Buttress and Arch Dam
3.1
Buttress dams
A buttress dam consists of a slopping u/s membrane which transmits the water load to
a series of buttress at right angle to the axis of the dam.
Buttress dam principally fall in to two groups, massive diamond or round-headed buttress
dams. The earlier but now largely obsolete flat slab (Amburson) & decked buttresses
constitute the minor types.
Relative to gravity dam, buttress dam has the advantages of saving in concrete, major
reduction in uplift and also offers greater ability to accommodate foundation deformation
without damage. However, the advantages offset by considerably higher finished unit
costs as a result of more extensive & non repetitive formwork required. It also requires
more competent foundation because of stress concentration.
1
Buttress and Arch Dam
Buttress analysis & profile design
Buttress dam analysis parallels gravity dam practice in being conducted in two phases
 Stability investigation
 Stress within the profile
2
Buttress and Arch Dam
The form of buttress dam has two important consequences w.r.t. primary loads.
 Uplift pressure confined to buttress head & result in modified uplift pressure
distribution; pressure relief drains are only necessary in exceptional cases
 Pwv vertical component of water load enhanced. The concept of stability against
overturning is no longer valid.
In structural terms, massive buttress constructed of a series of independent units, each
composed of one buttress head & a supporting buttress or web (length along the axis of
the dam of about 12-15 m for each unit). Structural analysis is therefore conducted w.r.t
the unit as a whole.
FSS or more usually FSF shear friction factor analyzed in same way as gravity profile with
comparable minimum values for these factors.
Stress analysis of a buttress unit is complex & difficult. Modern practice is to employ
finite element analysis to assist in determining the optimum shape for the buttress head to
avoid undesirable stress concentrations @ its function with the web.
Approximate analysis is possible by modified gravity method for parallel sided d/s webs.
The root of the buttress is usually flared to increase sliding resistance & control the
contact stress.
Profile design for buttress is not subject simplification as gravity dam. A trial profile is
established on the bases of previous experience. The profile details are then modified &
refined as suggested by initial stress analysis.
3.2
Arch Dams
The single –curvature arch dam & the double curvature arch or cupola were introduced
with concrete dams previously and the rock & valley conditions which various arch dam
were outlined in the first chapter.
Valley suited for arch dams
 Narrow gorges
 Crest length to dam height ratio should be less than / equal to 5
b  H ( Sec1  Sec 2 ) B
For Sr ≤ 5, arch dam may be feasibly
Sr 

H
H
B
F1
F2
H
b
Arch dam transfers its loads to the valley sides than to the floor. Overturning & sliding
stability have little relevance here. If the integrity & competence of the abutment is
assured, failure can occur only as a result of overstress. Arch dam design is therefore
3
Buttress and Arch Dam
centered largely up on stress analysis and the definition of an arch geometry which avoids
local tension stress concentration and /or excessive compressive stress. The area of
cupola dam offer great economics in volume of concrete.
Associated with saving may also be realized in foundation excavation & preparation, but
the sophisticated form of arch dam leads to very much increased unit costs. In case of
complex geology of abutment saving can also be negated by requirement of ensuring
abutment integrity under all conditions.
Arch geometry and profile.
The horizontal component of arch thrust must be transferred in to the abutment at a safe
angle β as shown in the figure below. In general abutment entry angle of 450 to 700 is
acceptable.
average rock cont our
ta
ng
en
t
a
Foundat ion rock cont ours
ί
F
Fig.: Angle between arch thrust and rock contour
Arch & cupola profiles are passed on a member of geometrical forms.
i) Constant radius profile: is the simplest geometry, U/s face of the dam is of
constant radii with a uniform radial d/s slope. It is apparent that central angle, 2θ,
reaches a max. @ Crest level.
In symmetrical valley minimum concrete volume when 2θ =1330, but entry angle
preclude this & 2θ ≤ 110. The profile is suited to relatively symmetrical U-shaped valley.
ii) Constant angle profile: Central angle of different arch have the same magnitude
from top to bottom & uses up to 70% of concrete as compared to constant radius
arch dam. But it is more complex as demonstrated in the figure. It is best suited to
narrow & steep-sided V-shaped valleys.
4
Buttress and Arch Dam
iii) Cupola profile. Has a particularly complex geometry & profile, with constantly
varying horizontal & vertical radii to either face.
Design & Analysis of Arch Dams
Loads on arch dams:
- Loads on arch dams are essentially the same as loads on gravity dams.
- Uplift forces are less important, if no cracking occurs it can be neglected.
- Internal stresses caused by temperature change, ice pressure, and yielding of
abutment are very important.
- An arch dam transfers loads to the abutments and foundations both by cantilever
action and through horizontal arches.
The design /analysis can be based on.
-The thin cylinder theory
-The thick cylinder theory.
-The elastic theory.
Thick & thin Ring (cylinder) theory.
-
The theory envisages that the weight of concrete & that of water on the dam is
carried directly to the foundation not to the abutment
The horizontal water load is borne entirely by arch action.
The discrete horizontal arch elements are assumed to form part of a complete ring
subjected to uniform radial pressure, Pw, from the water load & hence it is
assumed to have uniform radial deformation.
Thin Cylinder Theory
The theory assumes the arch to be simply supported @ the abutments & that the
stresses are approximately the same as in a thin cylinder of equal outside radius.
Consider thin ring 1-2 of unit height h = @ a depth of h below water surface.
Hydrostatic pressure acting radially against the arch is wh.
5
Buttress and Arch Dam
T
h
dh
Ru
Ri
t
F
F
B/2
B/2
Let
Ru = extrados radius
Ri = intrados radius
Forces parallel to stream axis
2F sin  = 2Ru sin. wh.
F = wh Ru
 h.R
F
The transverse unit stress  
 w u
T *1
T
 hR
For given stress the required thickness is T  w u

T
Since Ru = Rc+0.5T = Ri + T ;
 w hRc
 hR
 w i
  0.5 w h    w h
Condition for least volume of concrete
V= A.R2θ = T*1*R2θ
 hR
 h
T w
 KR ;
K w


2
 B

2 
V  KR   K 
 sin / 2 


dV
 0 , gives  = 1330341. (Most economical angle of arch with minimum volume)
d
2
For 2 =1330341;
R= 0.544B
Thick cylinder theory
At Radius R, the compressive ring stress is given by
6
Buttress and Arch Dam
Ru
Ri
T
Ru
R
Ri
T
Pu
pi
 Ru2  Ru2 Rd 2 / R 2 

  p w 
2
2

R

R
u
d


 ring stress is max @ d / s face
T  Ru  Rd is uniform at any elevation.
  h max 
2 w Z 1 Ru
Tr ( Ru  Rd )
2
2 w Z 1 Ru
 ( Ru  Rd )
( for R  Rd ) For design
2
Tr 
For analysis
Note in theory, T should diminish towards crown & increase towards abutments. In
practice, T usually is constant at any elevation on a simple arch profile, and correction for
maximum stress at abutment made by factor, Kr, determined as a function of θ & Ru /T
from curves.
For thin rings theory, therefore,
h 
K r  w Z1 Ru
Tr
at abutment.
Elastic Arch theory
This theory also assumes complete transfer of load by arch action only. Horizontal arch
rings are assumed fixed to the abutments, but acting independently of neighboring rings.
Effects of temperature variation on arch stress is considered. This method can be used for
preliminary design to determine adequacy of the section designed by the (cylinder theory)
The following formulae (modified by Cans equation) are used for calculating thrusts &
moments at the crown & abutments.
7
Buttress and Arch Dam
crown
?
p=
w
*
h
Ho
Mo
Ru
R
Rd
Ma
?
abu
tme
nt
Ha
Thrust @ crown
H o  PR 
where
PR
T2
2 sin 
 is in radians.
D
R
1 T 2  
sin 2 
2
  
D  
if shearis neglected.
  2 sin 
2  
2
12
R


 

T2
D  1 
2
 12R
Moment @ crown:
 
sin 2 
T2
sin 2
2
   
 ( 
)
  2 sin   3
2
2 
2
12R
 
 sin  
M 0   PR  H o R1 

 

if shear is included.
Thrust @ abutments: H a  PR  PR  H o  cos .
 sin

Moment @ abutments: M a  R PR  H o 
 cos 
 

After calculating thrusts & moments, stresses at intrados & extrados are calculated from
 H 6M 
 2 .
T 
T
 
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Buttress and Arch Dam
Advanced method of analysis /design
The assumptions made in elastic ring analysis simplified & discrete & independent
horizontal rings which are free of any mutual interaction and the uniform radial
deformation are both untenable. Early recognition of the importance of arch- cantilever &
arch- abutment interactions led to the development to trial load analysis (TLD) which is
similar to trial load twist analysis used in gravity dam. Finite element analysis (FEA) is
also extensively applied in arch dam analysis .Although FEA is most powerful reliable &
well proven approach it is a highly specialist analytical method demanding experience.
2.5 Concrete dams design features & construction
All analysis are founded mainly based on assumption w.r.t loading regime, material
response, structural mechanism etc. Application of the analytical methods introduced in
the preceding sections represents only the initial phase of the design process. The 2nd
phase is to ensure by good detailed design the assumptions made are fulfilled.
Design features divide in to three major categories
 Those related to seepage
 Those which accommodate deformation or relative movement
 Features related to structural continuity i.e. load transfer devices & possiblyThose which facilitate construction
Cut-off & foundation grouting


Cut-offs are formed by grouting
Shallow trenches constructed under heel of dam contribute to seepage control
Uplift relief drains
 Drainage holes d/s of grout curtain
 Holes are 75-100min.  & spacing of 3-5 centers & are drilled from inspection
gallery
 Uplift with in the dam relived by holes running full height & of at least 150
mm  to inhibit blocking by leached out material & located near to u/s face &
spaced at about 3m.
 Relief drain efficiency is a function of drain geometry i.e. spacing ,  distance
form u/s face
Internal design features
 Inspection gallery
 Collects inflow from seepage & inspection gallery.
 Also gives access to appurtenance structures
 Should not be less than 2x1.2m
 Adequate ventilation & lighting is required
 Transverse contraction joints ( inter- month invites)
 Vertical contraction joints are formed @ regular intervals of 12-15m.
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Buttress and Arch Dam


They permit minor differential moment
They are made necessary by shrinkage & thermal characteristics conc.
Construction joints (inter-lift joints)
 This is provided to prevent post construction shrinkage & cracking
 Lift height is generally 1.5- 2.0m
 Lift surface is generally constructed with a fall of about 4% towards the u/s face
Load transfer & continuity
Although gravity dams designed on the basis of free standing vertical cantilevers,
load transfer is affected by interlocking vertical shear keys on the construction joint
face. In the case of arch & cupola dams it is essential to provide horizontal continuity
to develop arch action. The construction joint are grouted after the structure is load
Pulvino
Pulvino or pad, which is heavy perimentral concrete, is constructed between the shell
of a cupola dam & the supporting rock to assist in distributing load in to the
abutments and foundation.
Concrete zoning
Different concrete mix can be need in facing & hearting of concrete dam.
3rd year
2nd year
1st year
14A
13A
12A
11A
10A
9A
8A
7A
12-15m
8B
7B
6B
6A
5A
5B
4A
3A
2A
4B
3B
2B
1A
5C
4C
3C
A,B,C= variable concrete quality
2C
1B
1C
Fig:Concrete zoning
Construction planning & excution
Detailed pre of all activities involve must be prepared well in advance of sit preparation,
with the objective of ensuring optimum availability & utilization of all resources the
acting divided in to:
Initial phase - site preparation
Second phase -river diversion
Third phase - foundation excavation & preparation
Fourth phase – construction operation
Final phase- completion of ancillary work
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Buttress and Arch Dam
Concrete for dams
The desirable characteristics comparable to concrete strength in concrete dams are
a) satisfactory density n& strength
b) durability
c) low thermal volume change
d) resistance to cracking
e) low permeability &
f) economy
The primary constituents of concrete are cement, mineral aggregate & water. Secondary
constituents employed for dams include pozzolans & selected other admixtures.
Cement: the hydration of unmodified ordinary Portland cement (ASTM) type I)
equivalent) is strongly exothermic. It is preferable to employ a low heat (ASTM type IV)
or modified ordinary Portland cement (ASTM) type II) if available. Thermal problems
can also be alleviated by the use of pozzolan- blended Portland cements (ASTM type 1P).
In the absence of special cements, partial replacement with pulverizing fuel ash (PFA)
and or/ cooling are also effective in containing heat build up.
Aggregates: used to act as cheap inert bulk filler in the concrete mix. Maximum size
aggregate (MSA) 75 -100mm is optimum, with rounded or irregular natural gravels etc,
preferable to crushed rock aggregates.
In the fine aggregates, i.e. < 4.67mm size, natural sands are preferable to crushed one’s.
Aggregates should be clean & free from surface weathering or impurities
Water: A general standard is that the water should be fit for human consumption.
Pozzolana: are siliceous aluminous substances which react chemically with calcium
hydroxide from the cement to form additional cementations compounds. PFA, an
artificial pozzolan is now universally employed. If available in partial replacement of
(25-50%) of cement. PFA reduces total heat of hydration & delays the rate of strength
gain. Long-term strength is generally enhanced, but strict quality control of PFA is
required.
Admixtures: The most common admixtures are air entraining agents (AEA). They are
employed to generate some 2-6% by volume of minute air bubbles, significantly
improving the long term freeze-thaw durability of the concrete. They also reduce the
water requirement of the fresh concrete & improve its handling qualities. Water reducing
admixtures (WRA) are sometimes employed to cut the water requirement, typically by 79%. They are also effective in delaying setting time under condition if ambient
temperatures.
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Buttress and Arch Dam
Characteristics of mass concrete for dams
Characteristics
Cement (C )+ PFA (F) kg/m3
F
%
CF
Water ( C+F) ratio
90 day compressive strength, c (
heating
150-230
NM
)
m2
tesile strength  t
(
c)
Compressive
Unit weight , c kN/m3
Modules of elasticity ,E (GN/m2)
Poisson ratio
Shrinkage (% at 1 year)
Coefficient of thermal expression (x10-6 per 0C)
Concrete mix
Facing
250-320
20-35
0.50-0.70
0-25
0.45-0.65
18-30
25-40
0.10-0.15
0.07-0.10
23-25
30-45
0.15-0.22
0.02-0.05
9-12
Roller Compacted Concrete Dams (RCC dams)
This is recent idea to improve concrete dam construction. The volume instability of mass
concrete due thermal effects imposes severe limitations on the size and rate of concrete
pour, causing disruption and delay through the need to provide contraction joints and
similar design features.
Variant of RCC
1. Lean RCC  Rolled dry lean concrete (RDLC)
Conceiving RCC as low cost fill material, offering the maximum possible economy
constituent with satisfactory strength and durability and suitability to continuous
construction technique
USA uses cement + Pozzolan (PFA) < 40%, 300mm layers
2. RCD method  closer to conventional hearting concrete developed in Japan.
Uses 700 – 1000mm layers
3. High past RCC  concept of dense, high past content material, and is
exemplified by high PFA content concrete. Used in USA & UK
Variant of RCC
RCC Type
Characteristics of RCC dams
Lean RCC
RCD
High past Convention
(RDLC)
RCC
al hearting
3
Cement (c)+ PFA (F) (kg/m )
100-125
120-130
>150
150-230
F/C+F (%)
0-30
23-35
70-50
20-35
Water: (C+F) ratio
1.0-1.1
0.8-0.9
0.5-0.6
0.5-0.7
2
8-12
12-16
20-40
18-40
c (MN/m )
3
23—25
22-25
unit wt (c) (KN/m )
0.3
lift
lift
layer thickness
0.7-1.0
1.5-2.5
sawn
sawn
formed
contraction joints
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Buttress and Arch Dam
The technique of RCC is advantageous compared with the traditional construction
technique of concrete dams, since it makes possible.
a) A reduction of the construction time due to
 High efficiency of the work site & high rate of placing of the concrete
 Possibility of increasing the number of machines
b) A reduction of construction cost due to:
 Low cement content
 Reduced formwork costs
 Elimination of cooling system for the concrete
 High degree of use of equipment & machinery
13