reforestation of barren areas also reduces erosion. These methods are very effective in
small areas, but in large areas, it is a slow process and the effects cannot be seen in short time.
The success of this method has been demonstrated in the Tungabhadra reservoir project in
India, the Gunating reservoir on the Yongding River in North China and Eel river basin in
California (U.S.A.) (UNESCO 1985). Construction of various structures such as check dams
on tributaries and gullies, stream bank revetments to reduce bank erosion and sills for bed
stabilization also help in reducing sediment entry into the reservoir.
2. Vegetative Screens: Vegetative screens, either natural or artificial at the head of the reservoir
reduce the velocity of flow and cause sediment deposition, thereby reducing sediment entering
in the reservoir. However, such screens have adverse effects in that they cause flooding of the
area and rise in water table. Such screens were used on the Pecos River above Lake McMillan,
and the Elephant Butte dam on the Rio Grande in U.S.A. and the Hongshan reservoir on the
Loaha River in North East China. The effects of vegetative screens have been discussed by Lara
(1960) and Maddock (1948).
3. Flow Regulation: Flow regulation is effected during floods by lowering the reservoir level by
opening bottom outlets under controlled or uncontrolled condition, so that flood waters
containing high sediment concentration are allowed to flow out and only water with less
sediment concentration is stored. This has been practised on the Heisonglin and Sanmenxia
reservoirs in China.
4. Venting of Density Currents: When conditions in the reservoir are favourable and density
current is formed, allowing it to pass through outlets is a good method of reducing sediment
deposition. This has been done in the case of the Elephant Butte and Lake Mead reservoirs on
the Colorado river, U.S.A., Iril Emda reservoir in Algeria, and Nebeur reservoir in Tunisia
among others. It is estimated that in most favourable conditions 5 to 20 percent of total
sediment entering the reservoir can be vented out in this manner.
311
Bed Level Variation in Streams
5. Drawdown Flushing: In this method the water level in the reservoir is lowered so that velocity
is increased and sediment deposition is reduced. Lowering of water level can also induce
erosion of deposited sediment. This has been done on many reservoirs such as the Ouchi–
Kurgan reservoir in USSR.
Recovery of Storage
This can be achieved by flushing, dredging or siphoning of deposited material
1. Flushing: Periodic emptying and flushing operations can be used in large reservoirs to recover
large percent of storage. This has been done on Hengshan reservoir in China and Sefidrud
reservoir in Iran.
2. Dredging: Generally dredging is undertaken when other methods are not effective, the
reservoir is relatively small and it is economical in terms of use of water e.g. when reservoir is
used for drinking water purposes or irrigation. This has been used in the case of few reservoirs
such as Akiba and Miusa reservoirs in Japan, Rand Mines reservoir in South Africa and Lake
Roslyn in Oregon in U.S.A.
3. Siphoning: Siphon dredging uses the hydraulic head difference between upstream and
downstream water levels of the dam to induce suction which removes sediment. This has been
done at Rioumajou dam in France.
References
Ananian, A.K. (1961) Determination de la Formation de Lit de Riviers Cree’ par Suite de l’abaissement de la Cote
de Leurs Bases d’Erosion. Proc. 9th Congress of IAHR, Dubrovnik (Yugoslavia), pp. 1102-1113.
Ansari, S.A. (1999) Influence of Cohesion on Local Scour. Ph.D. thesis, University of Roorkee, Roorkee (India).
Ansari, S.A., Kothyari U.C. and Ranga Raju, K.G. (2002) Influence of Cohesion on Scour Around Bridge Piers.
JHR, IAHR, Vol. 40, No. 6, pp 717- 729.
Bhalerao, A.R. and Garde, R.J. (2003) Design of Rip-rap for Protection Against Scour Around Bridge Piers.
Workshop on Bridge Scour, River Training and Protection Works, New Delhi (India), Oct. pp. 1-9.
Bolt, B.A., Horn, W.L., Macdonald, G.A. and Scott, R.F. (1975) Natural Hazards, Springer Verlag, Germany.
Bondurant, D.C. (1950) Sediment Studies at the Conchas Reservoir in New Mexico, ASCE, Proc. Separate, No.
29,
Borland, W.M. and Miller, C.R. (1958) Distribution of Sediment in Large Reservoirs. JHD, Proc. ASCE, Vol. 84,
No. HY2, Pt. 1, pp. 1587- 1 to 9.
Breusers, H.N.C., Nicollet, G. and Shen, H.W. (1977) Local Scour Around Cylindrical Piers. JHR, IAHR, Vol. 15,
No. 3, pp. 211-252.
Briaud, J.L., Ting, F.C.K., Gudavali, R., Perugu, S. and Wei, G. (1999) SRICOS: Prediction of Scour Rate in
Cohesive Soils at Bridge Piers. JGGE, ASCE, Vol. 125, No.4, pp 237- 246.
Brune, G.M. (1953) Trap Efficiency of Reservoirs. Trans. A.G.U., Vol. 34, No. 3, pp. 409-418.
Bull, W.B. (1985) Floods, Degradation and Aggradation. Chapter 10 in Flood Geomorphology (Eds. Baker, V.R.
Kochel, R.C. and Patton, P.C.), A Wiley Interscience Publication, John Wiley and Sons, N.Y. pp. 157-165.
CBIP (1975) Local Scour: A Review. Literature Review 34 Compiled by UPIRI, Roorkee (India).
Davies, B.E. (1974) Armouring of Alluvial Channel Beds. M.E. Thesis, University of Canterbury, Christchurch,
New Zealand.
312
River Morphology
Doyle, W.M., Stanley E.H. and Harbor, J.M. (2003) Channel Adjustments Following Two Dam Removals in
Wisconsin. W.R. Research. Vol.39, No.1, ESG 2, 1-15.
Egiazaroff, I.V. (1965) Calculation of Non-uniform Sediment Concentration. JHD, Proc. ASCE, Vol. 91, No. HY4, July, pp. 225-247.
Ettema, R. (1980) Scour at Bridge Sites. University of Auckland, Auckland, New Zealand, Rep. No. 117.
Evans, J.E., Mackey, S.D., Gottgen, J.F. and Gill, W.M. (2000) Lessons from a Dam Failure. Ohio Jour. of Science,
Vol. 5, pp. 121-131.
Galay, V.J. (1980) Engineering Aspects of River Bed Degradation. Annual Conference of Canadian Soc. of Civil
Engg, Winnipeg, H/7:1 -16.
Galay, V.J. (1983) Causes of River Bed Degradation. W.R. Research, Vol.19, No. 5, Oct., pp. 1057-1090.
Gangadharaiah, T., Sethia, B. and Sheshagiri Rao, R. (2003) Scour Protection Around Bridge Piers and
Abutments. Workshop on Bridge Scour, River Training and Protection Works, New Delhi (India), Oct. pp. 2741.
Garde, R.J. (1955) A Report on Degradation Below Dams. Report submitted to Civil Engg. Dept., Colorado A. and
M College, Fort Collins (USA).
Garde, R.J. and Kothyari, U.C. (1995) State of Art Report on Scour Around Bridge Piers. Report Submitted to
IIBE, Pune. 109 p.
Garde, R.J. and Ranga Raju K.G. (2000) Mechanics of Sediment Transportation and Alluvial Stream Problems.
New Age International Publishers, New Delhi.
Garde, R.J. and Ranga Raju K.G. and Kothyari, U.C. (1987) Effect of Unsteadiness and Stratification on Local
Scour. Research Report, Civil Engg. Dept., University of Roorkee (India).
Garde, R.J. Sahay, A. and Bhatnagar, S. (2004) Grain Size Distribution of Armour Coat. Proc. of Intl. Conference
on Hyd. Engg. Research and Practice, I.I.T. Roorkee (India), Oct.
Gessler, J. (1965) The Beginning of Bed Load Movement of Mixtures Investigated as Natural Armouring in
Channels. Laboratory of Hyd. Research and Soil Mechanics, Swiss Federal Institute of Technology, Zurich,
Rep. No. 69.
Gessler, J. (1970) Self Stabilizing Tendencies of Alluvial Channels. JWWHD, Proc. ASCE, Vol. 96, No. WW2,
pp. 235-249.
Gessler, J. (1971) Aggradation and Degradation. In River Mechanics (Ed. Shen, H.W.), Published by H.W. Shen,
Fort Collins, U.S.A. Vol. 1, pp. 8-1-24.
Gilbert, G.K. (1917) Hydraulic Debris in the Sierra Nevada. USGS Professional Paper No. 105, 154 p.
Harrison, A.S. (1950) Report on Special Investigation of Bed Material in a Degrading Bed. IER, Univ. of
California, Berkley, U.S.A., Series No. 33, Issue No. 1.
Hathaway, G.A. (1948) Observations on Channel Changes, Degradation and Scour Below Dams. Paper Presented
at 2nd Conference of IAHR, Stockholm, pp. 287-307.
Heinemann, H.G. (1981) A New Trap Efficiency Curve of Small Reservoirs. W.R. Bulletin, Vol. 17, No. 5, Oct.
Huber, E. (1991) Update : Bridge Scour. Civil Engineering ASCE (U.S.A.), Sept.
IRTCES (1985) Lecture Notes of the Training Course on Reservoir Sedimentation. Beijing (China).
Islam, M.N., Garde, R.J. and Ranga Raju, K.G. (1986) Temporal Variation of Local Scour. Proc. of IAHR
Symposium on Scale Effects in Modelling Sediment Transport Phenomenon, Toronto, Canada.
Jensen, P.Ph., Bendegom, L. Van, Berg, J. Van den, deVries, M. and Zanen, N. (1979) Principles of River
Engineering: The Non-Tidal Alluvial river. Pitman and Co., London, Chapter 4.
Kand, C.V. (1993) Scour-Sand, Clay and Boulders. Bridge Engineering (India), Vol. 9 and 10
Bed Level Variation in Streams
313
Kellerhals, R. Church, M. and Devies, L.B. (1977) Morphological Effects of Interbasin River Diversions. Paper
Presented at Hydro-technical Conference, Canadian Soc. Civil Engg. Quebec City.
Klaassen, G.J. (1995) Lane’s Balance Analogy. Proc. of 6th International Symposium on River Sedimentation,
New Delhi (India), pp. 671-686.
Kochel, R.C. (1985) Geomorphic Impact of Large Floods : Review and New Perspectives on Magnitude and
Frequency, Chapter II in Flood Geomorphology (Eds. Baker V.R.., Kochel, R.C. and Patton, P.C.) A Wiley
Interscience Publication, John wiley & Sons, N.Y., pp. 169-187.
Kothyari, U.C. (1989) Effect of Unsteadiness and Stratification on Local Scour. Ph.D. Thesis, Civil Engineering
Department, University of Roorkee (India).
Lane, E.W. (1953) Some Aspects of Reservoir Sedimentation. JIP, CBIP (India), Vol. 10, No. 2 and 5, April and
July, pp. 3-14.
Lane, E.W. (1955) The Importance of Fluvial Morphology in Hydraulic Engineering. Proc. ASCE, Paper 745, pp.
1-17.
Lara, J.M. (1960) 1957 Sedimentation Survey of Elephant Butte Reservoir. Bureau of Reclamation, USDI, U.S.A.
Little, W.C. and Mayer, P.G. (1972) The Role of Sediment Gradation on Channel Armouring, School of Civil
Engineering, Georgia Institute of Technology, Atlanta, Georgia (U.S.A.), ERC-0672.
Maddock, T. (1948) Reservoir Problems with Respect to Sedimentation. Proc. Federal Interagency Sedimentation
Conference, USDI, pp. 9-14.
Mahamood, K.C. (1987) Reservoir Sedimentation : Impact, Extent and Mitigation. World Bank Technical Paper
No. 71, 118 p.
Melville, B.W. and Sutherland, A.J. (1988) Design Method for Local Scour at Bridge Piers. JHE, Proc. ASCE, Vol.
14, No. 10, Oct., pp. 1210-1226.
Miraki, G.D. (1983) Sediment Yield and Deposition Profiles in Reservoirs. Ph.D. Thesis, University of Roorkee
(India).
Mittal, M.K. (1985) Parallel and Rotational Degradation. Proc. of 2nd International Workshop on Alluvial River
Problems. University of Roorkee, pp. 17-22.
Mohan, J. and Agarwal, A.K. (1980) Aggradation of Upper Ganga Canal. Proc. of 1st International Workshop on
Alluvial River Problems. Roorkee (India), pp.2-61-72.
Murthy, B.S., Surya Rao, S., Rajagopal, H., Tiwari, S.K. and Rajesh Kumar (1998) Flood and Sediment Routing in
River Systems Mathematical Models. Report Submitted to INCH by Civil Engineering Department, I.I.T.,
Kanpur, 159 p.
Namjoshi, A.G. (1992) Anticipated Scour Depth in Non-Alluvial/ Clayey Beds. Proc. Intl. Seminar on Bridge
Structure and Foundations. Conference Documentation 3, Vol. 2
NIH (1986) Sedimentation in Reservoirs. Report R.N. 26, National Institute of Hydrology, Roorkee, 98 p.
Odgaard, A.J. (1984) Grain Size Distribution of River-bed Armour Layer. Proc. ASCE, JHE, Vol. 110, No. 10, pp.
1479-1485.
Sahay, R.N., Pande, P.K. and Garde, R.J. (1980) Aggradation in Eastern Kosi Main Canal. Proc. 1st International
Workshop on Alluvial River Problems. Roorkee (India), pp. 2-73-78.
Scheuernlein, H. (1989) Critical Review of Various Methods to Prevent or Control Degradation in Rivers. Proc. of
4th International Symposium on River Sedimentation. Beijing (China), Vol. 2, pp. 1095-1102.
Shen, H.W. and Lu, J.Y. (1983) Development and Prediction of Bed Armouring. JHE Proc. ASCE, Vol. 109, No. 4,
pp. 611-629.
Stevans, J.C. (1938) Effect of Silt Removal and Flow Regulation on the Regime of Rio Grande and Colorado
Rivers, AGU, Pt. 2, pp. 653-661.
314
River Morphology
Swamee, P.K. and Garde, R.J. (1977) Progressive Reduction of Reservoirs Capacity Due to Sedimentation. Civil
Engg. Department, University of Roorkee, Research Report.
Todd, O.J. and Eliassen, S. (1940) The Yellow River Problem. Trans. ASCE, Vol. 105, pp. 346-416.
UNESCO (1985) Methods of Computing Sedimentation in Lakes and Reservoir : A Contribution to IHP-II Project,
A-2.6.1 Panel, Feb., 224 p.
Vetter, C.P. (1953) Sediment Problems in Lake Mead and Downstream on the Colorado River. Trans. AGU, Vol.
30, No. 2, April, pp. 291-295.
Wörman, A. (1989) Rip-rap Protection without Filters. JHE, Proc. ASCE, Vol. 115, No. 12, Dec. pp. 1615-1630.
Yearke, L.W.C. (1971) River Erosion Due to Channel Relocation. Civil Engineering (Canada), Vol. 4, No. 8, pp.
39-40.
Zhide, Z. (1991) Empirical Methods of Estimation of Loss of Reservoir Capacity. Lecture Notes of Regional
Training Course on Reservoir Sedimentation, New Delhi, pp. 3.6.1-3.6.34.
C H A P T E R
10
River Channel Changes
10.1
INTRODUCTION
It is seen in Chapter 9 that human interference in terms of change in Q, Qs or water surface slope in an
equilibrium stream can induce aggradation or degradation. Such changes in bed level also take place
because of change in land use, catastrophic floods, and tectonic or neo-tectonic activity. In this
discussion it was assumed that the channel width or plan-form remains unchanged. The changes in bed
level resulting from human interference were widely studied by engineers in the first six decades of 20th
century. Since then considerable interest has been evinced in changes in drainage pattern and channel
changes as can be seen from the works of Allen (1965), Leopold et al. (1964), Schumm (1969, 1971,
1977), Gregory (1977), and Gurnell and Petts (1995). These changes are briefly discussed herein.
Lewin (1977) classifies channel changes into two categories namely autogenic changes and
allogenic changes. Autogenic changes are the ones which are inherent in the river regime and involve
avulsion, channel migration, cut-offs and crevassing. Allogenic changes are the ones which occur in
response to system changes involving climatic fluctuations and altered sediment load or discharges, as a
result of human activity. If a channel is migrating in the valley created by it, some geomorphologists
consider such a stream, in regimen. Newson (1995) has given a sketch indicating the type of changes
that take place in the stream as it debouches from mountains and joins the sea. This is shown in Fig.
10.1; this figure indicates that avulsion is more likely to occur when stream is about to enter from steep
slope region into the plain with flatter slope. Bank erosion, bar formation and meander shifting occur in
the middle reaches, slumping of banks, building of flood plain and channel migration take place in the
lower reaches.
10.2
AVULSION
Horizontal instability of a single channel alluvial stream can take two forms, either avulsion or pattern
change. Avulsion is a sudden abandonment of part or whole of the stream for a new course at a lower
level of floodplain. This has occurred in the recent history of such streams as the Mississippi and the Rio
316
River Morphology
Upland
Knock-on effect of the
sediment system
Slope failure
Channel blockage
Channel aggrades
and bank erodes
Transfer
Erosion of banks as
bars acrete
Build up on bank
followed by collapse
Lowland
Erosion of banks
due to slumping
Conveyance loss of
Conveyance loss of
fines to floodplain
fines to floodplain
Fines washed out
to sea
Fig. 10.1
Alluvial stream problem problems involving erosion, deposition etc. (Newson 1995)
Grande in U.S.A., the Meandros in Turkey, the Rufiji in Tanganyika, the Kosi in India (Allen 1965), and
the Yellow river in China. In an aggrading stream or a stream shifting its position in meander belt, the
river bed rises and forms an alluvial ridge. Greater the height of the ridge above the floodplain, the more
likely it is that local crevassing will result in some permanent change in the stream course and it will
flow through one of the palaeo channels or carve a new course. As mentioned by Frisk (1944) the
Mississippi recently built in its floodplain at least five alluvial ridges along meander belts up to 80 km
apart.
Richards et al. (1993) consider the avulsive channel system, in which the key depositional process
involves the relationship between channels within the system, rather than the behaviour and properties
within a channel. In such a system there is areal sedimentation so that the basin fills relatively uniformly
over time scales of a few thousand years. Such a system exists in the Gangetic plain at the foothills of the
River Channel Changes
317
Himalayas. The mechanism of evolution of the present day avulsive systems includes (i) aggradation of
channel and floodplain by the accumulation of bed-load and suspended load, (ii) increasing but never
the less subtle topographic differences and flood overspills; and (iii) avulsion due to over spilling and
stream capture.
The Gangetic plain consists of 400-600 m thick alluvial deposit in the tectonically controlled
Himalayan foredeep basin. This area has experienced two earthquakes in 1934 and 1988 of magnitudes
8.4 and 6.5 respectively on the Richter scale. Avulsion has taken place at varying rates across the basin.
The higher rate of sediment supply in the northern margin of the Gangetic plain has caused rapid
aggradation and more frequent channel shifts on the Kosi mega-fan. Mega-fans are large size fans of
100-200 km in width and 100-150 km length in the humid environments. They are triangular in shape
with their apex at the gorge mouth, convex in form and are characterized by steep gradients (20 cm/km).
The Ganga plain consists of several fan and inter-fan areas viz. Yamuna-Ganga mega-fan, Sarda fan,
Gandak mega-fan and Kosi mega-fan. Inter-fan areas (intercones) are reverse in plan, tapering from
Himalayas, slightly concave at edges and with gradients 10 cm/km or less (Jain and Sinha 2003).
East-west trending Gangetic plain is characterized by geomorphological diversity in terms of
morphology, hydrology and sediment transport rates of the rivers. Most of the rivers such as the Ganga,
the Kosi and the Yamuna display braided as well as meandering plan-forms, and some such as the Kosi,
the Bagmati and the Rapti show change from braided to meandering pattern.
Further, most of the streams draining the area are known for their rapid and frequent avulsions albeit
with varying frequencies. As discussed in Chapter 13, the Kosi has migrated 110 km in 200 years before
it was embanked in 1963. (see Fig. 13.7). The primary reasons for this migration are high sediment load,
tectonic activity, frequent floods and general westward slope. The Sarda river has undergone shifting
and river capturing during the last 80 years (Tangri 2000) and the Gandak has migrated eastward by 80
km during the past 5000 years.
Data on lateral migration of alluvial steams were collected by Wolman and Leopold (1957). It was
found by them that while since streams showed continuing tendency for lateral migration over a period
of years, in some instances the stream channel maintained a reasonably stable position and had little
lateral movement over a long period of time. However, the same site experienced very rapid movement
during a succeeding period. In other words, the lateral movement can be continuous or discontinuous.
Further, it was found that in general larger streams seem have larger rates of migration. The migration
rate of the Kosi during 1936-1950 periods varied 0.18 km/yr to a maximum of 2.63 km/yr during 19221933. The Ramganga river in north India moved westward at 80.5 m/yr during 1795-1806 while it
moved eastward at 4.3 m/yr during 1806-1883 and westward at the rate of 4.0 m/yr during 1883-1945.
Table 10.1 gives data on lateral migration rates of some rivers across valleys.
In the case of the Yellow river in China, Chien (1961) has shown that the channel shifting (lateral
migration) varies with the fluctuations in discharge quantified as ratio of maximum flood discharge to
the bankful discharge. In the case of the Yellow river the migration rate varied from 20 m/day to 200 m/
day. Such large variation is due to heavy sediment carried by the river. He also found that the amount of
shifting is controlled by the spacing of constrictions or control points along the river.
Jain and Sinha (2003) have studied in detail the avulsive tendency of the river Bagmati using survey
of India topographic maps and satellite imageries. The Bagmati river draining north Bihar plains is an
anabranching stream with repetitive avulsive history. Figure 10.2 shows the avulsions in the Bagmati for
318
River Morphology
Table 10.1
Data on lateral migration rates of some rivers across valleys (Adapted from
Wolman and Leopold 1957)
River
Drainage
area km2
Period of
measurement
Rate of movement m/yr
Comments
Watts Branch near
Rockville Md.
10
1953-1956
0.60
From topographic map
North River, Va
128
1834-1884
2.44
Local observation
256 000
1795-1806
1806-1883
80.50 (W)
4.30 (E)
Ramganga river, India
Kosi river, India
…
1883-1945
4.00 (W)
Colorado river near
needles, California
437 000
150 years 18581883
1903-1942
750.00
243.00
30.00
For one bend
Yukon river, at Holy Cross,
Alaska
819 200
1896-1916
36.60
Local Observer
Missouri river, near Peru,
Nebraska
896 000
1883-1903
76.20
Rate varied from 15 m/
yr to 150 m/yr
2816 000
1930-1945
45.20
Mississippi river near
Rosedale, Mississippi
the past 230 years in which it may be noted that the river has shifted first towards east, then northeast,
south and southwest. The primary causes for the instability of the Bagmati are believed to be variability
in the peak discharge, frequent over-spilling and relatively high sediment load. Effect of channel
avulsion resulting in the abandonment of bridge on the Bagmati is shown in Fig. 10.3.
Avulsion of the Tigris
It is also interesting to discuss the avulsions of the Tigris and the Euphrates rivers in ancient
Mesopotamia (now known as Iraq). Mesopotamia is in fact one huge delta formed by joining of the
Tigris and the Euphrates to the Persian Gulf. The ancient city of Ur which was founded about 4000
years B.C. on the still marshy limits of the gulf and which served as a seaport during historical times,
now lies about 150 km inside (Garde 1978). The Tigris has undergone three shifts, see Fig. 10.4; the first
shift was between slightly south of Samara and slightly north of Baghdad. The old course shifted to the
new one in the 13th century. The second shift south of Ctesiphon is also shown. Both these shifts are
inferred by McAdams from the archaeological sites of the Parthian period (311 B.C.–226 A.D.). The
third shift is shown in the bottom figure. Presently the Tigris follows a winding course in the south-east
direction downstream of Baghdad for about 400 km. The combined river is then called Shat-al-Arab (the
Arab stream). However, in the Muslim period up to the 16th century, the Tigris came about 160 km
below Baghdad, then came straight south by a channel known as Shat-at-Hai to Wasit. Then 700 km
below Wasit the river lost most of its water by irrigation channels and finally became lost in the swamp.
319
River Channel Changes
Fig. 10.2
Avulsion of the Baghmati (Jain and Sinha 2003)
Fig. 10.3 Effect of avulsion in the Baghmati river
320
River Morphology
Fig. 10.4
Changes in the courses of the Tigris
Avulsion of the Yellow River (Xu Fuling 1982, Lin and Li 1986)
Another example of avulsion is the Yellow river in Peoples Republic of China. This river is known all
over the world for the heavy sediment load it carries with relatively small volume of runoff, and is often
known as “river of sorrow”. The Huanghe (or the Yellow river) which originates at Togo has an upper
reach of 3461 km with a drop of 3480 m; the major tributaries in this reach are the Datonghi, the Taohe,
the Huangshui, the Julihe and the Shanshuihe. This reach of the river carries relatively less sediment, the
total annual sediment load being only 11 percent of the whole river, while the annual runoff from this
reach is 56 percent of the entire river. The middle reach from Togto to Taohuayu is 1235 km long in
which the major tributaries the Wudinghe, the Yianshui, the Fenhe and others, flowing through Loess
region, discharge into the Yellow river. Hence this reach carries a heavy sediment load. From Taouayu to
the estuary is the lower reach after which the river joins the Bohai sea. This lower reach is 768 km long
and flows through a region in which more than 100 million people live. This reach has a flat slope of
321
River Channel Changes
0.000 125 and the flood discharge in this reach is 4000 m3/s to 5000 m3/s but can reach 10 000 m3/s.
Long-term average sediment concentration in the lower reach is 34 kg/m3 while the maximum observed
is 594 kg/m3. The sediment concentration in the tributaries can reach as high as 1000 to 1500 kg/m3. The
sediment transported has a size range of 0.002 mm to 0.05 mm. Because of the high concentration and
flat slope, almost 50 percent of the sediment carried by the lower Yellow river at Zhenzhou (see Fig.
10.5) is deposited in the river. As a result of this aggradation, the river bed between the flood
embankments is higher than the ground level outside by 3 to 5 m and is rising at an average rate of 0.1 m/
yr. At some places this difference is as large as 10 m.
he
eR
Ta
iyu
an
ob
Fe
eR
Jin
Yellow sea
R
Welhe R
e R Jinan
gh
n
ua
H
oh
Lanzhou
Yan'an
Lu
iR
hu
Xining
Beijing
Bohai sea
ns
Qi
Yin
chu
an
Wu
din
gR
Tuo
ket
uo
Huhehaote
Xi'an
Zengzhou
Fig. 10.5 The Yellow river
Levees or flood embankments in the lower reach of the Yellow river are about 1370 km long which
are attacked during the flood and breaches occur causing flooding of low lying areas and change in the
river course. This avulsive tendency in the lower reach of the Yellow river is present since historic times.
Changes in the course of the river since 2000 BC to the present time are shown in Fig. 10.6. As can be
seen, the river has swept over a big fan-shaped area between the Huaihe river in the south and the Haihe
river in the north. In the past 1000 years 1593 breaches of the levees have been recorded out of which 26
breaches resulted in extensive flooding and the river changing its course to a new channel.
To control floods, the levees have been raised by 2 to 6 m to a height of 10 m; they have also been
widened so that the top width is now 7 to 15 m and berms have been provided on the landside. Also to
provide additional protection, more than 300 km length of the levees has been provided with stone
pitching and more than 5000 short spurs have been constructed.
10.3
STREAM CAPTURE (WORCESTER 1948, LOBECK 1939)
Stream Capture results when one stream flowing in the lower region works head-ward and intercepts
head waters of the stream draining in higher area. The stream flowing at the lower level always has the
advantage. An example of stream capture is shown in Fig. 10.7. Figure 10.7 (a) shows the conditions
just before the capture. The river heading in the escarpment can, because of its steep gradient cut back
rapidly into the drainage area of the stream flowing on the plateau above, even if the rocks of the region
are all homogeneous and of equal resistance to erosion. Figure 10.7 (b) shows the condition shortly after
322
River Morphology
Beijing
ng
Julu
R
Wu
yi
ya
Fu
1
3
ya
ing
Zhanghe R
Pu
ing
R
Jinan
Dongping Lake
6
Heze
4
Yanjin
Zhengzhou
Xia
g
an
ot
Ga
Bohai sea
oq
2
3
0
R
Lij
in
o
tu
Hu
Ca
J
no
xia ingh
ai
n
Tianjin
Weishan Lake
Lankao
5
Shangqui Dangshan
7
Wo
h
Yin
h
eR
Ho
ng
he
eR
Xuzhou
Huaiyan
R
Huaihe
R
Yangzhon
Changian
Nanjing
0 About 2000 BC
0 1149 AD
0 602 BC
0 1494 AD
0 11 AD
0 1855 AD
0 1048 AD
0 1938 AD
Fig. 10.6 Historical migration of the Yellow river (Lin and Li 1986)
the capture. The captured stream has been diverted by the captor stream and now turns sharply at the
point of capture, known as the elbow of capture. The difference in level of the two streams results in a
waterfall. The captor stream has its discharge increased by the addition of captured stream and begins to
show signs of rejuvenation. Its gorge in deepened, and its tributaries on either side below the point of
capture cut back rapidly to form other gorges. The beheaded stream, having lost much of its discharge,
acquires mature characteristics. It develops small meanders, not suited to the size of its valley. It
becomes a misfit or underfit stream. Its tributaries build alluvial fans on the valley floor because the
beheaded stream in its shrunken condition can no longer transport its sediment load. Figure 10.7 (c)
shows the conditions long after the capture. The headwaters of the captor stream have all developed
gorges. The falls at the point of capture have retreated upstream to head of the diverted stream. With
further development all the falls and rapids disappear and the only evidence of capture remaining will be
the angular bend.
Stream capture also takes place in the case of stream migrating on the cone or the fan developed by
it due to sediment deposition. During its avulsion in a new course, the stream can capture smaller
stream. Similarly when the streams meander widely over flood plains, stream capture is common due to
lateral cutting and intersection of meanders.
323
River Channel Changes
Fig. 10.7 River capture (Lobeck 1939)
10.4
EROSION AT BENDS
Some studies have been carried out in the past to find out the variables which govern the rate of erosion
or migration of bends in alluvial rivers. Wolman (1959) has reported rates of erosion in cohesive river
banks and recognized the important of seasonality in the rates of erosion. Daniel (1971) has monitored
the effect of erosion in the form of changes in outer bank of meander bends along streams in Indiana.
According to Dury (1961) annual flood magnitude is of importance in this erosion, while Harvey (1975)
has commented on the effectiveness of intermediate discharge. Hughes (1977) made measurements on
three meander arcs on the river Cound in U.K. during 1972-74. This river has width to depth ratio of 15.
The rates of erosion were measured using 92 pegs and monitoring the distance of the bank line from
these pegs. The discharge during the study duration varied from 1.0 m3/s to 10.0 m3/s. It was found that
324
River Morphology
the two meander arcs having large bend radius had average erosion rates of 1.61 m/peg and 1.51 m/peg
while the third arc which had a smaller radius showed erosion rate of 1.9 m/peg.
It was also found that for discharge less than 2.0 m3/s the erosion rate of banks was minimum. For
discharges between 2.0 and 8.0 m3/s the erosion rate was moderate, and for discharge greater than 8.0
m3/s major erosion changes occurred. The corresponding return periods for 2 m3/s and 8.0 m3/s were
estimated as 10-12 times/yr and 1.5 yrs respectively. Similarly Hooke (1995) studied the migration of
bends on five streams in East Devon (U.K.) having catchment areas between 110 km2 and 620 km2. He
found the average rate of migration to be 0.37 m/yr while the maximum was 1.32 m/yr.
Studies of Nanson and Hickin (1983) and Hickin and Nanson (1984) throw light on the parameters
on which dimensionless migration rate M1/W, where M1 is migration rate in m/s and W is the channel
width, depends. According to them
F
GGH
Stream power, erosional resistance of concave bank material, height of
M1
r
=f
concave bank, sediment supply rate, c
W
W
I
JJK
Further, it stands to reason that average bed material size d should come in the picture and it can
assumed that sediment supply rate should be related to stream power QS. The above relation can then be
written as
M1
W
F
G
=fG
GG d
H
2
QS
, erosional resistance of concave bank material,
Dgs d
rf
I
J
h r J
,
D WJ
JK
c
where rc is the centerline radius of curvature of the bend, h is the height of concave bank above water
level and D is depth of flow. Further, Hickin and Nanson (1984) found that when rc/W = 2.5 the
migration rate of the bend is maximum. This maximum value of
to be a function of stream power,
M1
denoted by K is intuitively assumed
W
r
r
h
M1
and erosional resistance. Hence he has plotted
vs c for c
KW
D
W
W
ranging from 1.18 to 13.0 for bends and for which K =
bM g
1 max
W
was 0.02. The graph between
M1
and
KW
rc
is shown in Fig. 10.8 and it is anticipated that data for other bends would follow the same trend.
W
Nanson and Hickin (1983) have further stated that channel migration is discontinuous as a result of
seasonal fluctuations in flow; hence short-term migration rates are not indicative of the average
migration rate of the bend.
325
River Channel Changes
1.0
0.8
M1
KW
0.6
Beatton river data
0.4
0.2
0.0
0
2
4
6
8
10
12
14
rc/W
Fig. 10.8 Variation of
M1
r
with c
KW
W
The seriousness of bank erosion can be illustrated by discussing erosion upstream of the Farakka
barrage on the river Ganga (Majumder 2004), see Fig. 10.9. Farakka barrage was constructed across the
river Ganga in 1971 to divert 1135 m3/s (40 000 cfs) of water to its tributary, the Hooghly river, in order
to keep Kolkata port navigable throughout the year. This diversion has been effected by constructing a
3.8 km long feeder channel from Farakka barrage. Upstream of the barrage, the river slope is 0.000 06
and the bed is made of fine to medium sand. The flood discharge over the past 32 years has varied
between 36 290 m3/s and 77 778 m3/s. Further, while the distance between the permanent banks is about
16 km, the river width is about 2 km in the river reach upstream of the barrage.
Prior to the construction of barrage, the river was flowing straight from Rajmahal to the barrage site.
However in 1963 the course of the river started gradually shifting towards the left and attacking the
village on the left bank e.g. Panchanandpur about 20 km upstream of the barrage, see Fig. 10.9. The rate
of bank migration has varied from year to year, but over the past 30 years the apex of the bend has
migrated through approximately 8000 m giving an average rate of migration of 36.7 m/yr. Configuration
of the bend is such that the bend radius is about 14 km giving radius to width ratio of about seven. As a
result of migration of the bend to the east for the past six years, the area eroded has varied from 100 to
415 ha per year. The area being fertile it is thickly populated, and hence during a flood, loss of the order
of 500 to 1000 crores of rupees takes place. Further, to the northeast of Farakka barrage flow smaller
streams the Kalindri, the Pagla, the Old Bhagirathi, and the Mahananda. It is possible that if the
migration towards the east continues, the Ganga may capture the above mentioned streams one after
another and then flow along the Mahananda thus changing its course drastically. Hence some steps have
been taken to arrest this migration; these include building of retired embankments as erosion proceeds,
and construction of spurs. However, these measures seem to have only a marginal effect. It seems that
effective management of this problem should involve firstly the stabilization of the eroding bank by
giving proper slope to the bank and then providing bank protection. The next step that needs to be taken
is to reactivate the existing small channel on the right side so that it starts carrying increasing amount of
326
River Morphology
Mahananda
Bhagirati
Kalindri
2002
2001
2000
1999
1998
1997
NH34
Railway
Pagla
Panchanandpur
Farakka
barrage
1939
1922
Bhuti Diara
1967
1939
1922
Manikchak
Rajmahal
Fig. 10.9
Bank-line changes upstream of Farakka barrage on the Ganga
flow there by decreasing the flow along the left bank. This can be assisted, if necessary, by dredging
downstream of Rajmahal.
Hooke (1995) has summarized information about mechanisms of bank erosion. These are broadly
classified into three broad categories namely bank weakening, fluvial erosion or entrenchment, and
mass failure. Bank weakening can be due to pre-wetting downwards by precipitation front, inwards
from the river or upwards by the water table. Similarly bank weakening can occur by desiccation
condition of high temperature and low moisture which can lead to cracking and spalling. Similarly
freezing and thawing action can also make the bank more susceptible to erosion. Fluvial erosion can be
direct removal of non-cohesive material when flow and shear stress near the bank exceed a certain limit
during flood. Resistance to such type of erosion is affected by vegetation, composition and state of the
material and its cohesivity. Mass failure can be of two types. Shear, beam and tensile cantilever failures
occur mainly on composite banks. Initial fluvial failure takes place of basal coarse materials and then
failure of the upper fine blocks takes place. The second type of mass failure is shear failure. This occurs
in cohesive materials associated with increased bank angle and/or bank height, high moisture content
and pore pressures. Failure takes places after occurrence of peak flow.
10.5
NATURAL AND ARTIFICIAL CUT-OFFS
In most of the cases the meanders in alluvial streams are not stationary but move slowly in the direction
of flow. During the development and movement of meanders there is a gradual lengthening of meanders
which imparts a lateral movement to meanders. Hence in few cases movement of meanders is in lateral
direction thereby increasing the amplitude of meanders. Increased frictional and bank resistance tends
to halt the lateral movement. When the bend and bank resistance become too large for continued
River Channel Changes
327
stretching of the loop, it is easier for the flow to cut across the neck of the loop than to flow along the
bend, resulting in a natural cut off. The two ends of the loop that is cut get gradually silted up and give
rise to an oxbow lake. Usually small and narrow side channels are available within a neck of the
meander loop. These channels are either part of the main channel when the stream was flowing along
that course or are formed by spilling of floods over the banks. Cut-off may develop along these small
channels. The development of a small channel in the neck into a major natural cut-off primarily depends
on the assistance this channel receives from the major floods in increasing its cross-section. If a large
flood lasts for a relatively long period, the channel gets sufficient time to develop into a full waterway.
Development of such a natural cut-off requires two to three years, or probably even more time.
Natural cut-offs have occurred on the Mississippi river in U.S.A. and other rivers in the world. On
the Mississippi, natural cut-offs have taken place when the cut-off ratio i.e. arc distance along the bend
to the neck distance ratio, was between 8 and 10. Analysis of historical data on 145 natural cut-offs on
relatively smaller streams in England and Wales has shown (Lewis and Lewin 1983) that cut-offs have
occurred for rc/W ratio ranging from 1.0 to 12.0. However, a large number of these cut-offs have
occurred at rc/W values between 1 and 4. Assuming that the meander pattern is made up of arcs of a
circle, Chatley (1940) has shown that, from purely geometric point of view, cut-off occurs when MB =
(2 + 3 ) rc because at this value the neck distance will be zero.
According to Frisk (1944) natural cut-offs are of two types:
Neck Cut-off
This cut-off forms in response to river flow across the narrow neck of the over extended meander loop.
For neck cut-off to occur, the neck has to be narrow enough so that the flood water breaks through and
forms a cut-off. This type of cut-off rapidly abandons the old bend, forms an oxbow lake and is rapidly
silted up at its end since the sediment can then enter the oxbow lake only from local inflow or from over
bank flood flows; further deposited sediment consists of finer sediment, normally decreasing in size
with distance from the new channel.
Chute Cut-off
This type of cut-off forms in response to the development of a chute across a low lying swale within the
enclosed point bar area of an over extended meander bend. The old channel is abandoned slowly and
with the gradual reduction in flow, is filled with silt and sand material and finally with clay. These two
types of cut-offs are shown in Fig. 10.10. Friedkin (1945) noted in his flume tests that there was a
limiting size for each meander pattern and that, when for any reasons this size was exceeded, chute cutoffs invariably occurred. In natural streams they have been observed to occur during flood flows that
tended to follow a straight path and during lesser flows when either the loop in question or the adjacent
loop became excessively enlarged.
Artificial cut-offs are executed on the streams to reduce the stream length and thereby reduce the
flood heights and flood periods, and to shorten the travel distance and increase the manoeuvering ability
of water vessels during navigation along the bends. Pickles (1941) has estimated that if all the bends in
a typical alluvial river are cut-off, the average velocity in the stream will increase by about forty percent.
In the past artificial cut-offs have been executed on many rivers in the world such as the Mississippi, the
Arkansas and the Missouri rivers in U.S.A., the Tisza river in Hungary, the Hai river in China and some
328
River Morphology
Neck cut-off
Point bar
Chute cut-off
Fig. 10.10
Chute and neck cut-offs
streams in New Zealand. By execution of such cut-offs the length of the Mississippi has been reduced
from 720 km to 480 km and that of the Tisza from 1299 km to 745 km.
The execution of artificial cut-offs is done slightly differently in Europe and in U.S.A. In Europe,
the cut-off is made in the dry and to its full dimensions, and the river is allowed into it. American and
New Zealand practices are similar, in which a pilot channel of small cross-section is made which can
initially carry about 8 to 10 percent of flood discharge and it is allowed to develop by itself. This channel
develops fully in about 3 to 4 years. Pickles (1941) has given the following suggestions in the design and
execution of cut-offs.
i. The pilot channel should be tangential to the incoming flow as well as while leaving the cut.
ii. The pilot channel should be made on a slight curve, the curvature being less than the dominant
curvature of the river.
iii. Entrance to the pilot channel should be made bell-mouthed.
iv. Cut-off should be excavated to the mean river cross-section.
v. When a series of cut-offs is to be made, the work should progress from downstream to the
upstream.
When a cut-off is executed, there are some short term and some long-term changes in the rivers;
these need to be properly understood. As soon as the cut-off is executed the water surface slope within
the cut-off reach is increased. This causes M2 profile upstream of cut-offs and M1 profile downstream.
Further this change in water surface slope in the upstream reach will reduce the storage and the peak
discharge downstream of cut-off is likely to be increased. The long period change will be in the bed
profile. Reach upstream of the cut-off will experience degradation while that downstream will
experience aggradation.
The effectiveness of cut-offs as means of flood control is discussed by Pickles (1941). As
mentioned earlier, if all the bends are removed, the flow velocity is likely to be increased by about forty
percent. Whether the expenditure involved in straightening is justified as a flood control measure
depends on the width of the flood plain. If the flood plain is approximately 0.8 km wide of less, the
channel improvement using cut-off is justifiable because cost of levee construction will be prohibitive.
329
River Channel Changes
If the flood plain is 1.5 to 6.5 km wide, cut-offs together with levee construction are the accepted method
of flood protection. For every wide flood plain, flood protection is seldom attempted using cut-offs.
However, cut-offs can still be executed if the stream is used for navigation.
Lastly, it needs to be emphasized that when cut-off is executed the banks in that reach need
protection, otherwise stream will have a tendency to develop a meander loop again.
10.6
CHANNEL PATTERN CHANGES
Sinuosity is earlier defined as length of stream divided the length of the valley. The sinuosity values
range from 1 to slightly greater than 3.5. Analysis of American rivers by Leopold and Wolman (1960)
indicated that the sinuosity varied from 1.0 to 3.0. The average sinuosity of the Mississippi is 2.3 while
its maximum value at the Greenville Bends at Greenville was 3.3.
In single channel stream it is interesting to study variation in the sinuosity of the stream. Studies by
Schumm (1977) have indicated that the sinuosity is significantly affected by the differences in the flow
variation. To support this argument he has given example of two streams the Tanoro and the Guanipa.
The characteristics of these two streams are given below.
River
d mm
Tonoro
Guanipa
0.35
0.35
Mean annual
discharge Qma m3/s
11.34
17.00
Qmax m3/s
Qmax/Qma
Si
535.6
104.9
47.23
6.17
1.1
2.3
From this it seems that Qmax/Qma ratio is morphologically important in determining the sinuosity;
higher sinuosity is associated with lower value of Qmax/Qa.
Experiments in a laboratory flume by Khan (1971) have indicated that the sinuosity was function of
slope. For small slopes the channel was straight; when the slope exceeded a certain limit the channel
meandered and sinuosity increased with increase in slope and reached a maximum value. Further
increase in slope decreased the channel sinuosity and then the channel became straight and braided.
Similar variation between valley slope and sinuosity has been reported for the Mississippi between
Cairo (Illinois) and Head of Passes (Louisiana) by Schumm (1977). Schumm argues that the valley
slope reflects the past discharges and sediment loads while the channel slope corresponds to the present
discharge and sediment load variations. By plotting valley slope versus channel slope for some streams
and palaeo channels, he found that channels with low percentage of silt and clay in channels, had
sinuosity of unity and the two slopes were almost the same, while for channels with higher values of
percentage of silt and clay, channel gradient was smaller than valley gradient and streams were sinuous
with different sinuosity.
In a river system, it is many times found that for essentially constant discharge and sediment load,
change in river pattern or plan form occurs along the length. The fact that in many cases the channel
slope varies slightly but the slope of the valley changes explains this significantly. Within the valley;
there are reaches of valley floor that are steeper or gentler than the average stream gradient. This
happens wither due to tectonic movements or by the large difference between sediment load of the
tributary and the mainstream. Hence to maintain relatively constant gradient, the stream lengthens its
course on steeper reaches.
330
River Morphology
Agarwal (1983) analysed the field data and some laboratory data and found that sinuosity depends
on slope and discharge. Khan found that sinuosity is related to slope. Schumm (1977) has plotted
sinuosity against stream power toU and found that for low values of toU the channels are straight, then
for a certain range of toU channels meanders, the sinuosity increases and reaches a maximum value and
then decreases. Beyond another threshold value of toU, the stream braids. It is quite possible that
sinuosity would correlate well with dimensionless stream power QS/d2Ö(Dgs d/rf).
It many times happens that with time a river may undergo a complete change of morphology if
changes take place in discharge and sediment load. Schumm (1969) calls such change the river
metamorphosis. The changes taking place in bed elevations leading to aggradation or degradation have
been discussed in Chapter 9. Here change in plan form such as in meander length, sinuosity, and width
to depth ratio of the stream are briefly discussed. The geomorphic approach to such changes is based on
the work done by Schumm (1969, 1971 and 1977) and is briefly discussed below. Schumm’s work has
indicated that at characteristic discharge such as mean annual discharge,
W~
Q 0.38
M 0.39
S~
M - 0 .38
Q - 0.32
ML ~
Q 0.34
M 0.74
D~
Q 0.38
M 0.39
Si ~ M0.24
and assuming total bed material load ~
Qs »
U|
||
||
V|
||
||
W
...(10.1)
1
for constant discharge, one can write
M
W, ML , S
D, Si
...(10.2)
Here M is the percent of silt and clays in the bank material. By using plus or minus exponent to
indicate how various aspects of channel morphology will change if Q or Qs is increased or decreased,
the following relationships can be written
Q+ » W+, D+, ML+, S–
Q– » W–, D–, ML–, S+
Q+S » W+, D–, ML+, S+, S–i
Q–S » W–, D+, M–L, S– S+i
U|
|
V|
||
W
...(10.3)
331
River Channel Changes
Above equations indicate how W, D, ML and S change with change in mean annual discharge, and
how increase or decrease in Qs at constant discharge affect these variables along with sinuosity Si and
width to depth ratio F. Width to depth ratio of the channel is found to be mainly influenced by the type
of sediment load; as the load increases, F decreases and vice versa. Since in nature change in discharge
or sediment load will rarely occur alone, Schumm considers four possibilities and represents changes in
morphology that will result by the relationships
Q+ Q+S » W+, D±, ML+, S±, S–i, F+
Q+ Q–S » W±, D+, ML±, S–, S+i, F–
–
Q+S
–
Q–S
Q
Q
»W ,D ,
ML±,
S ,
»W ,D ,
M –L,
±
±
–
–
±
+
S
S–i ,
S+i ,
F
F–
+
U|
|
V|
||
W
...(10.4)
Schumm (1971) has further indicated that when channel width, depth, sinuosity and meander length
are required to be modified because of a hydrologic change, then a long period of instability could be
envisaged with considerable bank erosion and lateral migration occurring before stability is restored. A
couple of examples given by Schumm (1971) are briefly discussed here to emphasize the changes that
take place and time required to effect the change.
The length of the Mississippi river from the mouth of the Big Sioux river to the mouth of the Platte
river was approximately 400 km in 1804 while this length reduced to 240 km in 1935. This reduction is
attributed by Towl (see Schumm 1971) to the cutting of timber on the flood plain, and the great flood of
1881 and subsequent floods. These floods by reducing the length of river, steepened the slope and
widened the river cross-section.
It may be found that in a given reach of a stream the sinuosity has changed over a period of time.
This can happen when the river length changes over a period of time due to natural or artificial cut-offs,
or due to growth of the delta. Such changes in length will affect the slope and hence the sinuosity or
plan-form of the stream. Such fluctuations in the length of the Mississippi river have been found by
Winkley (1970) who showed the river length has changed from about 1680 km to 2056 km and then
reduced to about 1472 km over the past 2000 years. Schumm (1969, 1971) has given a few more
examples of changes in river morphology due to changes in hydrologic regime over a long period.
The other approaches is make judicious use of relationships and criterion discussed in the earlier
chapters to predict change in S, W, W/D ratio and plan-form when changes are effected in Q or QT or S.
Thus for a given discharge when S is changed, plan-form changes can be assessed using Lane’s Q vs S
criterion (see Eq. 9.1). Alternately Chang’s diagram (Fig.6.28) between Q and S/d1/2 can be used to
predict width, depth and plan-form. When aggradation or degradation takes place equilibrium depth,
width and width/depth ratio can be assessed using Eqs.(6.34) or (6.35) proposed by Garde et al.
However, it is difficult to predict the time required to effect such changes because the width adjustment
is rather slow and depends on the cohesivity of banks.
10.7
LONGITUDINAL GRAIN SORTING
As mentioned in Chapter 4, the size of bed material of alluvial streams reduces in the downstream
direction. This has been verified on a number of streams such as the upper Rhine, the Danube, the Niger,
332
River Morphology
the Mississippi, the Rio Grande and the Ganga. Sternberg attributed this to abrasion and developed
Sternberg’s law as given by Eq. (4.6) Similar reduction in size of bed material is also found on beaches
where littoral drift occurs. The phenomenon of abrasion has been discussed by Pettijohn (1957) in
relation to rates obtained on size reduction in laboratory experiments and reduction of bed material size
in the downstream direction in the streams. He has concluded that
1. Abrasion depends very much on the resistance of minerals to wear and on the diameter of
particles; the abrasion rate of gravel is much greater than that of sand.
2. Abrasion is also a function of the composition of the material tested.
3. Abrasion rates obtained in experiments by Lane, Daubree, Thiel and others show that abrasion
cannot generally be accepted as the sole cause of decrease of particle size in rivers.
Hence, it is believed that some sort of hydraulic sorting process can explain this reduction in size of
bed material of the streams in the downstream direction. Hydraulic sorting can be local over distances of
the order length of the bed-form or general over much larger lengths. Thus local sorting takes place over
dunes and in the bends. The general or longitudinal grain sorting primarily takes place because of spatial
variation of transport of different sediment sizes forming the bed material, and has been studied by Rana
et al. (1973), Diegaard and Fredsøe (1978) and Diegaard (1980).
Rana et al. (1973) considered a stream in which the longitudinal bed profile is in equilibrium i.e.
mean bed level of the stream does not change with time, and developed the model for longitudinal grain
sorting after making the following assumptions:
1. The flow is steady and constant along channel length.
2. The channel is wide and prismatic.
3. The channel profile is an independent variable and the channel slope decreases according to the
relationship
S = So e– a1
...(10.5)
in which S is the slope at distance L, So is slope at L = 0, and a1 is a constant.
4. The channel is in equilibrium but the channel bed has been initially formed by aggradation of
material transported from the upstream.
5. The bed material at any section in the reach has the same size and gradation as the bed material
discharge in the upstream section.
6. The bed material size at the most upstream section is known and is log-normally distributed.
The analysis is carried out in the following manner.
1. The bed material is divided into ten fractions and using Einstein’s bed-load fuction the total bed
material discharge and the ratio of total bed load to suspended load fractions is determined.
2. The median diameter and gradation of the computed bed material discharge at the upstream
section 1 is determined.
3. Knowing the bed material discharge, water discharge and bed material load gradation at section
1, the energy slope required at section 2 to maintain the some q and bed material discharge
between sections 1 and 2 is obtained.
333
River Channel Changes
4. For the slope obtained in step 3, L is determined using the slope, Eq. (10.5) And at this distance
section 2 is located.
5. The process is repeated taking section 2 as section1 and following steps 1 through 3 and the bed
material size at each section is obtained.
This size was found to decrease in the downstream direction and followed the law
d = do e–a1
and the value of a1 was found to vary with q and total bed material discharge. Further, for a given
combination of these values there was a reduction in the value of a within the bed material size range of
0.45 mm to 0.65 mm. It was also inferred by Rana et al. that if the major reduction in size of bed material
is assumed to be due to hydraulic sorting, then under the assumptions made in the analysis, the size of
bed material at any section would change with time.
A slightly different approach has been used by Diegaard and Fredsoe (1978) and Diegaard (1980).
The assumptions made by them are:
1. The channel is assumed to be prismatic and of constant width. Further, the discharge per unit
width is constant at all sections.
2. The longitudinal profile of the river bed is described by the exponential function
Z = Zo e–aL
where Z is bed elevation at L, Zo is bed elevation at L = 0 and a is constant.
3. The rate of sediment discharge at L = 0 is constant.
4. The median size d and its standard deviation s at the upstream section is known and follows
normal distribution law.
5. At the end of the river, the water surface level is assumed to be constant and there is no
backwater effect in the stream.
Using Engelund and Fredsoe’s equation for bed-load and using it for different size fractions,
fraction wise bed-load transport is calculated. Similarly fraction wise suspended load transport rate is
calculated using their method for determining reference concentration and Einstein’s method. The
model works as follows. The river divided into a number of reaches of length DL, and sediment transport
into a section qT (x) and sediment transport out of the section qT (x + DL) is calculated. The resulting
change in bed elevation is computed using the continuity equation for sediment. By using sediment
continuity equation for each size fraction, mixing it with the active layer of the bed (assumed to be 0.15
times the depth of flow) and resistance law of Engelund-Hansen, the size distribution of the bed material
as well as changes in bed elevation due to aggradation are computed at time Dt. However, the time scales
for grain sorting and changes in bed profile are much different and the bed profile changes very slowly.
Hence, grain sorting can be treated as a quasi-steady process.
Diegaard has used this model to predict the reduction in bed material size of the river Niger, the
Mississippi and the Rio Grande. His results for the Niger and the Mississippi rivers along with the
measured data points are shown in Fig. 10.11. It is found that the data scatter around mean predicted
curves, but in some cases the scatter is large. The scatter can be attributed partly to various simplifying
assumptions made in the analysis, sampling errors, and to the fact that joining of tributaries can vitiate
the results.
334
River Morphology
(a) Niger river
2
–4
q = 10.6 m /s, S = 1.07 ´ 10
d mm
1.0
Measured
0.8
Computed
0.6
0.4
0
100
200
300
L km
(b) Mississippi river (Vicksburg)
0.6
d mm
0.5
0.4
Computed
Measured
0.3
0.2
0
100
200
300
400
500
600
L km
Fig. 10.11
Variation of observed and computed diameter of bed material with length (Diegaard 1988)
References
Agarwal, V.C. (1983) Studies on the Characteristics of Meandering Streams. Ph.D Thesis, University of Roorkee,
Roorkee (India).
Allen J.R.L. (1965) A Review of the Origin and Characteristics of Recent Alluvial Sediments. Sedimentary, Vol. 5,
pp. 89-191.
Chatley, H. (1940) Theory of Meandering. Engineering (London), Vol. 149.
Chien, N. (1961) The Braided Stream of the Yellow River – Scientia Sinica – Vol. 10, No. 6, pp. 734-754.
Daniel, J.F. (1971) Channel Movement of Meandering Indiana Streams, USGS Professional, Paper 732-A.
Diegaard, R. (1980) Longitudinal and Transverse Sorting of Grain Sizes in Alluvial Rivers. Institute of
Hydrodynamics and Hyd. Engg., Technical University of Denmark, Series Paper 26, 106 p.
Diegaard, R. and Fredsoe J. (1978) Longitudinal Grain Sorting by Currents in Alluvial Streams. Nordic
Hydrology, Vol. 9, pp. 7-16.
Dury, G.H. (1961) Bankfull Discharge: An Example of its Statistical Relationships. Bull Intl. Association of
Hydrology, Vol. 5, pp. 48-55.
Ferguson, R.I. (1977) Meander Migration: Equilibrium and Change, In River Channel Changes (Ed. Gregory,
K.J.) John Wiley and Sons, Chichester, A Wiley Interscience Publication, Chapter 15, pp. 235-248.
River Channel Changes
335
Ferguson, R.I. (1981) Channel Form and Channel Changes. In British Rivers (Ed. Lewin J.). George Allen and
Unwin Ltd., London, Chapter 4, pp. 90-125.
Friedkin, J.F. (1945) Laboratory Study of the Meandering of Alluvial Rivers – USWES, Vicksburg, Mississippi
(U.S.A.), p. 40.
Frisk, H.N. (1944) Geological Investigations of the Alluvial Valley of the Lower Mississippi River. Mississippi
River Commission, Vicksburg, (Mississippi), U.S.A.
Garde, R.J. (1978) Irrigation in Ancient Mesopotamia. ICID Bulletin, Vol. 27, No. 2, pp. 11-22.
Gregory, K.J. (Ed.) (1977) River Channel Changes. A Wiley Interscience Pulication, John Wiley and Sons,
Chichester, (U.K.), 448 p.
Gurnell, A. and Petts, G. (Eds.) (1995) Changing River Channels. John Wiley and Sons, Chichester (U.K.), 440 p.
Harvey, A.M. (1975) Some Aspects of the Relations Between Channel Characteristics and Riffle spacing in
Meandering Streams. American Journal of Science Vol. 275, pp. 470-478.
Hickin, E.J. and Nanson, G.C. (1984) Lateral Migration Rates of River Bend. JHE, Proc. ASCE, Vol. 110, No. 11,
Nov., pp. 1957-1967.
Hooke, J.M. (1995) Processes of Channel Plan-Form Change on Meandering Channels in the U.K. In Changing
River Channels (Eds. Grunell, A. and Petts, G.). John Wiley and Sons, Chichester, pp. 87-115.
Hughes, H.J. (1977) Rates of Erosion on Meander Arcs. In River Channel Changes (Ed. Gregory K.J.) John Wiley
and Sons, Inc., A Wiley Interscience Publication, Chapter 12, pp. 193-206.
Jain, V. and Sinha R. (2003) River Systems in the Gangetic Plains and their Comparison with Siwaliks : A Review.
Current Science, Vol. 84, No. 8, 25 April, pp. 1025-1033.
Jain, V. and Sinha R. (2003) Hyperavulsive – Anabranching Bagmati River System, North Bihar Plains, Eastern
India, Z. Geomorphologie, N.F. Berlin, Vol. 47, No. 1., pp. 101-116.
Khan, H.R. (1971) Laboratory Study of River Morphology. Ph.D. Thesis, Colorado State University, Fort Collins,
(U.S.A.), 189 p.
Leopold, L.B. and Wolman M.G. (1964) River Meanders – Geol. Soc. of Am., Bull., No. 71, pp. 769-794.
Leopold, L.B., Wolman M.G. and Miller, J.P. (1964) Fluvial Processes in Geomorphology. W.H. Freeman and
Company, San Fransisco.
Lewin, J. (1977) Channel Pattern Changes. In River Channel Changes (Ed. Gregory, K.J.) John Wiley and Sons.
Chapter 8, pp. 167-184.
Lewis, G.W. and Lewin, J. (1983) Alluvial Cut-offs in Water and Borderlands, Special Pub., Intl. Assoc. of
Sedimentologists, Vol. 6.
Lin, P.N. and Li Guifen (1986) The Chanjiang and Huanghe. Circular No. 1, IAICES, Beijing. 17 p.
Lobeck, A.K. (1939) Geomorphology: An Introduction to the Study of Landscapes. McGraw Hill Book Co. Inc.,
New York, pp. 198-201.
Lu Jianyi (1982) Mouth of the Yellow River, Its Evolution and Improvement. The Yellow River Vol. 3, In Selected
Papers of Researchers on the Yellow River and the Present Practice (Ed. YACC) Oct. 1987, pp. 95-105.
Mazumder, S.K. (2004) Aggradation/Degradation of Ganga Near Farakka Barrage. National Symposium on
Silting of Rivers Held in New Delhi, C.W.C., 10 p.
Nanson, G.C. and Hickin, E.J. (1983) Channel Migration and Incision on the Beatton River. JHD, Proc. ASCE,
Vol. 103, No. 3, March, pp. 327-337.
Newson, M.D. (1995) Fluvial Geomorphology and Environmental Design. In Changing River Channels (Eds.
Gurnell, A. Petts, G.) John Wiley and Sons. Chapter 19, pp. 413-432.
Pettijohn, F.J. (1957) Sedimentary Rocks. Harper and Brothers, New York, 2nd Edition.
336
River Morphology
Pickles, G.W. (1941) Drainage and Flood Control Engineering. McGraw Hill Book Co., New York, Chapter 11.
Rana, S.A., Simons, D.B. and Mahmood, K. (1973) Analysis of Sediment Sorting in Alluvial Channels. JHD,
Proc. ASCE, Vol. 99, No. 11, No. pp. 1967-1980.
Richard, K., Chandra, S. and Friend, P. (1993) Avulsive Channel Systems: Characteristics and Examples. In
Braided Rivers (Eds. Best, J.L. and Bristo C.S.) Geological Society Publication No. 75, pp. 195-203.
Schumm, S.A. (1969) River Metamorphosis. JHD, Proc. ASCE, Vol. 95, No. HY1, Jan. pp. 255-273.
Schumm, S.A. (1971) Fluvial Geomorphology. In River Mechanics (Ed. Shen H.W.) Published by Editor, Fort
Collins (U.S.A.), Chapter 5, pp. 5.1 to 5.22.
Schumm, S.A. and Khan H.R. (1972) Experimental Study of Channel Patterns. Geol. Soc. of Am. Bull. Vol. 83, pp.
1755-1770.
Schumm, S.A. (1977) The Fluvial System. John Wiley and Sons, A Wiley Interscience Publication, New York,
Chapter 5.
Sinha, R. (1996) Channel Avulsion and Flood Plain Structure in Gandak-Kosi Interfan, North Bihar Plains, India.
Zeitscrift fûr Geomorphologie N.F. Supp. Bd. 103, pp. 249-268.
Tangri, A.K. (2000) Proceedings of the Workshop on Fluvial Geomorphology with Special Reference to Flood
Plains. IIT Kanpur, pp. 3.1 to 3.12.
Winkely, B.R. (1970) Influence of Geology on the Regimen of A River. ASCE, Natl. Water Resources Meeting
(Memphis) Preprint 1078, 35 p.
Wolman, M.G. and Leopold, L.B. (1957) River Flood Plains: Some Observations on Their Formation. Geo. Survey
Professional Paper 282-C, pp. 87-107.
Wolman, M.G. (1959) Factors Influencing Erosion of a Cohesive River Bank. Am. Jour. of Sciences, Vol. 257, No.
1, pp. 204-216.
Worcester, P.G. (1948) A Text Book of Geomoprhology. D Van Nostrand Co., New York, 2nd Edition, p. 150.
Xu Fuling (1982) A Brief Account of Changes of Course of the Lower Yellow River in Past History. The Yellow
River No. 3, In Selected Papers of Researchers on the Yellow River and the Present Practice (Ed. YRCC) Oct.
1987, pp. 47-52.Hug
C H A P T E R
11
Analytical Morphological Models
11.1 INTRODUCTION
Various changes that take place in the longitudinal profile of an alluvial river as a result of man-made or
natural disturbances introduced in the river are discussed in chapters nine and ten. Those can be studied
either by using a physical model or an analytical or a numerical model. If the changes taking place are
local, very often a physical model is used; however when the changes take place over large lengths and
are slow, thus requiring a very long time for attaining equilibrium or near equilibrium condition, it is
advantageous to use analytical or numerical models. Problems solved by using physical models with
movable bed include location of bridges, design of guide bunds, location and dimensions of spurs,
optimum design of sediment excluders and ejectors, execution of cut-offs, control of sediment entry into
canals and rejuvenation of dying channels. Design of physical movable bed model is based on the
determination of the dimensionless parameters that govern the process under consideration. These
parameters include ratios of lengths, velocities, mass densities, and forces. These need to be kept the
same in the model and the prototype so that the model satisfies the conditions of geometric, kinematic
and dynamic similarities. If all the corresponding length ratios have the same value in the model and the
prototype, the model is geometrically similar; otherwise it is geometrically distorted. Similarly, the
model can have material distortion or force distortion. Alluvial river models are usually distorted and
hence the designer of the model has to see what will be the effects of distortion on the behaviour of the
model and the interpretation of results from model to the prototype. Hence, designing a movable bed
model and interpretation of results from model to the prototype is still an art and each laboratory has its
own method of model design and interpretation of results. Further, each physical model may serve the
purpose of that specific problem only and cannot be used for other rivers.
Analytical and numerical models used to study the morphological changes are based on using
governing equations of motion namely, momentum equation, and continuity equations for flow and
sediment, and resistance and sediment transport relations. These equations are then combined and
solved for known initial and boundary conditions. To get analytical solutions, one has to make some
drastic simplifications. Such simplifications include one-dimensional flow, linearisation in respect of
338
River Morphology
friction, convective acceleration term, and sediment transport rate derivative, and assumption of
uniform sediment. In spite of these restrictions, under certain conditions analytical models provide
rough and useful results.
When one does not wish to make such simplifications, numerical models can be used where the
system of equations are solved using numerical techniques with known initial and boundary conditions.
Numerical models need calibration and proving with the past data; once the model is proved, it can be
used to make predictions. A number of such models are available and these differ from one another in
the degrees of sophistications used in its formulation (see Chapter 12).
This chapter includes a brief description of the governing equations for one-dimensional flows in
alluvial streams, their simplifications to get different analytical models and some of their applications.
De Vries (1993) initiated this approach and since then some investigators have used these models to get
results for a few practical problems.
11.2
BASIC ONE-DIMENSIONAL EQUATIONS
For solving problems concerning transient bed profiles in alluvial rivers, the basic equations that are
used are continuity equations for flow and sediment, dynamic (or momentum) equation, and resistance
and sediment transport relationships. These are derived or discussed below for one-dimensional flows
in which average velocity U, average depth D and sediment transport rate QT or qT are functions of x and
t; here QT = B qT where B is channel width and qT is volumetric sediment transport ratio per unit width.
(a) Continuity Equation for Flow
The continuity equation for flow, which is also called the equation for conservation of mass, when
written for open channels, states that the net rate of mass inflow into the control volume would result in
the rate of increase of mass within the control volume (see Fig. 11.1);
or
¶
¶
(rf A dx) +
(rf AU) dx + rf q¢ dx = 0
¶t
¶x
...(11.1)
Here rf is mass density of fluid which is taken as constant assuming sediment concentration to be
very small, A is the cross sectional area, U is the average velocity at a section and q¢ is the lateral in flow
rate per unit length from both sides. Taking rf as constant, Eq. (11.1) gives
¶ A ¶Q
+
+ q¢ = 0
¶t
¶x
...(11.2)
where Q = AU is the discharge in the channel. If lateral inflow is zero, the above equation takes the
form
¶A
¶A
¶U
+U
+A
=0
¶t
¶x
¶x
and for rectangular channel of constant width B, Eq. (11.3) reduces to
...(11.3)
339
Analytical Morphological Models
1
U
2
W.S
QT +
D
QT
¶QT
dx
¶x
h
Dz
Dx
Z
Channel bed
Datum
Fig. 11.1 Definition sketch for sediment continuity
¶D
¶D
¶U
+U
+D
=0
¶t
¶x
¶x
...(11.4)
since A = BD and D is the average depth of flow. This equation can be used for sediment-laden flows if
the sediment concentration
qT
is much smaller than unity; here qT and q are sediment and water
q
discharge per unit width.
(b) Continuity Equation for Sediment
The continuity equation for sediment can be derived in the same manner as the continuity equation for
flow. Here, the difference between the rates of sediment inflow and outflow from a control volume will
cause deposition on the bed or erosion from the bed, thereby changing the bed level, see Fig. 11.1.
Therefore,
and since
¶
¶
(B Z d x) +
(QT) d x = 0
¶t
¶x
QT = BqT
¶q T
1
¶Z
+
=0
¶t
1- l ¶x
a f
U|
|V
||
W
...(11.5)
Here B is assumed to be constant; qT is volumetric sediment transport rate and l is the porosity. This
equation is exact if qT represents bed-load only. When some material goes into suspension, an additional
term needs to be included in Eq. (11.5) to take into account change with respect to time of the suspended
¶
(DCs) where Cs is average concentration of suspended
¶t
load. If this term is not included when appreciable amount of suspended load is present, Eq. (11.5) is
sediment load in the control volume, viz.,
340
River Morphology
¶Z
¶ qT
is positive i.e., aggradation will occur if
is
¶t
¶x
negative i.e., qT decreases as x increases; in other words qT at section 1 is greater than qT at section 2.
approximate. Equation (11.5) indicates that
(c) One-dimensional Dynamic Equation
The dynamic equation for non-uniform and unsteady flow in an open channel is obtained from the
principle of conservation of momentum. With reference to Fig. 11.2, for the control volume ABCD,
Fig. 11.2
Definition sketch for momentum equation
(Rate of momentum outflow) – (Rate of momentum inflow) + (Change of momentum within the
control volume) = (Summation of components in the direction of flow of all the external forces acting on
the control volume)
These force components are (see Fig. 11.2)
Frictional force = – to P d x
Component of gravity force = r g A d x sin q
Component of pressure force in the direction of flow = – r g cos q
¶D
dx
¶x
Therefore the momentum equation takes the form
d
i
¶
¶
¶D
(rf A U) dt = – to P d x + rf g A d x sin q – rf g cos q
d x ...(11.6)
r f U 2 A dx +
¶x
¶t
¶x
Here U is the average velocity of flow over cross sectional area A, P is the perimeter, to is the
average shear stress on the perimeter, and q is the angle of inclination of channel bed. Assuming rf to be
constant and dividing all terms by (rf A dx), one gets
t
¶U U ¶U
¶U U 2 ¶ A
¶D
+
+2U
+
= – o + g sin q – g
cos q
¶t
¶x
¶x
A ¶x
A ¶x
rf R
...(11.7)
341
Analytical Morphological Models
However, according to Eq. (11.3)
1 ¶ A A ¶U
¶A
=–
–
U ¶t U ¶ x
¶x
...(11.8)
¶Z
and cos q » 1.0. Also B = constant for
¶x
rectangular channel for constant width. With these substitutions Eq. (11.7) becomes
Further, for small values of q, sin q »˜ tan q = So » –
t
¶U
¶U
¶D
¶Z
+U
+g
+g
=– o
¶t
¶x
¶x
¶x
rf R
...(11.9)
This is momentum equation and the assumptions made in its derivation are
i) constant width of rectangular channel;
ii) no lateral inflow;
iii) rf is constant which is true if
qT
is very small;
q
iv) flow being one dimensional, at a section we have average values of U and D, and hence
momentum correction factor b = 1.0, further pressure distribution is hydrostatic; and
v) q is very small.
(d) Resistance Relations
One can use either Chezy’s equation or Manning’s equation with constant value of C or n. Using
Chezy’s equation the term
gU 2
to
can be written as 2 and hence Eq. (11.9) takes the form
C R
rf R
gU 2
¶U
¶U
¶Z
+U
+g
=– 2
¶t
¶x
¶x
C R
...(11.10)
It may be mentioned that in alluvial streams a different resistance equation is applicable since bed
conditions change with the flow conditions. In unsteady, non-uniform flow C or n will be functions of
stage, x and t. However, for obtaining analytical solutions n or C is assumed to be constant.
(e) Sediment Transport Relation
¶ qT
in the continuity equation one must use a sediment transport formula. de Vries
¶x
recommends use of a relation of the type
To evaluate the term
qT = a U b
...(11.11a)
Here, a and b are assumed to be constant for the range of depth under consideration. Alternately,
some have used equation of the type
342
River Morphology
qT = a u*b
...(11.11b)
where a can be function of other parameters such as sediment size etc. but constant; here u* is the shear
velocity. It is further assumed that sediment size is uniform.
11.3
ANALYSIS OF WATER SURFACE AND BED WAVES
Combining Eqs. (11.11) and (11.5) one can write
¶Z
¶ f ¶U
+
=0
¶t
¶U ¶ x
...(11.12)
where qT = f (U). Further from Eqs. (11.4), (11.10) and (11.12) the following equation is obtained
LM
N
–U3w + 2 U U2w + g D - U 2 +
g ¶qT
1 - l ¶U
a
f
OP U – Ug ¶ q = 0
Q a1 - lf ¶U
t
...(11.13)
w
dx
is the celerity of the wave. Writing Eq. (11.13) in dimensionless form by introducing
dt
the dimensionless parameters
Here Uw =
M=
Uw
, Fr =
U
U
, and y1 =
gD
LM b OP ¶ q
N a1 - lf D Q ¶ U
T
one obtains
M3 – 2M2 + (1 – Fr–2 – y1 Fr–2) M + y1 Fr–2 = 0
...(11.14)
It may be mentioned that y1 is proportional to the sediment concentration. Equation (11.14) is a
cubic equation and hence has three roots namely M1, M2 and M3 and these are functions of Fr and y1.
These are given by
M1 = (1 + Fr–1) and it is dimensionless velocity of a small surface disturbance in the direction of
flow;
–1
M2 = (1 + Fr ) and it is dimensionless velocity of a small surface disturbance traveling in direction
opposite to the flow;
M3 =
y1
d1 - Fr i
2
when Fr is less than unity and it is the dimensionless velocity of bed form. It is
significantly affected by the sediment transport rate.
It is worth noting that when Fr is less than unity, M3 will be positive and the bed disturbance travels
in the direction of flow; however when Fr is greater than unity, M3 will be negative and the disturbance
moves in upstream direction. Figure 11.3 shows variation of |M| with Fr and y1. It can be seen from this
figure that M1 and M2 are much greater than M3 when Fr number is less than approximately 0.8.
Therefore, if the main interest is in the computation of flood or water levels, it is safe to assume M3 » 0
i.e., the bed is stationary. On the other hand, if one is interested in predicting the bed level variations, it
343
Analytical Morphological Models
10
1
M1
10
10
|M|
10
10
M2
M3
–1
y2 = 10
–2
10
–3
10
10
0
10
–5
0
10
–3
10
–4
–2
10
–4
10
–5
0.4
–2
10
0.8
Fr
1.2
–3
–4
–5
1.6
Fig. 11.3 Relative velocities in alluvial channel
can be assumed that |M1, M2| ® ¥ i.e., water depth and velocity variations occur very rapidly. In other
¶U
¶D
and
can be neglected with respect to other
¶t
¶t
terms in Eqs. (11.4) and (11.9). This is known as quasi-steady formulation. Another implication of
differences in relative values of M1, M2 and M3 is that the numerical analysis can be carried out in decoupled mode; it means that bed can be first assumed stationary and water levels computed using
momentum equation and then assuming water levels to be stationary, bed levels are computed using
continuity equation for sediment and sediment transport law.
words, flow can be considered quasi-steady and,
11.3
ANALYTICAL MODELS
The analytical models can be obtained from the quasi-steady formulation of the equations discussed
earlier i.e.,
U
gU 2
¶U
¶D
¶Z
+g
+g
=– 2
C D
¶x
¶x
¶x
U
¶D
¶U
+D
=0
¶x
¶x
1
¶Z
¶ qT ¶ U
=
=0
1 - l ¶U ¶ x
¶t
a f
qT = f (U)
U|
|
V|
||
W
...(11.16)
...(11.15)
...(11.12)
...(11.11)
344
River Morphology
These equations can be combined into one differential equation
¶ Z ¶ qT
–
¶t
¶U
F
I
GG g JJ
GH U - Uqg JK
2
1
¶Z
=
¶x 1- l
a f F
H
g Sf
qg
U- 2
U
I
K
¶ qT
¶U
1
1- l
a f
...(11.17)
The analytical models are obtained after linearisation of the above equations and therefore their
solutions give only the rough estimates of the correct solutions. The non-linearity arises from the terms
U2
U3
¶U
¶q
the friction term g 2 i.e., g 2 and the term T . Even though linearisation of these terms
C D
C q
¶x
¶U
introduces some error, it gives an advantage that resulting equations are amenable to analytical
solutions.
Taking original bed as the x axis and assuming small changes in the bed level i.e., Z << Do the initial
uniform flow depth, and various degrees of linearisation the following models have been obtained and
studied.
U
Parabolic Model
¶U
¶D
and
are neglected during the transient condition i.e., there is no draw down or
¶x
¶x
backwater profile and flow is uniform. Thus,
Here the terms
¶U
¶D
¶D
= 0,
= 0 and
=0
¶x
¶x
¶t
Hence, Eq. (11.16) reduces to
U3
¶Z
=– 2
C q
¶x
...(11.18)
Differentiating Eq. (11.18) with reference to x one gets
3U 2 ¶ U
¶2 Z
=
–
C2 q ¶ x
¶ x2
Further, according to continuity equation for sediment
1
1
¶Z
¶ qT
¶Z
¶ qT ¶ U
+
= 0 or
+
=0
1- l ¶x
1 - l ¶U ¶ x
¶t
¶t
a f
Hence, substituting the value of
a f
¶U
from Eq. (11.19), one gets
¶x
...(11.19)
345
Analytical Morphological Models
C 2 q ¶ qT / ¶ U
¶Z
–
3 1- l
¶t
U2
a
f
FG ¶ Z IJ = 0
H ¶x K
2
2
C 2 q ¶ qT / ¶ U
¶Z
¶2 Z
= Ko
where Ko =
2
3U 2 1 - l
¶t
¶x
a f
or
...(11.20)
Equation (11.20) is the diffusion equation – of the type used in heat conduction – and Ko is known
as the diffusion coefficient, which can be expressed as
FU I
f HUK
1 U ¶ qT / ¶ U
Ko =
3 So 1 - l
a
3
o
where Uo is the average velocity under uniform flow condition. If one uses the approximation U » Uo,
the above expression simplifies to
Ko =
b qTe
3 So 1 - l
a
f
...(11.21)
where qTe is the equilibrium transport rate. Equation (11.19) being parabolic in nature represents the
parabolic model for solving transient problems in alluvial streams. Vreugenhill and de Vries (1973)
stated that parabolic model is applicable when x is greater than 3 D/So when Froude number is small. It
may be mentioned that earlier Culling (1960) had used parabolic model probably for the first time by
¶Z
. He
¶x
developed solutions for simple hypothetical problems of channel erosion and development of
longitudinal river profiles using time invariant boundary conditions. In spite of the crude assumptions
made in the derivation of the parabolic model it gives useful results when applied with care, as shown
later.
It can be seen that Eq. (11.17) is of the form
assuming that bed load transport rate was directly proportional to local bed slope i.e., qTe ~
¶Z
¶Z
+ (M3 U)
= a (U)
¶t
¶x
in which (M3 U) represents celerity of bed wave and a (U) is a measure of damping of disturbance. If a
(U) is taken as zero, one gets an equation for the propagation of a simple wave the solution of which is
known. Thus, the so called wave model is represented by
¶Z
¶Z
+ (M3 U)
=0
¶t
¶x
...(11.22)
Analytical solution of the wave equation given above is possible if the equation is linearised i.e.,
(M3 U) and a (U) are taken as constants.
If the assumption of uniform flow during the transient stage is not made but still the linearisation is
done, one gets the hyperbolic model for river bed variation, namely
346
River Morphology
Ko ¶ 2 Z
¶Z
¶2 Z
–
– Ko
=0
M 3 U ¶ x ¶t
¶t
¶ x2
...(11.23)
Here Ko is the same as given by Eq. (11.21). It needs to be mentioned that in the derivation of Eq.
(11.23), a constant discharge is assumed whereas for parabolic model such assumption has not been
made. Vreugdenhill and de Vries recommend that hyperbolic model can be used for x less than 3 D/So.
Equation (11.23) can be written as
U M3 ¶ Z
¶
–
¶x
Ko ¶ t
FG ¶ Z + UM
H ¶t
3
¶Z
¶x
IJ = 0
K
here Ko, M3 and U are constants, U being taken as Uo. If
...(11.24)
UM3
is very small, the above equation can
Ko
be approximated to
¶
¶x
FG ¶ Z + UM
H ¶t
3
¶Z
¶Z
IJ = 0
K
by neglecting the first term in Eq. (11.24). The above equation can be integrated to yield the wave model
¶Z
¶Z
+ UM3
= constant
¶t
¶x
On the other hand, if
UM3
¶
is large, the second term in Eq. (11.24),
¶x
Ko
FG ¶ Z IJ can be neglected;
H ¶t K
then Eq. (11.24) reduces to parabolic model
¶2 Z
¶Z
= Ko
¶t
¶ x2
Thus the ratio
11.4
UM3
seems to play an important role.
Ko
SOME APPLICATIONS OF LINEAR MODELS
Parabolic Model
Let us first consider the parabolic model. Probably this method was first proposed by Culling (1960)
who assumed that sediment transport is proportional to terrain slope and combining it with the
continuity equation obtained the diffusion equation which is in fact heat conduction equation. He has
also proposed solution of diffusion equation for different boundary conditions. It may be mentioned that
a number of solutions of diffusion equation for different boundary and initial conditions are given by
Carslaw and Jaeger (1947).
347
Analytical Morphological Models
W.S
t=O
W.S
Changed lake level
¥
t = O, Z
t
Original lake level
t
Original bed level
=0
¥
Final bed
Transient bed profile
Fig. 11.4 Degradation due to lowering of lake level
De Vries (1975, 1993) has applied parabolic model to determine transient bed profiles in a stream
when the lake level to which it joins at the downstream end is suddenly dropped over a vertical height
Zo, see Fig. 11.4.
By neglecting the effects of drawdown one can assume that at t > 0 the flow is uniform. Measuring
x in up stream direction the boundary conditions are
Initial condition
Z (x, 0) = 0
Boundary condition
Z (x, t) = 0 as x ® ¥
and
Z (0, t) = – Zo
Equation (11.20) which is a partial differential equation can be reduced to ordinary differential
equation by substituting h =
x
2 Ko t
f ¢¢ + 2 h f ¢ = 0
where
Z
= f (h). The solution of this equation for the above boundary condition is
Zo
F
GH
x
Z
=–erfc
Zo
2 Ko t
I
JK
...(11.25)
Transient bed profiles are shown by dotted lines in Fig. (11.4). Vittal and Mittal (1980) have used
parabolic model for the prediction of degraded profile of the Ratmau torrent caused by trapping of
sediment in the upstream.
Soni (1975), Soni et al. (1980), Mehta (1980), Garde et al. (1981), Jain (1981), Gill (1983) and
others have used parabolic model to study aggradation of river bed due to overloading. Experiments
conducted by Soni and Mehta at Roorkee University in a 30 m long and 200 mm wide flume using
nearly uniform sediments of size of 0.32 mm, 0.50 mm and 0.71 mm and overloading ratio
D qT
from
qTe
348
River Morphology
Section of sediment injection
DQT
Qte
W.S.
Zo
Do
Transient bed profile at t > 0
Fig. 11.5
Us
Original bed
Aggradation due to overloading
0.50 to 16.0 form the basis of most verifications of parabolic and hyperbolic models. In these tests
equilibrium conditions were established for a given discharge and slope and equilibrium transport rate
qTe was determined. Then, for given increase in sediment load at upstream end, transient bed and water
surface profiles were obtained. In fact studies by Soni and Mehta have revived the interest in analytical
models since then and parabolic and hyperbolic models have been studied in greater detail.
With reference to Fig. 11.5 wide rectangular channel has uniform depth Do and velocity Uo and
equilibrium transport rate QTe for channel slope of So; the sediment supply rate at the upstream section is
increased by a constant rate DQT. Using the parabolic model, the initial and boundary conditions are (see
Jain 1981):
Z (x, 0) = 0 for t ³ 0
z
The second boundary condition can be obtained from the fact that sediment volume under transient
bed profile at time t is given by DqT t =
¥
o
DqT = (1 – l)
Substituting the value of
(1 – l) Z d x which on differentiation with t yields
z
¥
o
¶2 Z
¶Z
¶Z
from
= Ko
, one gets
¶t
¶t
¶ x2
DqT = (1 – l) Ko
But, since
=
D qT
1- l
a f
¶Z
dx
¶t
FG ¶ z IJ
H ¶ xK
o
FG ¶ z IJ at (¥, t) = 0, the second boundary conditions reduces to – K FG ¶ z IJ at (0, t)
H ¶ xK
H ¶ xK
o
349
Analytical Morphological Models
The solution of diffusion equation with these boundary conditions is
Z=
LMF K t I
a f MNH p K
2 D qT
Ko 1 - l
h=
in which erfc
1/ 2
o
2
p
z
¥
h
I OP
JK PQ
...(11.26)
2 D qT
p Ko 1 - l
...(11.27)
FG - x IJ - x erfc F
H 4 K t K 2 GH 2
2
exp
o
x
Ko t
e - h dh
2
From Eq. (11.26), Zo is given as that value of Z at x = 0, or
F K tI
a fH p K
2 D qT
Zo =
Ko 1 - l
1/ 2
o
or
Zo
=
Ko t
a f
Equation (11.26) can be written in dimensionless form as
af
2
Z
= e - h - h p erfc h
Zo
Further, if length of aggradation is that length l where
l = 3.2
...(11.28)
Z
= 0.01, one gets from Eq. (11.28)
Zo
...(11.29)
Ko t
Gill (1983) has solved the diffusion equation for aggradation due to overloading by the method
discussed above as well as obtaining the solution of diffusion equation by Fourier series. If So is the
initial slope, S¥ is the final slope of bed commensurate with increased sediment load, and L is the length
of the channel, the boundary conditions are
Z (x, 0) = S0 (L – x)
Z (x, ¥) = S¥ (L – x)
Z (L, t) = 0 which stipulates that bed at
down stream end remains unaffected
and
–
FG ¶ Z IJ
H ¶xK
=
x=o
qT¥
where qT¥ is the equilibrium
Ko 1 - l
transport rate
a f
U|
||
||
V|
||
||
W
...(11.30)
Assuming solution to be of the type
Z (x, t) = F (x) + f (x, t)
he found that
F (x) = S¥ (L – x)
Using the boundary conditions listed above, it is shown that f (x, t) is given as
...(11.31)
...(11.32)
350
River Morphology
f (x, t) =
b
8 L So - S¥
p
2
gå
¥
n = 1, 3, 5...
FG
H
IJ
K
1
- n2 p 2 Ko t
npx
exp
cos
2
2
2L
2L
n
...(11.33)
so that Eq. (11.31) becomes
Z (x, t) = S¥ (L – x) +
b
8 L So - S¥
p
2
gå
¥
n= 1, 3, 5,...
FG
H
IJ
K
- n2 p 2 Ko t
1
npp
exp
cos
2
2
2L
2L
n
...(11.34)
It is also shown that sediment transport rate satisfies diffusion equation, viz.
¶ 2 qT
¶ qT
= Ko
¶t
¶ x2
...(11.35)
and for the boundary conditions qT (o, t) = qT¥ and qT (x, o) = qTe
qT (x, ¥) = qT¥ and
a f
¶ qT L, t
= 0,
¶x
The solution of Eq. (11.35) is
F
GH
x
qT - qTe
= 1 – erf
qT¥ - qTe
2 Ko t
I
JK
...(11.36)
Adachi and Nakatoh (1969) have applied the diffusion equation for studying silting of reservoirs
and have obtained Fourier series solution. They have also determined the value of Ko at dominant
discharge for the river Tenryu in Japan.
Tsuchiya and Ishizaki (1969) have used a sediment transport formula of Sato, Kikkawa and Ashida,
namely
qB ~ u3*
and Manning-Strickler type resistance law and obtained the diffusion equation. Further, they have
applied this equation to predict river bed profiles upstream of Hongu dam on the Joganji river in Japan.
This dam on the torrential river was constructed in 1935 and was completely filled in 1939.
As mentioned earlier, Mehta and Soni have studied the application of parabolic model for
aggradation due to overloading. As shown by Jain (1981), for 0.32 mm data of Soni, transient bed
profiles obtained by theory using Ko values agreed reasonably well with observed data, even though for
large
x
values there was relatively more scatter. However, Mehta (1980) found that 0.50 mm and
2 Ko t
0.71 mm data gave considerable scatter on
x
Z
vs h =
plot when theoretical values of Ko were
Zo
2 Ko t
used. Hence, he modified the values of Ko for each run so that the transient bed profile matched with Eq.
351
Analytical Morphological Models
1.2
Different runs (d = 0.32 mm)
1.0
Z/Zo
0.8
0.6
0.4
0.2
0
Fig. 11.6
0
1.0
Variation of
0.2
0.3
0.4
0.5
0.6
h
0.7
0.8
0.9
1.0
1.2
Z
with h for aggradation due to overloading using modified values of K
Zo
(11.28). His modified values of Ko called K were found to be function of
f
1.1
FG Dq IJ . Figures 11.6 and 11.7 show variation of Z
Z
Hq K
T
Te
o
vs
a
f
K So 1 - l
D qT
and
=
qTe
qTe
a
f
K So 1 - l
x
and
=f
qTe
2 Kt
FG D q IJ as
Hq K
T
Te
obtained by Mehta. The need for modification of Ko to K has been attributed to the assumptions made in
the derivation of parabolic model.
Jaramillo and Jain (1983) applied linear parabolic model to channels of finite length. Park and Jain
(1984) have used computer based numerical experiments to determine the rate and extent of aggradation
of the bed resulting from overloading. For this they have used Karim and Kennedy’s sediment discharge
and friction factor relations. It was found that, if
of
Z
= exp (– h2) – h p erfc (h) is fitted for variation
Zo
Z
with h, the diffusion coefficient K and Zo were found to be functions of Co, So, DC and t as
Zo
K = 100.364 Co0.968 So–0.982 DC0.102
Zo = 100.11 DC0.960 Co0.517 So0.489 t0.50
Here, Co is the initial sediment concentration by volume, DC is increase in concentration, So is the
initial slope and t is time.
Application of parabolic model has been studied by Vittal and Mittal (1980) and Gill (1983a), for
degradation. Vittal and Mittal have applied parabolic model to predict transient bed profiles of the
Ratmau torrent in U.P., India. This torrent crosses the Upper Ganga Canal at Dhanauri where a level
crossing has been constructed in 1850 in which 192 m wide escape for the torrent and 72 m wide
regulator is provided for the canal (see Fig. 11.8). Initial bed slope of the torrent was 0.001558 and has
a maximum discharge of 2250.98 m3/s, while minimum flood discharge has been about 200 m 3/s. Over
352
River Morphology
4.0
K So (1 – l) qTe
3.2
2.4
Symbol
1.6
0.8
0
0
2
4
6
8
DqT/qTe
d mm
0.32
0.50
0.71
10
Investigator
Soni
Mehta
Mehta
12
14
16
Fig. 11.7 Variation of K So (1 – l) qTe with DqT/qTe
Fig. 11.8 Level crossing of Ganga canal and Ratmau torrent
the past 150 years the bed slope of the torrent downstream of the escape is decreasing as shown in Fig.
11.9 while the bed slope upstream of the escape has increased due to aggradation. Hence, it is concluded
that the cause of degradation in the lower reach of the torrent is due to reduction in sediment supply. In
the absence of detailed data they estimated the average transport rate using Engelund-Hansen’s relation
353
Analytical Morphological Models
Legend
Year
Notation
1845
1877
1924
1939
1947
1954
1966
1976
1977
Fig. 11.9 Reduction of bed elevation of the Ratmau torrent with time (Vittal and Mittal 1980)
and for various trap efficiencies 30, 40 and 50 percent, the bed profiles were computed for years 1924,
1947, 1954 and 1976, using parabolic model. The computed profiles for trap efficiency of 40 percent
agreed reasonably well with the observed ones, as can be seen in Fig. 11.10. It may be mentioned that
Vittal and Mittal used modified values of K as given by Soni and Mehta.
Gill (1983 a) has considered the case of degradation downstream of a dam where due to trapping of
sediment on the upstream of the dam, the sediment supply to the stream is suddenly reduced from qTe to
qT¥. Hence, the boundary conditions are
Z (x, o) = So (L – x)
Z (x, ¥) = S¥ (L – x)
and
FG ¶ Z IJ
H ¶xK
= – S¥ for t > 0
x=0
Here, S¥ is the equilibrium slope for reduced sediment supply rate qT¥. These boundary conditions
being exactly the same as those used for aggrading channels, earlier solutions also hold well in case of
degradation. These are
Z (x, t) = S¥ (L – x) +
b
8 L So - S¥
p
2
gå
¥
n = 1, 3, 5..
FG
H
n 2 p 2 Ko t
1
exp
4 L2
n2
IJ cos n p x
K 2L
Error function solution for infinitely long channels or relatively small times
...(11.37)
354
River Morphology
264
262
Original bed line
260
Bed elevation in m
258
Predicted profile for DqT/qT = 0.40
256
254
252
Observed profile
after flood of 1976
250
248
246
244
242
0
2
4
6
8
Distance in km
10
12
14
Fig. 11.10 Verification of bed level variation of the Ratmau torrent (Vittal and Mittal 1980)
LM
MN
Z (x, t) = So (L – x) – (S¥ – So) x e r f c
F
GH 2
I
JK
FG
H
Ko t
x
x2
exp -2
p
4 Ko t
Ko t
IJ OP
K PQ
...(11.38)
Studies by Hou and Kawahita (1987) have demonstrated that solutions to linear parabolic model
display unrealistically high values of sediment diffusion. They have numerically indicated that nonlinear parabolic model predicts even larger diffusion than the linear one. Consequently, the non-linear
model is applicable only when the exponent of empirical constant in the sediment transport formula
determined under equilibrium conditions is modified to include the non-equilibrium processes.
Hyperbolic Model
For sudden drop in the downstream bed level, Vreugdenhill and de Vries (1973) have obtained the
solution of linearised hyperbolic model (Ko and M3U constant) as well as parabolic model using the
technique of Laplace transforms and expanded the resulting solutions for large values of time. If
q=
M U x
x2
and to = 3 o , the expansions are:
2 Ko t
Ko
Hyperbolic model
LM
MN
I OP
JK PQ
F
GH
Z
»1–
Zo
2q
1
1
1
1- q
+
+ ...
p
8 t 2o 2 t o 6
Z
»1–
Zo
2q
q
1 - + ...
p
6
and parabolic model
LM
N
OP
Q
...(11.39)
...(11.40)
355
Analytical Morphological Models
It may be noted that the two expressions will be almost identical if q is smaller than 0.25 and/or, if
to is large (say greater than 10). The latter condition can be transformed into a workable criterion by
3 Do
.
So
Thus, parabolic model is a good approximation for large distances; the approximation may also be good
substituting the values of Ko and M3. Hence to greater than ten correspondents to l greater than
Z
with to and q for parabolic and
Zo
hyperbolic models and for asymptotic expansions are shown for degradation case in Fig. 11.11.
at small distances for small q i.e., large times. The variations of
0.7
0.6
Z/Zo
0.5
to = 1
0.4
0.3
2
0.2
0.1
0
0
4
6
to = 1
2
4
6
1
q
2
3
Parabolic model
id; asymptotic expansion
Hyperbolic model
id; asymptotic expansion
Fig. 11.11 Variation of
Z
with to and q according to parabolic and hyperbolic models (Vreugdenhil and de Vries 1973)
Zo
Linear hyperbolic model has been studied by Zang and Kawahita (1990) which is applicable to
alluvial channels of finite length and include a general case of an arbitrary function, of either sediment
transport or channel bed specified as an upstream boundary condition. They have shown that nonuniformity in both sediment transport rate and river bed is important for short time intervals. For large
times, the diffusion process becomes dominant and similarity solutions are acceptable. The linear
356
River Morphology
solutions provide fair predictions of river bed if the upstream loading DqT/qTe is less than 4.0. Linear
theory also indicates that the sediment celerity is constant, directly proportional to the sediment
transport rate and inversely proportional to the sediment transport rate and inversely proportional to
water depth. Non-linear hyperbolic model has been studied by Zang and Kawahita (1988).
Wave Model
The wave model was first used by Exner (1925) to explain the mechanism of formation of ripples in
alluvial channels. Assuming that acceleration in the flow causes erosion while deceleration would cause
deposition, Exner wrote the following equation
¶Z
¶U
+E
=0
¶t
¶x
...(11.41)
Here Z is the bed elevation, U is the average velocity at a section and E is the erosion coefficient. If
h represents the elevation of water surface above the datum, (h – z) represents the flow depth and for
constant Q and channel width B, the continuity equation for flow takes the form
(h – Z) BU = Q
...(11.42)
Assuming water surface to be horizontal and taking B as constant, the above two equations can be
combined to yield
EQ
¶Z
+
¶t
B h- Z
a
f
2
¶Z
=0
¶x
...(11.43)
which is the wave equation. Exner assumed that at t = 0 the bed elevation is given by
Z = ao + a1 cos
2p
l
F x - EQ tI
GH B a h - Z f JK
2
...(11.44)
The resulting bed undulations at various times are characterized by constant a1 and velocity of bed
forms equal to
a
EQ
B h- Z
f
2
. Since the crest of the wave moves faster than the trough, initial symmetrical
bed form becomes unsymmetrical with time, taking the approximate shape of ripple. The resulting bed
form has a flat upstream face and steep downstream face. Exner has further improved this analysis
taking into account water surface slope, friction and changes in channel width. However, the major
criticism against Exner’s analysis is that it does not explain as to how a plane bed would develop
symmetrical waves in the beginning.
Silva and Kennedy (1989) have used kinematic wave model to analyse river bed degradation
downstream of a section of an alluvial river where sediment discharge is cutoff. They have also included
the effects of bed coarsening and armoring by using validated mathematical expressions for these
phenomena. They assumed that sediment transport rate in a degrading stream is primarily a function of
depth of flow, say qT » f (D). This relation is modified to take into account bed coarsening and velocity
changes. Finally, Silva and Kennedy have obtained an implicit expression for D(x, t). This solution was
357
Analytical Morphological Models
compared with the solution obtained by IALLUVIAL software for specific problem and the agreement
was reasonably good. It may be mentioned that de Vries has used kinematic wave model for filling of
trench (see de Vries 1993).
References
Adachi, S and Nakatoh, T. (1969) Changes of Top-Set Bed in a Silted Reservoir. Proc. of 13th congress of IAHR,
Tokyo (Japan), Vol. 5.1, 3.16 – pp. 269-272.
Carslaw, H.S. and Jaeger, J.C. (1947) Conduction of Heat in Solids. Oxford University Press, New York, U.S.A.
Culling, W.E.H. (1960) Analytical Theory of Erosion. Jour. of Geology, Vol. 68, No. 3, pp. 336-344.
de Vries, M. (1965) Consideration About Non-steady Bed Load Transport in Open Channels. Proc. of 11th
Congress of IAHR, Leningrad, Vol. 3, 3.8 – pp. 1-11.
de Vries, M. (1975) A Morphological Time Scale for Rivers. Proc. of 16th Congress of IAHR, Sao Paulo, Brazil,
Vol. 2, B3 – pp. 17-23.
de Vries, M. (1993) Lecture Notes on River Engineering. Delft, 139 p.
Exner, F.M. (1925) Ûber die Wechuwirkung Zwischen Wasser und Geschiebe in Flûssen-Sitzber-Akad-Wiss.
Wien pt 1a, Bd 134
Garde, R.J., Ranga Raju, K.G. and Mehta, P.J. (1981) Bed Level Variations in Aggrading Alluvial Streams. Proc.
of 19th Congress of IAHR, New Delhi, Vol. 2, pp. 247-253.
Gill, M.A.(1983) Diffusion Model for Aggrading Channels. JHR, IAHR, Vol. 21, No. 5, pp. 355-268.
Gill, M.A. (1983a) Diffusion Model for Degrading Channels. JHR, IAHR, Vol. 21, No. 5, pp. 369-378.
Hou, Z. and Kawahita, R. (1987) A Nonlinear Mathematical Model for Aggradation in Alluvial Channel Beds.
JHD, Proc. ASCE, Vol. 113, No. HY3, pp. 353-369.
Jain, S.C. (1981) River Bed Aggradation Due to Overloading. JHD, Proc. ASCE, Vol. 107, No. HY-1, Jan. pp.120124.
Jaramillo, W.F. and Jain, S.C. (1983) Characteristic Parameters of Non-equilibrium Processes in Alluvial
Channels of Finite Length. Water Resources Research, Vol. 19, p. 952-958.
Mehta, P.J. (1980) Study of Aggradation in Alluvial Streams. Ph.D Thesis, University of Roorkee (Now I.I.T.
Roorkee).
Park, L. and Jain, S.C. (1984) River-Bed Profiles With Imposed Sediment Load, JHE, Proc. ASCE, Vol. 112, No.
4, April, pp. 267-279.
Silva, J.M. and Kennedy, J.F. (1989) Proc. of 4th International Symposium on River Sedimentation, Beijing
(China), Vol. 2, pp. 1072-1079.
Soni, J.P. (1975) Aggradation in Stream Due to Increase in Sediment Load. Ph.D. Thesis, University of Roorkee
(Now IIT Roorkee).
Soni, J.P., Garde, R.J. and Ranga Raju, K.G. (1980) Aggradation in Stream Due to Overloading. JHD, Proc.
ASCE, Vol. 106, No. HY1, Jan. pp. 117-132.
Tsuchiya, B. and Ishizaki, T. (1969) Estimation of River Bed Aggradation Due to Dam. Proc. of 13th Congress of
IAHR, Tokyo (Japan). Vol. 1, A-33, 297-304.
Vittal, N. and Mittal, M.K. (1980) Degradation of Ratmau Torrent Downstream of Dhanauri. Proc. of 1st
International Workshop on Alluvial River Problems, Roorkee (India), pp. 5-43-54.
Vreugenhill, C.B. and de Vries, M. (1973) Analytical Approaches to Non-steady bed Load Transport, Delft
Hydraulic Laboratory, Research Report S-78-III, 17 p.
358
River Morphology
Zang, H. and Kawahita, R. (1988) Non-linear Hyperbolic System and Its Solutions for Aggradaing Channels. JHR,
IAHR, Vol. 26, No. 3, pp. 323-342.
Zang, H. and Kawahita, R. (1990) Linear Hyperbolic Model for Alluvial channels. JHE, Proc. ASCE, Vol. 116,
No. 4, Apr., pp. 478-493.
C H A P T E R
12
Numerical Models for
Morphological Studies
12.1
INTRODUCTION
In the previous chapter analytical models for studying transient morphological processes have been
discussed. It may be recalled that a number of assumptions had to be made to obtain analytical solutions.
¶U
¶D
and
be omitted. Assumption of
¶t
¶t
steady state water flow is not valid while computing bed level changes during unsteady flow conditions.
It is also not strictly valid even if the discharge is constant, since water surface profile computations
depend on bed slope which varies with time. Further, the channel was assumed to be sufficiently wide
and of constant width. In addition, a constant value of Manning’s n or Chezy’s was assumed implying
that change in C or n due to changes in bed-forms during transient stage is neglected. Still further, the
bed material was assumed to be uniform or of small standard deviation so that it could be characterized
by d50 alone. As a consequence, effects of armouring and grain sorting were not included in those
models. Also, the sediment transport law used was in the simplest form namely qT ~ U n or qT ~ t on.
However, it must be accepted that in spite of these assumptions one gets solutions which are simple and
can be used as the first approximate solution to transients in alluvial streams. Hence, analytical solutions
have been obtained for degradation and aggradation at a dam, aggradation due to increase in sediment
load, withdrawal of water, and filling of trench.
However, when the above restrictions are violated the analytical solutions do not give acceptable
and accurate results. As such since about 1970 a number of numerical models have been developed to
solve problems of morphological changes in alluvial streams. This chapter is devoted to further
discussion of the governing equations, boundary conditions and the basic techniques of numerical
computation along with related aspects; a discussion of some available software packages and the
For example, flow was assumed to be quasi-steady so that
360
River Morphology
results obtained from them are also presented. In writing this chapter the author has heavily depended on
the excellent works of Cunge et al. (1980), de Vries (1993), and Murthy et al. (1998).
12.2
ONE-DIMENSIONAL EQUATIONS
One-dimensional form of the dynamic equation (St. Vennant equation) for unsteady flow in open
channels was derived in Chapter 11. As indicated by Cunge et al. (1980) this equation can be written in
different forms, depending on the choice of dependant variables.
(i) Q(x, t), D(x, t)
FG IJ
H K
¶Q
¶ Q2
¶D
+
+ gA
+ gA(Sf – So) = 0
¶t ¶ x A
¶x
...(12.1)
Here B = B (D) and A = A (D).
(ii) U (x, t), D(x, t)
¶U
¶U
¶D
+ g (Sf – So) = 0
+U
+g
¶t
¶x
¶x
...(12.2)
It may be mentioned that the channel cross section can be of arbitrary shape and may vary along the
length.
The continuity equation for flow is
¶ A ¶Q
+
=0
¶t
¶x
...(12.3)
when there is no inflow from the sides. This can be written as
¶A
¶A
¶U
=0
+U
+A
¶t
¶x
¶x
...(12.4)
The continuity equation for sediment is
(1 – l)
¶ A ¶ QS
+
=0
¶t
¶t
...(12.5)
(1 – l)
¶ Z ¶qS
+
=0
¶t
¶x
...(12.6)
which for wide channels reduces to
for wide channels. Here l is the porosity. If the bed of the channel is composed of non-uniform
sediment, this equation has to be applied for each size fraction; this is necessary for simulating
degradation and armouring. For i th reach and k th fraction of the sediment, one can write
D Zik
D qsk
1
+
=0
Dt
(1 - l ) D t
...(12.7)
361
Numerical Models for Morphological Studies
where D Zik = change in bed level in the i th reach due to imbalance in sediment transport capacity for the
k th fraction. Total change in k th reach is
m
D Zi =
åD Z
ik
...(12.8)
k =1
Resistance Law and Sediment Transport Law
As discussed in Chapter 5 a number of predictors are available for the resistance coefficient and
sediment transport rate, and some studies have been carried out to study their relative accuracy. With the
present state of knowledge prediction of average velocity U within ±20 to 30 percent error and
prediction of transport rate within ±40 to 50 percent error are considered acceptable. The effect of errors
in prediction of U or transport rate on the prediction of bed levels over long periods needs to be studied.
One can use either Chezy’s or Manning’s equation with constant C or n, or C or n changing with
changes in stage or discharge. One can also use any other resistance law which may involve prediction
of regime or a trial solution for U, or may be function of sediment transport rate.
Sediment Transport
In analytical models the transport equation of the form qT = mU n or qT = a t*b have been used. EngelundHansen formula corresponds to n = 5 while in Meyer-Peter and Müllers’ formula
n=3
FG1 - 0.047IJ
H t K
*
Some softwares such as HEC-6 has an option of choosing any one of the five or six formulae for the
computation of transport capability. Most of the sediment transport formulae in vogue are based on
some basic assumptions which include (i) the flow is steady and uniform, (ii) river-bed is in equilibrium,
(iii) there is negligible wash load transport, (iv) the sediment is uniform or with small standard
deviation, and (v) all size fractions are moving. In numerical modeling these formulae are used for
unsteady, non-uniform flow by replacing So by Sf . The validity of this extension of use is yet to be
verified.
Further, in most of these formulae it is assumed that sediment transport rate at any section is
governed by the local hydraulic conditions. When such an equation is used for computing transport rates
for different size fractions it is usually assumed that the transport rate of kth fraction of sediment size is
equal to transport rate for that size using a given formula multiplied by the fraction of that size range
available in the bed. This assumption may be acceptable if standard deviation of the bed material is
small and all the sizes are moving. However, for large standard deviations and partial transport of
sediment (during armouring process), the results will be affected due to sheltering effect for smaller
sizes and greater exposure for sizes larger than the average size.
Realising the complexities in sediment transport formulae and their accuracies, it is prudent to use a
simpler formula. Using some available data the engineer should try different formulae and choose the
one that gives acceptable results.
362
12.3
River Morphology
NUMERICAL SCHEMES OF SOLUTION
The differential equations governing morphological processes in alluvial streams can be solved either
by finite element method (FEM) or by finite difference method (FDM). Comparing these two methods
Zienkieweiz et al. (1975) have observed that for slow flow, where convective terms are insignificant,
FEM was superior. They also found that with high velocities, when the convective terms become
important, and in transient problems, FDMs retain some superiority. Similarly in the preliminary stages,
studies by Palaniappan (1991) indicated that FEM did not have any superiority over FDM in one
dimensional alluvial stream transients. Cunge et al. (1980) also expressed similar view that in modeling
of river dynamics FEM has not found wide spread applications and it is found that the method has no
advantage over finite difference one-dimensional models. The real strength of FEM is in solving 2-D
and 3-D problems.
One of the FDMs viz. the method of characteristics is discussed in detail by Abbott (1966) and
Cunge et al. (1980). This method requires very small time steps, whereas in alluvial stream transients
computations involve very large times such as 10 to 30 years. Hence while the method of characteristics
can be used for flood propagation involving a few days, it is uneconomical and hence not suited for
computation of bed level variations in alluvial stream involving large times.
Two methods of computation are available in the other finite difference scheme: these are the
explicit method and the implicit method. In the explicit method a variable at (n + 1) the time level is
expressed fully in terms of known quantities at n th time.
Two schemes of explicit finite difference method that are often used are the Lax scheme and the
Leap-frog scheme. With reference to Fig. 12.1 in the Lax scheme the time derivative and space
derivative are expressed as
f jn + 1 - [a f jn + (1 - a )( f jn+ 1 + f jn- 1 )]
¶f
=
¶t
Dt
...(12.9)
n
n
¶ G (G j + 1 - G j - 1 )
=
2D x
¶x
...(12.10)
where a is the weighting coefficient. Substituting these in the continuity type equation for sediment, one
gets
f j n + 1 = a f j n + (1 – a)
LM f
MN
n
j +1
n
+ fj -1
2
OP - D t (G
PQ 2 D x
n
j +1
n
+ Gj - 1)
...(12.11)
Thus f can be calculated for (n + 1) time level for known values of f and G at nth level.
In the Leap-frog scheme the time and space derivatives are expressed as
n
n
( f jn + 1 - f jn - 1 )
¶f
¶ G (G j + 1 - G j - 1 )
=
and
=
2
2D x
¶t
¶x
...(12.12)
363
Numerical Models for Morphological Studies
t
(n
1)
n
(n + 1)
j
1
j
j+1
Fig. 12.1 Computational grid
and substitution in sediment continuity equation gives
fj n + 1 = fj n – 1 –
Dt
(Gnj+ 1 – G nj– 1)
2Dx
...(12.13)
When Dt/Dx = g Do and a = 0 both the schemes give exact solution of fully linearised flow
equations.
The finite difference implicit scheme can be written in general form as
and
y f jn++11 + (1 - y ) f jn + 1 - y f jn+ 1 + (1 - y ) f jn
¶f
=
Dt
¶t
...(12.14)
q G nj ++11 - G nj + 1 + (1 - q) G nj + 1 - G jn
¶G
=
¶x
Dx
...(12.15)
When the weighting coefficient y = 0.50 and the coefficient q is given a value between 0.5 and 1.0
(and preferably slightly greater than 0.50) it represents Preissmann 4-point scheme. There are a few
variations in this scheme also. The implicit method involves solution of a matrix resulting in escalation
of cost of computation.
12.4
CLASSICIATION OF ONE-DIMENSIONAL MODELS
One-dimensional mathematical models are quite useful in prediction of bed and water surface profiles,
average depth, velocity and transport rate as a function of x and t. These have been used for solving
problems such as
i) bed level variation during flood in lower reaches of the river;
ii) sedimentation upstream of a dam;
364
River Morphology
iii) degradation downstream of a dam;
iv) modification of a river profile due to construction of embankments and execution of cutoffs;
v) changes in river morphology due to addition or withdrawal of sediment or water;
vi) long-term evolution of river bed.
One-dimensional numerical models can be classified depending on whether quasi-steady or full
unsteady flow equations are used, and on whether uncoupled or coupled scheme of computation is used.
In quasi-steady models the terms
case where
¶D
¶U
and
are neglected. As pointed out earlier, this excludes the
¶t
¶t
¶U
¶D
is very small but
has to be considered. This situation arises for a river with a
¶t
¶t
reservoir where, Q being a function of t, there is storage which is a function of
¶D
. In unsteady flow
¶t
case these terms are retained.
In uncoupled scheme of solution the continuity equation and the dynamic equation for flow are
solved along the river course for time Dt assuming that the bottom elevations Z (x) do not change during
D t; the solution consists of water stages, water discharges and average velocity at the end of time
interval Dt. Then using the water depth, velocity and slopes that are computed at the nodal points, the
transport capacities are computed at the nodal points, and using sediment continuity equation, changes
in bed elevation DZ and new bed profile are computed over the whole reach at the end of Dt. The process
is then repeated for the next Dt. Since in this scheme the water flow equations and sediment continuity
equation are uncouples during Dt, it is called uncoupled scheme. When the Froude number is less than
0.60 or so (which is usually the case in alluvial rivers), the velocities of propagation of water wave are
much greater than that of bed wave propagation and hence this scheme of computation is justified in
many cases.
In quasi-steady coupled models, the quasi-steady equations for full momentum equation and the
continuity for flow and the sediment continuity equation are solved using implicit finite difference
scheme. The resulting non-linear algebraic equations are solved simultaneously to achieve coupling
between water flow and sediment movement. In a similar manner unsteady uncoupled, and unsteady
coupled one-dimensional models can be described.
In all the four types of one dimensional models discussed above, one can use either the explicit or
the implicit scheme of computations. However, it may be noted that most of unsteady coupled models
use implicit scheme to solve the governing equations. Although large computational time steps can be
used with these schemes, they involve solution of a system of equations using matrix inversion during
each computational step. Lyn (1987) has suggested that complete coupling between full unsteady flow
equations and sediment continuity equation is desirable in the cases where the conditions are changing
rapidly at the boundaries. Lyn’s results along with those of Yen et al. (1995) support the view that
uncoupled models with quasi-steady flow have considerable utility in solving alluvial stream transients.
Their accuracy can be improved by using more reliable methods of computing sediment transporting
capacity, armouring processes, and friction factor predictors.
The investigations by Cui et al. (1996) and de Vries (1993) indicate cost effectiveness of explicit
schemes. Cui et al. (1996) compared the numerical results obtained using coupled and quasi-steady
365
Numerical Models for Morphological Studies
uncoupled models for the cases where Froude number is close to unity and also for cases in which
upstream water discharge, sediment inflow rate and the downstream water level varied strongly. There
was a very good agreement between numerical results obtained using the two models, although
uncoupled models are inherently unstable than the coupled ones. Hence, uncoupled explicit schemes are
many times preferred and due consideration is given to the convergence and stability.
Some One-Dimensional Models
A number of one-dimensional numerical models have been developed and used since 1970’s for solving
transients in alluvial streams. Some of the models are listed below giving name of the model, developer
of the model, and its description, see Table 12.1.
Table 12.1 Summary of some one-dimensional models for mobile bed simulation
Name
Developer
Details
1. Delft Hydraulics
Laboratory
de Vries et al.
Quasi-steady, one-dimensional, qT = aUb, n or C
assumed constant
2. SOGREAH CHAR-2,
CHAR-3
Cunge et al.
Quasi-steady, 4-point implicit scheme to solve
coupled system.
3. HEC-2 with sediment
routing
Simons et al.
Quasi-steady, uncoupled, uses M.P. and Müller’s or
Einstein’s equation for sediment transport; armouring
effect included
4. KUWASER
Simons et al.
Quasi-steady, qT = aUb Dc, uncoupled.
5. UUWSR
Tucci et al.
Unsteady, uncoupled, uses 4-point implicit scheme for
flow and explicit scheme for sediment qT = aU b Dc
6. HEC-6
Thomas
Quasi-steady, variable Manning’s n, choice of sediment
transport formula, armouring included, uses explicit
scheme.
7. FLUVIAL – II
Chang and Hill
Unsteady, uncoupled, width changes allowed, Graf or
Engelund-Hansen formula for sediment transport, uses
explicit scheme for sediment and implicit scheme for flow.
8. HRS Wallingford
Bettess and While
Quasi-steady, uncoupled, uses Ackers-White or
Engelund-Hansen transport formula, implicit scheme,
armouring included.
9. IALLUVAL
Karim, Kennedy et al.
Quasi-steady, partially decoupled, single load mechanism,
saturated capacity, armouring included, multi-size predictor.
10. RESSED
Chen
Quasi-steady, fully decoupled, single load mechanism,
multi-size predictor.
11. CHARIMA
Holly et al.
Unsteady flow, partially coupled, single load mechanism,
saturated capacity, single size predictor.
12. MOBED
Krishnappan
Unsteady, flow, fully coupled, single load mechanism,
single size predicator.
13. FLUVIAL – II
Chang
Unsteady flow, fully decoupled single load mechanism
non-saturated capacity, multi-size predictor.
14. SEDICOUP
Holly and Rahuel
Unsteady flow, fully coupled, separate bed-load
mechanism, non-saturated capacity, multi-size predictor
366
River Morphology
Out of all these models, HEC-6 is discussed here in detail followed by a brief account of
CHARIMA. This is followed by two applications of HEC-6 to study effect of levee spacing on bed
elevations in the Kosi and sedimentation studies upstream of a dam in India.
12.5
CONVERGENCE AND STABILITY (CUNGE ET AL. 1980)
The basic idea of convergence is that the discrete solutions to the governing flow equations should
approach the exact solutions to those equations when Dx and Dt approach zero. However, since the full
non-linear partial differential equations do not have analytical solutions, it is impossible to directly
compare analytical and numerical solutions for convergence. Hence, the numerical method is tested on
the corresponding linear form of equations to obtain information about the convergence of the scheme.
For linear equations the convergence is ensured if the conditions of Lax theorem are satisfied. The
theorem states:
“Given a properly posed initial-value problem and a finite difference approximation to it that
satisfies the consistency condition, stability is the necessary and sufficient condition for
convergence”.
Consistency means that the finite difference operators approach differential equations when Dx and
Dt lend to zero. Numerical stability means that the solutions obtained using the numerical scheme are
bounded, that a small rounding-off error remains small during computational steps however long and
never become as large as the prescribed significant number. Thus stability means the errors introduced
by small perturbations remain smaller than a prescribed value.
In studying the numerical stability, two partial differential equations
and
¶U
+g
¶t
¶D
+ DO
¶t
¶D
=0
¶x
¶U
=0
¶x
U|
V|
|W
...(12.16)
are used. When the numerical scheme is utilized, the numerical computations can have different
harmonics resulting from the truncation errors, and if during the computations | C + U |
Dt
Dt
is
or C
Dx
Dx
always kept less than one, the damping factor for all the harmonics will be less than one and hence the
solution will be stable. This condition is known as Courant condition or Courant-Friedrichs-Levy (CFL)
condition. CFL condition of stability is directly linked to the theory of method of characteristics.
Courant number Cr is less than one expresses the fact that the computational point (n + 1, j) lies within
the domain of determinacy of the point of intersection of two characteristics from the neighbouring
point at nDt level.
In general explicit methods are conditionally stable, Courant condition limiting the permissible time
step Dt. Implicit methods, on the other head, can generally be made unconditionally stable. Preissmann
and Delft Hydraulics Laboratory methods are unconditionally stable if q ³ 0.50. Because of conditional
stability of implicit schemes, they have been used often.
367
Numerical Models for Morphological Studies
12.6
BOUNDARY CONDITIONS (CUNGE ET AL. 1980, DE VRIES 1993)
The boundary conditions required for solving alluvial stream transients are in four forms, namely initial
conditions, upstream conditions, downstream conditions and internal conditions. These are briefly
discussed below.
Initial Conditions
At time t = 0 the bed elevation Z at all places 0 < x < L must be known i.e., Z (x, 0) is known. In the case
of a meandering channel, since the bed level varies across the width, it is reasonable to take average bed
elevation there. In flood problems initial water level along the river length should be known.
Upstream Conditions
Two conditions are imposed at the upstream; the first is variation of Q with t should be known, i.e.,
Q (0, t); this is inflow hydrograph and is needed for solving the momentum equation. Inflow hydrograph
is usually obtained from historic data for as many years as possible. The other upstream condition
needed is regarding variation of incoming sediment load with time, i.e., Qs (0, t). This is prepared from
suspended load measurements. Since it is difficult to measure the bed load, it can either be calculated
using one of the bed-load equations or estimated and added to Qs (0, t) so that it represents bed material
discharge. This is needed for solving the sediment continuity equation. Alternatively one can prepare
relationship between measured bed material discharge and Q and use it.
Downstream Conditions
For sub-critical flow, downstream water level must be known in order to determine the water surface
profile for known bed elevation and discharge. This usually follows from discharge rating curve
h = h (Q). However if the bed level at x = L changes with time due to erosion or deposition, then the
downstream condition can be placed far downstream so that the bed level does not change during the
time of interest.
Internal Boundaries
If within 0 < x < L one or more of the parameters are discontinuous, then the internal boundary
conditions are required. Such situations arise in cases such as withdrawal of discharge DQ (t),
withdrawal of sediment load DQs (t), change in river width, confluences and bifurcation. These
discontinuities can create discontinuity in bed elevation.
Thus, if two streams 1 and 2 join and form the stream 3 the conditions to be satisfied are
Q1 + Q2 = Q3
QT 1 + QT 2 = QT 3
UV
W
...(12.17)
For a bifurcation of river 1 into two streams 1 and 3
Q1 = Q2 + Q3
QT 1 = QT 2 + QT 3
UV
W
...(12.18)
Further, the distribution of Q1 into Q 2 and Q3 should be such that the stage discharge relations for
the two branches 2 and 3 lead to the same water level at the point of bifurcation. The local geometry of
the branches determines the ratio QT2/QT 3.
368
River Morphology
Consider the problem of aggradation upstream of a dam. If x is measured from the dam in the
upstream direction,
Initial condition: Z (x, 0) should be known for 0 = x and L
Downstream boundary condition: D (0, t) should be specified for all t
Upstream boundary condition: Q (¥, t) should be specified and Qs = f (¥, t) should also be given
0 £ x £ L and t = 0.
In the similar manner boundary condition for degradation downstream of dam can be given. If x is
measured from the dam in the downstream direction,
Initial condition: Bed level and water level should be known for 0 = x and L at t = 0
Upstream boundary condition: at x = 0
QT (0, t) = QT for t < 0
QT (0, t) = QT 1 for t > 0 where QT 1 < QT
QT (L, t) = QTe for L large value of L
12.7
CHANNEL CROSS-SECTIONS AND METHOD OF EROSION OR
DEPOSITION
Even with the assumption of one-dimensional flow, the channel cross section can be irregular and can
have floodplain on one or both the sides of the main channel as shown in Fig. 12.2.
n1
n2
n5
n3
n4
Fig. 12.2
Channel with floodplain
In such a case the channel is usually divided into a number of sub-sections each having a different
value of n or C. Defining the conveyance K as
Q=
1
AR2/3 Sf1/2 = K S f
n
one can write Q = Q1 + Q2 + Q3 …….
where Q1, Q2, Q 3 … are discharges in each subsection and Q is the total discharge. Hence
K
S f = S Ki
S f or K = S Ki
Further, it is recognized that the floodplain areas often act as storage zones. They store water whose
velocity in the general direction of flow is nil. Hence, models such as HEC-6 define a movable bed
width at each section and erosion or deposition occurs in that width only.
369
Numerical Models for Morphological Studies
Fig. 12.3 Methods of deposition
In a one-dimensional model even though the flow is one-dimensional sediment movement is three
dimensional in nature because of secondary circulation and presence of beds. However, to simplify the
analysis the sediment transport is assumed to be one-dimensional. Also when erosion or deposition
occurs within a section, it can be assumed to occur in one of the following three ways as shown in
Fig. 12.3.
1. the cross section rises or falls through DZ without change in shape;
2. only those parts of the cross section which are below water level move up or down;
3. attempt is made to distribute sediment laterally in relation to tractive force (Chang and Hill
1976) or based on other information.
As discussed later in HEC-6, movable bed width is identified at each section and effective width
between two sections is also determined. Then knowing the volume of sediment to be deposited or
eroded in time Dt, bed level change DZ is computed.
12.8
MODELING OF ARMOURING
Starting with Harrison (1950) a number of laboratory investigations have been carried out by
investigators such as Hasan (1965), Jaswant Singh (1974), Gessler (1967), Little and Mayer (1972),
Garde et al. (1977) Shen and Lu (1983), Odgaard (1984) and Garde et al. (2004). Most of these studies
were aimed at the prediction size distribution of the armour coat for known size distribution of the
parent material and the initial flow conditions. The results of some of these investigations have been
described in Chapter 10.
Garde et al. (1977) conducted laboratory studies to determine time variation of surface layer of a
degrading stream. It was found that the major part of coarsening takes place in a relatively short time;
thereafter the process is very slow. If do and df are the median sizes of the parent material and the final
surface layer, and dt is the median size of the surface layer at any time t, they found that
(1 - F ) = 0.32 (t / t0 . 75 ) - 0 .17 for t / t0 . 75 < 0.40
and (1 - F ) = 5.5 (t / t 0 . 75 ) - 3. 40 for t / t0 . 75 < 4.0
U|V
|W
...(12.19)
Here F = (dt – do)/(df – do). The final value df varied along the length according to Sternberg’s law.
Here t 0.75 is the time at which F = 0.75. To use the above equation one must know df and t 0.75. Borah
(1989) has also proposed a method for predicting the depth of degradation.
370
River Morphology
Some attempts have been made to study the time evolution of the armour coat, which is required in
any mathematical model used for predicting time variation of erosion and deposition.
In HEC-6 model (1993) developed by Thomas and Prashun (1977) the armouring process is
analysed assuming the bed to consist of two layers: (1) the active layer which predicts the bed surface
degradation and armouring, and (ii) the inactive layer beneath the armour layer. Using Manning’s
equation for U, Strickler’s equation for Manning’s n, and the condition for insignificant sediment
transport as proposed by Einstein viz. y = Dgs d/to = 30, an equilibrium depth De is defined as the
minimum water depth required for a given particle size d to be immobile on the bed, and is given by
De = (q/10.21 d1/3)6/7
...(12.20)
2
in which q is expressed in ft /s, De in ft, and d in mm.
When the bed is composed of a mixture of different sized particles, the erosion depth Dse required to
accumulate one particle size thick layer of coarse non-moving material is calculated using the equation,
Dse = 2 SAE.d/3Pc
...(12.21)
Here SAE is the ratio of surface area of potential erosion to the total surface area (which is also taken
as equal to the ratio of erodible material remaining in the active zone to the total volume in inactive
zone) and Pc is the fraction of the bed material coarser than size d, which can be determined from the
known size distribution curve of the bed material, which is divided into different segments starting from
the coarsest fraction as shown in Fig. 12.4.
100
1
Percent finer
2
3
4
5
6
9
8
7
d mm
Fig. 12.4
Segmented size distribution curve of bed material
Consider the segment 1-2 and determine the equilibrium depths Deq1 and Deq2 for sizes 1 and 2
respectively using Eq. (12.20). If the actual depth of flow Dw is less than Deq2.1, the straight line segment
from 1 to 2 in Fig. 12.4 determines the value of Pc and then the final equilibrium depth is calculated as
Deq = Dw + Dse. If Dw is greater than Deq2, computations move to segment 2-3 and so on, until either the
proper segment is located or the smallest particle size in the bed material is sufficient for armouring the
bed, in which case scour or erosion does not occur. The depth between bed surface and equilibrium
depth is the active layer (see Fig. 12.5), and below the equilibrium depth and the erodible limit is the
inactive layer. The thickness of the active layer changes with change in U, Dw and slope.
371
Numerical Models for Morphological Studies
W.S
Deq1
Dw
Deq = Dw + Dse
Deq
Deq2
Active layer
Inactive layer
Fig. 12.5
Definition sketch
Ashida and Michiue (1971), Bayazit (1975) and Palaniappan (1991) use the concept of mixing
volume on the bed surface to simulate the armour coat. In these models when sediment flows out of a
mixing volume, an equal quantity by weight is added to the mixing volume in each computational step.
The added sediment has the same grain size distribution as that of the current surface.
Armouring procedures used in CHARIMA (Holly et al. 1990) are identical to those used in
IALLUVIAL. It is assumed that as the armouring develops with increasing degradation, the bed surface
is segregated into two parts: armour coat and part of the bed containing movable size fractions. Hence
fraction of the bed covered by non-moving particles Af (t) at any time t can be used as a measure of the
degrading bed. This process depends on the size distribution of the bed material and its variation with
depth, intensity of water discharge and sediment transport, formation and height of bed undulations, and
the stochastic character of the sediment movement. According to the analysis of Karim et al. (1983),
Af (t, k) is given by
Af (t, k) = Af (t – 1, k) + CA (t, K )×(1 – l) D Z(t)×
Pk
dk
...(12.22)
= 0 when k £ l (t)
and
Af (t) =
å
m
k = l(t )
A f (t , k )
Here Af (t, k) = fraction of the bed area covered by particle size interval k at any time t; DZ (t) =
incremental depth of degradation during current time interval; l (t) = index for lowest grain size interval
which is immobile according to Shields’ criterion, and forms the armour coat at time t; CA (t, k) = a
positive coefficient; Pk = fraction of bed material in the k th fraction, and m = total number of fractions.
The constant CA (t, k) = 1.9 for plane bed while the following empirical equation is used for CA (t, k)
CA (t, k) = 1.902 ad qk
to take into account the effect of bed forms on armouring. Here ad is a function of dune height to water
depth ratio and hence of t*/t*c; ad = 1.0 when t*/t*C = 1.0 and when t*/t*c = 1.5. Its variation between
these two limits is given by a function. Also qk is the probability of k th sediment size fraction to remain
on the bed.
372
River Morphology
Armouring of the bed surface tends to reduce the sediment transport capacity of the flow and
reduces the average height of dune and mixed layer. This reduction is assumed to be linear in
CHARIMA.
qsa = qs (1 – Af [t])
qsa =
H
(1 – Af [t])
2
Here qsa and qs are the transport rates with and without armouring; Tm is the mixed layer thickness
and H is the dune height.
12.9
HEC-6
HEC-6 is a one-dimensional quasi-steady uncoupled model designed to simulate and predict long term
changes in river bed profile over moderate times. It was developed by W.A. Thomas of the Corps of
Engineers of U.S.A. in 1976 and since then the model has been improved upon a few times; the latest
version 4.1 was presented in 1993. It handles a river system consisting of the main, tributaries, and local
inflow or outflow points. Hence the model can analyse network of streams, channel dredging and
various levee and encroachment alternatives. It faithfully deals with sub-critical flows and approximates
the super critical flow by normal depth.
Input Data
The input data include the geometric data, the sediment data and the hydrologic data. The geometric
data include cross-sections along the length of the reach, Manning’s n values, movable bed width in
each section and depth of sediment material in the bed. Each cross section is defined by a maximum of
100 points with station and elevation data. Typical cross-section is shown in Fig. 12.6 indicating main
channel, left and right over banks, movable bed limit and erodible-bed.
Left
over bank
Main channel
Right
over bank
Movable bed limit
Bed material
available for scour
Fig. 12.6
Channel details
Numerical Models for Morphological Studies
373
The conveyance limits are also specified so that section beyond those limits does not contribute to
water conveyance. The channel is divided into a number of sub-sections for each one of which
Manning’s n can be specified which can vary with stage of the discharge. For given water level, the
effective depth and effective width are defined. Hence for given Q, velocity can be computed.
The sediment data include fluid and sediment properties, inflowing fraction wise sediment load
data, the size distribution of the stream bed material, sediment transport capacity’s relationships, and
unit weight of sediment. The sediments are classified into silt, clays, sands and boulders using
classification of the American Geographical Union. These are divided into different size ranges and are
represented by the geometric mean size. Sediment transport rates for sizes up to 2048 mm are computed
and material coarser than 2048 mm only participates in armour coat formation. The sediment inflow
data at the upstream section is given as QT vs. Q curve according to size class. Other properties of
sediment that are needed such as relative density, shape factor, unit weight and fall velocity are also
specified. The sediment transport capacity at each section is calculated by using one of the alternatives
provided in HEC-6 programme; these include methods of Toffaleti, modifications of Laursen’s method
by Madden, and Copeland, Yang, DuBoy’s transport function, Ackers-White, Colby, Meyer-Peter and
Müller.
The hydrologic data include water discharges, temperature, downstream water surface elevations
and flow duration. To reduce the number of time steps used to simulate a given time period, the
continuous flow hydrograph is treated as a sequence of discrete steady flows; this is sometimes known
as computational hydrograph.
Boundary Conditions
HEC-6 needs specification of upstream as well as downstream boundary conditions and internal
boundary conditions. The upstream boundary conditions that are needed are discharge vs. time discrete
hydrograph, corresponding water temperature and sediment discharge data. HEC-6 provides three
options for downstream boundary conditions. These are: (i) rating curve giving Q versus water surface
elevation data, (ii) water surface elevation as a function of time, or (iii) a combination of the first two
options. The second option is used with reservoirs where water surface elevations are a function of time.
The internal boundary conditions are specified at the internal points within the reach at which water
surface elevations may be specified. This is usually done either by specifying a constant head loss for all
discharges, or by specifying a rating curve at the internal boundary.
Method of Calculation
Since HEC-6 is a quasi-steady, uncoupled model, it first uses one-dimensional energy equation for
computing the water surface profile, starting from downstream section and moving upstream, using
standard step method. Knowing the initial bed levels at all the sections, and water surface elevation at
downstream section 1, the following equation is solved for water surface elevation at section 2.
WS2 + a2
U 22
U2
= WS1 + a1 1 + he
2g
2g
...(12.23)
Here WS1 and WS2 are water surface elevations, a is the energy correction coefficient based on the
distribution of average velocities in the subsections and he is the head loss due to friction and expansion
374
River Morphology
(a 2 U22 - a1 U12 )
where Ce is specified. Equation (12.22) is
2g
solved by assuming WS2 and comparing the terms on the left and right hand side of the equation; a
maximum of twenty iterations are carried out. The computations are performed at all sections and
hydraulic parameters U, D and W are computed. For computing the sediment capacity, effective depth
and effective width are used which are defined as follows:
or contraction; the latter is computed as Ce
N
Effective depth (EFD) =
åD
av ai
2/3
Dav
1
N
åa D
i
Effective width (EFW) =
2 /3
av
1
( EDF ) 5 / 3
where ai = flow area of each trapezoidal element, Dav = average depth of each trapezoidal element, and
N = total number of trapezoidal elements in a sub-section.
Knowing velocity, depth and movable bed width at each section these are converted into
representative values in each reach for their use in calculating transport capacity. This is done as
follows:
Interior points:
U|
|
W = 0.25 W ( I - 1) + 0.5 W ( I ) + 0.25 W ( I + 1)|
||
S = 0.5[ S ( I ) + S ( I + 1)]
||
For upstream boundary:
U = U ( I ), D = D ( I ), W = W ( I ), S = S ( I )
V|
Downstream boundary:
||
S = 0.5[U ( I ) + U ( I + 1)]
||
D = 0.5 [ D ( I ) + D ( I + 1)]
W = 0.5[W ( I ) + W ( I + 1)]
||
S = S (I)
W
U = 0.25 U ( I - 1) + 0.5 U ( I ) + 0.25 U ( I + 1)
D = 0.25 D ( I - 1) + 0.5 D ( I ) + 0.25 D ( I + 1)
...(12.24)
Now the sediment transport capacities at any section at a given time are calculated using one of the
equations listed earlier and the computations proceed from the upstream towards the downstream
direction. Sediment continuity equation is then used in finite difference form. With respect to Fig. 12.7,
one can write
375
Numerical Models for Morphological Studies
Section
t
4
3
2
1
Time
p
Dt
p
L4
Ld
x
(Upstream)
(Downstream)
Fig. 12.7
Definition sketch
Bsp (Ysp¢ - Ysp )
Gu - Gd
+
=0
0.5 ( Lu + Ld )
Dt
where Gu and Gd are upstream and downstream transports of sediment in time Dt, in (vol./time), and
Bsp is width of movable bed at P,
Ysp and Y¢sp are depths at sediment before and after the time step at P
Gu is size wise sediment load entering the section and
Gd is calculated considering the transport capacity at P, sediment in flow, availability of material in
the bed and armouring.
The time step can be variable, a fraction of a day for high flows to several days or month for low
flows. It should be such that during the time step the bed level change is less than 0.3 m or 10% of depth
of flow whichever is smaller. The gradation of the bed material is recalculated after each time interval by
computing the fraction of bed material size available in the active bed. When scour or deposition occurs
during a time step Dt, HEC-6 adjusts the cross-section elevations within the movable bed portion of the
cross-sections. For deposition, the stream bed portion is moved vertically only if it is within the movable
bed specified and is below water surface. Scour occurs only if it is within movable bed, within the
conveyance limits, within the effective flow limits and below water surface. Once scour or deposition
( volume of sediment eroded or deposited)
gives change in bed elevation
effective width ´ length of control volume ( Lu + Ld )
in time Dt. When bed scours, armouring process may start which has been discussed earlier. For other
details one may see HEC-6 user’s manual (1993).
limits are known,
Model Output
HEC-6 gives a variety of outputs which include hydraulic data for each trial elevation in each backwater
computations at all the sections, volume of sediment entering and going out of each reach, trap
376
River Morphology
efficiency, bed level changes, water surface elevations, sediment transported at each section along with
its gradation, and bed material surface composition at each time step. It also gives some additional
information.
Model Calibration
Numerical models such as HEC-6 usually need calibration with the known conditions. During the
calibration of the model, the constants in the equations, time step, sediment transport and resistance
formulae used are changed so that the historical conditions are simulated. The known conditions used
for calibrating the model can be water levels and or bed levels at certain times. Such a calibration also
accounts for any inaccuracies in hydraulic and sediment load data as long as consistently the same
techniques of measurements are used. Once the model is calibrated it is assumed that it will predict the
results for the future with reasonable accuracy. However, it may some time happen that such data for
calibration of the model are not available; in such a situation the modeler has to use his past experience
in choosing the coefficient and the equations.
Limitations of HEC-6
HEC-6 programme has the following limitations:
i) The model being one-dimensional, development of meanders and lateral bank erosion cannot
be accounted for.
ii) Further, bifurcation of flows and closed loops (i.e., flow around islands) cannot be modelled.
iii) Only one junction or local inflow is permitted between consecutive sections; and
iv) The model analyses long term erosion or deposition; hence analysis of the single flood events
must be done with great caution.
12.10
CHARIMA
This one-dimensional model was developed at Iowa Institute of Hydraulic Research (U.S.A.) in 1988 to
study braided river channel network of the Sestina river in Alaska. The model can simulate processes
such as sediment sorting, bed armouring, flow dependent friction factor, and alternative flooding and
drying of perched channels. In addition to the assumptions made in St. Vannant equation, channel
network (i.e., total number of channels and their inter connections) is assumed to remain same and
cross-sections rise and fall during deposition of degradation. The effect of bends cannot be accounted
for in the model and lateral inflow be accounted for by channels joining at regular intervals. The model
has been used for flow analysis by CWPRS (1999).
Governing Equations
In addition to continuity equations for flow and sediment, and momentum equation for unsteady flow,
CHARIMA requires
Sediment discharge predictor:
F1 (Q, A, d50, Sf , D, Qs, ASF) = 0
Friction factor predictor:
F2 (Q, A, d50, Sf , D, Qs, ASF) = 0
Channel geometry predictor:
A = A (D, x)
B = B(D, x)
377
Numerical Models for Morphological Studies
Hydraulic sorting:
n
D 50
® d 50n + 1
Armouring of bed surface:
ACF N = ACF N + 1
Here Sf is the energy slope and ACF is a coefficient.
Solution Procedure
The solution of these equations is obtained in decoupled mode. CHARIMA follows Preissmann implicit
scheme to discretise the water flow and sediment continuity equations. In the first stage sediment
discharge equations, friction factor equation, channel geometry equations and discretised equation for
water flow are solved in hydraulic sweep. During this sweep the bed elevation Z, d50, armouring
coefficient ACF are held constant assuming the bed to be temporarily stationary. During this stage at
grid point C, water flow, water level, and the sediment transport capacity for each size fraction of the bed
material are computed.
In the stage 2, discretised sediment continuity equation is solved in downstream sweep to get new
bed levels at each grid point i. The sediment discharge Qsn +1 computed in stage 1 is treated as constant
assuming that it is unaffected by bed evolution process, armouring, and grain sorting. In this stage
accounting procedure is executed using aggradation or degradation computed in stage 2 (i.e. sorting of
bed material to compute new d50 and new armouring factor ACF n + 1). This procedure is uncoupled
because it assumes that these processes occur sequentially and not concurrently in given Dt. CHARIMA
essentially follows the following flow chart.
Load boundary conditions
Time loop
Compute W.L., discharge etc.
solve continuity and momentum
equations
Compute friction factor
and sediment discharge
Compute bed level changes
n
using sediment continuity eq .
Execute sorting and
armouring procedure
Fig. 12.8 Flow chart for CHARIMA
Iteration loop
378
River Morphology
During execution of CHARIMA the sediment load capacities can be determined from anyone of the
sediment transport formulae of Karim and Kennedy, Engelund and Hansen, modified Peter Ackers and
White formula, or the power law predictor. Dune height can be obtained either from Yalin’s relation or
Allen’s relation. It also takes into account and model
i) hydraulic sorting of bed material;
ii) changes in the composition of bed material;
iii) armouring of the bed surface or armouring factor ACF which is defined as the fraction of bed
surface area covered by non-moving particles;
iv) effect of bed forms on armouring;
v) effect of armouring on sediment discharge and the mixed layer thickness.
Armouring process used in CHARIMA is briefly discussed earlier. Many of the procedures and
relations used in CHARIMA are those used in IALLUVIAL model developed at Iowa Institute of
Hydraulic Research (U.S.A.) CHARIMA has been used to study long-term evolution of the Missouri
river reach between Gavins point dam and Rulo (Nebr), a reach of about 313 km, short term prediction
of bed evolution of the Cho-Shui river system in Taiwan and the Sestina river in Alaska. For details of
the model one can refer Holly et al. (1990).
12.11
APPLICATIONS OF HEC-6
To illustrate the applications of the above-mentioned numerical models, two applications of HEC-6 will
be briefly discussed here. The first relates to the aggradation of the Kosi river in the leveed reach, while
the second is concerned with aggradation upstream of a dam in India.
Aggradation of the Kosi
The river Kosi which is a major tributary of the Ganga originates in Nepal and flows through the state of
Bihar before it joins the Ganga at Kursela. The morphology of the Kosi is discussed in detail in Chapter
13 and the index map of the Kosi can be seen there; the Kosi has been known for its lateral migration
which has been attributed to excess sediment load it carries, eastward slope of the region and tectonic
and neo-tectonic activity in the region. To control frequent flooding and lateral migration the barrage
was constructed at Bhimnagar and embankments on both sides were built between the barrage and the
place called Mansi. Downstream of Mansi, the river is embanked only on the eastern side upto Koparia.
Between 1964 and 1974 it was found that approximately 50 percent of the sediment load of the Kosi was
deposited upstream of the barrage and the major part of the remaining load was deposited in between
levees thereby raising the bed levels.
The spacing between eastern and western embankments varies significantly along 100 km reach
that seems to be responsible for bed level variations. Table 12.2 lists the cross-section number, distance
from the barrage in km and levee spacing in meters.
At the request of Ganga Flood Control Commission the Kosi problem was investigated at the
University of Roorkee (Now IIT Roorkee) by Garde et al. (1990) to study:
1. causes of frequent breaches in the embankments;
2. bed level changes that are likely to occur in the embanked reach up to 2005;
379
Numerical Models for Morphological Studies
Table 12.2
Levee spacing at selected reaches on the Kosi
Cross-section number
Distance from the barrage, km
Levee spacing m
33
41
48
53
63
65
67
69
75
81
87
91
1.27
11.25
23.25
31.25
48.00
53.75
55.50
60.00
68.75
78.50
84.25
94.25
7458
7323
5505
11335
12722
15600
18540
17434
11156
9279
7972
8853
3. bed level changes that are likely to occur if spacing between the embankments is reduced
selectively; and
4. calculate sediment load brought into the Ganga by the river Kosi during 1985-2005 with and
without forward embankments.
Figure 12.9 shows the leveed portion and the locations of different sections. The slope of the river
between the barrage and 40 km downstream is about 5.5 ´ 10–4 and it reduces to 2.70 ´ 10–4 upto Mansi.
The median size of bed material is 0.25 and has a standard deviation of 1.45. For very low flows the river
is braided but at medium and high flows it flows in a single channel within embankments; hence it was
treated as unbraided in the model.
Fig. 12.9 Leveed portion of the Kosi
380
River Morphology
Analysis of the past records gave average monthly discharges which varied 13 170 cfs (373 m3/s) in
January to 167 365 cfs (47 544 m3/s) in the month of July. From the discharges available, ten daily
computational hydrograph was prepared. On the basis of measurements of average suspended sediment
concentration data at the dam site, the relationship between sediment discharge G in tons/day and Q in
cfs was obtained in the form
G = a Qb
...(12.25)
in which a and b varied as follows:
Table 12.3 Values of a and b in Eq. (12.25)
Range of d in mm
Range of Q in cfs
D less than 0.075 mm
a
5000 = Q = 30 000
30 000 = Q = 40 000
b
4.33 ´ 10
–13
0.012
3.86
1.53
0.075 < d < 0.15 mm
a
B
1.08 ´ 10
–9
–5
2.043 ´ 10
2.86
1.89
D > 0.15 mm
a
b
2.89 ´ 10
–9
2.76
1.84 ´ 10
–6
2.13
After a few trial runs it was decided to use Laursen-Madden’s equation for determining sediment
transport capabilities. The model was calibrated using bed level data in the leveed portion for the period
1975-1984. Values of Dx and Dt were determined from the following considerations. A typical flood
wave would take about 7 hours to cover 200 km reach. The time step Dt chosen was much greater than
this, namely 10 days during the monsoon period and 30 days during non-monsoon period, while Dx
equal to 10 km was used. For downstream control the water levels at Kursela were estimated from
analysis of the Ganga river data and used in HEC-6.
Bed level profiles during 1975-1984 were used with the above mentioned Dx and Dt values and the
best value of Manning’s n which could satisfactorily estimate those bed levels was found to be 0.20; this
value was used in further studies.
For the bed level predictions between 1985-2005, monthly discharges were generated using
Thomas-Fiering model and using characteristics of monthly flow data from the historic data available.
Analysis of Data
Detailed analysis of cross sections at various times and the occurrence of breach at any section,
indicated that prior to the actual breach, the deep channel gradually shifted towards the embankment
near that section. The average lateral rate of deep channel shifting was about 200 m/yr. It was therefore
recommended that the cross-sectional data in the leveed reach be monitored every year after flood
season and the places where the deep channel is close to the embankment be determined. The sections
downstream of that would be prone to breaching.
Bed Level Variations
Observations of the longitudinal profiles in the leveed reach for different years indicated that
aggradation or bed lowering occurring from section to section was primarily due to the variation in
width between levees along the river length. It was found that if a narrow section was followed by a
381
Numerical Models for Morphological Studies
3
1995
2005
2000
Bed elevation m
2
1
0
Scheme 6
1
Barrage
2
0
Leveed portion
20
Fig. 12.10
40
60
80
100
120
km from barrage
140
160
180
200
Rise and fall in bed levels in the Kosi with 1984 as the basis
wider section, the material scoured from the narrow reach was deposited in the wider reach causing
aggradation. Taking 1984 bed profile as the basis, bed profiles were obtained by using HEC-6 for the
years 1990, 1995, 2000 and 2005. The rise and fall in bed levels along the river reach with respect to
1984 levels (both leveed and not leveed) are shown for the years 1995, 2000 and 2005 in Fig. 12.10. It
can be seen that maximum rise in the bed level at about 2.6 m is likely to occur at about 48 km from the
barrage (section 63) in the year 2005. The computation of water levels indicated that the water level
between sections 63 and 91 will be about 1.37 m to 2.13 m below the top of the levee.
A number of proposals for reducing the spacing between the levees thereby reducing aggradation
were considered and tested using HEC-6. These were:
i) uniform reduction in width to 90 percent of the present;
ii) uniform reduction in width to 80 percent of the present;
iii) uniform reduction in width to 70 percent of the present;
iv) reduction in width to 70 percent of the present width in 12 km reach between sections 63 and
69;
v) reduction in width between sections 53 and 75 to 75 percent to 0 percent width;
vi) reduce width between sections 67 and 75 gradually from 70 percent at section 69 to 0 percent at
section 75.
The first three proposals were rejected because these caused increased deposition and rise in water
level at most of the sections. Schemes (v) and (vi) are shown in Fig. 12.11. Effect of scheme (vi) on the
bed levels within the leveed reach and the downstream of it can be seen in this Fig. 12.10. It may be
noted that the proposed scheme (vi) does not significantly alter bed levels downstream of leveed reach,
and significantly brings down rise in bed levels between sections 63 and 75. At critical section 63
aggradation reduces from 2.59 m to 1.71 m in 2005.
382
River Morphology
N
Eastern flood embankment (existing)
50
53
We
ste
at
ir
ive
r
75
Ba
g
m
59
63
rn fl
ood
(exi emba
Forward
stin
g) nkmen
embankment
t
as per scheme-V and VI
Fig. 12.11
67
69
Forward
embankment
as per scheme-VI
71
Forward
embankment
as per scheme-V
Recommended spacing of levees in the Kosi
The study also indicated that if the jacketing proposal (vi) is adopted, the sediment load entering the
Ganga may increase from (9.8 ´ 107) tons/yr to (.1 ´ 108) tons/yr, which seems to be only a marginal
increase in view of the high discharges in the Ganga at Kursela.
Sedimentation Studies Upstream of a Dam
As a second example of application of HEC-6, computation of sediment deposition profiles upstream of
a dam is discussed. The dam under discussion is located on a river in Southern India and has a height of
35.3 m and length of 1560 m. Average riverbed slope in 275 km reach is 0.000091 and bed material of
size 0.90 mm and sg of 5.5. At about 240-250 km upstream of dam the irrigation scheme and diversion
weirs are in operation. Hence it was required to be found out if sedimentation in the upstream of the dam
would affect the function of these diversion structures and would raise the flood levels beyond
acceptable limits. Since further details about operation of the dam were not available, it was assumed
that full reservoir level of 519.6 m will be maimed and flood discharges will be released accordingly.
Ten daily discharge hydrograph flows varied from 125 m3/s in June to 3150 m3/s in July and about
100 m3/s in October. The inflow sediment discharge obtained from suspended load measurements was
represented by the equation
Qs = 1.5 Q1.65
in which Qs is expressed in tones/day and Q in m3/s. A tributary joining just upstream of the dam, having
ten-daily discharge variation from 40 m3/s to 200 m3/s was also modeled. The Manning’s for the main
channel and the flood plain were estimated to be 0.025 and 0.05 from the meager data available. The bed
profiles obtained for 10, 20 and 30 years of operation, for a constant water level of the dam, obtained by
using HEC-6 are shown in Fig. 12.12. It was found that the bed levels at 245 km upstream of the dam
where lift irrigation scheme is in operation would rise by about 2.20 m in 30 years. When the maximum
383
Numerical Models for Morphological Studies
Fig. 12.12
Transient bed profiles upstream of the dam
observed flood of 13 320 m3/s was passed over 30 year bed profile with 519.6 water level at the dam, the
flood levels rose by nearly 2.0 m within 60 to 260 km upstream of the dam.
References
Abbott, M.B. (1966) An Introduction to the Method of Characteristics. Thames and Hudson, London.
Ashida, K. and Michiue, M. (1971) An Investigation of River Degradation Downstream of a Dam. Proc. of 14th
Congress of IAHR, Paris, Vol. 3.
Bayazit, M. (1975) Simulation of Armour Coat Formation and Destruction. Proc. of 16th Congress of IAHR, Sao
Paulo (Brazil), B 10, pp. 73-78.
Borah, D.K. (1989) Scour Depth Prediction Under Armouring Conditions. JHE, Proc. ASCE, Vol. 115, No. 10, pp.
1421-1425.
Chang, H.H. (1982) Mathematical Model for Erodible Channels. JHD, Proc. ASCE, Col. 108, No. HY5, pp. 678688.
Chang , H.H. and Hill, J.C. (1976) Computer Modelling of Erodible Flood Channels and Deltas. JHD, Proc.
ASCE, Vol. 102, No. HY9, pp. 1464-1477.
Chen, Y.H. and Simons, D.B. (1975) Mathematical Modelling of Alluvial Channels. Proc. of Symposium on
Modelling Techniques, ASCE, San Francisco, pp. 466-483.
Chen, Y.H. and Simons, D.B. (1980) Water and Sediment Routing for the Chippewa River Network System. Proc.
of International Conference on Water Resources Development, Taipei (Taiwan), Vol. 2.
384
River Morphology
Correia, L.R.P., Krishnappan, B.G. and Graf, W.H. (1992) Fully Coupled Unsteady Mobile Boundary Flow Model.
JHE, Proc. ASCE, Vol. 118, No. 3, pp. 476-494.
Cui, Y., Parker, G. and Parola, C. (1996) Numerical Simulation of Aggradation and Downstream Fining. JHR,
IAHR, Vol. 34, No. 2, pp. 185-204.
Cunge, J.A. Holly, F.M. and Verwey, A. (1980) Practical Aspects of Computational Hydraulics. Pitman
Publishing Ltd., London, 420 p.
CWPRS (1999) Mathematical Model Studies for Proposed Storm Water Drainage System of Central and North
Region of Vasai-Vihar. Central Water and Power Research Station, Khadakwasla, Pune. Tech. Report 3655,
65 p.
De Vries, M. (1993) Lecture Notes on River Engineering, Delft International Course, Delft, 139 p.
Garde, R.J., Ali, K.A.S. and Diette, S. (1977) Armouring Process in Degrading Streams. JHD, Proc. ASCE, Vol.
103, No. HY9, pp. 1091-1095.
Garde, R.J., Ranga Raju, K.G., Pande, P.K., Asawa, G.L., Kothyari, U.C. and Srivastava. R. (1990) Mathematical
Modelling of the Morphological Changes in River Kosi. Hyd. Engg. Section, Civil Engg. Dept., University of
Roorkee, Roorkee, 92 p.
Garde, R.J. Sahay, A. and Bhatnagar, S. (2004) Armour Coat Formation in Parallel Degradation. Report Prepared
for Indian National Science Academy, CWPRS, Pune., 45 p.
Gessler, J. (1967) The Beginning of Bed Load Movement of Mixtures Investigated as Natural Armouring in
Channel. Translation T-5, W.M. Keck Laboratory of Hydraulics and W.R., Caltec (U.S.A.).
Harrison, A.S. (1950) Report on Special Investigation of Bed Sediment Segregation in a Degrading Stream.
University of California, Inst. of Engineering Research, Berkeley (U.S.A.), Series 33, No. 1.
Hasan, S.M. (1965) Experimental Study of Degradation. M.E. Thesis, Civil Engg. Dept., University of Roorkee,
Roorkee.
Holly, F.M., Yang, J.C., Schwarz, P., Hsu, S.H. and Einhellig, R. (1990) CHARIMA – Numerical Simulation of
Unsteady Water and Sediment Movement in Multiply Connected Network of Mobile Bed Channels. Iowa
Institute of Hydraulic Research, Iowa, Rep. No. 343.
Karim, M.F., Holly, F.M. and Kennedy, J.F. (1983) Bed Armouring Procedure in IALLUVIAL and Application to
the Missouri River. Iowa Institute of Hydraulic Research, Iowa, Rep. No. 269.
Krishnappan, B.G. (1985) Modelling of Unsteady Flow in Alluvial Streams. JHE, Proc. ASCE, Vol. 112, No. 2,
pp. 257-265.
Little, W.C. and Mayer, P.G. (1972) The Role of Sediment Gradation in Channel Armouring. School of Civil
Engineering, Georgia Institute of Technology, Atlanta (U.S.A.).
Lyn, D.A. (1987) Unsteady Sediment Transport Modelling. JHE, Proc. ASCE, Vol. 113, No. 9, pp. 1-15.
Murthy, B.S., Surya Rao, S., Rajagopal, H., Tiwari, S.K. and Kumar, R. (1998) Flood Estimation Routing in River
System : Mathematical Models. Report Submitted to INCH, IIT Kanpur, Kanpur, 151 p.
Odgaard, A.J. (1984) Grain Size Distribution of River Bed Armour Layers. JHE, Proc. ASCE, Vol. 110, No. 10,
pp. 1479-1485.
Palaniappan, A.B. (1991) Numerical Modelling of Aggradation and Degradation in Alluvial Streams. Ph.D.
Thesis submitted to University of Roorkee, Roorkee.
Rahuel, J.L., Holly, F.M., Chollet, J.P., Belleudy, P.J. and Yang, G. (1989) Modelling of River Bed Evolution for
Bed Load Sediment Mixtures. JHE, Proc. ASCE, Vol. 115, No. 11, pp. 1521-1542.
Shen, H.W. and Lu, J.Y. (1983) Development and Prediction of Bed Armouring. JHE, Proc. ASCE, Vol. 109, No.
4, pp. 611-629.
Numerical Models for Morphological Studies
385
Singh, J. (1974) Variation of Bed Material Size in Degrading Channel. M.E. Thesis, University of Roorkee,
Roorkee.
Thomas, W.A. and Prashun, A.L. (1977) Mathematical Modelling at Scour and Deposition. JHD, Proc. ASCE,
Vol. 103, No. 8, pp. 851-863.
U.S. Army Corps of Engineers (1993) HEC-6 : Scour and Deposition in Rivers and Reservoirs. User’s Manual,
Hydraulic Engineering Centrer, Davis, (U.S.A.) 164 p. with Appendix.
Yen, K.C., Li, S.J. and Chen, W.L. (1995) Modelling Non-uniform Sediment Fluvial Process by Characteristic
Method. JHE, Proc. ASCE, Vol. 121, No. 2, pp. 159-170.
Zienkieveiz, J.C. Gallagher, R.H. and Hood, P. (1975) Newtonian and Non-Newtonian Viscous Incompressible
Flow- Temperature Induced Flow-Finite Element Solution. MAFELAP.
C H A P T E R
13
Morphology of Some Indian Rivers
13.1
RIVER SYSTEMS IN NORTH INDIA
From the point of view of morphology of rivers in alluvial material, the Indian rivers originating from
the Himalayas and flowing through thick alluvial stratum need special mention. These rivers broadly
belong to three basins, namely the Indus basin, the Ganga basin and the Brahmaputra Basin (Rao 1979).
The Indus system of rivers comprises the main river Indus and its tributaries the Kabul, the Swat,
and the Kurram joining from the west, and the Jhelum, the Chenab, the Ravi, the Beas and the Sutlej
joining from the east. The five tributaries from the east join the Indus which flows 960 km before joining
Arabian Sea. The Indus river originates in Tibet near Manasarovar Lake, passes through the mountain
ranges of Kashmir and Gilgit, enters Pakistan and emerges out of the hills near Attock. From Attock to
its mouth in the Arabian Sea, south of Karachi, it traverses a distance of about 1610 km out of its total
length of 2880 km. The eastern tributaries pass through northwest part of India namely through
Kashmir, Punjab and Himachal Pradesh and then flow out to join the Indus in Pakistan.
The Himalayas in the north, and the Vindhyas in the south bound the Ganga basin. The Ganga is not
known by this name either in the beginning or at the end of its length. Downstream of the confluence of
the Alaknanda and the Bhagirathi at Dev Prayag, the river is known as the Ganga. After traversing a
distance of 250 km the river descends on to the plains at Rishikesh, and passing through Hardwar and
Narora it meets the river the Yamuna at Allahabad. It further passes through Varanasi, Patna and
Bhagalpur and then turns towards south. Upstream of Varanasi the Ganga is joined from the north by
major tributaries the Ramganga, the Gomti and the Tons, and from the south by the Chambal, the Betwa,
the Sinda and the Ken. Downstream of Varanasi, when the river enters Bihar, other important tributaries
like the Ghagra, the Gandak, Son, the Bagmati and the Kosi join from the north. In the lower Ganga
basin only the Mahananda joins the Ganga. Of all these tributaries the Kosi is known for its instability
due to high sediment load and braided plan-forms; hence its morphology is discussed later. About
hundred kilometers downstream of Rajmahal the river ceases to be called Ganga. It bifurcates into
Bhagirathi the lower portion of which below Kalna is called the Hooghly which continues in India and
the Padma, which flows in Bangladesh and forms the southern boundary between India and Bangladesh
Lucknow
Kanpur
Kabul
Ahmedabad
Kolkata
Nagpur
Morphology of Some Indian Rivers
Delhi
Jhelum
Chenab
Mumbai
Beas
vi
Ra
Lakshadwip
Bhakra
Nangal
Chenab
Sutlej
Andaman and
Nicobar
Islands
Chennai
Sri Lanka
Tsangpo
Indus
Sarda
Delhi
Ganga
Yamuna
Chambal
Gandhi
Sagar
I
Narmada
Narmada
Allahabad
d
Kosi
Gandak
Brahmaputra
Kosi
Kurusela
Son
Betwa
n
Ghaghara
i
Mahanadi
a
Hirakud
Kolkata
Fig. 13.1 Basins in Indo-Gangetic plain in Indian subconinent
387
388
River Morphology
for some distance. After traversing 220 km further down in Bangladesh the Padma is joined by the
Brahmaputra at Goalundo and after meeting the Meghana 100 km downstream, the Ganga joins the Bay
of Bengal. Figure 13.1 shows a sketch of these basins in the Indian subcontinent.
The Brahmaputra river rises in the Kailash range of the Himalayas at an elevation of about 5000 m.
It is about 2880 km long. After flowing about 1600 km parallel to the main Himalayan range, it enters
India and after traversing 720 km joins the Padma at Goalundo. The combined stream is then known as
the Padma. In Tibet and India a number of tributaries join Brahmaputra. The Brahmaputra is known for
its instability, floods, and bank erosion causing innumerable miseries to the people living in north-east
India. Hence, the morphology of the Brahmaputra is also discussed later.
There are certain common characteristics of rivers in these basins namely the Kosi and the
Brahamputra which are responsible for their morphological behaviour. These rivers are fed by rainfall
as well as snowmelt; hence, their hydrographs have in general two peaks. Further, major parts of their
catchment lie outside India; as a result, India can do very little in terms of soil conservation measures as
well as construction of dam etc., without active cooperation from neighbouring countries. Further, these
streams originate or pass through fragile Himalayas which erode fast, and hence they carry relatively
heavy sediment load. Also, the entire Himalayan belt from Kashmir to Assam being tectonically active
with frequent earthquakes and neotectonic movements, the morphology of rivers in these regions is
affected by tectonic activity. It may be mentioned that there are a number of subsurface transverse faults
in the region, which influence the morphology of the streams. Further, hilly areas are prone to
landslides, which occur because of unstable hill slopes, earthquakes and intense rainfall. As a result,
heavy sediment load enters these streams.
The streams in these regions are classified by Jain and Sinha (2003) into three categories namely
mountain-fed, foothills-fed and plain-fed streams. These differ significantly in morphological,
hydrological and sediment transport characteristics. Mountain-fed rivers are generally multi-channel,
and braided systems, characterized by many times higher discharges and sediment load in comparison to
single channel sinuous foothill-fed and plains-fed river systems. Mountain-fed rivers such as the Ganga,
the Gandak and the Kosi transfer large quantities of sediment from their source areas of high relief and
consequently form large depositional areas (e.g., fans) in plains. The foothill-fed rivers (the Bagmati
and the Rapti) and plain-fed rivers (the Gomati and the Burhi Gandak) derive their sediments from
foothills and plains and a large proportion of this material is re-deposited in the plains after reworking.
It may also be pointed out that many rivers in Ganga basin show tendency towards avulsion.
KOSI
13.2
INTRODUCTION
The river Kosi, which is a major tributary of the Ganga and which is the life line of the state of Bihar in
North India, originates at an elevation of about 6000 m in the Himalayas and finally discharges into the
Ganga at Kursela, see Fig. 13.2. Plate 1 shows the aerial view of the Kosi. The river is also sometimes
called the Saptakosi with seven tributaries namely the Sun Kosi, the Arums, the Tamur, in the upper
reaches and the Trijuga, the Balan, the Kamla and the Bagmati in the plains. In Sanskrit literature this
river is referred to as the Kaushiki. It may be mentioned that Kaushiki was the legendary ascetic low-
389
Morphology of Some Indian Rivers
N
nd
ak
riv
er
Tibet
river
ara
n
So
er
ir
r
er
India
North Bihar
Badiaghat
a
Gang riv
Darjeeling
Barahakshetra
Chatra
Barrage
Jogbani
ive Nirmali
r Kamrail
rive
Patna
riv
at
W
es Balan river
te
rn
ste
em
rn
ba
em
nk
ba
m
nk
en
m
en
t
t
er
riv
agh
gm
Tribeni
Ea
ak
nd
Ga
Gh
Ba
Ka
ml
ar
ive
r
Nepal
Monghyr
32 miles
Pumea
Katihar
Kursela
ri
Mahananda ver
Kosi
Sikkim
Ta
m
Ar
Sun
ur
un
r
Khatmandu
riv
er
ive
r
Ga
MT Everest
Rajmahal
Scale
Fig. 13.2
Kosi river basin
caste woman who, after being left by her Brahmin lover, became frivolous and went to various places in
quest of pleasure. Hence, there is considerable similarity between the ever-wandering Kosi river and
Kaushiki. The river Kosi traverses a total distance of 468 km passing through Tibet, Nepal and India.
The Kosi is known for shifting its course laterally and thus creating problems of flooding and causing
considerable loss to human lives, cattle, property, public utilities and agriculture. Hence the river is
known as the “Sorrow of Bihar”. The Kosi is also one of the largest braided rivers in the world.
The Kosi catchment consists of the Himalayas in the eastern part of Nepal and Tibet. The transHimalayan portion is a high plateau while the Himalayan portion comprises mountain ranges running
eastward separated by cross-ribs. Portions of the catchment above the elevation of 4900 m are covered
by perennial snow, the snowline being at 3000 m in winter and 4500 m in summer. It may be mentioned
that ten percent of the Kosi catchment is perpetual snow zone of Himalayas and this has a major effect
on the nature of annual flood hydrograph. The catchment area within India is flat and lies in the
Gangetic plains. Out of the remaining, seventy percent is under cultivation and a very small percent
under forest cover in India.
The Kosi forms an inland delta or fan in the Gangetic plain (Gole and Chitale, 1966). The apex of
the fan is a few kilometers downstream of Chatra, the base extending over a distance of 120 km and
height being about 100 m. It has a slope from north to south and west to east. Kosi fan covers an area of
16 000 km2 lying partly in Nepal and partly in north Bihar. It lies between altitudes of 152 m and 34 m
390
River Morphology
Plate 1 Aerial view of the Kosi
391
Morphology of Some Indian Rivers
above the sea level. This fan is covered by old courses of the Kosi now occupied by smaller streams
(known locally as dhars), old channel lakes (known locally as chaurs), oxbow lakes and dune-like
mounds along the abandoned courses of the Kosi. Their existence is due to the westward shifting of
Kosi through 112 km in 223 years (Gole and Chitale 1966).
13.3
CATCHMENT CHARACTERISTICS AND GEOLOGY
The Kosi basin falls within longitude 85° to 89° (E) and latitude 25° 20’ to 29° (N). On its north is the
Tsangpo (Brahmaputra) and on the south is the Ganga river. On eastern side is the ridge separating it
from the Mahananda catchment and on the west is the ridgeline separating it from the Gandak/Burhi
Gandak catchment. There is an 87 m drop in elevation in the 160 km reach between the Chatra gorge
and Kursela near the confluence with the Ganga. The total catchment area of Kosi is 95 156 km2 out of
which 20 376 km2 lies in India. Thus, nearly eighty percent of total catchment of the Kosi lies in Tibet
and Nepal. The rivers the Trijuga, the Kamla Balan, the Bhutahi Balan and the Bagmati are the
tributaries, which join the Kosi from the right in the plains in Bihar. The distribution of the catchment
area in the Kosi river system is given in Table 13.1.
Table 13.1
Kosi including hilly tributaries
Kamla Balan
Bagmati
Trijuga
Bhutai Balan
Total
Distribution of catchment area in Kosi river system
In India (km2)
Out side India (km2)
Total (km2)
11 070
2980
6320
20 370
63 430
2465
7080
706
1105
74 786
74 500
5445
13 400
706
1105
95 156
The three hilly tributaries are the Arun, the Sun Kosi and the Tamur. The Arun Kosi is the longest of
the hilly tributaries, which drains the Mount Everest. Its catchment area is 34 650 km2 and it contributes
37 percent of flow and 36 percent of sediment load of the Kosi at Tribeni. The Sun Kosi is the second
longest tributary. Its catchment area is 19 000 km2 and it contributes 44 percent of flow and 42 percent
of sediment load of Kosi at Tribeni. Tamur Kosi drains Mount Kanchanjunga; its catchment area is 5900
km2 and it contributes 19 percent of flow and 22 percent of sediment load of Kosi at Tribeni.
The Bagmati originates in Sheapore range hills at an elevation of 1500 m and has a catchment area
of 13 400 km2 and length of 589 km. The Kamla Balan originates in Nepal and has a catchment area of
5445 km2 almost half of which is in the plains. Its length is 320 km. The Trijuga and the Bhutai Balan
have catchment areas of 706 km2 and 1105 km2 respectively.
The geology of the Kosi basin can be divided into three parts, namely the geology of the Mount
Everest and the Kanchanjunga, which lie in the upper northern most part and form the upper catchment,
the Siwalik deposits which lie towards south of Mount Everest and up to Chatra, and the terraces below
Chatra. The upper-most part is made up of folded Jurassic strata composed of black shales and
argillaceous sand stones. This stratum is 100 to 150 m thick, and contains calcarius, pyrites and ferrous
partings. Underlying the Jurassic shales are dark limestones and below it thick series of metamorphosed
392
River Morphology
limestone, quartzites etc. The Siwalik deposits are alluvial detritus derived from wastes from mountains
which are swept down by streams and deposited at their foot. These former alluvial deposits have been
involved in the upheavals of the Himalayas because of which they may have been folded and elevated
into their outermost foothills. Weathering of Siwalik rocks has been proceeding at an extraordinarily
rapid rate since their deposition. Because of this, the topography produced is made up of very large
escarpments and dip-slopes separated by broad longitudinal valleys intersected by deep meandering
ravines. The terraces below Chatra are made up of conglomerates and thick beds of sand, boulders and
shales. The Kosi flood plain is made up of alluvial deposits in the form of a trough, which is tectonic in
nature and is formed in front of Himalayan chains. Hence, during the past and present times it is
subjected to slow neo tectonic movements and earthquakes (NIH 1994). Figure 13.3 shows the
geological map of the Kosi basin.
13.4
GEOTECTONICS
The entire Kosi basin area has been the subject of study by Bordet, Gansser, Hagen and Akiba et al. (see
Gohain and Parkash, 1990). The major north dipping thrusts – the Main Central Thrust and Main
Boundary Thrust – are present in the area and are active even at present. One can see from Fig. 13.3 a
major fault FF’ at the edge of the Kosi fan which causes an offset of the Siwaliks by about 20 m. This
area has also experienced over 45 earthquakes of magnitudes ranging from 4.0 to 8.3 on Richter scale,
the most severe earthquake being the one that occurred on 15th Jan. 1934 and was of magnitude 8.3; this
Kosi alluvium
Alluvium of the Ganga River
F¢
Alluvium of the other south,
southeast and east flowing streams
Younger alluvial piedmont
Older alluvial piedmont
Upper Siwalik sediments
Middle siwalik sediments
Archaean
Burhi
Gandak R
Lesser Himalayan Rocks
Kosi R
Faults lineaments
Ganga
Faults after raiverman et. al., 1983
0
20 km
Fan boundary
Scale
Fig. 13.3 Geological map of the Kosi alluvial fan and adjacent area (Gohain and Parkash 1990)
393
Morphology of Some Indian Rivers
earthquake had its epicenter within 100 km of Barakshetra where a high dam was earlier proposed on
the Kosi. This earthquake was felt all over north Bihar and Nepal and the cities of Munger and Bhatgaon
(in Nepal) were completely destroyed while the cities of Patna, Kathmandu and Darjeeling felt the
shocks of the earthquake. Kosi basin is also subjected to slow neotectonic upheaval, which may be
partly responsible for the westward migration of Kosi.
13.5
HYDROLOGY
The Kosi catchment is fed by monsoon rainfall as well as snowmelt. As mentioned earlier ten percent of
the catchment up to Chatra is above perpetual snow zone of the Himalayas. Kosi catchment gets rainfall
due to monsoon, which begins around June, and retreats in the middle of October. This accounts for
eighty percent of the annual rainfall. During April and May, thunderstorms occur in the catchment. The
annual rainfall decreases from 1200 mm at the foothills to 350 mm on the southern slopes of the
Himalayas. In the Tibetian catchment it is about 250 mm while in the lower parts of the Kosi catchment
it varies from 1380 mm to 1500 mm. July and August provide the maximum rainfall. Mookerjee and
Aich (1963) have estimated that 74 percent of the discharge of Kosi can be accounted for by the
precipitation in the form of rainfall. Analysis of peak flow in Kosi indicates that the peak flow can be ten
times as large as the mean discharge in a single year. Flow duration curve for the Kosi at Barakshetra is
given by Gohain and Parkash (1990). Its approximate coordinates are given in Table 13.2
Table 13.2
3
Flow duration curve for Kosi at Barakshetra
Monthly average discharge in m /s
300
400
600
700
1400
3600
4300
4800
5800
Percent of time equaled or exceeded
100
80
60
50
40
20
10
5
1
The average annual runoff at Barakshetra is estimated to be 53 040 Mm3 out of which 80 percent is
contributed from June to October. The minimum annual runoff at the same place is approximately 38.83
Mm3.
Discharge and Sediment Measurements
It was only after 1947 that the government agencies realised the necessity of having adequate and
accurate flow and sediment data for the management of Kosi and established gauging sites. At present
the Kosi has eight sediment and gauge-discharge observation sites. These are at Barakshetra, Bhim
Nagar barrage, Baltara and Basua on the Kosi, on the Sun Kosi, the Arun and the Tamur at Tribeni, and
at Machhuaghat on the Arun. The annual peak flows observed at Barakshetra between 1948 and 1978
are listed by NIH (1994). These are given in Table 13.3.
It can be seen that the maximum observed flow at Barakshetra was 25 880 m3/s in 1968 and water
surface elevation for this discharge was observed to be 132.18 m.
Analysis of sediment load carried on the Kosi at Barakshetra for the period 1948-1981 has revealed
that on the average it carries 95 Mm3 of sediment annually, of which coarse, medium and fine sized
materials are 18.95, 25.11 and 55.94 percent respectively. Similar measurement made at Baltara
between 1973-1981 have given average sediment load as 57.35 Mm3 of which coarse, medium and fine
394
River Morphology
Table 13.3
Peak flows in m3/s at Barakshetra during 1948–1998
13587
12283
9647
11226
9646
5424
24236
7198
10825
10718
9829
14322
11346
8379
7085
8309
8842
9456
13343
9170
10223
7190
5441
10514
25880
11428
7792
8171
9257
7538
7651
8142
9209
7990
14831
6987
10570
10769
13880
9489
6912
11332
7136
5979
6660
12186
7783
8818
13391
6949
are 8.2, 19.8 and 72.0 percent respectively. Garde et al. (1990) analysed the sediment load data at the
barrage and found that the sediment load in Tons/day is related to Q in m3/s as
QT ~ Q3.86
for sediment finer than 0.075 mm
QT ~ Q2.86 for 0.075 < d < 0.15
QT ~ Q2.76 for d > 0.15 mm
Sediment load in tons/day
These are shown in Fig. 13.4. It is observed that sediment concentration of the Kosi increases in the
head reach up to Hanuman Nagar. This increase is primarily due to increase in fine fraction due to
10
5
10
4
10
3
Fine sediment
(d < 0.075 mm)
Medium sediment
(0.075 < d < 0.15 mm)
Coarse sediment
(d ³ 0.15 mm)
Scatter
of data
10
2
10
1
Scatter
of data
Scatter
of data
0
Datum 10
3
4
5 ´ 10 10
10
5
3
5 ´ 10 10
4
5
3
10 5 ´ 10 10
Q cfs
4
10
5
Fig. 13.4 Relation between sediment load and Q at the barrage on the Kosi
10
6
395
Morphology of Some Indian Rivers
erosion of Belka hill region. Beyond Hanuman Nagar however, the sediment concentration
progressively reduces due to deposition of coarse and medium fractions. At Kursela where the Kosi
joins the Ganga, the average sediment concentration is only 24 percent of that at the gorge. This
progressive deposition causes great instability in the river (Godbole 1986).
13.6
SEDIMENT SIZE AND SLOPE
Garde et al. (1990) have analysed the data collected from three boreholes at different cross sections of
the now embanked Kosi. These bore holes were at the left, right and the center of leveed portion. This
size distribution is shown in Fig. 13.5. It can be seen that d50, d84.1 and d15.9 sizes are 0.25 mm, 0.37 mm
and 0.175 mm respectively giving geometric standard deviation sg =
F
GH
d84.1
d
1
=
+ 50
d50
d15. 9
2
I as 1.455. On
JK
the same figure are plotted data given by CWPRS, Pune. The Central Water Commission has divided the
entire reach of Kosi in four segments and the slope in each reach has been given as follows during 1982.
100
Left bank
Centre
80
Right bank
Percent finer
CWPRS data
60
40
20
0
0.06
0.08 0.10
0.2
0.4
0.6
0.8
1.0
d in mm
Fig. 13.5
Size distribution of bed material of the Kosi at section 63
2.0
396
River Morphology
Extent of reach (in km) below Chatra
Bed slope
0 – 42 km
42 – 68 km
68 – 134 km
134 – 160 km
0.001 400
0.000 716
0.000 450
0.000 110
The longitudinal section of the Kosi river as obtained in 1975 is shown in Fig. 13.6. It can be seen
that between Chatra and the barrage at Bhim Nagar the average bed slope is 9.38 ´ 10 – 4, between the
barrage and up to next 32 km downstream the average slope is 5.5 ´ 10– 4, while downstream for the next
64 km the average bed slope is 2.70 ´ 10 –4. The differences in the slopes between 1975 and 1982 are
evidently due to aggradation/degradation.
106
Chatra
98
90
9.38 ´ 10
–4
Bed Levels m
82
74
Barrage
5.50 ´ 10
66
–4
58
50
2.70 ´ 10
–4
42
Datum 34
0
16
32
48
64
80
96
Distance in km from Chatra
112
128
144
Fig. 13.6 Longitudinal profile of the Kosi
13.7
MORPHOLOGY OF THE KOSI
Investigators have opined that quite possibly, in the earlier times the Kosi joined the river Mahananda
through the present course of the river Parman near Araria in Purnea district. This view is supported by
the presence of long stretch of depression varying in width from 30 m to 60 m passing from Forbesganj
397
Morphology of Some Indian Rivers
side towards Araria. However, since 1736 the river has shifted towards the west through 112 km in 223
years. In this process, it has deposited sand over 7680 km2 land in Bihar and 1280 km2 in Nepal making
the land almost infertile. Positions of the Kosi during different years are shown in Fig. 13.7. The shifting
has always been towards the west and the average shifting rate has varied from 0.19 km/year to 1.8 km/
year with an average rate of 0.478 km/year at Purnea to Belhi. It can be seen in Fig. 13.7 that the river
has shifted westward by abandoning its old channels. Since the Kosi carries high sediment load, much of
the sediment gets deposited during the recession of the flood thereby choking mouths of some of the
channels. As a result, during the next flood the river activates a new channel which gets developed with
the passage of time. Observations indicate that when the Kosi was in flood, the water spread over 16 to
Fig. 13.7
Lateral migration of the Kosi river
398
River Morphology
32 km laterally. In the dry season, the river flowed in a number of channels; some of these were deep and
others shallow, indicating that the river was braided in nature. The flow velocity during flood used to be
so high in deep channels that a large animal such as an elephant could be washed down. The country
area looked like a series of islands. In 1883 there was apprehension that Kosi may suddenly change its
course and flow in the abandoned channels on the east. Shillingford in 1885 published a paper in the
Asiatic Society of Bengal and opined that the eastward movement of the Kosi would probably be
accomplished in one great swing and cause great loss to property and life.
Some probable reasons for the westward movement of the Kosi have been proposed. The one earlier
mentioned is the differential deposition of sediment during the recession of flood causing closure of
some channels and opening newer ones in the next flood. The second reason that is often quoted is the
general westward slope on the Kosi flood plain. Lastly, it is already mentioned that the Kosi plain and
adjoining areas are subjected to earthquakes and neotectonics that can cause this shift.
13.8
MANAGEMENT OF THE KOSI
To reduce the flood and sediment problems of the Kosi a number of expert committees have given their
recommendations a few among them being those of Inglis, K.L. Rao, Leopold and Maddock, Kanwar
Sain and Mitra. Along with these reports there were some review committees of Central Water
Commission of the Govt. of India. They generally agreed that for the proper management of Kosi, the
following recommendations be implemented.
1. Catchment area treatment for the Sun, the Arun and the Tamur tributaries; it is estimated (see
Carlson 1985) that the average rates of denudation of Tamur, Sun Kosi and Arun catchments
are 2.56, 1.43 and 0.51 mm/year, which are quite high and are the source of large sediment load
of the Kosi.
2. Construction of a high dam in Nepal which would arrest a large percentage of coarse sediment
and reduce aggradation downstream. It will also provide for flood control, power generation
and irrigation in Nepal.
3. Construction of a barrage at Hanuman Nagar near Bhim Nagar at a distance of 48 km
downstream of Chatra. This would reduce water surface slope between Chatra and the barrage
and thus reduce excessive bank erosion between Chatra and the Barrage.
4. Construction of afflux bunds upstream of the barrage and flood embankments downstream of
the barrage.
5. Construction of canals on both sides of the barrage for the development of Irrigation of 1.05
Mha. and power generation of about 20 000 kW.
The first two recommendations have not been implemented because these areas of catchment and where
a large dam was to be constructed lie in Nepal. The construction of the barrage was started in 1959 and
completed in 1963. Afflux bunds have been provided on the upstream of the barrage on the east and
west. Afflux bund on the east is 40 km long while that on the west is 14 km long which prevent
inundation due to ponding in non-monsoon season and afflux caused by the barrage obstruction during
the flood time. These are shown in Fig. 13.8. Some of the details of barrage are as follows.
Total length
= 1150 m
No. of bays at barrage
= 46 each of 18.3 m width,
399
Morphology of Some Indian Rivers
Fig. 13.8
Kosi flood embankments
No. of under sluice bays = 6 on the left and 4 on the right each18.3 m widths
Spillway gates
= 16 Numbers of 18.3 m ´ 6.4 m
The maximum discharge at barrage is about 14 000m3/s and minimum of 1000 m3/s. To provide
water for irrigation and generate waterpower, irrigation canals have been taken from the barrage. The
one on the east is known as Eastern Kosi main canal while that on the west is known as Western Kosi
main canal. Right from the beginning both these canals are facing severe problems of sedimentation.
This is illustrated by discussing about Eastern Kosi Main Canal whose head works has 32 tunnels
covering four bays of the barrage. The canal was designed to carry 424.5 m3/s; however subsequently a
sediment ejector was provided at 646 m downstream of the head regulator; hence the discharge at head
regulator was increased to 485 m3/s to provide for flushing water requirement for sediment ejector as
400
River Morphology
discussed by Sahai et al. (1980). The canal discharge decreases from 424.5 m3/s to 40.5 m3/s over a
length of 41.3 km. In the same distance the bed width changes from 189.7 m to 19.8 m, the full supply
depth changes from 3.5 m to 2.13 m and slope from 0.99 ´ 10 – 4 to 1.333 ´ 10 – 4. Also at 3600 m
downstream of the head regulator there is 4 m drop, which is used for generation of power. This canal
runs in heavy cutting from the head regulator to about 9.15 km downstream.
While the power house was under construction, the canal discharge was gradually increased from
44 m3/s in 1964 to 251 m3/s in 1969. Extensive sediment deposition took place in the 41.15 km reach;
the yearly sediment volume deposited being 0.14 to 0.25 Mm3. It has been found that both the sediment
excluder and ejector have failed to function properly. The Western Kosi Main Canal is also plagued with
similar problems (Sinha 1986).
Flood-Embankments
Construction of flood embankments was taken up in 1955 and was completed in 1959. These are 144
km long on the left bank and 123 km long on the right bank, and are designed for flood discharge of 24
000 m3/s which is a flood of about 150 year return period. The right bank embankment will be extended
up to Kursela except where the Bagmati and the Kamla join Kosi. The left bank embankment has been
extended up to Koparia, see Fig. 13.8. These embankments provide flood protection to 0.214 Mha in
India and 51,400 ha in Nepal.
Sedimentation studies have shown that upstream of barrage the bed slope changed from 0.00 061 to
0.00 042 between 1963 and 1968. It was also estimated (Chitale 2000) that between 1963 and 1970,
35.05 Mm3 of sediment was deposited in 10 km reach upstream of the barrage giving an average depth
of deposition of 0.40 m in eight years.
It has also been found that during 1963-1970 there was a general lowering of bed level downstream
of barrage for a length of 23 km. Further downstream there was tendency towards aggradation.
Earlier studies by Sanyal (1980) and others indicated significant aggradation in the lower reaches of
the Kosi. Concerned about the continuous aggradation in lower reaches of the embanked reach of the
Kosi, Ganga Flood Control Commission, Govt. of India referred the problem to University of Roorkee
which used HEC-6 1-D model to study aggradation by using Laursen-Madden relation for sediment
transport and Dx = 10 km, Dt = 10 days for non-monsoon and 30 days for monsoon periods. Table 12.2
gives the levee spacing at various sections downstream. The model was calibrated using 7 year’s data of
discharges and river cross sections for the period 1975-82 and then the model was run for the period
1984 to 2005, using discharge data generated using Thomas-Fiering model. The model indicated a rise
in the bed level by about 2.44 m with reference to 1984 bed levels bringing the water level within 1.37
m to 2.13 m of the top of the embankment near Nirmali. Hence, it was concluded that the primary reason
for aggradation was large spacing between the levees. Aggradation can be offset by either reducing the
spacing between levees, or by providing spurs. Some have suggested giving proper slope to the stream
in different reaches so that aggradation can be avoided; however the latter solution does not seem to be
practicable.
The morphology of the river-bed in the leveed reach from Gopalpur to Koparia has been studied by
Gohain and Parkash (1990) by field investigation and also by interpretation of black-white air photos
with a scale of 1:25 000. They have identified the following topographic levels and larger bed features.
401
Morphology of Some Indian Rivers
flood em
bankment
91
Eas
tern
69
r
rive
Ba
gm
63
ati
75
81
53
87
41
Barrage axis
33
Level 1 : Active channel course with low bars;
Level 2 : 0.5 to 0.9 m higher than water surface on level 1 during low flows; no vegetation,
submerges with a small increases in flow.
Level 3 : About 1 m higher than level 2, sparsely vegetated, submerged during high flows of flood.
Level 4 : Between 0.5 and 0.8 m higher than level 3, it comprises the surface the islands and banks.
These levels are best developed in the braided reach of the river. The Kosi with the artificial
embankments is a confined braided stream. Figure 13.9 shows braided reach downstream of the barrage.
Levels 2 and 3 are relatively unstable and are dissected intensively every year during the flood. Grass
and shrubs along the reach cover level 4. Extensive agricultural activities and settlements are seen on
this level and these are flooded when discharge at Barakshetra exceeds 8400 m3/s. Considering a
distinct change in the slope of flow duration curve at about 1000 m3/s. (see Table 13.2), it is interpreted
that levels 1 and 2 correspond to low flows in November–February period while levels 3 and 4
correspond to monsoon discharges. Gohain and Parkash found that there are a number of channels at
any section that can be divided into primary channels which are deep and carry water even at low stages.
Usually there are one or two primary channels. The sub-channels are defined as part of the river-bed
which has only bars with level 2, hence at high flow these get submerged.
Western flood embankment
Fig. 13.9
Braided reach in leveed portion of the Kosi river downstream of barrage
Channel Patterns
In the Zone 1 between Chatra and Karaya, a distance of about 20 km, the slope is 0.000 45 and one
primary braided channel is present. Zone 2 is from Karaya to Dumra, a distance of about 96 km. Here the
slope is 0.000 48. This is the main braided zone of the river, having two primary channels and a few
meandering channels on level 4. Zone 3 is a 40 km reach from Dumra to a few km upstream of Koparia
in which average slope is 0.0001. One straight channel of sinuosity 1.01 to 1.16 is present. Zone 4
extends for a distance of 160 km downstream of Zone 3 up to Kursela. Here the mean slope is 0.000 05
402
River Morphology
and the stream meanders all along its course. Point bars and sidebars are a common occurrence.
Abandoned channels with chute cutoffs and neck cutoffs are common in flood plain.
13.9
PRESENT DAY PROBLEMS OF THE KOSI
One of the major problems faced on the Kosi is breaching of sections of embankment almost every year
leading to huge maintenance cost. It is found that the deep channel takes a different course every year
and affects new reach of levees. Since it is very difficult to predict the behaviour using a mathematical
model, every year after the flood has receded, bed levels are taken at different sections and the bed in the
movable bed physical model is laid for the new condition. The model is then run for flood discharge to
identify the sections of the embankment that are likely to be attacked during the next flood season.
Protection works are undertaken on the basis of the above study as well as on the basis of advice of highlevel committee, which visits the site before the monsoon. The protection methods include direct
strengthening of embankment or construction of spurs. The physical model studies are carried out at
Central Water and Power Research Station, Pune (India).
The second aspect of concern is the continuing aggradation taking place in the major length of
leveed reach. Even though reduction of spacing between levees can reduce or stop aggradation, no
action has been taken. Aggradation can reduce if sediment is stored upstream behind a large dam;
however no serious effort is made in this direction also.
The third concern is about the malfunctioning of both the canals taking off from barrage, as a result
of which there is under utilization of the irrigation potential that has been created.
Also, water-logging problems have occurred in the Eastern Kosi command area and there are also
problems related to proper drainage behind leveed reach.
BRAHMAPUTRA
13.10
INTRODUCTION
The Brahmaputra is one of the largest rivers in the world and is known for its high floods and sediment
load, flood damages and instability. The river originates near Manasarovar at an elevation of about 5000
m. Within 160 km of this lake are also the sources of two other largest rivers in the Indian subcontinent,
namely the Indus and the Ganges. The Sutlej, a large tributary of the Indus also originates in this area.
Figure 13.10 shows the course of the river Brahmaputra, while Plate 2 shows the aerial view of the
Brahmaputra. The Tibetan portion of the Brahmaputra is known as the Tsangpo, it is called Siang and
then Dihang when it enters Arunachal Pradesh in India. The words Siang and Dihang mean the “big or
great river”. Brahmaputra means son of the God Brahma. It is interesting to know that Brahmaputra is
probably the only river having masculine name. Near the upstream border of Assam, just upstream of
Sadiya it is joined by two tributaries the Dihang and the Lohit. Here the river turns in the westerly
direction and flows through India passing along the cities of Kobo, Dibrugarh, Jorhat, Tezpur,
Guwahati, Dubri and Goalpara, and then turns towards south. After flowing for about 337 km the
Brahmaputra joins the Padma at Goalundo in Bangladesh.
The total length of the Brahmaputra up to the confluence with the Padma is 2 880 km out of which
1625 km is in Tibet, 918 km in India and 337 km in Bangladesh. Similarly the river has a catchment area
N
Tsangpo
Morphology of Some Indian Rivers
From manasarowar
Bhutan
Himalaya
N5
N1
Dhuri
N2
North lakhimpur
Barpeta
Goalpara
N8
N3
N4
Mangaldoi
N7
N6
Teepar
Sibsagar
Guwahati
Silighat
Embankments
hi
ai
S2
tk
S1
N
ag
a
pa
Meghalaya plateau
Fig. 13.10
S3
Jorhat
lls
India
S4
Dibrugarh
Gamirighat
Embankment
Scale
1 cm = 20 km
Nomenclature of the rivers
North bank
Soutth bank
N1 Manas
S1 Kapil
N2 Pagladiya S2 Dhanairi
N3 Pachnoi
S3 Dessng
N4 Jia bhargil S4 Lohit
N5 Ranganadl
N6 Jladhol
N7 Dihang
N8 Dibang
Brahmaputra river system along with the embankments
403
404
River Morphology
Plate 2 Aerial view of the Brahmaputra basin
405
Morphology of Some Indian Rivers
of 29 300 km2 in Tibet, 19 500 km2 in India, 4500 km2 in Bhutan and 4700 km2 in Bangladesh, thus
making a total of 58 000 km2 drainage area up to the confluence with the Padma.
As the Brahmaputra flows through India, large and small tributaries join the river both from the
north and from the south. In the entire course of its journey, the Brahmaputra receives as many as 22
major tributaries in Tibet, 33 in India and 3 in Bangladesh. The northern tributaries come from higher
rainfall region, pass through fragile Himalayas and have steeper slopes. In general, they carry high
sediment concentration comprising cobbles, coarse gravel and sand. These tributaries are braided and
have migrating channels over major portion of their lengths. Some of the important tributaries of the
north are the Subansiri, the Ranganadi the Jia Bhareli, the Sankosh, the Pagladiya and the Manas. The
tributaries on the south bank emerge from comparatively lower levels from Naga-Patki, Khasi and Garo
hill ranges and flow towards north or north-west at flatter slopes. These tributaries have deep
meandering channels and they carry relatively finer sediment at smaller concentrations. Some of the
south bank tributaries are the Lohit, the Buri Dihing, the Desang, the Kopili and the Dikhu. These are
shown in Fig. 13.10. It may be mentioned that the Brahmaputra is closer to the hills on the south
probably because the river has been pushed southwards during the past because of sediment deposition
on the northern side. Another characteristic that is worth noting is that in general, the north bank, at
many places is at a higher elevation than the south bank by three to ten meters as noted by Baruah
(1969). The Brahmaputra valley width has a minimum value of 60 km and an average value of 86 km,
while the river width varies from 15 to 19 km. Within India the Brahmaputra is braided for most of its
length except where its width is restricted and the river is stable with well-defined nodal points. Such
restrictions in width occur at a number of places; these locations and average width in km are listed in
Table 13.4. These constrictions in the channel would create backwater and changing water surface
profile along the river, thereby causing tendency towards aggradation especially for medium flows. At
other places the river width varies from 5 000 m to about 19 000 m. Typical cross sections at Pandu and
Pancharatna where the river is constricted and at Jogighopa where it is much wider are shown in
Fig. 13.11.
Table 13.4
Location
Murkong - Selek
Near Dibrugarh
Near Dikhumukh
Near Helem
Silghat
Near Tezpur
North of Dihang
Downstream of Laterisuti
Mirkhameri
Guwahati
Near Pandu
Hathimura
Jogighopa
Chandor Dinga
Constrictions in the Brahmaputra (Baruah 1969)
Total width (km)
1.92
2.08
1.60
2.0
2.56
2.40
1.36
2.56
2.56
1.44
0.90
1.15
1.36
2.00
3.00
Width of perennial channel (km)
0.16
0.80
0-.48
0.72
0.32
1.76
1.04
1.36
0.72
0.72
1.15
0.90
1.12
1.12
0.56
406
River Morphology
41
Elevation (m)
38
35
32
29
26
23
20
0
500
1000
1500
2000
2500
Chalnage (m)
Cross Section of Brahmaputra at Pancharatna
60
Elevation (m)
55
50
HFL = 47.40 m
45
40
35
30
25
0
500
1000
1500
2000
2500
3000
3500
Chalnage (m)
Cross Section of Brahmaputra at Pandu
38
HFL = 36.12 m
Elevation (m)
36
34
32
30
28
26
24
22
0
1000 2000 3000 4000 5000 6000 7000 8000
Chalnage (m)
Cross Section of Brahmaputra at Johlghopa
Fig. 13.11 Typical cross sections of the Brahmaputra
407
Morphology of Some Indian Rivers
13.11
RIVER CHARACTERISTICS
River Slope
The longitudinal profile of the Brahmaputra as given by Goswami (1985) is shown in Fig. 13.12. The
slopes of the river prior to 1950 and in recent times are given by Baruah (1969), and by WAPCOS
(1993) respectively. These are listed below.
Range
Slope
Kobo to Dibrugarh
Dibrugarh to Neamati
Neamati to Silghat
Silghat to Guwahati
Guwahati to Goalpara
Goalpara to Dubri
Reach between Kobo to Dubri
Reach within Bangladesh
5000
0.000 300
0.000 182
0.000 135
0.000 115
0.000 1136
0.000 105
0.000 147
Reduces from 0.000 09 to 0.000 03
Manasarowar
4000
China
Elevation m
Shigatse
Tesla dihong
3000
Pe
2000
1000
Enters India
Pasighat
Enters
Bangladesh
Pandu
0
28
24
20
16
12
Distance in 100 km
8
4
0
Fig. 13.12 Longitudinal profile of the Brahmaputra bed
Recent alluvial deposits comprising clay, silt, sand and shingle cover the major part of the
Brahmaputra valley. The average thickness is about 300 m. Drilling at Pasighat bridge and for oil wells
in Ningru plains of Arunachal Pradesh have provided useful data about the thickness and nature of
alluvial deposits. These borings show repeated sequences of clay, fine sand, coarse sand, coarse sand
with cobbles, pebbles and boulders. Figure 13.13 shows the borehole data on the Dihang near Pasighat,
408
River Morphology
Pictorial
representation
R.L. in meters
155.190
153.190
Strata description
Filled up sand
Sandy soil mixed with gravel and boulders
150.190
60 to 70% of boulders in compacted red soil
148.190
70 to 80% Boulders (1500 mm to 3000 mm)
144.190
Boulders medium and large size (300 mm 3000 mm)
140.190
139.190
138.190
137.190
Boulders of size upto 1200 mm
Boulders of size upto 800 mm
Silt and sand mixed gravel
Silt sand and shingles (size about 63 mm)
129.800
Silt sand and gravel (size 50 mm to 5000 mm)
128.300
Silt sand and boulders
(size between 800 mm to 1000 mm)
127.900
Boulders (size between 600 to 1000 mm)
Fig. 13.13
Bore log data for bed material on the Dihang near Pasighat
Morphology of Some Indian Rivers
409
which illustrates the stratified nature of sediment deposits. Presence of coarse fractions would be helpful
in controlling the scour around hydraulic structures such as bridge piers, as well as excessive
degradation due to formation of an armor coat. Bed material in the Brahmaputra river mostly comprises
silt and fine sand. Goswami (1985a) has reported the size distribution of bed and bar material in the
Brahmaputra river at Dibrugarh, Salmara, Hatimura, Guma, Goalpara and Pandu. The median size of
the samples varied from 0.03 mm to 0.30 mm; such a large variation is probably due to the fact that some
samples were collected on the bars while others in the depressed portions. Recently several more
samples were collected by WAPCOS (1993) over a long stretch. It was found that median size of the bed
material varied from 0.223 to 0.085 mm with an average of 0.16 mm and the standard deviation varied
from 1.294 to 2.043 with an average of 1.476. The average size at Pancharatna was 0.138 mm with the
standard deviation of 1.52. Pancharatna is between the outfalls of Manas and Dubri. At Pancharatna
10% of the material is finer than 0.06 mm and only 2% of material is coarser than 0.40 mm.
Normally the median size of the sediment decreases in the downstream direction due to abrasion
and sorting; however, such tendency is not noticed in the case of the Brahmaputra. There is no
systematic reduction of median size of bed material along the river length. This is attributed to the
number of tributaries joining Brahmaputra on its way and mixing of their bed material with that of the
Brahmaputra. Also abrasion is unlikely to be unimportant in the Brahamputra since most of the
sediment moves as suspended load.
The bed material of the Brahmaputra river is composed mainly of varying proportions of fine sand
and silt, with only occasional presence of small amount of clay, less than 5% (Goswami, 1985). Particle
size distribution of bank material at Dibrugarh, Hatimura and Dubri, given by Goswami shows that sizes
range from 0.001 mm to 0.20 mm with d50 between 0.05 to 0.15 mm. The vertical profiles generally
include two distinct parts – a relatively fine-grained top stratum and a coarser substratum. The coarse
sediments probably represent channel bars and islands accreted laterally through wandering channel,
and the finer sediments represent vertical accretion from over bank flow.
Bank Instability
The bank line of the Brahmaputra is extremely unstable for most of its length. Bank failures are rampant
and seem to be function of the hydraulic character of the flow and the engineering properties of the bank
material. According to Coleman (1969) several factors are responsible for short-term changes in the
bank line. These are
i) rate of rise and fall of water level;
ii) number and position of channels active during the flood stage;
iii) angle at which the talweg approaches the bank line;
iv) amount of scour and deposition that occurs during flood;
v) formation and movement of large bed forms;
vi) cohesion and variability in the composition of bank material;
vii) intensity of bank sloughing; and
viii) relationship of abandoned river courses to present-day channel.
Shear failures in the upper bank material seem to be by far the most widespread model of bank
failures. This is caused either by undercutting of the upper bank material by the current during high
flows, producing an over-hanging cantilevered block which eventually fails, or by over steepening of
410
River Morphology
the bank materials due to migration of talweg closer to the bank during falling stages. High moisture
content, low percentage of clay and good sorting of the bank materials in the Brahmaputra make them
highly susceptible to erosion by the river.
13.12
SEISMICITY AND LANDSLIDES
Brahmaputra basin is located in a geodynamically unstable region characterized by active faults and
continuing crustal movements. According to plate tectonics the Indian plate moving in the north –
northeasterly direction is under thrusting the Eurasian plate and is causing deformation and instability in
the Brahmaputra basin. It is believed that many E-W and transverse faults that dissect the Meghalaya –
Mikir blocks are active and are responsible for high seismicity. In the 60 years prior to 1980, over 450
small and large earthquakes have taken place in this area. Their distribution is as follows
Richter magnitude
No. of earthquakes
8 or greater
7–8
6–7
5–6
3
15
167
270
Major earthquakes in this region appear to be separated by quiescent periods of about 30 years
(Goswami, 1985). Among the earthquakes that have taken place in the region, the two most severe
earthquakes were those of 1897 and 1950. The 1897 earthquake of Richter magnitude of 8.7 had its
epicenter in Shillong plateau. It was felt over 450 000 km2 and its effects were noticed even after ten
years. The entire lower portion of the basin up to Goalpara district was affected. The 1950 earthquake of
intensity 8.7 occurred on 15th August and its epicenter was at 50 km north east of India’s border. Its
effects are very well recorded by Gee (1951). The following description is taken from his paper
“Many hills, a few hundred meters in height were shattered from top to bottom, their sides
crushing down into the valley below. Rivers, both small and large became blocked by huge
dams of rock, earth and vegetation, and in cases ceased the flow. Even the Subansiri, which had
swollen with monsoon rains practically dried for few days. Then came the bursting of dams,
one by one in some cases, in other cases simultaneously. Vast flood waves surged down the
valley carrying everything below them.
In some cases lakes thus formed in the hills by these temporary dams endured for longer period.
Thus at the head waters of the Tidding river, a tributary of the Lohit, a lake nearly 6.5 km in
length and 0.40 km wide was formed and lasted throughout the winter of 1950 and spring. It
disappeared in 1951 monsoon. Seventy five of the hills in 27 000 km2 area were mutilated by
land slides. About half of the landslides appeared to have occurred on the day of the earthquake
and remaining subsequently when heavy rain occurred.
The Dihang became so silted up that its tributaries, the Jigiapani, Deopani and Ghurmura could
not enter it. These were diverted by the newly formed silt banks of the Dihang up to the town of
Sadiya. Lohit was silted up to the extent of one to two meters while Brahmaputra was silted up
to two to three meters at Murkong Selek and at Dibrugarh. This earthquake had radically
411
Morphology of Some Indian Rivers
altered the slope of Brahmaputra, stopping the flow temporarily and bringing about flooding
and rapid accumulation of enormous volume of sediment in the channel. The low water level
rose by as much as 3 m at Dibrugarh as a result of this earthquake”.
The sediment deposited in the river as the result of the earthquake moved downstream at a low
velocity as sediment wave, and its effects were noticed even in 1971.
In addition to the tectonic activity, neotectonic effects have also been noticed as reported by Valdiya
(1999). Leveling observations made three times during 1910-1976 have indicated that blocks of
Guwahati-Dergaon section have been consistently rising up at the rate of 0.30 mm to 4.5 to 31 mm per
year at Dergaon (30 km west of Jorhat). Similar uplifting activity is noticed in Guwahati-Goalpara
sector. Such movements gradually change the slope of the stream and can cause aggradation or
degradation.
Along with the earthquake, landslides also influence significantly the morphology of alluvial
streams. Landslides in the Himalayan region of India occur during the monsoon season. Further, it has
been observed that reactivation of old Himalayan landslides, invariably occurs during the monsoon
season after heavy and/or prolonged rains. It has been observed that in all those cases of large landslides
in Himalayan region, the rainfall ratio defined as
ER =
Average 24 hour, 2 year rain fall
Average annual rainfall
is greater than 0.08. In fact ER greater than 0.08 and earthquake magnitude greater than 7.0 have
produced all the large landslides in this region, see Garde and Kothyari (1989). Figure 13.14 shows
map-showing landslide – prone regions of India, while Fig. 13.15 shows locations of epicenters of high
magnitude earthquakes. Foothill region of Arunachal Pradesh is characterized by tightly folded mega
structures of alternate stratified layers in which building up of pore pressure is responsible for slope
failures. As mentioned earlier, such land slides brought down heavy debris during 1950 earthquake
resulting in stream blockages, stream diversion and aggradation.
13.13
CLIMATE AND HYDROLOGY
The annual rainfall in the Brahmaputra catchment varies from 100 cm to 400 cm; the map showing
isohyets is shown in Fig. 13.16. Most of the rainfall occurs during June to September. The eastern part of
the catchment experiences pre-monsoon thunder-showers during March-May period. Of the total annual
rainfall, about 60 to 70 percent falls during the monsoon period, while 40 to 30 percent occurs during
pre-monsoon season. Only a small percentage of rainfall occurs during the winter. Analysis of storms
has indicated that majority of storms are of 2, 3 or 4 days duration.
Natural vegetation in the Brahmaputra basin varies with altitude from tropical evergreen and mixed
deciduous forests within the valley and foothills to alpine meadows and steppes in the higher ranges,
and in Tibet about 20 percent of the Brahmaputra valley is forested.
Discharge data are collected at 33 stations on the north bank tributaries, 58 on the south bank
tributaries and about 60 stations on the main river where gauge discharge or gauge-discharge-sediment
measurements are made.
412
River Morphology
Devastating landslide
Landslide – pone areas
Earthquake of magnitude between 7.0 to 8.0
Main central thrust
Main boundary thrust
Earthquake of magnitude more than 8.0
36°
ER = 0.085
Srinagar
Shimla
32°
Dehradun
ER = 0.105
28°
ER = 0.08
Delhi
Gangtok
ER = 0.115
Lucknow
ER = 0.09
24°
68°
72°
Fig. 13.14
76°
80°
84°
88°
92°
Imphal
96°
Land slides-prone areas in India (Garde and Kothyari 1989)
36°
Fault
Ridge
Earthquake of magnitude 5.0 to 6.9 on Richter scale
Earthquake of magnitude 7.0 to 8.0 on Richter scale
Earthquake of magnitude more than 8.0
on Richter scale
32°
28°
24°
68°
72°
76°
80°
84°
88°
92°
Fig. 13.15 Locations of epicenters of high magnitude of earthquakes in India
96°
413
Morphology of Some Indian Rivers
N
Bhutan
West
Bengal
350
300
0
50
250
200
250
180
s
A
m
a
s
350
250
Brahmaputra
nd
la
aga
25 300
0
0
14
500
400
300
300
30
250
0
2 0
150
Burma
16
0
18
0
N
0
Bangladesh
400
350
300
Arunachal
0
40
35000
3
0
35
20 0 20 40 60 80 100
km
250 200
Fig. 13.16 Isohyetal map of Brahmaputra valley and adjoining highlands
Rao (1979) has prepared a diagram showing contribution of mean annual runoff by different
tributaries to the Brahmaputra and variation of mean annual runoff along the Brahmaputra. This is
shown in Fig. 13.17, which shows that contribution of the Subansiri, the Jia Bhareli, the Manas and the
Sankosh from the north, and the Buri Dihang, the Dikshu, the Dhangiri, and the Kopili from south are
significant.
Regional flood frequency approach has been used by Jakhade et al. (1984) who found that the
Brahmaputra basin rivers can be grouped in two hydro meteorologically homogenous zones A and B.
Broadly zone A covers Manas to Dihang in the north and Burhi Dihing in the south. Zone B covers all
the southern tributaries in the valley below Burhi Dihing, Sankosh in the north and the main river below
Pasighat. Goswami (1985) has analysed annual flood discharge data at Pandu for the years 1971-1974
using log-Pearson type III distribution. His analysis gives the mean annual flood at Pandu as 51 156 m3/
s with a recurrence interval of 2.1 years while bankful discharge which just overtops the banks has the
magnitude of 34 940 m3/s with a recurrence interval of 1.02 years. It may be mentioned that the
maximum observed flood occurred in 1962 and was 72 784 m3/s while minimum observed discharge is
1757 m3/s. Flood frequency analysis carried by WAPCOS (1993) has given floods of 25, 50 and 100
years return period at Pandu as 65 692, 68 964 and 72 028 m3/s respectively. It needs to be mentioned
that difference in water levels between 25 and 100-year floods is less than 1.0 m and hence a large area
gets flooded even with floods occurring once in 2 or 3 years.
Analysis of flood data on the Brahmaputra has also shown that the magnitude and time of
occurrence of maximum flood in the tributaries play an important role in maximum discharge and its
occurrence at various places along the Brahmaputra. The depth of river, measured from the top of the
414
River Morphology
Sankosh (O)
16556
Manas (85)
32258
Goalundo
Dhubri
Dhansiri (270)
2295
Jia Bhareli (338)
28890
Subansiri (430)
57296
Dihang
186290
Tezpur
Kobo
589000
510450
Jogighopa
Bangladesh
India
359241
Guwahati
Pandu
Bhurbandka
Dibang
39085
268936
Bessamara
Dikshu(505)
3511
Kopilikalang(220) Dhansiri(420)
6084
8640
Dibru
garh
Lohit
46564
Buri Dihang(540)
10996
Disang(515)
5010
Notes: Figures represent average annual runoff in Mm
Figurehs in bracket indicate chainage from India–Bangladesh border upstream
Fig. 13.17 Average annual runoff of the Brahmaputra (Rao 1979)
River
Ganga at Harding Bridge (India)
Godavari at Dhauleshwaram (India)
Brahmaputra at Pandu (India)
Padma at Chandpur (Bangladesh)
Amazon at Obidos (Brazil)
Mississippi at Columbia (U.S.A.)
Q max/A m3/s km2
0.067
0.280
0.297
0.114
0.048
0.03
bank varies from 4.6 m in a crossing near Dibrugarh to approximately 30 m near the mouth of the Manas
river. At the latter location, the river is confined to a single channel. Low water depths in bends where a
single channel exists vary from 12 to 21 m. In passing it may be mentioned that the ratio of maximum
observed discharge per unit catchment area is quite large in the Brahmaputra river as compared to other
rivers in the world as can be seen from the above table.
13.14
RESISTANCE TO FLOW AND SEDIMENT TRANSPORT
Resistance analysis has been carried out in a given reach at Pancharatna gauging station. Manning’s n
value is found to vary from 0.05 to 0.03 for low flows and it reduces 0.04 – 0.02 for high discharge of the
order of 30 000 m3/s. The depth at the deepest section at Pancharatna is about 15 m for a discharge of
around 35 000 m3/s. WAPCOS (1993) had used different methods of predicting resistance and found
that Garde–Ranga Raju and Engelund’s methods give better results than the methods of Sugio and
Paris. Since Manning’s n values are much greater than 0.011 obtained by using Strickler’s equation, it
415
Morphology of Some Indian Rivers
can be inferred that the bed is covered with dunes for low and medium flows. Some measurements were
made in 144 km reach upstream of Dubri during the month of May 1989. The data indicated bed
undulations of height about 8 m occurring at a wavelength of 8 to 10 km. Superimposed on these were
smaller undulations or bed forms. Coleman (1969) has reported some echo-sounding measurements on
the Brahmaputra in Bangladesh at Sirajang, Nagabari and Aricha throughout one flood season.
Coleman observed ripples (height a few cm to 30 cm), mega-ripples (height ranging from 0.30 m to 1.5
m and length ranging from 3 m to over 150 m), and dunes (height ranging from 1.5 m to 7.5 m and wave
length ranging from 40 m to 480 m). He also found sand waves with heights ranging from 7.5 m to 15 m
and wave length ranging from 180 m to 900 m; their maximum speed was about 30 m per hour.
Relatively high values of n at medium and large flows in the Indian portion of the Brahmaputra indicate
the presence of fairly large bed-forms. The larger n values at very low flows are due to formation of
islands in braided regime.
Most of the suspended sediment measurements are carried out at 0.6 depth and concentration there
is taken as the average suspended sediment concentration. This is divided into three size fractions: fine,
medium and coarse. The assumption of taking concentration at 0.6 depths as the average concentration
may be satisfactory for fine sediment, but it can underestimate sediment load in medium and coarse
fractions. Usually suspended sediment discharge Qs is related to the corresponding water discharge and
a relation of the form Qs = a Qb established for each river. Using mean monthly values of Qs and Q,
Goswami (1988) found b to be 1.78 and 2.53 at Pandu for 1971-76 and 1977-79 data respectively. The
analysis of suspended load indicate that the river carries relatively more fine material compared to
medium and coarse size fractions. The percentage of fine sediment varies from 70 to 90. Using sediment
measurements at Pandu for 1955 to 1980, Goswami (1985) found the sediment yield at Pandu to be 804
tons/km2/year while at Bahadurgarh in Bangladesh it is 1128 tons/km2/year. The major tributaries
contributing high rates of sediment yield are given in Table 13.5 along with their catchment areas.
Table 13.5
Tributary
Dibhing
Subansiri
Ranganadi
Jia Bhareli
Dhansiri (N)
Puthimari
Pagladiya
Beki (Manas)
Lohit
Buri Dihing
Erosion rates at the tributaries of the Brahmaputra (Goswami, 1985)
Catchment area A km 2
12 120
27 400
3077
11 300
1657
1787
38 300
36 300
22 077
4923
Sediment yield in Tons/km2/year
3765
959
1569
4721
463
2887
1883
1581
1960
1129
It can be seen that the tributaries from the north bank have almost three times the sediment yield of
south bank tributaries. This is due to different geologic conditions, rainfall and the character of
sediment. Similarly, for the catchment of the size of the Brahmaputra, its sediment yield is three to four
times that of many rivers of the world.
416
River Morphology
No bed-load measurements have been made on the Brahmaputra. However, some efforts have been
to estimate it by Goswami (1988) using well-known bed-load equations of Schoklitsch, Kalinske,
Meyer-Peter and Müller, Einstein, and Bagnold. It may however be mentioned that these equations have
been developed using very coarse material whereas the bed material of the Brahmaputra is very fine.
Hence the results are questionable. WAPCOS (1993) has used total-load equations of Samaga, Ranga
Raju et al. and Laursen and computed total load; knowing measured suspended load, ratio of QB/QS was
obtained for various discharges at Pandu. The average of these results indicate the following:
Q m3/s
3600
9600
18 800
36 000
QB/Q s
0.053
0.501
0.189
0.087
Even though the results are erratic, above analyses of Goswami and WAPCOS indicates that, the
assumption that the river carries 10-15 percent of suspended load as bed-load may be a good
approximation.
On the basis of yearly sediment transport rate, estimates have been made of the annual depth of
erosion in different catchments. These are tabulated below.
River
Amazon
Mississippi
Yangtze
Ganga
Brahmaputra
Kosi
Average erosion rate in mm/year
0.09
0.07
0.33
0.57
0.41 to 0.81
1.88
It can be seen that average rates of erosion are quite high in the Kosi and Brahmaputra catchments.
Goswami (1988) studied the discharges which carry significant amount total suspended load and found
that flow events which occur one day or more in a year carry on the average 65.5 percent of the total
suspended load, while flow events which occur 7.0 days in year carry on the average 31.25 percent of
total suspended load. Thus he showed that maximum flows do not necessarily carry the maximum
percent of yearly sediment load.
Information about flow duration curve and sediment transport rates can be utilized to determine the
characteristic discharges for the stream. It has been mentioned that bankful discharges at Pancharatna
and Pandu are approximately 30 000 m3/s and 27 000 m3/s respectively while the mean annual
discharges at these stations are 16 154 and 15 756 m3/s. The bed generative discharge at Pancharatna is
estimated to be 56 000 m3/s.
13.15
PLAN-FORMS
As mentioned earlier, for the major part in India the Brahmaputra is braided. The configuration of the
channel undergoes major changes in response to variations in the flow and sediment load. During
Morphology of Some Indian Rivers
417
November to March when the river discharge is low, the channel is highly braided with a number of bars
and islands. After April-May when discharge starts increasing these islands and bars get submerged and
river looks straight. It is interesting to note that when low flow data are plotted on t * vs. WS/D criterion
of Agarwal, these data indicate braided plan form, while t * vs. WS0.2/D criterion of Kishi indicates
presence of multiple bars. In general, in the case of braided rivers, the number of channels formed by
islands depends on width to depth. Figure 13.18 shows the braided pattern at Dibrugarh in 1928, 1976
and 1987. The changes in the channel patterns and their numbers as well as changes in islands in their
shape and number may be noted. The braiding index defined by Brice as the ratio of twice the sum of
lengths of bars and islands in a reach to the length of the reach measured mid-way between the banks has
been calculated at Dibrugarh and upstream of Palasbari by Goswami (1988) and found to be between 5
and 7 indicating the highly braided nature of the river.
Some of the islands formed are small and they get submerged and changed as flood level rises; new
or modified islands are formed during the recession of floods. However, some islands become
permanent and can grow due to vegetation grown on them. Majule is one such and is the largest island
in the Brahmaputra, north of Jorhat at the confluence of the Subansiri with the Brahmaputra. The island
is about 80 km in length along east-west direction 10 to15 km in north-south direction, and is habitated
by 140 000 people. Originally it was 1245 km2 in area prior to 1950 earthquake and due to continuous
erosion its area was reduced to 924 km2 in 1971 and to 880 km2 in 1993. This is a matter of great
concern to engineers (see NIH, 1998) and efforts are being made to control erosion.
Another aspect of changing islands is the change of talweg of main branch of the braided river with
change in flow. This change is large during medium flows, relatively little during high flows, and very
erratic during the falling stages i.e. during November to March. This is very important when the river is
used for navigation. This aspect of wandering of the talweg and its relation to bank erosion has been
discussed by Coleman (1969). With the Brahmaputra carrying heavy load of sediment, bed condition
changes rapidly and drastically with change in flow. Deposition of sediment at one place causes erosion
at other place and triggers changes in talweg from one position to another within the bank-line. Study of
stage and position of talweg at Sirajgang (Bangladesh) indicated that during the rising stage the
amplitude of movement of the talweg is large, as much as 3000 m and the movement is gradual; during
the peak-flows it is relatively small and the talweg remains more or less stable. However, during the
falling stage the talweg movement is irregular and sudden in fashion.
During low water stage the main channel in a braided river, which carries large portion of the
discharge, is commonly situated near one of the river-banks and is slightly curved moving from one
bank to other. During the rising stage when the flow increases rapidly, while the flow tends to follow the
deep channel, it is not able to develop rapidly to accommodate increasing flow and hence there is
tendency for bank-cutting and sloughing. This action helps migration of the talweg in lateral direction.
Bank sloughing depends on the nature of the bank material. In as much as the nature of bank material
varies along the length, sloughing is not uniform; hence the erosion of the banks is different at different
locations thereby changing the river path. The shifting of the talweg is also influenced by the movement
of sand bars and mid-channel islands. This occurs most frequently during the falling stage and the shift
is erratic and sudden. Shifting of the talweg close to the bank causes bank erosion.
418
River Morphology
N
1928
Sonarighat
Dibrugarh
Bur
i dih
ang
r
(a)
1976
0
5
ru
jan
Scale
rive
Dib
Mai
10
rive
r
rive
r
20 km
N
Sonarighat
Dibrugarh
ang
Mai
jan
r
0
(b)
1987
5
10
rive
r
er
Scale
riv
rive
bru
i dih
Di
Bur
20 km
N
Sonarighat
Dibrugarh
Bur
i dih
(c)
Fig. 13.18
ang
rive
r
Ma
ija
Scale
0
5
10
20 km
Di
nr
bru
ive
r
riv
er
Plan form of the Brahmaputra near Dibrugarh in years 1928, 1976 and 1987
419
Morphology of Some Indian Rivers
13.16
FLOODING AND FLOOD PROTECTION
Floods in Assam valley seem to have increased in frequency and intensity since 1950 earthquake when
the hills were mutilated to a great extent. Floods are caused due to heavy rainfall in the mountains and
valley, and melting of snow in the mountains. Eighty to ninety percent of rainfall occurs during May to
September during which time snow also melts. Considerable construction activity and deforestation
brings down large quantities of sediment along with the flow which is responsible for aggradation in
some reaches. The valley being wide and flat, an increase of 1 m water level during normal annual flood
inundates large areas of flood plain. Encroachment on flood plain and islands accentuates the flood
problem. Based on the analysis of satellite imageries it is found that during 1988 flood, flood plain 10 to
50 km in width on northern side and 5 to 30 km wide on southern side was inundated. When the
Brahmaputra level is high the tributaries are not able to drain into the main river and cause inundation in
their valleys due to backwater effect. Handique and Borgohain (1991) have given the statistics of flood
damage in Assam valley as indicated below.
Table 13.6
Flood damages during 1953-1989 in Assam valley (Handique and Borgohain, 1991)
Total area affected in M ha
Crop area affected in M ha
Damage to crops in crores Rs
Total damage to crops, houses and public utilities in crores Rs
Lives lost
Maximum (1988 figures)
3.823
334.10
663.84
232
Average
0.97
26.67
54.67
38
Another effect of floods is erosion of banks which causes embayment. This sometimes continues till
it joins the neighboring tributary. This results in shifting of outfall of the tributary. This is particularly
true for south bank tributaries, since slope of tributaries on the south is flatter than that of tributaries on
the northern side of the Brahmaputra river.
To protect certain areas from flooding embankments (or levees) have been built on the northern and
southern side of the river. Between 1954 and 1989 embankments over a total length of about 940 km of
embankments have been constructed at critical reaches on both sides, these are shown in Fig. 13.10.
These levees have top width ranging from 2.5 to 4.6 m, river side slope 3:1 and country side slope 2:1
and 8:1 with berm. Usually the free board is about 1.5 m. These levees are subjected to erosion and
breaches at many places during high floods necessitating frequent costly repairs, and provision of spurs.
Over 300 breaches have occurred since the levee system was established. Since earlier embankments
were constructed with inadequate data, these had to be raised and strengthened as the data on higher
floods were obtained. Some towns also had to be protected by dykes. The present day system of
embankments provides protection to about 14 000 km2 of about 30 000 km2 of the total flood prone area.
Many times the embankments have been cut by lateral erosion, not at the highest flood but at
somewhat lower stages and hence the low lying areas have been flooded even though the level of water
in the river is below that of the embankment. As mentioned earlier, floods in the tributaries are also
caused when the Brahmaputra river flows at a higher level than the tributaries thereby causing
backwater in them.
420
River Morphology
To overcome the problems of flood control, bank protection, maintaining navigation channel for
river commerce and to protect cities, towns and other man-made structures, various types of works have
been constructed. These are (see Weller, 1970).
1. Bandals: These are made from bamboo poles driven 1 to 2 m into river bottom and spaced at 0.5
to 1.0 m center to center. Mats of woven bamboo 0.8 m ´ 0.5 m are placed on bamboo poles
near the water surface. Bandals are inclined 30° – 40° with current. These slow down the
current and induce deposition, direct the flow into proposed channel and provide adequate
depth for navigation.
2. Bottom Panels: Bottom panels are structures arranged on the bottom at such angles to flow so
as to divert bottom current out of existing channel and induce accretion in that area. Each panel
is composed of corrugated metal sheets 1.0 m high and 4 to 5 m long. They are placed against
bamboo poles driven 0.6 to 1.0 m apart.
3. Bamboo Palisading: this is composed of a row of bamboo poles 7.5 to 10 cm in diameter placed
closely together and driven 1.2 to 1.5 m into the river bed and 1.8 to 2.4 m of bamboo extended
above the bed. This structure is strengthened by split bamboo placed horizontally at 0.3 m apart
and tied to the vertical bamboo poles with wire. The structure is also adequately braced. This is
placed immediately offshore and approximately parallel to the bank to be protected.
4. Bamboo spurs.
5. Tree spurs.
6. Anchored trees.
7. Tree Branch Revetment: This is a method of bank protection in which a mattress of tree
branches is placed against the bank to arrest erosion. Three or four branches of trees each 3.0 to
3.6 m long are tied together by wire and weighted with stones placed in sacks. This assembly is
anchored to the bank with wire ropes and sunk to the river bottom. Other bundles are placed,
each over lapping the last until the line of branches is extended from deep water to the bank.
8. Floating rafts and cages made from bamboo.
9. Permeable screens made from bamboo.
10. Timber and stone spurs.
11. Stone revetment in which 15 to 25 cm diameter crushed stones are placed with a thickness of
0.5 to 0.6 m on 1 V: 1.5 H slope.
Figure 13.19 shows bamboo porcupine spur, permeable pipe spur and RCC porcupine screen used
on the Brahmaputra.
13.17
DRAINAGE OF HINTER LANDS
Because of inadequate hydrologic data in the earlier times, adequate numbers of sluices have not been
provided in the embankments as a result of which there occurs drainage congestion in some areas,
because the natural drainage from protected areas is cut off. It may also be mentioned that physiographic
features of the region as a whole are responsible in causing, at least partly, widespread floods. The valley
is surrounded on all sides by hills and mountains with only one inadequate outlet near Dubri though
which the entire discharge of the Brahmaputra must pass. The rivers in the region are also marked by the
absence of lakes that exercise moderating influence on floods.
Morphology of Some Indian Rivers
Fig. 13.19 Some river training structures on the Brahmaputra
421
422
River Morphology
13.18
RIVER BED CHANGES IN BRAHMAPUTRA
Bed level changes in the Brahmaputra have been studied by different methods. Panchang (1964) plotted
the yearly-observed low water level and observed flood level at Dibrugarh for the period 1912 to 1963,
see Fig. 13.19, on which he also indicated the occurrence of earthquakes of moderate and severe
intensity. WAPCOS (1993) report extended the range of data up to 1966. This figure clearly shows the
gradual rise of high flood level; however since these levels are for different flood discharges, one has to
examine the trend of yearly lowest water levels. Since daily low water stages for the season are believed
to be comparable from year to year the same can be taken as a reflection of river bed from year to year.
This curve in Fig. 13.20 shows lowering of bed during 1914-1918 at the rate of 143 mm/year, 1918-1922
period shows gradual aggradation of bed at the rate of 210 mm/year. Similarly during 1947-51 there is
rapid aggradation at 832 mm/year. These changes are partly due to occurrence of earthquakes in the
region and passage of bed-wave in the downstream direction.
The other approach is based on sediment balance using continuity equation for sediment, according
to which during a given time
RSInflow of sediment UV + RSInflow of sediment fromUV - RSOutflow fromUV = RS Net storage or UV
T from upstream W T in between tributaries W T the reach W Tloss of sedimetnW
This method was used by Goswami (1985); his studies have indicated that during the period study
1971-1979, the Bessamara–Burabandha, and the Pandu–Jogighopa reaches have undergone excessive
aggradation, while the Ranaghat–Bessamara and the Bhurabandha–Pandu reaches have experienced
some degradation. WAPCOS (1993) had also collected the cross-sectional data at 65 stations along the
length of the Brahmaputra for the period 1957-1989. On the basis of the analysis of these data WAPCOS
concluded that there was no significant deposition or erosion in different reaches; however the erosion
Earthquake with strong intensity felt in Assam
106
Earthquake with mild intensity felt in Assam
Yearly observed highest W.L.
Water level m
104
100
(1951 - 66)
y = 112.37 + 0.058x
(1931 - 66)
y = – 0.44 + 0.0536x
102
Yearly observed lowest W.L.
98
96
1910
1915
1920
1925
1930
1935
1940
1945
1950
Years
Fig. 13.20 Brahmaputra water levels at Dibrugarh (1913 – 66)
1955
1960
1965
Morphology of Some Indian Rivers
423
or deposition was not uniform in different reaches. Aggradation of 5 cm/year to erosion of 7 cm/year
was observed at different locations during 1957-1971. During 1971-1977 about 11.3 cm/year erosion
has taken place. During 1981-1989, aggradation of 2.7 cm/year on the average is noticed; this
aggradation has taken place upstream of Dibrugarh at the rate of 16.8 cm/year during this period. During
1959-1989, on the average aggradation has occurred at most of the places at the rate of 1.8 cm/year. On
the whole it was concluded that large quantities of sediment, which entered the Brahmaputra in 1950,
moved downstream till 1971 and hence deposition is indicated at various places. After 1971 up to 1981,
the sediment is eroded at decreasing rate and started aggradation after 1981 up to 1989. It is felt that
additional data are needed to study aggradation/degradation problem in the Brahmaputra and relating it
to flow conditions as well as channel contractions and expansions.
13.19
DEVELOPMENT PLANS
The development plans and activities in the Brahmaputra basin are designed to find the solution to
problems discussed earlier and to make the maximum use of the water resources for the betterment of
people in the region. Specifically the plan focuses on
1. control of floods;
2. aggradation of river channel;
3. drainage problem of hinter land;
4. extending embankments and controlling breaches as well as bank cutting and thereby
protecting towns on the banks of the stream; and
5. development leading to extension of irrigation, water power and navigation.
To achieve these objectives Brahmaputra Board has been established in 1981 and has been given
the responsibility of preparing the master plan for development. In the first phase of development
additional hydrologic, hydro meteorological and micro-earthquake recording stations are being
established. Modernization of flood forecasting network is also being done. Construction of additional
length of embankments and improvement of the existing ones are being undertaken. Further, new
schemes for the removal of drainage congestion are identified and will be undertaken.
In the second phase, multipurpose dam projects on the tributaries Pagladiya, Dihang and Subansiri
and watershed management and soil conservation programmes will be undertaken. The recent studies
(see Goswami, 2004) indicate that even though Brahmaputra basin as a whole has a forest cover of 59
percent, in some parts such as Assam it is only 20 percent and is reducing due to deforestation. Shifting
cultivation involving slash and burn technique of agriculture, being widely practised in the hills of North
–East and Bhutan, is also a major cause of land degradation and excess sediment. Hence, watershed
management programme would control sediment load and reduce aggradation problem.
The Brahmaputra has been serving, for a long time, as an important means of communication in
Assam (India), and this water route was linked to Kolkata, Bihar and U.P. Assam used to transport oil,
tea, jute, timber, coal, paddy and rice by inland waterways. Prior to 1950 earthquake, 93 percent of tea
and 90 percent of jute crop used to be transported to Kolkata by river. However, after 1950, due to
extensive deterioration of the Brahmaputra channel due to earthquake, and the establishment of
effective rail and road transport, these percentages gradually dropped to 65 for tea and 25 for jute in
1965. By 1990 the total inland waterways transport was only 2 to 3 percent of total traffic by road, rail
and inland waterways transport.
424
River Morphology
Even though the first steam boat service on the Brahmaputra started only thirty years after the first
steam boat service started on the Mississippi in 1801, the inland navigation developed much faster on
the Mississippi because of massive and sustained investments on the water course and development of
navigation over 150 years. On the other hand, the Brahmaputra remained essentially in its natural,
unregulated and undisciplined state, with the only major concern for flood control. Hence, in the recent
times Inland Waterways Authority of India and the Directorate of Inland Water Transport of Assam have
taken some initial steps to carry preliminary studies (see IWAI 1990) to develop water transport on the
Brahmaputra and its tributaries. There are a number of inland ports on the Brahmaputra such as
Dibrugarh, Neamati, Tezpur, Guwahati, Pandu, Jogighopa, and Dubri. However, modern facilities of
permanent nature for cargo handling do not exist in any of these ports; hence these are being planned.
Plans are being formulated for fully utilizing the potential of the Brahmaputra for inland water transport.
In the first stage design vessel of 100 m length, 12 m width and 2.5 to 3.0 m draft are suggested. To make
the river fully navigable, a number of actions need to be taken such as stabilization of river course,
checking formation of shoals, providing minimum depths and widths at low flows, adequate bend radii
and moderate velocity.
13.20
ROLE OF DREDGING
There is some discussion as to the role of dredging in the management of the Brahmaputra river. In the
past (see Baruah and Gogoi, 2004) experimental dredging has been used in the Chimna area near
Palasbari, 30 km downstream of Guwahati in 1974-75. The objective was to control erosion of the
embankment system, which was in danger. It was proposed to dredge cut a channel of 30 m width, and
7 km length to channelise the flow and reduce the flow through channel near northern bank. However,
before the work of dredging was completed, flash flood came. It was later found that the proposed
channel did not develop. However, dredging at Alikash area 40 km from Guwahati on the south side of
Brahmaputra, to control erosion by dredging a pre-aligned channel of length 2.24 km, width 50 m and
side slope 1V:2H was successful. Similarly dredging has been used on come tributaries to change the
local flow, remove blockages or opening mouths of the tributaries. However, it is the considered opinion
that dredging on the main river over long stretches to reduce aggradation is not feasible and economical.
However, when the river is used for navigation and generates adequate resources, dredging can be
used to maintain minimum depths at critical sections and for other local adjustments of the section.
References
Baruah, B.B. (1969) Flood and Erosion Control in the Brahmaputra Valley by Making Use of Natural Features,
Central Fuels Research Institute, 59 p.
Baruah, B. and Gogoi, P.K. (2004) Experiences of Dredging in Brahmaputra and Tributary, Seminar on Silting of
Rivers, Problems and Solutions, CWC, New Delhi, 6 p.
Bristow, C.S. (1993) Sedimentary Structures Exposed in Bar Tops in the Brahmaputra River, Bangladesh. In
Braided Rivers (Eds. Best, J.L. and Bristow C.S.) Geol. Society, Special Publication No. 75m, pp. 277-289.
Carlson B. (1985) Erosion and Sedimentation Processes in Nepalese Himalays. International Centre for Integrated
Mountain Development (ICIMOD), Occasional Paper No. 1, Khatmandu, Nepal.
Morphology of Some Indian Rivers
425
CBIP (1986) Seminar on Morphology of Ganga River. Central Board of Irrigation and Power, New Delhi,
November, 146 p.
Chitale, S. V. (1984) Kosi -The Problem River of North Bihar. Journal of Irrigation and Power of CBIP, Vol.41,
no.2, April, pp.197-202.
Chitale, S. V. (2000) Future of the Kosi River and the Kosi Project. Journal of Institution of Engineers (India), Vol.
81, December, pp.109-114.
Coleman, J.M. (1969) Brahmaputra River: Channel Processes and Sedimentation. Sedimentary Geology, Vol. 3,
pp. 129-239.
CWPRS (2002) Mathematical Model Studies for Proposed Bridge on Kosi River at NH-57 Crossing (Bihar).
Central Water and Power Research Station, Technical Report No. 3926, Sept.
Dhanju, M.S. (1976) Study of Kosi River Flood Plains by Remote Sensing. Hydrology Review, vol.2, No.4,
October, pp. 43-48.
Garde, R.J. and Kothyari, U.C. (1989) Land Slides and Their Effects on River Regime, Proc. 4th Intl. Symposium
on River Sedimentation, Beijing (China), Vol. 2, pp. 819-831.
Garde, R. J., Ranga Raju, K. G., Pande, P.K., Asawa, G. L., Kothyari, U. C. and Srivastava R. (1990) Mathematical
Modelling of the Morphological Changes in the River Kosi. Civil Engg. Department, University of Roorkee
(Now IIT Roorkee), 58p.
Gee, E.P. (1951) The Assam Earthquake of 1950. Jour. Of Bombay Natural History Society, Vol. 50, No. 3, pp.
629-635.
Godbole, M.L. (1986) Morphology of the Gandak and the Kosi Rivers – A Comparison. Seminar on Morphology
of Ganga. CBIP, New Delhi, November, pp. 29-51
Gohain, K. and Parkash B. (1990) Morphology of the Kosi Megafan. Chapter 8 in Alluvial Fans: A Field Approach
(Ed. Rachocki, A. H. and Church, M.) John Wiley and Sons Ltd., pp.151-177.
Gole, C.V. and Chitale, S.V. (1966) Inland Delta Building Activity of Kosi River. JHD, Proc. ASCE, Vol. 92, No.
HY-2, March, pp. 111-126.
Goswami, D.C. (1985) The Pattern of Sediment Yield from River Basins of the Brahmaputra System, N.E. India.
The North Eastern Geographer, Vol. 71, Nos. 1 and 2, pp. 1-11.
Goswami, D.C. (1985a) Brahmaputra River, Assam, India: Physiography, Basin Denudation and Channel
Aggradation. W.R. Research, Vol. 21, No. 7, July, pp. 959-978.
Goswami, D.C. (1988) Estimation of Bed-Load Transport in the Brahmaputra River, Assam. Indian Journal of
Earth Sciences, Vol. 15, No. 1, pp. 14-26.
Goswami, D.C. (1988) Magnitude and Frequency of Fluvial Processes in the Brahmaputra Basin, Assam: Some
Observations. Geomorphology and Enviironment, The Allahabad Geographical Soc., Allahabad (India), pp.
203-211.
Goswami, D.C.(1990) Morphology of Brahmaputra (Cyclostyled Unpublished Lecture Notes).
Goswami, D.C. (2004) Alluvial Regime and Channel Morphology of the Brahmaputra River : Some Observations.
Seminar on Silting of Rivers, Problems and Solutions, CWC, New Delhi, 8p.
Handique, G.R. and Borgohain, J.K. (1991) The Brahmaputra River System, The Senteniel, April 13.
Handique, G.R. and Borgohain, J.K. (1991) Long Term Projects. The Senteniel, April 20.
IWAI (1990) Detailed Report for Development of Inland Water Transport on national Waterway No. 2, Inland
Waterways Authority of India Report.
Jain, V. and Sinha, R. (2003) River Systems in the Gangetic Plains and Their Comparison with Siwaliks: A
Review. Current Science, Vol. 84, No. 8, April, pp. 1025-1033.
426
River Morphology
Jakhade, G.S., Murthy, A.S. and Sethurathinam (1984) Frequency Floods in Brahmaputra Valley. Journal of
Irrigation and Power, CBIP (India), Jan., pp. 41-47.
Mookerjea D, and Aich, B.N. (1963) Sedimentation in Kosi -A Unique Problem. Journal of Institution of
Engineers (India) vol.43. b) Godbole, M.L. Morphology of the Gandak and the Kosi Rivers -A Comparison.
pp39-S2.
NIH (1998) Majuli River Island: Problems and Remedies – North Regional Research Centre, National Institute of
Hydrology, Guwahati, 27p.
NIH (1994) Erosion, Sedimentation and Flooding in River Kosi. National Institute of Hydrology, Roorkee, SR -26,
229p.
Panchang, G.M. (1964) High Floods in Brahmaputra – A Retrospect. Journal of Irrigation and Power, CBIP
(India), Jan., Vol. , pp. 67-71.
Rao, K.L. (1979) India’s Water Wealth: Its Assessment, Uses and Projections. Orient Longman Limited. 267p.
Sahai, R.N., Pande, P.K. and Garde, R.J. (1980) Aggradation in Eastern Kosi Main Canal. Proc. of 1 st Intl.
Workshop on Alluvial River Problems, University of Roorkee (Now I.I.T., Roorkee), 2-73 to 78.
Sanyal, N. (1980) Effect of Embankment of River Kosi. Proceedings of 1st International Workshop on Alluvial
River Problems, Roorkee.
Sinha, R.K. (1986) Morphology of the River Kosi, M. E. thesis, Water Resources Development Training Centre,
University of Roorkee (Now IIT Roorkee), 51 p.
Sinha, R. (1995) Sedimentology of Quaternary Alluvial Deposits of Gandak-Kosi Interfan, North Bihar Plains.
Journal of Geol. Society of India, vol.46, November. pp. 521-532.
Sinha, R., Friend P.F. and Switsur, V. R. (1996) Radiocarbon Dating and Sedimentation Rates in the Holocene
Alluvial Sediments of the North Bihar Plains, India. Geol. Magazine, Vol.133, No.1, pp.85-90.
Valdiya, K.S. (1999) Why Does the River Brahmaputra Remain Untamed? Current Science, Vol. 76, No. 10, 25
May, pp. 1301-1305.
WAPCOS (1993) Morphological Studies of Brahmaputra River. Unpublished Report Prepared by Water and
Power Consultancy Services (India) Ltd., New Delhi.
Weller, H.E. (1970) Brahmaputra River Bank Protection in India. Journal of Irrigation and Power, CBIP (India),
April, Vol. No., pp. 177-189.
C H A P T E R
14
Rivers and Environment
14.1
INTRODUCTION
Streams in natural condition generally exist in a state of dynamic equilibrium, in which the amount of
sediment delivered to the channel from the drainage basin is in long-term balance with the capacity of
the stream to transport sediment; in such a case, channel dimensions and slope remain fairly invariant
and over a period of time there is neither aggradation or degradation. In such streams, a balance also
exists between communities of aquatic organisms inhabiting in the stream and the biochemical
processes that recycle nutrients from natural pollution sources to the water. The physical processes such
as aeration, dispersion, currents and sedimentation, chemical processes such as photosynthesis,
metabolism, and biological processes such as biological flocculation and precipitation act together and
naturally purify water. Aerobic purification processes require free oxygen, and are dominant in natural
streams, although anaerobic processes occur as well where free oxygen is absent.
Organic matter and nutrients in the streams are decomposed and resynthesised through chemical
reactions in association with aquatic organisms. The material is transformed by cycles of nitrogen,
carbon, phosphorus and sulphur in aerobic decomposition. These processes create Biological Oxygen
Demand (BOD) that depletes the dissolved oxygen in water. Re-oxygenation is effected through
aeration, absorption and photosynthesis. Riffles and other turbulence creating units such as dunes, bars,
and bends in the stream enhance aeration and oxygen absorption.
Fish and other aquatic organisms that utilize dissolved oxygen in water for respiration may
suffocate if oxygen concentration is severely depleted. Excessive loading of streams with organic matter
and nutrients can create significant biochemical oxygen demand and reduce dissolved oxygen to critical
levels.
Pollution sources can be grouped into point sources and non-point sources. Domestic sewage and
industrial wastes are called point sources because they are generally collected by a network of pipes and
channels and carried to a single point of discharge. Pollution by point sources can be prevented by
passing the pollutant through a properly designed waste treatment plant prior to discharging it into the
stream. On the other hand, urban and agricultural runoffs are characterized by multiple discharge points.
428
River Morphology
Treatment of non-point source wastes is generally difficult. Nutrient enrichment causes rapid
multiplication of algae, blooming, death and decomposition during the low flow periods resulting in
severe depletion in oxygen and fish kills. The aquatic organisms inhabiting natural streams can be
classified into:
Aquatic plants:
These include seed bearing plants, mosses and liverworts, ferns, horse tails and
algae.
Aquatic organisms: Moulds, bacteria and viruses.
Aquatic animals:
These include vertebrates and invertebrates
Vertebrates:
Fish and amphibians
Invertebrates:
Mollusks (Mussels, snails, slugs) and anthropoids (insects spiders, mites), worms
and protozoa
Streams in their natural state tend to maintain equilibrium between populations of aquatic
organisms and available food. The population dynamics of aquatic organisms in a stream ecosystem
involves substrate utilization, food web, nutrient spiraling and the growth curve. The waste organic
substances in the stream form the substrate on which micro organisms grow and become part of the food
web. Growth of micro organisms follows sequent portions of the growth curve including nutritionally
unrestricted exponential growth, nutritionally restricted growth, and stationary or declining growth due
to environmental conditions.
The circulation, capture, release and recapture of nutrients is known as nutrient spiraling. The
ability of the stream to a assimilate nutrients and store them in the living tissue of plants and animals is
termed as the assimilative capacity of the stream. The streams, which have a relatively high assimilative
capacity, are known as healthy streams and this is needed for maintaining good water quality. The
presence of larvae of stoneflies, caddisflies and dragonflies generally indicates good quality of water,
whereas large populations of rat-tail, maggot, blood worm and sewage fungus indicates polluted water.
Conditions or health of a stream ecosystem is reflected by its biological activity. Biological integrity is
defined as the ability of an aquatic ecosystem to support and maintain a balanced, integrated, adaptive
community of organisms having a species composition, diversity and functional organization
compatible to that of the natural habitats of the region. The main factors and some of their important
chemical, physical and biological components that influence and determine the integrity of surface
water resources are:
i) Flow Regime: Precipitation, run-off, high and low flows, stream velocity, base flow, land use,
etc.
ii) Habitat Structure: Channel morphology, pool-riffle sequence, bed material, slope, in stream
cover, canopy, substrate, width/depth ratio, sinuosity, bank stability, etc.
iii) Energy Source: Sunlight, organic matter inputs, nutrients, seasonal cycles, primary and
secondary production.
iv) Chemical Variables: Dissolved oxygen, pH, temperature, alkalinity, solubility, adsorption,
hardness, turbidity and nutrients.
v) Biotic Factors: Reproduction, disease, parasitism, feeding, predation and competition.
Any natural disturbance or human activity that affects one or more of the above factors will affect
the biological integrity and hence water quality.
Rivers and Environment
14.2
429
ACTIONS CAUSING DISTURBANCE IN STREAM SYSTEM AND
THEIR IMPACTS (OSMG 2004)
Stream system can be affected by human actions or natural disturbances in the catchment, in the stream
corridors or in the stream. These actions include:
i) Deforestation, construction activity and agricultural activity in the basin.
ii) Construction of dams and reservoirs and other hydraulic structures such as energy dissipators,
spillways, hydro-power plants, bridges, irrigation outlets, locks, bank protection works and
embankments.
iii) Development of water resources projects, water-power projects and thermal projects along
stream banks.
iv) Development of irrigation, flood plains and uplands.
v) Stream canalization for navigation and flood control using methods such as cut-offs, stream
straightening and flow diversion.
vi) Dredging of channels and disposal of dredged material.
vii) Use of streams for discharging urban sewage, industrial wastes and heated discharges.
As a result of the above mentioned actions causing disturbance in the stream system, the following
changes may take place in the stream ecosystem:
i) Changes in physical and chemical aspects of water quality and in-flow regime.
ii) Modification of channel and ecosystem morphology.
iii) Excessive non-point source pollution including sedimentation and nutrient enrichment.
iv) Deterioration of stream substrate quality and stability.
v) Destabilization of stream banks and bed.
vi) Modification of water temperature regime by removal of tree canopy, induction of thermal
discharge, and alteration of base flow regime.
vii) Introduction of exotic species that disrupt dynamic balance.
viii) Problems arising out of displacement and resettlement of population such as transfer of
diseases.
It is not possible to discuss the impacts of all these activities on river channels and water quality in
the context of the theme of the text. Hence, only effect of construction of dams and reservoirs and power
plants, and some aspects of pollution of river waters will be discussed here.
14.3
ENVIORNMENTAL EFFECTS OF HYDRAULIC STRUCTURES
When one wants to study the effects of hydraulic structures on the environment, one should study the
probable effects on water quality, land, atmosphere and society. Parameters to be studied for water
quality have already been mentioned in general earlier and details are given in sections 14.4 and 14.8.
As regards the land one should consider salts, sedimentation, erosion, aggradation or degradation,
vegetation, landslides and reservoir induced seismicity, terrestrial animals, ground water levels and
recreation. The aspects related to atmosphere are air pollution, humidity, temperature and evaporation.
Social aspects will be many which may include displacement, development and prosperity.
430
River Morphology
It is necessary to ensure that the identified effects are truly significant and that some significant
effects have not been overlooked. TCEEHS (1978) recommends the effects be described by one of the
four numbers 1, 2, 3, 4 to indicate the dependence; thus
1. Variable may be increased by causal factor,
2. Variable may be decreased by causal factor,
3. Variable may be increased or decreased by causal factor, and
4. Variable is unaffected by causal factor.
The hydraulic structures that can be considered include reservoirs, dams, outlets, energy
dissipators, power plants, bridges, sediment excluders and ejectors, embankments, spurs and channel
rectification works such as cut-offs, channel contractions and dredging.
14.4
DAMS AND RESERVOIRS
Since ancient times dams have been constructed on streams and reservoirs have been formed. Generally
dams and reservoirs serve many purposes such as flood control, power generation, supplying water for
irrigation, drinking and industrial use, navigation and recreation. Since independence, India has
witnessed rapid growth in the construction of large dams and elaborate canal networks. Over 4000
projects have been constructed in last five decades and 700 projects have been proposed to meet
increased demand for power and achieve larger irrigation potential (Raghuvanshi et al. 2000). This
activity has caused several social, ecological and economic problems.
As a result of completion of such water resources projects, the society is greatly benefited in terms
of dependable and clean drinking water, greater availability of food, better health, sanitation and
increased per capita income; availability of increased power has also resulted in greater industrial
activity and better living standards. Tourism and recreational facilities created by water resources
projects have led to social and cultural improvements e.g., Brindavan gardens, Ramganga garden,
Kalinadi Kunj, Jaikwadi garden and Gobindsagar reservoir. (Goel and Agarwal, 2000). Flocking of rare
species of birds and increase in wild life have also been reported near Ramganga, Rihand and Matatila
reservoirs.
As against these beneficial effects, a number of adverse effects have also been reported. Formation
of reservoirs due to construction of dams submerges large areas including those of forests and a number
of people are ousted from submerged areas. Table 14.1 gives some data on submergence, ousted number
of people and installed power capacity.
Thus, it can be seen that as a result of construction of these dams, large areas including forests have
been submerged and ousted a large number of people from their homes. Resettlement and compensation
to inhabitants of the submerged areas include determination of areas that will be submerged, evaluating
compensation for their properties, selection of alternative sites for settlement and distribution of land.
Such considerations were not made in the case of the Volga lake in Ghana which submerged about 8200
km2 area. The submergence area was greatly underestimated. Similarly, in the case of the Roseires
reservoir on the Blue Nile river in Sudan, only a few months before submergence people were asked to
move and submergence was underestimated by two metres (Murthy 1976). Submergence of forest areas
affects the habitat of many wild life species as can be seen from Table–14.2.
431
Rivers and Environment
Table 14.1
Submergence areas and number of oustees under some existing and proposed
hydroelectric projects (Raghuvanshi et al. 2000)
Project
Total area of
submergence
Forest area
submerged (ha)
Number of oustees
Installed capacity
(MW)
Narmadasagar
91 348
40 332
150 000
1000
Ukai – Kakrapur
60 000
22 260
50 000
300
Bargi
36 729
18 000
114 000
90
Sardar Sarovar
34 996
11 640
45 515
690
Omkareshwar
9393
2471
12 295
390
Idukki
6475
6475
4500
230
Tehri
5200
1600
85 600
2400
Table 14.2
Sr.
No.
Submergence of forests and wild life habitats under hydroelectric projects
(Raghuvanshi et al. 2000)
Project name
Forest area under
submergence (ha)
Characteristic wild life species in
submergence zone
1.
Narmadasagar multipurpose project
40 332
Tigers, sambar, chital, fishing cat and
otter
2.
Sardar Sarovar multi-purpose project
11 600
Four horned antelope, crocodile and
otter
3.
Idukki hydroelectric project
6475
4.
Parmbikulam Aliyar project
2800
Tiger, elephant, gaur
5.
Kariakutty Karapara multi-purpose project
1690
Lion tailed macaque, nilgiri langur,
tiger, elephant, sloth bear, gaur
6.
Tehri hydroelectric project
1600
Himalayan mountain sheep
7.
Rajghat irrigation project
990
Tiger, black buck, crocodile, great
Indian bustard
8.
Ramganga hydroelectric project
280
Tiger, elephant, hog bear, gharial
Elephants
Two other environmental effects of construction of large dams for water storage and its utilization
are water logging and salinization, and water-borne diseases. About 2 to 3 million ha of land every year
is going out of production due to salinity problems. Water logging results primarily from inadequate
drainage and over irrigation, and to a lesser extent, from seepage from canals and ditches. Water logging
concentrates salts, drawn up from lower portions of the soil in the plant’s rooting zone. The build up of
sodium in the soil is particularly detrimental form of salinization which is difficult to rectify. The
irrigation-induced salinity can arise as a result of use of any irrigation water, irrigation of saline soils,
and rising levels of saline ground water combined with inadequate leaching.
Water-borne or water related diseases are commonly associated with the introduction of irrigation.
The diseases most directly linked with irrigation are malaria, bilharzias, filaria, cholera, gastroenteritis,
viral encephalitis and goitre. Other irrigation related health risks include those associated with increased
432
River Morphology
use of fertilizers, herbicides and pesticides. The occurrence of these diseases in the population have
been noticed in Ghana, Nigeria, Egypt, Ethiopia and other countries.
Large versus Small Dams
Construction of large dams and reservoirs usually entails enormous costs and displacement of a large
number of people as can be seen from Table 14.1. Resettlement of these oustees is many times neglected
and hence leads often to protests, hunger strikes, stoppage of work and costly litigations that further
delay the work. Unfortunately, people who are likely to be affected are not consulted or taken into
confidence. Further, we do not have a National Rehabilitation Policy and credible implementing and
monitoring procedures for rehabilitation. There is always a complaint that these people do not get fair
compensation and a guaranteed share in the prosperity that the project brings. These conditions need
immediate improvement.
Considering these effects, many environmentalists argue that instead of building one large dam, a
few small dams should be built. However, this idea is not feasible for the following reasons (Indiresan
2000).
i) A number of small dams cannot control floods or generate electricity as a high dam can.
ii) Per 1000 m3 of storage, the capital cost for large, medium and small dams varies in the ratio of
approximately 1:3:6; hence it will be costlier to build smaller dams than a single large dam for
achieving the same storage.
iii) Other things being equal, doubling height of dam increases the storage by about eight times and
power potential sixteen times; hence it is better to build large dams when feasible.
iv) Since rainfall in India is erratic and occurs in 3 or 4 months, water needs to be stored to meet
irrigation, water supply and power needs especially when drought occurs. This is unlike in
Europe where precipitation occurs all through. Hence large dams are needed.
v) Evaporation loss in India is about 1.2 to 1.4 m annually; hence, storage required has to be large.
Further, it has to be realized that providing food, drinking water and power to millions of people is
more important than preventing displacement of a few thousand people. This is not to say that the
legitimate needs and aspirations of the oustees should be overlooked. Similarly, legitimate actions have
to be taken to protect the environment. In the three gorges project about one third of the investment has
been set aside for rehabilitation and environmental protection. Considering all these aspects it may
prudent to have good mix of large and small dams for the development of water resources in the country.
Reservoir Induced Seismicity
It has been found all over the world that in some cases, after the reservoir is filled, the adjacent areas are
subjected to reservoir-induced earthquakes (Kolhi and Bhandari 1991, Gupta 1992). Such reservoir–
induced earthquakes have occurred after impoundment of the Shivajisagar lake formed by Koyna dam
and at Bhatsa dam in Maharashtra, and at Sriramsagar dam on the Godavari in India. Such earthquakes
have also occurred at Hsinfengkian reservoir in China, at lake Mead formed by Hoover dam on the
Colorado river in U.S.A., Nurek and Tokgotul reservoirs in Russia, Aswan dam in Egypt and at many
other places.
A few details about reservoir-induced earthquakes at Koyna dam can be given. The Koyna dam of
height 103 m and the Shivajisagar reservoir are located in peninsular India about 200 km from Pune.
Rivers and Environment
433
Soon after impoundment of the reservoir in 1962, the nearby area started experiencing earth tremors and
the frequency of these tremors increased from the middle of 1963 onwards. These tremors were
accompanied by sounds similar to those of blasting. Between 1963 and 1967, five earthquakes occurred
which were strong enough to be recorded by many seismological observatories in India. The major
earthquake at Koyna occurred on December 10, 1967, which had a focal depth of 10 km ± 2 km and had
a magnitude of 6.0. This earthquake claimed about 200 lives, injured over 1500 people and rendered
thousands homeless. It also caused damage to hoist tower of the dam and developed horizontal cracks
on both the upstream and downstream faces of a number of monoliths, and damaged a large number of
houses, bridges and culverts.
Realising the socio-economic importance of reservoir induced seismicity, UNESCO formed a
working group on these phenomena and since then a number of symposia on reservoir-induced
seismicity have been organized. A number of theories/explanations have been suggested to explain why
and under what conditions the seismicity is caused. Investigation of fluid injection-induced earthquakes
at the Rocky Mountain Arsenal near Denver, Colorado, (U.S.A.) during 1960’s and Evan’s work on the
mechanism of triggering earthquakes by increase of fluid pressure have helped in understanding the
phenomenon of reservoir-induced seismicity. Gough and Gough have explained triggering of
earthquakes due to incremental stress caused by water load in the reservoir. Gupta et al. (see Gupta
1992) identified the rate of increase of water level, duration of loading, maximum levels reached and the
duration of retention of high water levels among the important factors affecting the frequency and
magnitude of reservoir-induced earthquakes. Other studies by Nyland, and Bell and Nur have also
indicated that the three main effects of reservoir loading relevant to inducing earthquakes are (i) the
elastic stress increase that follows the filling of the reservoir; (ii) the increase in pore fluid pressure in
saturated rocks due to decrease in pore volume caused by compaction in response to elastic stress
increase; (iii) and pore pressure changes related to fluid migration. It is also found that reservoir-induced
earthquakes are associated with shear fracturing of rocks. The shear strength of rocks is related to the
ratio of the shear stress along the fault to the normal effective stress across the fault, the latter being
equal to normal stress minus the pore pressure. Hence, increase in pore pressure can trigger earthquake
if rocks are under initial shear stress. During the past four decades, scientists have gained some
knowledge about RIS but a lot more needs to be learned. It may be mentioned that the largest reservoirimpoundment triggered earthquakes have exceeded magnitude of six. On the basis of RIS observations
on a number of dams, it has been well established that major RIS events are produced by enhanced
foreshock activity. Such analysis has indicated that, if two earthquakes of magnitude greater than 4
occur at RIS site within a short interval of say 2-3 weeks, there is an enhanced probability for occurrence
of earthquake of magnitude greater than 5. Studies have suggested that in the case of a large reservoir
(volume in excess of 1000 Mm3 usually impounded behind a dam height greater than 100 m) it is
desirable to carry out geological mapping for the entire reservoir area to determine faults and
competence of rocks (Gupta 1992).
14.5
WATER QUALITY IN RESERVOIRS
Construction of a dam forms a reservoir the capacity of which is progressively reduced due to
sedimentation. Since depending on the capacity to inflow ratio for the reservoir, the water is stored in the
reservoir for different time periods before it is released; the quality of water in the reservoir is different
from that flowing in the stream. The following factors need to be considered in the study of water quality
in reservoirs (TCEEHS 1978).
434
River Morphology
Temperature
Temperature plays an important role in controlling many hydraulic, chemical and biological
phenomena. In this regard, the temperature range as well as rate of temperature change are important.
The temperature affects the behaviour of biological organisms, and the rates of chemical and
biochemical reactions. A 10°C rise in temperature approximately doubles the reaction rate. Similarly,
thermal stratification takes place in deep reservoirs. Near the water surface is the layer known as
epilimnion in which temperature is fairly constant and it is in aerobic condition. Near the bottom is a
cold-water layer known as hypolimnion in which there is depletion of dissolved oxygen. Rise in
temperature upto a certain limit may increase the growth rate of fish and beyond that limit a rapid die-off
takes place. Warm water fish may survive in temperature higher than 34°C. At higher temperature, fish
may starve due to increased rate of respiration and higher food requirement. Temperature is also found
to affect reproduction ability, digestion and longevity of fish.
Turbidity
The turbidity of water due to suspended material reduces the light transmission characteristics of water.
Hence, increase in turbidity decreases the algae growth. Suspended solids can also clog gills of fish and
cover benthic organisms.
pH
pH is the logarithm of the reciprocal of hydrogen ion concentration in water and it normally varies from
6 to 9. A value of pH less than seven indicates acidic liquid while value greater than seven indicates
alkaline liquid. pH plays an important role in many chemical and biological reactions. Extremes in pH
as well as fluctuations in its value can have adverse effect on aquatic life. Anaerobic activities in the
hypolimnion of some reservoirs can reduce pH resulting in slightly acidic waters.
Salinity
Dissolved solids can enter the reservoir through the inflowing water or through ground water
infiltration. Salinity of the reservoir water can also increase as a combined result of high evaporation
rates and long detention times. High salinity water entering a reservoir can establish density
stratification patterns similar to thermal stratification. In such cases mixing of oxygen-rich surface
waters into oxygen-depleted bottom water is inhibited at the interface named chemocline. Water of
increased salinity may result in discharges that are less suited as a source of water for industrial and
irrigation uses. In addition, higher the salinity, the lower is the oxygen saturation concentration for
water.
Dissolved Oxygen (DO)
Dissolved oxygen concentration in water plays an important role in determining the quality of
discharged water. Adequate DO is necessary for the life of aquatic organisms and fish. Equilibrium
concentration of DO resulting when water is in contact with air is known as saturation concentration and
this is directly proportional to pressure and inversely proportional to salinity and temperature.
Ultimately DO concentration is equal to net oxygen sources and sinks affecting the aquatic system.
Oxygen is obtained by water by photosynthetic activity by aquatic plant and re-aeration from the
atmosphere. Dissolved oxygen is consumed by the following processes: (i) biochemical oxygen demand
Rivers and Environment
435
resulting from oxidation of nitrogenous and carbonaceous matter; (ii) respiration by benthic organisms,
fish, zooplankton and other species; (iii) chemical oxygen demand resulting from oxidation of methane,
hydrogen sulphide and certain other compounds of iron and manganese; and (iv) inflow of water with
low dissolved oxygen. When dissolved oxygen concentration becomes very low, toxic and noxious
substances can be generated and in extreme case fish kills can result.
Iron and Manganese
The source of these metals in impounded water can be from geological out croppings in reservoir
bottom, from inflow of tributary streams, ground water infiltration, and decomposition of organic
material by biological action. For drinking water, their concentrations should be limited to 0.30 mg/ l
and 0.05 mg/ l respectively.
Phosphorus
Phosphorus is an essential nutrient for the growth of aquatic plants; but only a small amount is required
for this growth. Orthophosphate form of phosphorus is readily taken up and assimilated by
phytoplankton and periphyton. Reservoirs tend to reduce phosphorus content of water discharged
through mechanisms of biological uptake and assimilation, chemical precipitation and physical
adsorption. Most soluble phosphorus released to the water results from decomposition of sediments.
Under anaerobic conditions, high concentrations of phosphorus occur in the hypolimnion of reservoir. If
this water is released downstream, it can result in algae blooms which reduces the dissolved oxygen.
Nitrogen
If dissolved nitrogen concentration in water is very large it can cause gas bubble disease in fish in which
gas bubbles develop under skin, in the fins, tail and mouth, and behind eye-balls. This can lead to gas
embolism and death.
Nitrogen is available in water in five forms: Nitrogen gas, organic, nitrite, nitrate and ammonia
nitrogen. The nitrogen cycle can operate either in aerobic or anaerobic conditions. Under aerobic
conditions, nitrates are reduced to ammonia form and then assimilated in cellular form. Under anaerobic
conditions, different reactions take place in nitrogen cycle and nitrates are reduced to ammonia and then
under certain conditions to nitrogen gas, a process known as nitrification. In aquatic nitrogen cycle,
other process that may take place is nitrogen fixation in which molecular nitrogen, in the presence of
energy source, is incorporated into biological material.
Vaidya et al. (2004) have analysed the water quality data from two reservoirs–Panchet and Ujjani–
in the Bhima basin in Maharashtra (India). Panchet is located in the hilly regions and is less affected by
human activity; Ujjani on the other hand is a much larger reservoir and is affected by quality and
quantity of water received from upstream industrial areas. Over a year phosphorus as orthophosphate,
phytoplankton and secchi disk depths indicating clarity of water were measured. High concentration of
soluble reactive phosphate or orthophosphate helps in growth of algae and depletion of dissolved
oxygen. In both reservoirs orthophosphates over the entire depth varied between 0.10 to 0.25 mg/ l ,
while secchi depth in monsoon and in winter ranged 0.8 to 2.0, and 2.0 to 4.0 m respectively.
436
14.6
River Morphology
THERMAL AND HYDRO-POWER PLANTS
Often thermal and nuclear power plants are built near reservoirs or rivers. These plants release a large
amount of heat as waste heat. Part of it is released in air through chimneys and the remaining heat is
extracted by cooling water circulated in condensers. This heated water passes through an open channel
and then is discharged into a cooling pond such as reservoir or a stream. The temperature of cooling
water rises through 8°–10°C during the passage through condensers. Discharge of this water back into
the reservoir or stream poses a major engineering and environmental problem. As discussed earlier
temperature change causes physical, chemical and biological effects on aquatic organisms, as well as
the thermal structure of water body. Hence, Environmental Protection Act 1986 stipulates that the
temperature rise of cooling water discharge from thermal power stations to the receiving body should
not be more than 5°C higher than the intake water temperature.
The water body receiving heated discharge is usually divided into two zones: (i) small near field of
high temperature where dissipation of heat takes place primarily due to entrainment of cold water from
the surrounding, and (ii) large far field with relatively lower temperature where head loss is due to
evaporation and radiation. Since temperature continuously decreases as one goes away from discharge
point, Maharashtra Pollution Control Board states that the temperature in the receiving water at 15 m
from the discharge point shall not be more than 5°C above the ambient temperature.
Vaidhankar and Deshmukh (1992) who carried out survey of reservoir temperatures at Obra,
Jatpura and Korba thermal power stations found temperature rise of 5°C or more over relatively short
distance. The length of initial mixing zone for deep pond of Obra was about 100 m while for shallow
reservoir of Korba it was 500 m. Further depending on the depth of reservoir, vertical stratification was
found to exist with temperature difference of 3° to 10°C between bottom and the surface.
As regards the hydropower plants, a few environmental problems can be briefly mentioned. Water
passing through the turbines entraps nitrogen and water released downstream in some cases is found to
be super saturated with nitrogen (El-Shami 1977). This causes gas-bubble disease and increase in fish
mortality rate in the tail race channel. In some cases, the turbine water releases have low dissolved
oxygen concentration partly due to inflow water having low dissolved oxygen and additional depletion
of oxygen in the hypolimnion of the reservoir. Since a depletion of DO concentration below a certain
limit is harmful to aquatic organisms, in extreme cases artificial re-aeration can be resorted to. This was
studied in laboratory and pilot field tests on Fort Patrick Henry dam in U.S.A. (Ruane et al. 1977). In this
case, laboratory and small-scale field studies were conducted to select the most promising diffuser on
the basis of oxygen transfer efficiency, operation and maintenance problems and economics. The
selected diffuser from small-scale experiments was tested in a pilot scale tests and then modifications
were made in it.
Change in discharge releases in the downstream channel because of construction of hydropower
plant on a stream can cause some positive and some adverse effects. Drastic reduction in flow in the
downstream channel will reduce plant and animal populations associated with the area. Further,
regulated flow in the downstream channel could prevent the adverse effects on the aquatic habitat, given
that a certain minimum flow is always maintained.
Rivers and Environment
14.7
437
RECREATION
With rapid growth in population, the demand for outdoor recreation is continually increasing. Since
water-oriented activities play an important role in outdoor recreation, rivers and reservoirs are
increasingly used for fishing, hunting, boating and other water sports. Sedimentation and erosion can
seriously hamper these activities, increase the maintenance cost and reduce the life of such facilities. A
few of the problems associated with recreation that are caused by erosion and sedimentation are briefly
discussed below (Bondurant and Livesey (1965):
1. Deposition of inert silt and sand is sterile as far as propagation of either fish or fish food is
concerned. Similarly, thin deposits of fine sediment and sludge seal the surface against
circulation of water and oxygen and can wipe out hatches of various food species. Formation of
normal reservoir delta also tends to inhibit reproduction of fish that travel to open river
upstream of reservoir to spawn.
2. Small inlets to reservoirs, known as coves, are ideal sheltered places for boat docks and
launching ramps. If these are blocked by sedimentation, recreation can be hampered. Such
deposition can also occur due to littoral drift caused by wave action. Adequate provision of a
dyke can control the situation.
3. Erosion of bank line by wave action is also undesirable from the point of view of recreation.
Hence, if bank line is eroding, proper bank protection needs to be given.
4. Fishing and boating are also practised in the clear water releases below a dam. Many times sand
bars in such area are used for docking and launching of boats. If such bars are not protected,
they are likely to be washed away in a degrading stream.
14.8
STREAM POLLUTION
Rivers while they flow from mountains to plains and then to the sea experience withdrawals of water
along their courses for agricultural, industrial or municipal use. Similarly, on their way pollution in the
form human and animal waste, agricultural drainage water and industrial effluents are discharged in
them. If the existing pollution in flow is greater than the natural assimilative capacity of the stream, the
quality of water deteriorates in the downstream direction, as is the case in many Indian rivers. Pollution
results in loss of aquatic flora and fauna leading to loss of livelihood for river fisher folk, impact on
human health from polluted water, loss of habitat for many bird species, and loss to inland navigation
potential. Further, many Indian rivers are linked with history and religions beliefs of the people and are
used for bathing and religious rites. Hence, people expect the rivers to be clean and unpolluted.
However, since many cities and villages on the stream banks do not have sewage and wastewater
treatment facilities, untreated sewage and industrial wastewater are dumped in the rivers. Floods tend to
wash down this polluted water but in lean season, the problem is aggravated. Table 14.3 lists the major
pollutant categories and principal sources of pollutants.
The major pollutant categories are briefly discussed below. Anything that can be oxidized in
receiving water uses molecular oxygen in water and consumes dissolved oxygen (DO). Human wastes,
food residue, waste from food processing and paper industries, crop residues, leaves etc. fall in this
category. Nitrogen and phosphorus are the major nutrients required for growth. Problem arises when
they become excessive and the food web is grossly disturbed. Excessive nutrients lead to growth of
438
River Morphology
Table 14.3
Major pollutant categories and principal sources of pollutants (Davis and Cornwell 1998)
Point sources
Pollutant category
Domestic wastes
Non-point sources
Industrial wastes
Agricultural
runoff
Urban runoff
Oxygen demanding material
Yes
Yes
Yes
Yes
Nutrients
Yes
Yes
Yes
Yes
Pathogens
Yes
Yes
Yes
Yes
Suspended Solids/Sediment
Yes
Yes
Yes
Yes
Salts
No
Yes
Yes
Yes
Toxic Metals
No
Yes
No
Yes
Toxic Organic Chemicals
No
Yes
Yes
No
Heat
No
Yes
No
No
algae, which in turn becomes oxygen-demanding material when they die. Major sources of nutrients are
detergents, fertilizers and food processing wastes. Pathogenic organisms are micro organisms found in
wastewaters and include bacteria, viruses and protozoa excreted by diseased persons and animals.
Excess of pathogenic organisms in water make it unfit for drinking and swimming. Organic
suspended solids may exert demand on oxygen. Inorganic suspended solids create problems for fish
spawning. Colloidal suspended material reduces penetration of light in water. High concentration of
dissolved solids make the water unfit for drinking if its concentration increases beyond a certain level,
even crops can be damaged and soils may become unfit for agriculture. Toxic metals and toxic organic
compounds enter rivers through agriculture runoff, urban runoff and industrial wastes. These include
pesticides, herbicides and zinc. These are concentrated in food chain and are very harmful to aquatic
species and human beings. As discussed earlier heat is discharged in reservoirs and rivers by thermal
power plants and also by some industrial processes. It can be beneficial to some aquatic fish while
harmful to others.
The general parameters determined from laboratory analysis, to evaluate water quality and degree
of pollution are pH, conductivity, BOD, Nitrate-N, Nitrite-N, and fecal coliform. The general
parameters estimated once a year or so include phenophelne alkalinity, total alkalinity, dissolved solids,
total suspended solids, nitrogen, hardness, fluoride, phosphate, chlorides etc. Similarly, micropollutants in water and sediment that are determined when needed include heavy metals, cyanide, total
iron and pesticides.
14.9
RIVER ACTION PLANS
For maintaining the quality of river water, the pollution levels in the Indian rivers have been obtained by
monitoring a limited number of physical, chemical and biological parameters, which could determine
the changes in the characteristics of water. In view of the deterioration in water quality over the past few
years, the Government of India has taken initiative to improve the water quality of the Ganga and other
rivers, and given water quality criteria for designated best uses (DBU) as listed in Table 14.4. A brief
mention may be made of Ganga Action Plan, which was launched in 1985 to prevent pollution of the
439
Rivers and Environment
Table 14.4
Water quality criteria for designated best uses
Class
Parameters
pH
DOMg/l
BODl
mg/l
Total coliform
MPN/100 ml
Free
ammonia
mg/l
6.5 or more
2.0 or less
50
-
A
Drinking water source without
treatment but with disinfection
6.5 – 8.5
B
Outdoor organized bathing
6.5 – 8.5
5.0 or more
5.0 or less
500
-
C
Drinking water source after
treatment and disinfection
6.5 – 8.5
4.0 or more
3.0 or less
5000
-
D
Wildlife and fisheries
6.5 – 8.5
4.0 or more
-
-
12
E
Irrigation, Industrial cooling and
controlled waste disposed
6.5 – 8.5
Electrical conductivity 22-60µ mho/cm Sodium
absorption ratio 26 Boron: 2.6 mg/l
Ganga river and improve its waste quality. The plan was initiated after the initial survey by Central
Pollution control Board which indicated that out of the total pollution load on account of the municipal
sewage, 80 percent came from class 1 towns having population over 100 000. The plan was cast to
restore river water quality to the following standards.
BOD
not greater than 3 mg/l
DO
not less than 5 mg/l
Total coliform
not greater than 10 000 MPN per 1000 l
Fecal
not greater than 2500 MPN
To accomplish this task, 281 schemes have been sanctioned under Ganga Action Plan, which
include interception and diversion schemes, sewage treatment plants, low-cost toilets and electric
crematories. With the completion of these schemes, improvement has been notices in levels of BOD and
DO. Hence, second phase of GAP and NRCP (National River Conservation Plan) has been started
along 18 interstate rivers.
14.10
STREAM RESTORATION
Stream restoration and mitigation is a process that involves recognizing natural and human induced
disturbances that degrade the form and function of the stream and riparian ecosystems or prevent its
recovery to a sustainable condition. Restoration includes a number of activities designed to enable
stream corridors to recovers dynamic equilibrium and function to maintain channel dimensions, pattern
and profile so that over a period of time the stream channel does not degrade or aggrade. FISRWG
(1998) identifies three levels of stream improvement: (a) restoration (b) rehabilitation and (c)
reclamation.
Restoration is defined as the establishment of the structure and function of ecosystems. Ecological
restoration involves returning an ecosystem as closely as possible to the pre-disturbance conditions and
function. Restoration also implies that it will provide the highest level of aquatic and biological diversity
possible. The basic principles of stream restoration include:
440
River Morphology
1. analysis of channel history and evolution;
2. analysis of cause and effect of change;
3. analysis of current condition;
4. development of specific restoration goals and objectives prior to design;
5. holistic approach to account for channel process, riparian and aquatic function;
6. consideration of passive practices such as fencing against livestock;
7. natural channel design to restore function.
Rehabilitation is defined as a procedure for making the land useful again after a disturbance. It
involves the recovery of ecosystem functions and processes in a degrading habitat. Rehabilitation
establishes geological and hydrologically stable landscapes that support biological diversity.
Reclamation is defined as a series of activities intended to change the function of an ecosystem, such as
changing wetland to farmland.
Restoration principles, practices and methods of monitoring are being evolved on the basis of
studies on small and medium sized streams in some western countries such as U.S.A. and U.K. The
structures used in stream restoration include vegetation, wood, and constructed rock and wood
structures. In U.K. (see Brookes 1995) river restoration project (RRP) was formed to promote
restoration of rivers for conservation, recreation and amenity. The project utilizes the expertise of river
ecologists, engineers, planners, fisheries biologists and geomorphologists to establish demonstration
projects to show how restoration techniques can be utilized to recreate natural ecosystem in damaged
river corridors (Brookes 1995). Research needs to be carried out to study their effectiveness in
degrading and aggrading streams, and to extend the methods to larger streams.
References
Bondurant D.C. and Livesey, R.H. (1965) Sedimentation Aspects in Recreational Planning. JHD, Proc. ASCE,
Vol. 91, No. HY5, Pt. 1, Sept. pp. 51-64.
Brookes, A. (1995) River Channel Restoration: Theory and Practice. In Changing River Channels (Eds. Gurnell,
A. and Petts, G.) John Wiley and Sons, Chichester, pp. 369-388.
Davis, M.L. and Cornwell, D.A. (1998) Introduction to Environmental Engineering. WCB McGraw Hill
Company, 3rd Edition.
El-Shami, F.M. (1977) Environmental Impacts of Hydro Electric Power Plants. JHD, Proc. ASCE, Vol. 103, No.
HY9, Sept., pp. 1007-1020.
FISRWG (1998) Stream Corridor Restoration: Principles, Processes and Practices. Federal Inter Agency Stream
Restoration Working Group. National Technical Information Service, Springfield, Va (U.S.A.).
Gupta, H.K. (1992) Reservoir Induced Earthquakes. Development in Geotechnical Engineering, No. 64, Elsevier
Book Co., Amsterdam, 364 p.
Goel, R.S. and Agarwal, K.K. (2000) River Valley Projects and Environment: Concerns and Management in India
context. In Environmental Impacts Assessment in Water Resources Projects (Ed. Goel, R.S.), Oxford and IBH
Publishing Co., New Delhi, pp. 71-87.
Indiresan, P.V. (2000) Dams or Damn: Perceptions and Facts. In Environmental Impacts Assessment in Water
Resources Projects (Ed. Goel, R.S.), Oxford and IBH Publishing Co., New Delhi, pp. 89-103.
Rivers and Environment
441
Kolhi, S. and Bhandari, R.K. (1991) Reservoir Induced Seismicity in Peninsular India. Proc. Institution of
Engineers (I) Civil, Vol. 72, pp. 47-55.
Murthy, B.N. (1976) Men-made Lakes and its Effects on Ecosystem. CBIP (India), Miscellaneous Publication No.
6, 26 p.
OSMG (2004) Natural Stream Processes. Ohio Stream Management Guide No. 3, 8 p.
Raghuvanshi, A., Mathur, V.B. and Mukherjee, S.K. (2000) Hydropower Projects and Challenges to Wildlife
Conservation in India – An Overview. In Environmental Impacts Assessment of Water Resources Projects
(Ed. Goel, R.S.) Oxford and IBH Publishing Co., New Delhi, pp. 389-401.
Ruane, R.J., Vijander, S. and Nicholas, W.R. (1977) Aeration of Hydro Releases at Fort Patric Henry Dam. JHD,
Proc. ASCE, Vol. 103, No. HY10, Oct. pp. 1135-1145.
TCEEHS (1978) Environmental Effects of Hydraulic Structures. Task Committee on Environmental Effects of
Hydraulic Structures. JHD, Proc. ASCE, Vol. 104, No. HY2, Feb. pp. 203-221.
Vaidhankar, D.V., and Deshmukh, D.N. (1992) Environmental Effects of Hot Water Releases From Power Plants
and Some Practical Aspects of Regulation Acts in India. Proc. of 1st National Symposium on Environmental
Hydraulics, CWPRS, Pune (India), June 1992, pp. 274-293.
Vaidya, S., Swain, K.K., Kamble, K.J. and Basu, A.K. (2004) Tropic State of Panchet and Ujjani Reservoirs in
Relation to Phosphorus Concentration and Other Factors. International Conference on Hydraulic
Engineering: Research and Practices. IIT Roorkee (India), Vol. 2, Oct. pp. 407-416.
C H A P T E R
15
Data Requirements for
Morphological Studies
15.1
INTRODUCTION
When one plans to develop the water resources of the basin and utilise them fully, it is necessary to have
the master plan for the development which will take into account the needs of the population at present
and in near future, and the potential for development of the water resources. Such a plan may include
conservation of water for irrigation, domestic and industrial use, power generation, flood control to
protect certain areas from flooding, and channel improvement for stabilizing the river channel to make
the whole or part of the stream navigable. It may also include use of water bodies for recreational
purposes and environmental management of the basin. Further these developments may have to be
carried ou