1
Chapter 1
INTRODUCTION
1.1. Background
Lang Creek dam is an earthfill dam located in Southern California. The dam was
constructed to protect the downstream residential areas from high season floods. Floods
induced by dam break can cause serious loss of lives and significant economic losses. To
recognize the possible causes of dam break, a detailed knowledge of dam breakage
processes and flood propagations are required.
Performing a sensitivity analysis of dam break parameters helps to study the
relationships among the parameters that are involved in dam breach and flood
propagation processes. The methods applied in conducting the sensitivity analysis of dam
break parameters include hydrologic and hydraulic routing techniques. These techniques
help to predict dam-break breaching outflow hydrographs and flood wave propagation,
and provide the information regarding the wave front arrival time, inundated area, and
flow depth.
This study, sensitivity analysis of dam breach parameters using Lang Creek dam
as a testing basis, involved estimating the key parameters, time to dam failure, side slope
of breach, downstream Manning coefficients, and channel bed slopes. The process of
estimating the parameters was done based on literature reviews [12]* and historical data
collections [19]*. The influences of parameters on peak flows were analyzed at the
specified reaches stations and dam site. Two applications software, the HEC-1 applied in
2
the reservoir components of the study and HEC-RAS applied in unsteady flow routing
through the downstream reaches, were utilized to carry out the study.
1.2. Purpose
This study was prepared to evaluate the relative effects of dam breach and
downstream river parameters on the peak discharges at the dam site and specified
locations in the downstream channel. Based on the type of flow routing techniques and
parameters used, the objectives of the sensitivity analysis were grouped into two phases.
Phase 1:

To investigate the sensitivity of maximum discharges for given changes in
time to dam failure in hours (TFH), and side slope of dam breach (SS) at the
dam site.

To evaluate the combined effects of changes in time to dam failure and side
slope of breach on maximum discharges and determine the controlling
parameter at the dam site.
Phase 2:

To examine the sensitivity of peak flows for specified Manning coefficients
and time to dam failure at specified reach stations; to test the combined
effects of changes in Manning coefficients and time to dam failure on peak
flows, and determine the controlling parameter at specified reach stations.
3

To study the sensitivity of peak flows for given changes in channel bed slopes.
In order to carry out the sensitivity analysis, Lang Creek Dam, reservoir data, and
downstream river data were utilized in the study as a testing basis.
4
Chapter 2
GENERAL DESCRIPTION OF STUDY AREA
2.1. Location
Lang Creek detention basin is located downstream of Westlake Boulevard, near
Lang Ranch, in the city of Thousand Oaks, Ventura County, California. See Figure 2.1 –
vicinity map of the Lang Creek Dam.
Figure 2.1 - Vicinity map of Lang Creek detention basin [19]
5
The Lang Creek basin dam is an earth fill dam with crest elevation of 1040.8 feet.
The study area includes Lang Creek debris and detention basin, the contributing
watershed upstream of the basins, and the affected area downstream of the basins.
Figure 2.2 – Lang Creek detention basin watershed map [19]
6
2.2. Physical characteristics of Lang Creek dam
The physical characteristics of Lang Creek detention basin and dam were
summarized in Table 2.2.1. The Table below contains data gathered from previous
studies and provided by the dam owner.
Table 2.2.1- Lang Creek reservoir and dam characteristics [19]
Lang Creek Dam and Reservoir Descriptions
Reservoir Characteristics
Maximum Water Surface Elevation (ft.)
Full Storage Capacity (acre-ft)
Maximum Surface Area (Acre)
Drainage Area (square miles)
Dam Characteristics
Type of Dam
Height of Dam (ft.)
Elevation of Crest (ft.)
Length of Crest (ft.)
Elevation of Spillway (ft.)
Spillway Capacity (cfs)
Spillway Width (ft.)
Type/Size
1034
345
13.6
3.63
Earth Fill
62.8
1040.8
345
1034
N/A
17
The dam was constructed by the Ventura County Watershed Prevention District
with the city of Thousand Oaks in 2004. It was built to relieve the city of Thousand Oaks
from flooding during high storm events. The dam is connected to a Lang Creek channel
at the downstream side. The channel has an approximate length of 6.49 miles before it
joins Arroyo River.
7
Chapter 3
THEORY OF DAM BREACH ANALYSIS
3.1. Historical background
Floods resulting from dam failures led to catastrophic and tragic consequences in
the past. The catastrophic flooding due to dam failures in the 1960’s and 1970’s brought
about the passage of the National Dam Safety Act. Since then [18], a number of state and
federal governments have been working to develop robust computer programs that would
help to design new dams or evaluate existing dams.
The actual failure mechanics of dam failure have not been well understood for
either earthen or concrete dams. In earlier attempts to predict downstream flooding due to
dam failures, it was usually assumed that the dam failed completely and instantaneously.
Some investigators of dam-break flood waves assumed the breach encompasses the entire
dam and that it occurs instantaneously. Others, such as Army Corps of Engineers (1960),
have recognized the need to assume a partial failure rather than complete breaches. [12]
Several researchers have devolved regression equations to estimate breach size,
shape, and time to dam failure from historical dam breach information. [9][11][18] A few
researchers have tried to develop computer models to simulate the physical breaching
process. [8][10][1][2] Since the passage of the “National Dam Safety Act” [18], US
Army Corps of Engineers has been proactively working in developing a number of
computer models that have capabilities to perform dam breach analysis and river system
routing. Such as, HEC-1 and HEC-RAS modeling software, applied in Lang Creek dam
breach sensitivity analysis.
8
3.2. Major steps in dam break analysis
3.2.1. Information gathering
In this starting step, information on the reservoir, the dam’s structure, and
downstream reaches are researched. The following data are required to complete the
study: [12]
a. Hydrologic information such as precipitation patterns, snow and snowmelt
characteristics, watershed characteristics, and topographic data.
b. Reservoir characteristics such as storage capacity, surface area, normal and
maximum pool elevations, inflows, etc.
c. Physical characteristics of the dam and spillway such as construction type,
height, crest length, crest elevation, toe elevation, spillway type, spillway
width, elevation and capacity, etc.
d. Type, size and characteristics of downstream hydraulic structures such as
dams, bridges, culverts, railroads or highway crossings, etc.
e. The location and type of downstream development such as schools, highways,
railroads, parks, etc.
3.2.2. Size and hazard classification of dam
Depending on the size and hazard potential, dams can be classified into three
categories: small, intermediate, and large. The height of the dam and the volume of the
reservoir determine the size category of a certain dam.
9
Table 3.2.1- Classification of dam based on height and reservoir volume [12]
Size of dam
Small
Intermediate
Large
Dam height
(feet)
Less than or equal 40
Less than or equal to 100
100 plus
Volume of the reservoir
(acre-feet)
Less than or equal 1000
Less than or equal 50,000
50,000 plus
Dams can also be classified according to their hazard potential. This depends on
the number of human lives that are threatened, and the economic loss inflicted on the
downstream areas in the event of dam failure. There are three categories: low, significant,
and high hazard.
Table 3.2.2- Classification of dam based on hazard potential [12]
Category
Low
Significant
High
Loss of life (Extent of
development):
None expected (no permanent
structures for human habitation)
Few (no urban developments and no
more than a small number of
inhabitable structures)
More than a few
Economic loss:
Minimal (undeveloped to
occasional structures or
agriculture
Appreciable (no stable
agriculture, industry, or
structures)
Excessive (extensive
community, industry, or
agriculture)
3.2.3. Inflow design flood hydrologic analysis
The main objective of this step is to estimate the inflow design flood (IDF) to
reservoir and to determine the most probable type of failure. Depending on the amount of
IDF, different modes of dam failure will be assumed. If the dam is overtopped by the
inflow hydrograph, then the failure shall be assumed to be an overtopping failure,
otherwise a “sunny day” shall be assumed. The design floods need to be verified and used
10
as IDF hydrographs and routed through the reservoir using HEC-1 to determine the dambreak breaching hydrographs.
Table 3.2.3 - Recommended inflow design floods [12]
Hazard
Size
Inflow Design Flood (IDF)
Small
50 - 100 year
Low
Intermediate
100 - 0.5 PMF
Large
0.5 PMF - PMF
Small
100 - 0.5 PMF
Significant
Intermediate
0.5 PMF - PMF
Large
PMF
Small
0.5 PMF - PMF
High
Intermediate
PMF
Large
PMF
Where PMF is Probable Maximum Flood
3.2.4. Types of dam failure
The types of dam failure include: [12]
a. Overtopping failure: the overtopping type of failure is most likely to occur when the
reservoir’s water surface elevations exceeds the top of the dam due to significantly large
amount of IDF inflows into the reservoir. This commences as a gradual erosion of
embankment for earthen dams. Overtopping occurs when there is insufficient flood
storage of reservoir, low spillway capacity, or it is modeled by using the broad-crested
weir equation.
b. Normal pool failure: also referred to as a “sunny day” failure because it occurs
independent of rain events, even on sunny days, is initiated by erosion of material due to
piping, earthquakes, slope instabilities, foundation weaknesses, or other structural
11
weaknesses. Hydraulically, this type of failure is often modeled as a combination of
orifice and weir flow.
3.2.5. Dam breach parameters and analysis
The objective of this step is to calculate and verify the outflow breach hydrograph
resulting from a dam failure. The most typical breach characteristics are the shape, final
depth and width, side slopes, breaching time (failure time) and the rate at which the
breach develops. Table 3.2.4 shows the parameters in the development of breach for
hypothetical failure of dam.
Table 3.2.4 - Dam-break breaching parameters [12]
Breaching
Parameter
Average Width
of Breach (BB)
Side Slope
Saide
Slopeofof
the Breach
the
(Z)
(1: Breach
Z)
Time of Failure
in Hours (TFH)
Values
Type of Dam
0.5 HD <BB <3 HD
BB = 0.8 * Crest Length
BB = Multiple of Monolith Widths
BB = Crest Length
0<Z<2
Z= 0
0.25 <Z < 2
1<Z<2
0.1 < TFH <3.0
0.1 < TFH < 0.3
Earthen, Rock fill
Slag, Refuse
Masonry, Gravity
Concrete, Arch
All
Masonry, Gravity
Earthen, Rock fill
Slag, Refuse
All
Masonry, Gravity, Slag, Refuse
Earthen, Non Engineered, Poor
Construction
Earth, Engineered, Conmpacted
0.1 < TFH < 0.5
0.3 < TFH < 3.0
Note: TFH – time to dam failure in hour
BB - Average breach bottom width (ft)
HD – Dam height (ft)
Z or SS – Side slope of the dam breach
A. Shape of breach [12]
12
For the hypothetical dam failures the shape of the breach is usually approximated
as geometric shape such as rectangle, triangle, trapezoidal or parabola. The shape of the
breach is greatly dependent on the type of dam. For earth or rock-fill dams, a trapezoidal
shape is common. For concrete arch dams usually the shape of the breach will be the
same as the shape of the dam.
B. Breach size
As the dam breach advances, the dimensions of the breach keep increasing. For an
earth fill dam, usually a trapezoidal breach shape, overtopping failure starts as a small
breach and progresses at a linear or non-linear rate down the height of the dam as shown
in Figure 3.2.1.
Figure 3.2.1 - Overtopping breach dimensions [10]
For piping failures, the breach starts as a rectangle at some specified elevation
from the crest as shown in Figure 3.2.2. The breach width and height grow until the
elevation of the top of the breach is the same as the crest elevation, at which point the
13
breach is identical to an overtopping failure. The range of acceptable parameters for both
the overtopping and breaching cases are shown in Table 3.2.4.
Figure 3.2.2 - Piping breach dimensions [9]
ho
=
the breach top elevation at time t , feet
hd
=
elevation at the top of the dam, feet
hb
=
the breach bottom elevation at time t, feet
hbm
=
lowest breach bottom elevation at time t, feet
hf
=
specified center-line elevation of the pipe, feet
b
=
maximum breach bottom width at time t, feet
C. Breaching time
Breaching time refers to the time elapsed since the initial breach formation until it
reaches its terminal size. The failure time for earth dams ranges from six minutes to three
hours. Concrete dam failures are much more rapid, and have a time range of six to
14
eighteen minutes. The time of failure most commonly depends on the size of the dam,
types of materials used for construction, and the structural strength of the embankment.
D. Rate of failure [12]
The rate of breach expansion, increase in depth and width, is called rate of failure.
This rate can progress at a linear or non-linear rate. The progress of breach bottom
elevation hbt at a rate of P defined by Fread according to this equation:
Hbt = hd – [(hd - hbm) (tb / t)p]
for
0 < tb < t
Where:
Hbt
=
breach bottom elevation at a specified time tb, feet
hd
=
elevation at the top of the dam, feet
t
=
breach formation time, hours
hbm
=
lowest breach bottom elevation at time t, feet
p
=
rate of failure (1 < p < 4)
Also, the relationship between the breach bottom width b and its progress rate P is given
according to the equation:
Bt = bm (tb / t)p
Where:
Bt
=
breach bottom width at time tb, feet
bm
=
maximum breach bottom width at time t, feet
p
=
rate of failure (1 < p < 4), most commonly the rate of failure P is
assumed to be linear; P is equal to one for both cases.
E. Determining outflow hydrograph [12]
15
There are a few recommended computer programs to calculate the breach outflow
hydrograph, in addition to manual calculations. Manual calculations are usually the
approximate method for calculating the outflow hydrograph. For overtopping failures, the
breach outflow hydrograph can be computed by the broad-crested weir flow equation.
Neglecting the correction factor for the velocity of approach and downstream
submergence effects, the broad-crested weir equation will take the form:
Qj
=
3.1 bj (hwj – hbj)1.5 + 2.45 Z (hwj – hbj)2.5
Qj
=
the outflow from the dam (cfs) at time step j
bj
=
the breach bottom width (ft) at time step j
hw
=
water surface elevation in the reservoir (ft, m.s.l) at time step j
hbj
=
the breach bottom elevation at time step j, in feet
Z
=
side slope of the breach; Z: 1 = horizontal: vertical
Where:
On the other hand, for piping failures, the breach shape is approximated as a
rectangle and the following orifice equation can be used:
Qj
=
9.6 bj (hp – hbj) (hwj – hdj)0.5
Qj
=
outflow through the breach at time step j, in cubic feet per second
bj
=
breach bottom width in feet at time step j
hp
=
elevation of the vertical centerline of the breach in feet
hbj
=
elevation of the bottom of the breach in feet at time step j
hwj
=
elevation of the water surface elevation in the reservoir in feet at
Where:
16
time step j
hdj
=
equal to the pipe center line elevation as long as the downstream
tail water elevation is at or lower than the centre line of the pipe.
Otherwise it is equal to the downstream tail water elevation at
time j.
F. Dam-break maximum breaching outflow verification
After the analysis is completed and the hydrograph developed, it is necessary to
check the reasonableness of the maximum breaching outflow Qmax. There are a few
commonly known techniques to check Qmax: historical predictor equations, parametric
models, physically based erosion methods, direct comparison techniques, customized
prediction equations, classical equations, FERC recommended equations and current
OES recommended equations. The rule of the thumb is to check Qmax obtained in one
method with the result of the other techniques.
3.3. Streamflow and reservoir routing
The process of routing is used to predict the temporal and spatial variations of a
flood hydrograph as it moves through a river reach or reservoir. The effects of storage
and flow resistance within a river reach are reflected by changes in hydrograph shape and
timing as the floodwave moves from upstream to downstream. Figure 3.3.1 shows the
major changes that occur to a discharge hydrograph as a floodwave moves downstream.
Routing serves the useful purpose of deriving the hydrographs from rainfall distributions,
estimating the water yield at a specified point, developing design elevations of flood
17
embankments, studying the effect of a reservoir on the modification of a flood peak,
determining the size of spillway, and other flow related objectives.
Figure 3.3.1 - Discharge hydrograph routing effects [20]
In general, routing techniques may be classified into two categories: hydraulic
routing, and hydrologic routing. Hydraulic routing techniques are based on the solution of
the partial differential equations of unsteady open channel flow. These equations are
often referred to as the Saint Venant equations or the dynamic wave equations.
Hydrologic routing employs the Continuity equation and an analytical or an empirical
relationship between storage within the reach and discharge at the outlet.
18
3.3.1. Hydrologic routing techniques [7]
Hydrologic routing techniques combine the continuity equation with some
relationship between storage, outflow, and inflow. These relationships are usually
assumed empirical, or analytical in nature. In its simplest form, the Continuity equation
can be written as inflow minus outflow equals the rate of change of storage within the
reach:
I-O=
S
t
Eq. (3.3.1)
Where:
I = the average inflow to the reach during t
O = the average outflow from the reach during t
S = storage within the reach
For the purpose of this study, the Modified puls reservoir routing method of HEC1 was selected to conduct reservoir routing. The Modified puls method applied to
reservoirs consists of a repetitive solution of the Continuity equation. It is assumed that
the reservoir water surface remains horizontal, and therefore, outflow is a unique function
of reservoir storage. The Continuity equation, Eq. 3.3.1, can be manipulated to get both
of the unknown variables on the left-hand side of the equation:
(
S1
O2
S2
+
)=(
2
t
t
+
I1  I 2
O1
) - O1 +
2
2
Eq. (3.3.2)
19
Since “I” is known for all time steps, and O1 and S1 are known for the first time step, the
right-hand side of the equation can be calculated. The left-hand side of the equation can
be solved by trial and error. This is accomplished by assuming a value for either S2 or O2,
obtaining the corresponding value from the storage-outflow relationship, and then
iterating until Eq. 3.3.2 is satisfied. However, this iterative procedure can be done using a
computer program that would produce fast and accurate results. With this premises,
HEC-1 hydrologic routing program was used in the Lang Creek Reservoir Routing Study.
3.3.2. Hydraulic routing techniques [7]
In hydraulic routing, the flow is described through a set of hydrodynamic
differential equations of unsteady-state flow and simultaneous solutions of those
equations lead to determination of the outflow hydrograph. Hydraulic routing is based on
the principles of hydraulics in which flow is computed as a function of time at several
locations along the conveyance system. It involves complexities of varying degrees.
The HEC-RAS computer program uses equations that describe 1-D unsteady flow
in open channels, the Saint Venant equations consist of the Continuity equation and the
Momentum equation. The solution of these equations defines the propagation of a
floodwave with respect to distance along the channel and time.
The Continuity equation originates from the law of conservation of mass. In
figure3.3.2, q is the lateral inflow rate per unit length of channel. Q and A stands for
initial discharge and cross-sectional area. All variables are functions of time and space.
20
q
Q-
 Q x
.
 x 2
A
Q+
x
 Q x
.
 x 2
So
Figure 3.3.2 - Control volume for the Continuity equation [7]
q
y
q Fg
FH
FH
A
Ff
x
Figure 3.3.3 - Control volume for the Momentum equation [7]
21
Inflow = (Q -
 Q x
.
) t
 x 2
Outflow = (Q +
+ qxt
 Q x
.
) t
 x 2
The rate of change in volume stored within the element is equal to the change in crosssectional area multiplied by the length of section and time, i.e.
Storage change =
A
xt
 t
According to the conservation law:
Input – Output = Rate of change in volume
Substitute the inflow, outflow and storage change in the conservation law and divide
by x ,
A Q

q
t x
Eq. (3.3.3)
For a unit width b of channel with v average velocity, the continuity equation can be
written as:
y
y
v q
v  y

t
x
x b
Eq. (3.3.4)
22
The Momentum equation is the x-direction is produced from a force balance on the river
element, according to Newton’s second law of motion. The following three main forces
are acting on area A as shown in Figure 3.3.3.
 
 yA
x
x
Hydrostatic:
FH =  
Gravity:
FH = ASox
Friction:
FH = - ASfx
The rate of change of momentum is expressed from Newton’s second law as:
F=
d
mv 
dt
Where the total derivative of v with respect to t can be expressed
dv v
v

v
dt t
x
After equating the sum of the three external forces and make some simplifications for
negligible lateral inflow and a wide channel, the equation can be rearranged to yield a
complete Momentum equation:
Sf  So 
y v v 1 v


x g x g t
Eq. (3.3.5)
23
Where
 = specific weight of water
y = distance from the water surface to the centroid of the pressure prism
Q = inflow
A = Cross-sectional flow area
v = average velocity of water
x = distance along channel
b = water surface width
y = depth of water
t = time
q = lateral inflow per unit length of channel
Sf = friction slope
So = channel bed slope
g = gravitational acceleration
The Continuity and Momentum equations are considered to be the most accurate
and comprehensive solution to 1-D unsteady flow problems in open channels.
Nonetheless, these equations are based on specific assumptions, and therefore have
limitations. The assumptions used in deriving the 1-D unsteady flow equations are as
follows: [3]
a. Velocity is constant and the water surface is horizontal across any channel
section.
24
b. All flows are gradually varied with hydrostatic pressure prevailing at all points in
the flow, such that vertical accelerations can be neglected.
c. No lateral secondary circulation occurs.
d. Channel boundaries are treated as fixed; therefore, no erosion or deposition
occurs.
e. Water is of uniform density, and resistance to flow can be described by empirical
formulas, such as Manning’s and Chezy’s equation.
f. Solution of the full equations is normally accomplished with an explicit or
implicit finite difference technique. The equations are solved for incremental
times (t) and incremental distances (x) along the waterway.
25
Chapter 4
MODELING AND SENSITIVITY ANALYSIS METHODOLOGIES
4.1.
Data gathering and processing
Most of the original data gathered and compiled by the dam owner were used in
this sensitivity analysis. The main purpose of gathering data in creating a modeling
methodology was for defining the size, type, elevation and storage relations of the subject
dam, and the geometries of the downstream river reaches. Data gathered for modeling
were grouped into the following categories:
Reservoir characteristics: The reservoir characteristics consist of reservoir storage
elevation curve and reservoir surface area elevation curve (See Figure 4.3.2, Stage –
Storage Capacity – Surface Area Curves), reservoir storage capacity in acre-feet at
normal water storage pool elevation, surface area in acres at normal water storage pool
elevation. The summary of Lang Creek reservoir and dam characteristics were presented
in Table 2.2.1.
Dam characteristics: This category includes data about name of dam, dam type, dam
size, location of the dam, elevation of downstream toe of dam, design water storage pool
elevation, maximum flood surcharge elevation, spillway crest elevation, crest of dam
elevation, and height of the dam measured from downstream toe to the crest, and
category of the dam. See Table 2.2.1, for the detail of Lang Creek reservoir and dam
characteristics.
General Information: This category of data is for general information purposes. It
includes jurisdictions of the dam owner (city, town, and county area), geographic
26
information, watershed boundary, and others. See Chapter Two for detail of geographic
information.
Downstream Information: Data gathered under this category includes bank stations, reach
stations, downstream developments, cross section plots, Manning roughness coefficients,
and other pertinent hydrostructures. See appendix B for detail information on river
stations and bank stations, and other hydraulic properties.
Inflow Hydrograph: The inflow hydrograph data category includes the 10-year 24-hour
flood events hydrograph provided by the dam owner. [19] In addition, it includes a
modified “sunny day” hydrograph used to breach the Lang Creek Dam. See appendix A –
for Lang Creek dam breach HEC-1 inflow data.
4.2.
Sensitivity analysis flow chart
The analysis of dam breach involved using different computer application
software. The software was used to model hydrologic and hydraulics of different
waterways that include natural streams, man-made canals, reservoirs and others.
Depending on the level of study and extent of expected accuracy, modelers can select
appropriate type of modeling software. In this study, two types of application software
were used to perform the dam breach sensitivity analysis at the dam site and its
downstream reaches.
Dam-break analysis assumed in this study caused sever breaching outflow
hydrograph at the dam site, this study also incorporated the breaching outflow
hydrograph routing through its downstream channel. In order to meet this scope of study,
27
the Lang Creek Dam and its downstream river was used as a testing dam and was
modeled in two components, reservoir and river components. The reservoir component of
the study was studied using HEC-1. The river component was studied using HEC-RAS.
A sensitivity analysis flow chart using the Lang Creek Dam and its downstream river as a
testing basis was presented in Figure 4.21. The flow diagram described and presented the
overall modeling approaches and assumed scenarios. Also, it showed the matrices used to
analyze the relative importance of one or more of the parameters which were thought to
have significant influences on the dam-break inundation phenomenon.
4.2.1. HEC-1 modeling
As shown in Figure 4.2.1, HEC-1 computer program was used for half of the
sensitivity analysis study using the Lang Creek Dam as a testing basis. The model
assumes a single inflow to the reservoir of the Lang Creek Dam in addition to defining
the physical characteristics of the dam and reservoir. As indicated on the flow diagram,
five different scenarios of time to dam failure in hours (TFH) were assumed to evaluate
the sensitivity of outflow hydrographs to these changes. See Appendix A for the HEC-1
inputs and outputs data for this part of the study.
Additionally, four side slopes of dam breach were assumed to examine their
responses of peak outflows at dam for the aforementioned changes. The combined effects
of side slope and time to dam failure in hours changes on peak outflows at the dam were
also evaluated using HEC-1 hydrologic modeling software. Moreover, the outputs of
HEC-1 modeling, combinations of the five time to dam failure in hours (TFH1-5)
scenarios and a single side slope of breach (SS3) resulted in five dam-break outflows
28
hydrographs, which were used as input hydrographs to HEC-RAS for studying the
relationships among river flow parameters. See Appendix A for the HEC-1 inputs and
outputs data for this part of the study. Also, see Chapter five for discussions and
summary of multi-plan computer outputs of the modeling.
4.2.2. HEC-RAS modeling
As shown in the second half of the flow diagram, the HEC-RAS hydraulic
modeling software was used to execute unsteady flow river routing of dam breach
hydrographs through the downstream channel. The five dam-break outflow hydrographs
generated from HEC-1 were the prime inputs in this modeling. In HEC-RAS modeling,
each routing hydrograph was varied with five different Manning’s n values and resulted
in twenty five computer runs. The outputs were analyzed to evaluate sensitivity of
downstream peak flows to change in Manning’s n values for a given TFH. See Figure
4.2.1 for the testing scenarios matrix, and see Appendix B for the HEC- RAS input and
output data for this part of the study.
Additionally, three channel bed slopes were tested in the modeling under TFH1
(0.25hr to dam failure) dam-break hydrograph. This matrix resulted in five computer
runs. The relationships among peak flows and change in channel bed slope for a specified
TFH were investigated for each scenario. See Figure 4.2.1 for the testing scenarios
matrix, and see Appendix B for the HEC- RAS inputs and outputs data for this part of the
study.
29
Gathering Data
Reservoir Routing
TFH 1
TFH 2
TFH 3
TFH 4
SS1
TFH 5
SS2
SS3
SS4
Q1&TFH1 –
relation,
given SS3
Q2&TFH2, relation,
given SS3
Q3&TFH3,relation,
given SS3
Q4&TFH4,relation,
given SS3
Q5&TFH5,relation,
given SS3
SS1 (Q1-5TFH1-5)
SS2 (Q1-5TFH1-5)
SS3 (Q1-5TFH1-5)
SS4 (Q1-5TFH1-5)
River Routing
CHS1
N1
N2
N3
N4
N5
CHS2
CHS0riginal
CBS3
Q1-5, & TFH15, - relation,
given N1 &
SS3
Q1-5, & TFH15,- relation,
given N2 &
SS3
Q1-5, & TFH15, relation,
given N3 &
SS3
Q1-5, & TFH15, relation,
given N4 &
SS3
Q1-5, & TFH15, relation,
given N5 &
SS3
Notes:
Q1-5: Number of hydrographs produced based on a given relation, i.e.,
outflow hydrograph 1 2 …..5
TFH1-5: Time to dam failure in hours, TFH 1 to 5 = 0.25, 0.5, 1.0, 2.0, and
3.0 hrs respectively
SS1-4: Side slope of breach, SS 1 to 4 = 0.25, 1.0, 2.0, & 2.5 respectively
Manning coefficient N 1 to 5 = 0.04, 0.035, 0.0375, 0.045 & 0.05
respectively.
CBS – channel bed slope CBS 1 to 4 = 0.95So, 0.975So, 1.025So, and
1.05So respectively
Figure 4.2.1 – Sensitivity analysis flow chart
CBS4
CBS1, (N1, Q1TFH1)
CBS2, (N1, Q2TFH1)
CBS3, (N1, Q3TFH1)
CBS4, (N1, Q4TFH1)
CBSoriginal, (N1, Q5TFH1)
30
4.3.
Dam breach analysis procedures
The parameters of dam breach depend on type of the dam and mode of failure.
The shape and duration of the breach, together with the size of the dam and the reservoir,
would determine, to a great extent, the characteristics of the breach outflow hydrographs.
Overtopping mode of failure was assumed in this study and modeled by using the broadcrested weir equation. The dam-break breaching elevation was assumed at 6 inches above
the top of the dam [12]. Hydraulic analysis of dam breach includes two primary tasks, the
prediction of the reservoir outflow hydrograph and the routing of that hydrograph through
the downstream valley.
4.3.1. Predicting the outflow hydrographs
For flood hydrograph estimation, the breach modeled by defining acceptable dam
breach parameters was the core of this project. Predicting the outflow hydrographs at the
dam location was done using HEC-1 under different scenarios. See Appendix A for HEC1 input data and different scenarios. The process of predicting the outflow hydrograph
was a multi-steps approach and began with defining the reservoir characteristics, physical
description of Land Creek Dam, and its detailing breach characteristics.
4.3.1.1. Describing reservoir characteristics
Description of reservoir geometry was the first step in the analysis of dam breach.
The original data taken from the dam owner were input in the HEC-1 model. See
Appendix A for input data. Collected data included reservoir surface area rating curves,
stage-storage capacity – surface area curves, and spillway rating curve. See following
Figure 4.3.1 and Figure 4.3.2.
31
Figure 4.3.1 – Lang Creek spillway rating curve and area-capacity curves [19]
Figure 4.3.2 – Stage – storage capacity – surface area curves [19]
32
4.3.1.2. Identifying physical descriptions of dam
This step included the identification of dam height, dam crest width, spillway
elevation and width, weir flow coefficient, and coefficient of discharge. In this study,
data about the physical characterizes of the Lang Creek Dam were imported from the
dam owner’s dam inundation mapping report [21] and used as input in HEC-1 modeling.
See Table 2.2.1 - Lang Creek Reservoir and Dam Characteristics, and Appendix A –
HEC-1 input data.
4.3.1.3. Determining inflow hydrograph to the reservoir
This step involved deriving an inflow design flood from a probable maximum
precipitation. The inflow design flood is expected to cause the dam to breach in order to
analyze the worst case of dam breach analysis. For Lang Creek Dam, the inflow design
flood hydrograph provided by the dam owner, 10-year 24 hours flood events, didn’t raise
reservoir’s surface water elevation to overtop the dam.[21] As a result, modified
hydrograph was used in addition to setting the initial water surface elevation in the
reservoir equal to the dam crest elevation.
4.3.1.4. Estimating dam breach characteristics
The dam breach core characteristics are:
a. Shape of the breach: Since Lang Creek Dam is an earth-fill dam, a trapezoidal
shape of breach was assumed in this study. See Table 2.2.1, Lang Creek Dam and
reservoir characteristics, and Appendix A for input data and Table 4.3.1 Dam-break
Breaching Parameters.
b. Breach bottom elevation (Hb): By assuming the possible worst case, the breach
33
bottom elevation was set to be equal to the reservoir minimum elevation. See Appendix
A HEC-1 input data.
c. Average breach bottom width (b): In this modeling, the breach bottom width
was estimated based on empirical formula provided by “DAMBRK Modeling
Methodology”. [12] The breach bottom width remained the same in all cases. For well
constructed earthen dam “b” is given by:
2Hd  b  5Hd
Where:
Hd: height of the dam.
d. Side slope of breach (SS): the slope parameter Z or SS identifies the side slope
of the breach, i.e., 1 vertical: Z horizontal. The Z value ranges from 0.25 to 2.0 for
earthen dam [8] [12]. Its value depends on the angle of repose of the compacted and
wetted materials through which the breach develops. A trapezoidal shape was specified
with various combinations of Z values. The four Z values, 0.25, 1.0, 2.0 and 2.5 were
used to simulate reservoir routing and examining the relationships between peak
breaching outflows and change in Z values at the dam site. For multi-variables or
parameters of dam breach sensitivity analysis, the analysis flow chart was presented in
Figure 4.2.1 while the inputs and outputs of breaching parameters were presented in
Table 4.3.1.
e. Time to Failure in hours (TFH): Based upon NWS (National Weather Service)
recommendation, the typical TFH for earthen dam is given by:
0.3  TFH  3.0
in hours,
34
Where:
TFH = time to dam failure in hours
In this study, five different TFH were used to analyze the sensitivity of peak
breaching outflows at the dam site due to change in TFH. As shown in the schematic
modeling diagram Table 4.3.1, five different TFH: 0.25, 0.5, 1.5, 2.0, and 3.0 hour were
used to simulate five breaching scenarios.
Additionally, these five TFH were simulated for each Z value and resulted in
twenty different peak breaching outflows. The relationship among these three parameters,
peak flow, TFH and Z were further analyzed to compare the result with existing
condition. See Appendix A for input data. Table 4.3.1 summarized the inputs and outputs
of dam-break breaching parameters.
Table 4.3.1 - Summary of inputs and outputs of sensitivity analysis
Resevoir
Inflow
TFH
t1
t2
t3
IDF
t4
t5
Z value
SS1
SS2
SS3
SS4
HEC-1
HEC-1
Output - one Output - two
(Qsst)
(Qsst)
Q11
Q21
Q31
Q31
Q41
SS1
SS2
SS3
SS4
Q12
Q22
Q32
Q42
SS1
SS2
SS3
SS4
Q13
Q23
Q33
Q43
SS1
SS2
SS3
SS4
Q14
Q24
Q34
Q44
SS1
SS2
SS3
SS4
Q15
Q25
Q35
Q45
HEC-RAS
inflow data
(QSSt)
Q31
Q32
Q32
Q33
Q33
Q34
Q34
Q35
Q35
Manning
n
HEC-RAS
output - one
n1
n2
n3
n4
n5
n1
n2
n3
n4
n5
n1
n2
n3
n4
n5
n1
n2
n3
n4
n5
n1
n2
n3
n4
n5
Q11
Q12
Q13
Q14
Q15
Q21
Q22
Q23
Q24
Q25
Q31
Q32
Q33
Q34
Q35
Q41
Q42
Q43
Q44
Q45
Q51
Q52
Q53
Q54
Q55
HEC-RAS
Input data
(QSStn)
Channel bed Slope
(CBS)
Q311
CBS0riginal
CBS1
CBS2
CBS3
CBS4
Q321
Q331
Q341
Q351
HEC-RAS
Output - two
(QSStnCBE)
Q3110
Q3111
Q3112
Q3113
Q3114
35
4.3.2. Routing breach outflow hydrographs through downstream reaches
Dam-break flood hydrograph is a dynamic and unsteady phenomenon. Therefore,
the preferred approach is to utilize a fully developed Unsteady State flow routing model.
The HEC-1 Flood Hydrograph package provides the capability to compute and route the
breaching outflow hydrographs through downstream natural stream, but its channel
routing is to hydrologic methods. In order to accurately model the flows, the unsteady
flow computer program, HEC-RAS was used to route breaching outflow hydrographs
through natural waterways.
The implicit formulation of the St. Venant equation is well-suited from the
standpoint of accuracy for formulating unsteady flows in a natural channel. Therefore,
HEC-RAS was chosen for unsteady state flood routing, and this technique simultaneously
computes the discharge, water surface elevation, and velocity throughout the river reach.
The following parameters are crucial in running HEC-RAS to perform unsteady flow
routing:
4.3.2.1. Defining channel geometry and boundary conditions
During modeling of the downstream channel of the Lang Creek Dam using HECRAS, the first step was to establish the external boundary conditions. The upstream
boundary was selected at a location such that it was independent of the downstream
conditions. The downstream boundary was selected at a location that was independent of
flow conditions below the boundary. The last downstream cross section was set at a
reasonable distance and a normal depth was chosen to define the downstream boundary
conditions. [3]
36
Figure 4.3.3 - Schematic of single river with number
After the routing reach was established by the boundary locations, cross sections
were obtained to represent the reaches. Cross section locations were measured from
upstream to downstream. The cross sections were numbered sequentially from upstream
to downstream as shown in Figure 4.3.3. Next, the initial conditions at each cross section
were established.
For the purposes of this study, default values of expansion and contraction
coefficients were used throughout the unsteady state analysis. The program by default
assigns a value of 0.3 and 0.1 for expansion and contraction coefficient, respectively.
This decision was made due to geometric similarities among cross sections and
Manning’s roughness coefficients provided by the dam owner.
4.3.2.2. Selecting Manning coefficients, “n” values
37
Manning’s coefficient n is used to describe the resistance to flow due to channel
roughness caused by sand/gravel bed-forms, bank vegetation and obstructions, bend
effects, and circulation-eddy losses and so on. The Manning’s coefficient n values
provided by the dam owner for the channel reaches between specified cross-sections were
used as a reference basis of the sensitivity analysis.
In unsteady state river routing simulation, results were often very sensitive to the
Manning n values. Selection of the Manning n was aimed to reflect the influence of bank
and bed materials, channel obstructions, irregularity of the river banks, especially
vegetation, and to minimize potential biasness of the results.
Table 4.3.2 – Selected Manning coefficients, “n” values
River station
(miles)
0
0.91
1.25
1.69
2.06
2.49
3.19
3.76
4.67
5.35
6.49
8.5
Dam owner n –
value
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
12.5% decrease
0.035
0.035
0.035
0.035
0.035
0.035
0.035
0.035
0.035
0.035
0.035
0.035
5.0% decrease
0.0375
0.0375
0.0375
0.0375
0.0375
0.0375
0.0375
0.0375
0.0375
0.0375
0.0375
0.0375
5.0% increase
0.045
0.045
0.045
0.045
0.045
0.045
0.045
0.045
0.045
0.045
0.045
0.045
12.5% increase
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
Note: Left, right and main channel are assumed to have the same manning values.
Based on field investigations and references for selecting the Manning
coefficients, Chow (1959)[15] and Henderson(1966)[14], five “n” values were used to
study the relationships among peak flow, time to failure (TFH), and Manning n at two
specified locations along the downstream river.
4.3.2.3. Dam-break outflow hydrographs
Five different outflow hydrographs derived from five TFH during HEC-1 analysis
were used as inflow hydrographs for the downstream river routing. As shown on flow
38
chart Figure 4.3.1 and Table 4.3.1, each breaching outflow hydrographs was in
conjunction with five different Manning n values and produced twenty five independent
computer runs. See Appendix A for dam-break flood hydrographs. Additionally, the same
dam-break breaching outflow hydrographs were used to study the sensitivity of peak
flows due to change in channel bed slopes.
4.4.
Flood hydrograph routing
Flood routing can predict the temporal and spatial variations of a flood wave
through a river reach and/or reservoir. This sensitivity analysis consisted of reservoir and
downstream channel. The hydrologic routing and hydraulic routing were used to conduct
flood routing through the reservoir and downstream channel.
4.4.1. Hydrologic routing
The hydrologic routing involved the balancing of inflow, outflow, and storagedischarge relation through use of the continuity equation. This application of hydrologic
routing was used for reservoir routing. The reservoir component initiated by receiving
upstream inflows and routed these inflows through a reservoir using Storage Routing
Methods. [2] Storage Routing Methods in HEC-1 required data that define the storage
characteristics of the routing reservoir.
The 10-year 24-hour inflow hydrograph to the reservoir provided by the dam
owner did not cause the reservoir’s water surface elevation to go above the top of the
dam. In order to carry out this project, the IDF was modified and used artificial inflows
with the water surface just before failure set to the crest elevation of the dam. In addition
39
to IDF, the shape of breach, average width of breach, side slope of breach, breaching
time, and other dam breach parameters were identified and predefined for generating the
breaching outflow hydrographs by HEC-1 computer software.
Lang Creek
Reservoir
Dam
Dam
Reach 1
Distance 0.91mile
RC1
Reach 2
Distance 0.34 mile
RC2
Figure 4.4.1 – Schematic of Lang Creek reservoir and reaches
Figure 4.4.1 is a schematic of Lang Creek reservoir and reaches used in HEC-1
reservoir routing. As shown in Figure 4.4.1, two reaches were defined at the immediate
downstream of the dam which helped to increase the accuracy of the breaching outflow
hydrographs at the dam site. [3] The HEC-1 hydrologic routing subroutine was applied in
modeling and performing the Lang Creek dam-break parameters sensitivity analysis. See
Appendix A for detail input parameters and assumptions.
4.4.2. Hydraulic routing
40
Dam-break outflow hydrographs were used as inputs to the river routing through
the immediate downstream reaches of dam site. By the very nature, dam-break outflow
hydrographs are highly unsteady flows that require a full unsteady flow routing method.
In order to fully define an unsteady hydrograph, St. Venant equations should be used to
analyze the routing floodwave propagation. Thus, the HEC-RAS hydraulic routing
subroutine was adopted to route the dam-break outflow hydrographs though the Lang
Creek Channel.
In order to carry out the hydraulic routing through the Lang Creek, the
downstream cross sections data were imported from the dam owner study that included
all cross sections geometries, Manning coefficients, reach lengths and boundary
conditions. The boundary conditions included all of the external boundaries of the
system, as well as the internal locations and set the initial flow and storage area
conditions at the beginning of the simulation. Since the Lang Creek downstream channel
was modeled as an open-ended reach, the downstream boundary condition was set as a
normal depth. As recommended in HEC-RAS user manual for this option of boundary
condition, the last cross section was placed far enough such that any errors it produced
would not affect the results at the study reach. [3] See Figure 4.4.2- for the detail
information about downstream channel geometries.
Lang_Creek_DAMBRK Sensitivity Analysis
Plan:
1) S-orig
Flow:
8.5
8
7.59
7.25
Legend
WS Max WS
Ground
Bank Sta
6.81
6.44
6.01
5.58
5.31
4.74
3.83
3.15
2.01
0
Figure 4.4.2 – 3D-view of downstream channel geometries
41
42
Chapter 5
RESULTS AND DISCUSSIONS OF SENSITIVITY ANALYSIS
The sensitivity analysis using Lang Creek Dam as a testing basis involved testing
a number of dam breach parameters. The parameters defined for the reservoir and river
component of the analysis were prepared based on existing data and some empirical
formulas developed by Fread and Froehlich. With the aid of hydrologic and hydraulic
modeling software, reservoir and river flow routings were carried out to establish
relationships among the characteristics influencing a peak flow at the dam and specified
location in the downstream. The findings were discussed in the following sub-sections.
Maximum breach discharge (Qmax), breach development time in hours (TFH), and
side slope of breach (SS or 1: Z) were the three principal parameters analyzed at the dam
site in the first half of this study, reservoir component. The second half, river component,
of sensitivity analysis focused on identifying and analyzing the influences of change in
downstream reach parameters, i.e. Manning coefficients and channel bed slopes, on peak
flows for a given breaching outflow hydrograph.
5.1.
Time to dam failure (TFH) versus maximum breach discharges (Qmax) for a
given side slope of breach
The HEC-1 dam-break subroutine was used for testing the sensitivity between
TFH and Qmax. The results of testing were summarized in Table 5.1.1-2, and appendix A
for the detail outputs of HEC-1 dam-break subroutines.
43
Table 5.1.1 – Maximum discharge and time to dam failure at dam site
Time of breach
development (hr)
Side slope of breach
(1:Z)
Maximum dicharge
(cfs)
0.5To
To
2To
4To
6To
1 : Zo
1 : Zo
1 : Zo
1 : Zo
1 : Zo
25893
14172
7832
4336
3038
Note: To and Zo represent typical values and equal to 0.5hr and 2 respectively.
Table 5.1.2 – Percent change in max discharge and time to dam failure at dam site
Time of breach
development (hr)
Side slope of breach
(1:Z)
Change in max
discharge (%)
0.5To
To
2To
4To
6To
Zo
Zo
Zo
Zo
Zo
82.7
0.0
-44.7
-69.4
-78.6
Note: To and Zo represent typical values and equal to 0.5hr and 2 respectively.
In this sensitivity analysis, five different TFH were used for HEC-1 dam-break
computer runs and resulted in five dam breaching outflow hydrographs. Figure 5.1.3 –
five dam breach hydrographs for a given side slope of breach (1:2) with five different
TFH. Also, Appendix A showed the detail of HEC-1 dam-break outputs, and Table 5.1.1
showed the maximum breach discharge varied with TFH with a given side slope Z.
Based on results in Table 5.1.1-2, the peak discharge decreased when TFH
increased. A 50 % reduction in TFH (To to 0.5To) resulted in 82.7 % increase in peak
discharge at the dam site. Whereas, a 500 % increase (To to 6To) in TFH resulted in 78.6
% reduction in peak discharge at the same site. The rate of increase in peak flow relative
44
to change in TFH was very drastic compared to the rate of decrease which was slightly
steady as shown in the above table. This trend showed in the following figures and a best
fitted equation.
Breach Development time and Maximum Discharge
Maximum Discharge (cfs)
30000
25000
20000
15000
10000
5000
0
0
0.5
1
1.5
2
2.5
3
3.5
Time to dam failure (hr)
Figure 5.1.1 – Time to dam failure and maximum discharge at dam site
Percent change in max discharge vs time to dam failure
100.0
Change in max flow (%)
80.0
60.0
40.0
20.0
0.0
-20.0 0
0.5
1
1.5
2
2.5
3
3.5
-40.0
-60.0
-80.0
-100.0
Time to dam failure (hr)
Figure 5.1.2 – Percent change in max discharge and time to dam failure at dam site
45
Figure 5.1.1 and 2 depicted graphical relationships between the two parameters.
An equation developed based on best fitted trend line showed existence of non-linear
function between TFH and Qmax for a given side slope of breach at dam site.
Qmax = 7836TFH-0.86
Where:
Qmax: maximum discharge at the dam
TFH: time to dam failure in hours
The equation revealed the qualitative influence of change in dam breach
development time on the maximum discharge at dam site. As shown above and
mentioned in Chapter Three section 3.2.5, estimation of breaching hydrograph was a
multi-variable analysis that involved using empirical formula, historical data and a lot of
personal experience. Despite all of these, the above results confirmed that predicting dam
breach outflow hydrographs was dependent on and sensitive to a minor change in dam
breach development time. The finding of this sensitivity analysis agrees with the dam
breach study references such as those written by Fread and Froehlich [9] [11], and this
verifies the results.
Outflow hydrographs for a given time to dam failure @ dam
30000
25000
Outflow (cfs)
20000
15000
10000
5000
0
0
20
40
60
80
100
120
140
Time (x3mins)
0.5To
To
2To
4To
6To
Figure 5.1.3 - Five dam breaching outflow hydrographs for a given side slope
46
47
5.2. Side slope of breach (SS) versus maximum breach discharges (Qmax) for a given
time to dam failure
The HEC-1 dam-break subroutine was applied and resulted in the following
summarized data for the two variables, Qmax and SS, at the dam provided that TFH
remained the same. Appendix A presented the detail outputs of HEC-1 reservoir routings.
Table 5.2.1 – Side slope of breach and maximum discharge at dam site
Time of breach
development (hr)
To
To
To
To
Side slope of breach
(1:Z)
0.125Zo
0.5Zo
Zo
1.25Zo
Maximum dicharge
(cfs)
14654
14399
14172
14085
Note: To and Zo represent typical values and equal to 0.5hr and 2 respectively.
Table 5.2.2 – Percent change in max discharge and side slope of breach at dam site
Time of breach
development (hr)
To
To
To
To
Side slope of breach
(1:Z)
0.125Zo
0.5Zo
Zo
1.25Zo
Change in max
discharge (%)
3.4
1.6
0.0
-0.6
Note: To and Zo represent typical values and equal to 0.5hr and 2 respectively.
The shape parameter (Z) identified the side slope of the breach, i.e., 1 vertical: Z
horizontal. For this study a trapezoidal shape of breach was assumed, and breach bottom
elevation was set to remain constant in all cases as discussed in Chapter Four section 4.3.1.4. The sensitivity analysis between side slope of breach and maximum discharge
was done based on the above mentioned conditions.
Results in Table 5.2.1-2 indicated that the maximum discharge increased as the
side slope of breach decreased at the dam site. An 87.5% decrease in side of slope of
48
breach (Zo to 0.125Zo) resulted in 3.4% increase in maximum discharge at the dam
relative to original data. Whereas, a 25% increase in SS (Zo to 1.25Zo) value produced
0.6% decrease in maximum discharge at the dam site. The rate of increase in peak flow
for a given percent change in SS was higher compared to the rate of decrease as shown in
the above tables. However, the increments of percent change in peak flow were very
small compared to the corresponding percent changes in SS. This observation was
further illustrated in Figure 5.2.1-2.
Max discharge vs side slope of breach
14700
Max discharge (cfs)
14600
14500
14400
14300
14200
14100
14000
0
0.5
1
1.5
2
2.5
Side slope of breach (1:Z)
Figure 5.2.1 – Side slope of breach and maximum discharge at dam site
3
49
Percent change in max discharge vs side slope of breach
4.0
change in max discharge (%)
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5 0
0.5
1
1.5
2
2.5
3
-1.0
Side slope of breach (1:Z)
Figure 5.2.2 – Percent change in max discharge and side slope of breach at dam site
Figure 5.2.1 and 2 depict the influence of side slope of breach on maximum
discharge at the dam location. As the Z value decreased or the side slope of breach
became steeper, the maximum discharge at the dam increased at a steady rate as shown in
the above figures. It was obvious that when the Z value increases or breach slope
becomes flatter, the area of breach increases. The wider conveyance area means decrease
in velocity for a given flow. The rate of increase or decrease in conveyance area with
respect to velocity determined the rate of outflow. However, the results of this sensitivity
analysis indicated that the maximum discharge at the dam site decreased as the Z values
increased under the condition, TFH was remained constant.
Further qualitative analysis of the relationship between the two variables is shown
in the following equation. The best fit equation developed from Figure 5.2.1-2, and it
described the sensitivity of peak discharge to Z values and defined as follows:
50
Qmax = 14339Z-0.0169
With
R2 = 0.9724
Where:
Qmax: maximum discharge at the dam
Z: side slope of dam breach
The best fit equation showed estimated non-linear relationship between the two
parameters, and this evaluation agreed with the coefficient of determination R2 which
indicated the level of the equation’s accuracy. Similarly, many literatures like US Army
Crops Engineering Manual 1110-2-1420[18], FLDWAV [10] and DAMBRK [8] manuals
consistently agreed with the finding of this study. These literatures confirmed that the
aforementioned results and findings are acceptable.
5.3. Relative effects of time to dam failure (TFH) and side slope of breach (SS) on
maximum breach discharges (Qmax)
The HEC-1 dam-break subroutine was applied to test the sensitivities between
TFH and Qmax with given SS, and SS and Qmax with given TFH at the dam site. Appendix
A presented detail outputs of HEC-1 dam-break subroutines. The summary results were
tabulated – Table 5.3.1 – 2.
51
Table 5.3.1 – Effects of time to dam failure and side slope on peak flows at dam
Breach hydrograph
based on (hr)
0.125Zo
Side slope of breach, SS (1: Z)
0.5Zo
Zo
1.25Zo
Peak flow (cfs)
0.5To
26704
26285
25893
25747
To
14654
14399
14172
14085
2To
8089
7956
7832
7787
4To
4450
4395
4336
4320
6To
3113
3074
3038
3024
Note: To and Zo represent typical values and equal to 0.5hr and 2 respectively.
Table 5.3.2 – Percent change in max discharge for a given time to dam failure and side
slope of breach at dam site
Breach hydrograph
based on TFH (hr)
0.5To
To
2To
4To
6To
Side slope of breach, SS (1: Z)
0.125Zo
0.5Zo
Zo
1.25Zo
Change in peak flow (%) relative to typical value
88.4
85.5
82.7
81.7
3.4
1.6
0.0
-0.6
-42.9
-43.9
-44.7
-45.1
-68.6
-69.0
-69.4
-69.5
-78.0
-78.3
-78.6
-78.7
Note: To and Zo represent typical values and equal to 0.5hr and 2 respectively.
Table 5.3.1 and 5.3.2 show how the peak discharge at the dam site reacted to
change in the two parameters, time to dam failure and side slope of breach. The tables
show four conditions of side slope of breaches. Each side slope of breach was combined
with five time to dam failure and produced five maximum discharges at the dam site.
This analysis was done four times for the four Z values as shown in the above tables.
Results in Table 5.3.1 – 2 revealed that the peak discharge increased by 88.4%
when the time to dam failure reduced by 50% whereas side slope of breach decreased by
87.5%. On the other hand, a 500% increase in time to dam failure (To to 6To) and 25%
increase in side slope of breach (Zo to 1.25Zo) resulted in 78.7% reduction in maximum
52
discharge at the dam site. Similarly, a 50% decrease in time to dam failure and a 25%
increase in side slope of breach resulted in 81.7% increase in maximum discharge.
Maximum discharge vs time to dam failure for given side slopes of breach
30000
27500
25000
Maximum discharge (cfs)
22500
20000
17500
15000
12500
10000
7500
5000
2500
0
0.00
1.00
2.00
0.125Zo
3.00
Time to dam failure (hrs)
0.5Zo
4.00
Zo
5.00
6.00
1.25Zo
Figure 5.3.1 – Effects of time to dam failure and side slope on peak flows at dam site
Percent change in peak flow vs time to dam failure for given side slopes of breach
100.0
Change in maximum discharge (%)
80.0
60.0
40.0
20.0
0.0
0.00
-20.0
1.00
2.00
3.00
4.00
5.00
6.00
-40.0
-60.0
-80.0
-100.0
0.125Zo
Time to dam failure (hrs)
0.5Zo
Zo
1.25Zo
Figure 5.3.2 – Percent change in max discharge versus time to dam failure for specified
side slopes of breach at dam site
53
Further graphical sensitivity analysis was done to determine a controlling
parameter that influenced the maximum discharge at the dam site the most. Figure 5.3.1
and Figure 5.3.2 illustrate the trend existed between the parameters at the dam site. The
two figures depicted that the change in side slope of breach resulted in closely spaced
graphs for a wide range of change in time to dam failure. This implied that the maximum
discharge at the dam site was highly sensitive to the TFH than Z.
5.4. Manning coefficient versus peak flows in existing channel for specified time to
dam failure
The downstream river routings were carried out by HEC-RAS computer program
for five dam-break breaching outflow hydrographs under five TFH scenarios with side
slope factor Z equal to two. The HEC-RAS unsteady flow routing was run to investigate
the overall impacts of change in time to dam breach on the downstream reach peak flows
for given manning coefficients at specified locations between reaches. Appendix B
presented the detail inputs and outputs for downstream channel routing. This analysis was
executed based on existing Manning coefficients and channel geometries data provided
by the dam owner.
54
Table 5.4.1 – Downstream peak flows for five TFH breaching outflow hydrographs
River Sta.
(miles)
0.5To
Qmax (cfs)
25893
20271.23
18709.37
17420.82
15205.26
14000.91
12928.92
12222.29
11761.45
10388.74
8813.7
7942.21
6563.12
0
0.5
0.91
1.25
1.69
2.06
2.49
2.92
3.19
3.76
4.67
5.35
6.49
Assumed time to dam failure for inflow hydrographs
To
2To
4To
6To
Peak flow (Qmax)
Qmax (cfs)
Qmax (cfs)
Qmax (cfs)
Qmax (cfs)
13944
7766
4314.33
3031
12251.44
7337.21
4225.15
3000.67
11928.2
7235.32
4205.49
2991.54
11683.38
7194.03
4194.05
2986.84
11294.61
7070.76
4181.41
2982.24
10994.26
7002.19
4170.12
2978.64
10597.88
6911.79
4156.59
2973.61
10247.64
6830.81
4147.32
2970.12
10002.27
6783.89
4134.38
2966.26
9229.91
6594.76
4080.54
2948.3
8121.33
6238.07
3996.64
2919.48
7409.53
5951.63
3933.75
2886.42
6280.88
5366.47
3710.33
2812.73
Manning coeff.
(original value, No)
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
Note : To represents original time to dam failure value equal to 0.5hr.
Peak flow profiles vs River Sta. for a given inflow hydrograph
30000
Peak flow (cfs)
25000
20000
15000
10000
5000
0
0
1
2
3
4
5
6
7
River station (miles)
0.5To
To
2To
4To
6To
Figure 5.4.1 – Peak flow profiles for five TFH breaching outflow hydrographs
As shown in Table 5.4.1, five different unsteady flow routings were done using
HEC-RAS to produce peak flows at respective river stations. Similarly, Figure 5.4.1
shows the five peak flow profiles generated from five breaching outflow hydrographs that
had five different dam breach development times at the dam site. The tabular and
55
graphical analyses of the outputs revealed that the peak flows starting at the dam run in a
similar manner all the way to downstream reach end. It was obvious that smaller time to
dam failure resulted in a higher dam breach hydrograph as discussed above, and the
maximum discharge at the dam sustained its peak throughout the river routing.
The second part of this analysis was done to evaluate the relationship between
Manning coefficients and peak flows for a given TFH breaching outflow hydrograph.
According to the dam owner data, the downstream left, main and right channel sections
of the whole reach had the same Manning coefficients. This analysis assumed four
additional Manning coefficients based on reasonable assumptions and literature reviews.
Appendix B presented HEC-RAS inputs data and outputs for different Manning values.
The following tables and figures showed the influence of change in Manning coefficient
on the peak flows along the river.
As shown in Table 5.4.2 and Figure 5.4.2, the peak flow profiles starting from the
dam site down to the downstream end of the channel showed smooth transitions that
implied the gradual effects of change in Manning value. The sensitivity analysis results
indicated that the HEC-RAS run with a smaller Manning coefficient resulted in higher
peak flows for the entire reach length as shown in the Table and Figure 5.4.2.
56
Table 5.4.2 – Peak flows at different river stations for five Manning values
Assumed manning coeff.
0.9375No
No
Peak flow (Qmax)
Qmax(cfs)
Qmax(cfs)
25893.0
25893.0
20751.1
20271.2
18791.6
18709.4
17692.7
17420.8
15565.0
15205.3
14423.9
14000.9
13401.8
12928.9
12618.6
12222.3
12174.7
11761.5
10877.3
10388.7
9209.7
8813.7
8290.5
7942.2
6862.9
6563.1
5390.4
5152.0
0.875No
River Sta.
(miles)
Qmax(cfs)
25893.0
20678.3
18403.1
17635.6
15740.9
14821.0
13750.3
12769.0
12378.7
11235.6
9592.9
8627.9
7162.3
5634.7
0
0.5
0.91
1.25
1.69
2.06
2.49
2.92
3.19
3.76
4.67
5.35
6.49
8.5
1.125No
1.25No
Qmax(cfs)
25893.0
20443.6
18234.8
16934.8
14642.8
13368.3
12130.4
11462.9
10994.8
9622.6
8139.5
7315.8
6018.4
4751.6
Qmax(cfs)
25893.0
20061.4
17632.1
16325.2
13960.7
12674.9
11396.6
10720.6
10291.8
8965.3
7528.3
6780.0
5551.1
4400.4
Note : No represent original manning coeff equal 0.04.
Peak flow along river for a given manning value
30000.0
Peak flow (cfs)
25000.0
1.25No
20000.0
1.125No
15000.0
No
0.9375No
10000.0
0.875No
5000.0
0.0
0
1
2
3
4
5
River station (miles)
6
7
8
9
Figure 5.4.2 – Peak flow profiles based on five different Manning values
Further analysis was done to investigate the percent change in peak flows for a
given change in Manning coefficient relative to baseline flow generated from existing
Manning coefficients. Table and Figure 5.4.3 depict the summary of the findings. The
57
results showed a similar trend of increasing in percent change in peak flow down to
downstream end of the channel. As shown in Table 5.4.3, a 12.5 % decrease in Manning
coefficients resulted in a change in peak flows that ranged from 0% at the upstream and
9.4% at the downstream end of the channel. Whereas, a 25% increase in Manning
coefficients resulted in a change in peak flows that ranged from 0% at the upstream and 14.6% at the downstream.
Table 5.4.3 – Percent change in peak flows for given Manning values
River Sta.
(miles)
Assumed manning coeff.
0.9375No
No
Percent change in peak flow @ given sta.
Qmax(%)
Qmax(%)
0.0
0.0
2.4
0.0
0.4
0.0
1.6
0.0
2.4
0.0
3.0
0.0
3.7
0.0
3.2
0.0
3.5
0.0
4.7
0.0
4.5
0.0
4.4
0.0
4.6
0.0
4.6
0.0
0.875No
Qmax(%)
0.0
2.0
-1.6
1.2
3.5
5.9
6.4
4.5
5.2
8.2
8.8
8.6
9.1
9.4
0
0.5
0.91
1.25
1.69
2.06
2.49
2.92
3.19
3.76
4.67
5.35
6.49
8.5
1.125No
1.25No
Qmax(%)
0.0
0.9
-2.5
-2.8
-3.7
-4.5
-6.2
-6.2
-6.5
-7.4
-7.6
-7.9
-8.3
-7.8
Qmax(%)
0.0
-1.0
-5.8
-6.3
-8.2
-9.5
-11.9
-12.3
-12.5
-13.7
-14.6
-14.6
-15.4
-14.6
Note : % change relative to original flow data and No represent original manning coeff equal 0.04.
Percent change in peak flow along river for a given manning value
15.0
change in peak flow (%)
10.0
5.0
0.0
0
1
2
3
4
5
6
7
8
9
-5.0
-10.0
-15.0
-20.0
River station (miles)
0.875No
0.937No
No
1.125No
1.25No
Figure 5.4.3 – Change in peak flow profiles based on five different Manning values
58
Figure 5.4.3 shows the profiles of percent change in peak flow for specified
Manning coefficients along the river relative to the baseline. The profiles revealed that
the change in peak flow became more pronounced at reach stations located away from the
dam site. According to the above Figure 5.4.2-3 and Table 5.4.2-3, the peak flow
increases as the Manning coefficient value decreases. The relationship between the two
parameters have been discussed and studied by researchers such as Chow [15] for years.
Based on their finding, the two variables had inverse relationship as indicated in
Manning’s equation. This confirmed the consistency of this analysis with literatures.
5.5. Effects of time to dam failure and Manning coefficient on peak flows at specified
river stations
This part of sensitivity analysis was designed to combine the two scenarios
considered in the above sub-section, section 5.4, in order to determine the controlling
parameter. Two reach stations were selected to conduct a thorough investigation in
identifying the biggest peak flow influencing parameter, Manning value or time to dam
breach. Reach station 6.81 and 4.74 were selected and results of different computer runs
were tabulated as follows.
Table 5.5.1 – Peak flows for different Manning and TFH values @ Sta. 6.81.
Breach hydrograph
based on TFH (hr)
0.5To
To
2To
4To
6To
0.875No
15740.9
11476.6
7194.9
4202.6
2990.3
0.9375No
No
1.125No
Peak flow (cfs) @ sta. 6.81
15565.0
15205.3
14642.8
11411.7
11294.6
10968.4
7130.2
7070.8
6988.7
4191.0
4181.4
4156.1
2985.7
2982.2
2973.1
1.25No
13960.7
10677.8
6898.8
4131.7
2965.2
Note :No & To represent original manning coeff and time to dam failure, & equal 0.04 and 0.5hr repsectively.
59
Table 5.5.2 – Change in peak flows for different Manning and TFH @ Sta. 6.81
Breach hydrograph
based on TFH (hr)
0.5To
To
2To
4To
6To
0.875No
3.5
1.6
1.8
0.5
0.3
0.9375No
No
1.125No
Percent change in peak flow (%) @ sta. 6.81
2.4
0
-3.7
1.0
0
-2.9
0.8
0
-1.2
0.2
0
-0.6
0.1
0
-0.3
1.25No
-8.2
-5.5
-2.4
-1.2
-0.6
Note : % change relative to original flow data @ sta. 6.81 and N o & To equal to 0.04 and 0.5hr respectively.
Table 5.5.3 – Peak flows for different Manning and TFH values @ Sta. 4.74
Breach hydrograph
based on TFH (hr)
0.5To
To
2To
4To
6To
0.875No
11235.6
9695.2
6815.1
4123.3
2963.9
0.9375No
No
1.125No
Peak flow (cfs) @ sta. 4.74
10877.3
10388.7
9622.6
9484.2
9229.9
8687.1
6705.9
6594.8
6433.4
4101.3
4080.5
4038.6
2956.1
2948.3
2929.2
1.25No
8965.3
8218.8
6258.4
3989.2
2913.5
Note :No & To represent original manning coeff and time to dam failure, & equal 0.04 and 0.5hr repsectively.
Table 5.5.4 – Change in peak flows for different Manning and TFH @ Sta. 4.74
Breach hydrograph
based on TFH (hr)
0.5To
To
2To
4To
6To
0.875No
8.2
5.0
3.3
1.0
0.5
0.9375No
No
1.125No
Percent change in peak flow (%) @ sta. 4.74
4.7
0
-7.4
2.8
0
-5.9
1.7
0
-2.4
0.5
0
-1.0
0.3
0
-0.6
1.25No
-13.7
-11.0
-5.1
-2.2
-1.2
Note : % change relative to original flow data @ sta. 4.74 and No & To equal to 0.04 and 0.5hr respectively.
As shown in Table 5.5.1 and 2, a decrease in time to dam failure by 50% (To to
0.5To) and 12.5% (No to 0.875No) decrease in Manning coefficient resulted in 3.5%
increase in peak flow at reach station 6.8. Similarly, a 500 % increase in time to dam
failure and 25% increase in Manning value resulted in 0.6 % reduction in peak flow at the
same reach station. Table 5.5.3 and 4 show the same pattern for reach station 4.74. A
50% decrease in time to dam failure and 12.5 % decrease in Manning value resulted in
8.2% increase in peak flow at station 4.74. Overall observation of the results in the above
60
tables indicated that the change in peak flow at the two stations was highly sensitive to a
minor change in Manning coefficient than time to dam failure. This finding was further
illustrated in the following figures.
Peak flow vs time to dam failure for given Manning values @ Sta. 6.81
17500.0
Peak flows (cfs)
15000.0
12500.0
10000.0
7500.0
5000.0
2500.0
0.0
0
0.5
1
0.875No
1.5
2
Time to dam failure (hr)
0.9375No
No
2.5
3
1.125No
3.5
1.25No
Figure 5.5.1 – Peak flow profiles for given Manning values and TFH @ Sta. 6.81
Percent change in peak flows relative to original flows @ Sta. 6.81
6.0
Change in peak flow (%)
4.0
2.0
0.0
0
0.5
1
1.5
2
2.5
3
-2.0
-4.0
-6.0
-8.0
-10.0
Time to dam failure (hr)
0.875No
0.9375No
No
1.125No
1.25No
Figure 5.5.2 – Change in peak flow profiles for given Manning values
and TFH @ Sta. 6.81
3.5
61
Peak flow vs time to dam failure for given Manning values @ Sta. 4.74
12000.0
Peak flows (cfs)
10000.0
8000.0
6000.0
4000.0
2000.0
0.0
0
0.5
1
0.875No
1.5
2
Time to dam failure (hr)
0.9375No
No
2.5
3
1.125No
3.5
1.25No
Figure 5.5.3 – Peak flow profiles for given Manning values and TFH @ Sta. 4.74
Percent change in peak flows relative to original flows @ Sta. 4.74
10.0
7.5
Change in peak flow (%)
5.0
2.5
0.0
-2.5
0
0.5
1
1.5
2
2.5
3
3.5
-5.0
-7.5
-10.0
-12.5
-15.0
Time to dam failure (hr)
0.875No
0.9375No
No
1.125No
1.25No
Figure 5.5.4 – Change in peak flow profiles for given Manning values
and TFH @ Sta. 4.74
The above figures demonstrate that as the Manning coefficient and time to dam
failure decrease, the peak flow increases at the two reach stations. The controlling
parameter between the two variables was shown in the figures. Particularly, the percent
62
change in peak flow profiles at the two reach stations, Figure 5.5.2 and 5.5.4, indicate the
influence of a minor change in Manning coefficient on the peak flow. In the analysis of
natural waterway, there were a number of unpredictable conditions that prohibited
making general conclusions about the river hydraulic parameters. Since the downstream
flows changed with time and space, it was difficult to describe the relationships among
the three parameters empirically at this level of study. However, the graphical and tabular
results at the two stations indicated that the peak flow had inverse relation with Manning
coefficient and time to dam failure, i.e., the smaller time to dam failure and Manning
value are, the higher the peak flow is.
5.6. Channel bed slope (So) versus peak flows in existing channel under a specified
time to dam failure
The last part of sensitivity analysis involved studying the reactions of peak flow
to change in channel bottom slopes that changed the corresponding downstream channel
elevations. As shown in Table 5.6.1, four channel bed slopes were considered in the
analysis. Appendix B presented the detail of HEC-RAS inputs and outputs data.
63
Table 5.6.1 – Existing and assumed channel bed slopes
Reach Sta.
River Sta.
(mile)
8.5
8
7.59
7.25
6.81
6.44
6.01
5.58
5.31
4.74
3.83
3.15
2.01
0
0
0.5
0.91
1.25
1.69
2.06
2.49
2.92
3.19
3.76
4.67
5.35
6.49
8.5
Assumed channel bed slopes
So - existing
S1 = 0.950So
S2 = 0.975So
S3=1.025So
S4 = 1.050So
0.001386
0.001386
0.003064
0.003874
0.003874
0.004405
0.004405
0.004405
0.003323
0.002081
0.002081
0.001661
0.001661
0.001317
0.001317
0.002911
0.003680
0.003680
0.004184
0.004184
0.004184
0.003157
0.001977
0.001977
0.001578
0.001578
0.001351
0.001351
0.002987
0.003777
0.003777
0.004294
0.004294
0.004294
0.003240
0.002029
0.002029
0.001620
0.001620
0.001420
0.001420
0.003140
0.003971
0.003971
0.004515
0.004515
0.004515
0.003406
0.002133
0.002133
0.001703
0.001703
0.001455
0.001455
0.003217
0.004068
0.004068
0.004625
0.004625
0.004625
0.003489
0.002185
0.002185
0.001744
0.001744
Note: So represents existing or baseline channel bed slope provided by dam owner.
Similarly, Figure 5.6.1 shows the profiles of the four channel bed slopes
considered in the analysis relative to the existing channel bed.
Existing and assumed channel bed slopes
1000.00
980.00
960.00
Elevation (ft)
940.00
So
920.00
1.05So
900.00
1.025So
880.00
0.975So
860.00
0.95So
840.00
0
1
2
3
4
5
6
7
8
9
River station (miles)
Figure 5.6.1 Profiles of existing and assumed channel bed slopes
64
The existing channel bed slope was used as a baseline to develop four additional
bed slopes that helped to investigate the relationship between channel bed slopes and
peak flows along the channel. In this analysis, the breaching outflow hydrograph
generated by 0.25hr of TFH was used to perform the unsteady flow routing through the
downstream reaches. Appendix B showed the detail of inputs and outputs data for this
analysis. The summary of computer runs for the assumed channel bed slopes are shown
in the following tables.
As shown in Table 5.6.2 and 3, the peak flows along the river changed as the
channel bed slopes changed. A 5% decrease in channel bed slopes resulted in changes in
peak flows that ranged from 0% at the upstream to -24.8% at the downstream. Similarly,
a 5% increase in channel bed slopes resulted in changes in peak flows that ranged from
0% at the upstream to 20.0% at the downstream. In order to supplement the tabular
results and produce robust findings, the peak flow profiles were created along the river
for specified channel bed slopes, shown in Figure 5.6.2 and 5.6.3.
Table 5.6.2 – Peak flows for specified channel bed slopes
Peak Flow (cfs)
Reach Sta.
River Sta.
(mile)
So - existing
S1 = 0.950So
S2 = 0.975So
S3=1.025So
S4 = 1.050So
8.5
8
7.59
7.25
6.81
6.44
6.01
5.58
5.31
4.74
3.83
3.15
2.01
0
0
0.5
0.91
1.25
1.69
2.06
2.49
2.92
3.19
3.76
4.67
5.35
6.49
8.5
25893
21142.12
19268.23
18077.92
15957.52
14420.62
13241.21
12408.22
11856.72
9143.9
7539.86
6770.19
5927.17
5296.71
25893
21096.24
19213.05
18078.24
15893.99
14151.29
12676.23
11892.07
11362.94
7575.79
5806.45
5137.23
4455.81
4030.61
25893
21116.71
19228.56
18192.81
15862.62
14253.46
12985.99
12228.94
11700.82
8333.36
6889.69
6111.76
5319.31
4771.15
25893
21153.89
19330.75
18290.26
16109.76
14492.77
13332.29
12460.6
11995.78
10444.5
8314.27
6967.22
6385.12
5374.97
25893
21190.29
19349.76
18380.42
16270.31
14623.59
13438.54
12636.88
12125.22
10791.89
9045.36
7916.52
6702.61
5571.31
Note: So represents existing or baseline channel bed slope provided by dam owner.
65
Table 5.6.3 – Change in peak flows for specified channel bed slopes
Reach Sta.
8.5
8
7.59
7.25
6.81
6.44
6.01
5.58
5.31
4.74
3.83
3.15
2.01
0
River Sta.
(mile)
0
0.5
0.91
1.25
1.69
2.06
2.49
2.92
3.19
3.76
4.67
5.35
6.49
8.5
So - existing
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Change in peak flow along river (%)
S1 = 0.950So S2 = 0.975So S3=1.025So
0.0
0.0
0.0
-0.2
-0.1
0.1
-0.3
-0.2
0.3
0.0
0.6
1.2
-0.4
-0.6
1.0
-1.9
-1.2
0.5
-4.3
-1.9
0.7
-4.2
-1.4
0.4
-4.2
-1.3
1.2
-17.1
-8.9
14.2
-23.0
-8.6
10.3
-24.1
-9.7
2.9
-24.8
-10.3
7.7
-23.9
-9.9
1.5
S4 = 1.050So
0.0
0.2
0.4
1.7
2.0
1.4
1.5
1.8
2.3
18.0
20.0
16.9
13.1
5.2
Note: So represents existing or baseline channel bed slope provided by dam owner.
Figure 5.6.2 and 5.6.3 are the graphical representation of the above two tables.
Analysis of the graphs showed that the variation in peak flows was not noticeable at the
dam site, but effects of change in channel bed slopes became more prominent at the reach
stations distant from the dam site. The influence of change in channel bed slopes were
consistent from upstream to downstream end as shown in Figure 5.6.2 and 3.
The computation results shown in the above tables and figures revealed that the
peak flow along the channel was very sensitivity to a minor change in channel bed slopes,
example at river mile 5.0, there was a significant variation in peak flow for a small degree
change of So. As indicated in Manning equation [15], the peak flow and channel bed
slope have a direct non-linear relation. This implied that as the channel bed slopes
increased by certain coefficients, the peak flow increased by certain multiplier which was
consistent with the finding of this study.
66
Percent change in peak flows along river for given channel bed slopes
25.0
20.0
Change in peak flow (%)
15.0
10.0
5.0
0.0
-5.0
0
1
2
3
4
5
6
7
8
-10.0
-15.0
-20.0
-25.0
-30.0
River station (miles)
So
0.950So
0.975So
1.025So
1.050So
Figure 5.6.2 Change in peak flows along the river for given channel bed slopes
9
Peak flow profiles along river for given channel bed slopes
30000
Peak flows (cfs)
25000
20000
15000
10000
5000
0
0
1
2
3
4
5
6
7
8
9
River station (miles)
S0
0.95So
0.975So
1.025So
1.050So
Figure 5.6.3 – Peak flow profiles along the river for specified channel bed slopes
67
68
Chapter 6
CONCLUSIONS AND RECOMMENDATIONS
6.1.
Conclusions
The results of Lang Creek Dam breach sensitivity analysis demonstrated that dam
breach analysis is a broad subject and requires a large degree of precautions in selecting
appropriate parameters and flow routing techniques. Additionally, the study revealed that
predicting the pattern of the sensitivity testing outputs becomes more complex as more
parameters are incorporated in the analysis.
A minor change in dam breach characteristics and downstream river parameters
resulted in a significant increment in peak flows at the dam site and specified reach
stations in downstream channel. The rates of increments in peak flows were not uniform
in the specified sensitivity analyses. This observation indicated that the peak flows were
sensitive to changes in time to dam failure, side slope of breach, Manning coefficient, and
channel bed at various degrees.
Based on the Lang Creek Dam breach sensitivity analyses results, which were
obtained through application of HEC-1 and HEC-RAS subroutines, the following
conclusions were made on the relationships among the key dam breaching parameters
and open channel parameters.

A 50 % reduction in TFH resulted in 82.7 % increase in peak discharge at the
dam site. Whereas, a 500 % increase in TFH resulted in 78.6 % reduction in
peak discharge at the same site. This implied that when the dam collapsed
69
rapidly, the peak discharge became high at the dam site. This concluded that
the maximum discharge at the dam site was very sensitive to change in TFH.

An 87.5% decrease in SS resulted in 3.4% increase in maximum discharge at
the dam site. Whereas, a 25% increase in SS value produced 0.6% decrease in
maximum discharge at the dam site. As the side slope of dam breach became
steeper or breach area became smaller, the maximum discharge at the dam site
became relatively higher. This concluded that maximum discharge at the dam
site was slightly sensitive to change in SS.

The peak discharge at the dam site increased by 88.4% when the TFH reduced
by 50% and SS decreased by 87.5%. Based on the test results, evaluation of
the relative influences of the two parameters on the maximum discharge
demonstrated that the peak discharge was highly sensitive to a smaller change
in TFH than SS at the dam site.

The peak flows in the downstream reaches were directly related to maximum
dam-break breaching outflow hydrographs. The smaller time to dam failure
resulted in a higher dam breaching hydrograph, and the maximum discharge at
the dam site sustained its peak throughout the downstream river.

A 12.5 % decrease in Manning coefficients resulted in changes in peak flows
that ranged from 0% at the upstream and 9.4% at the downstream end of the
channel. Whereas, a 25% increase in Manning coefficients resulted in change
in peak flows that ranged from 0% at the upstream and -14.6% at the
70
downstream. The results suggested that the peak flows in the channel were
highly sensitive to changes in Manning coefficients.

A 50% decrease in TFH and a 12.5% decrease in Manning coefficient resulted
in 3.5% increase in peak flow at reach station 6.8. Similarly, a 500 % increase
in TFH and a 25% increase in Manning value resulted in 0.6 % reduction in
peak flow at the same reach station. A similar observation made at a different
station, reach station 4.74, showed that a 50% decrease in time to dam failure
and 12.5 % decrease in Manning value resulted in 8.2% increase in peak flow.
These results indicated the relative influences of the two parameters on the
peak flow at the specified reach stations. Based on the results, the peak flows
in the channel were highly sensitive to changes in Manning coefficient than
time to dam failure.

A 5% decrease in channel bed slopes resulted in changes in peak flows that
ranged from 0% at the upstream to -24.8% at the downstream. Similarly, a 5%
increase in channel bed slopes resulted in changes in peak flows that ranged
from 0% at the upstream to 20.0% at the downstream. These results concluded
that the peak flows in the channel were highly sensitive to a minor change in
channel bed slopes, i.e. as the channel bed slopes became flatter, the peak
flows became higher.
71
6.2.
Recommendations
Sensitivity analysis of dam breach and open channel parameters using Lang Creek
as a testing basis involved making a number of assumptions based on literature reviews
and historic data. In the real world, there is a large degree of uncertainty associated with
the breach parameters and breaching outflow estimation. It would be helpful to minimize
the ambiguities associated with breach parameters estimation using different modeling
software and analysis techniques for obtaining a wider range of dam and reservoir
characteristics and downstream river characteristics data.
In this study, only one dimensional unsteady flow routing technique was used to
carry out the sensitivity analysis in the downstream river. Similarly, the old version of
hydrologic modeling software was applied to perform the reservoir routing. There are a
number of limitations and assumptions in the modeling software. It would be helpful to
utilize a different version of the software and enhance the findings of this study.