Download Do Current Breach Parameter Estimation

DO CURRENT BREACH PARAMETER ESTIMATION TECHNIQUES PROVIDE
REASONABLE ESTIMATES FOR USE IN BREACH MODELING?
Sanjay S. Chauhan1, David S. Bowles2 and Loren R. Anderson3
Utah State University and RAC Engineers & Economists
1.0
Introduction
Dam breach inundation characteristics, including flood wave travel times, are needed
for preparing Emergency Action Plans and as a basis for estimating the consequences of dam
failure for use in Dam Safety Risk Assessments. For the emergency preparedness
applications there is an apparent tendency towards overestimating the extent of inundation in
the interest of conservatism. However, for risk assessment applications the emphasis should
be on obtaining reasonably realistic estimates of all inundation characteristics. The scale of
estimated consequences associated with dam failure, and especially estimates of potential life
loss in close proximity to the dam, can be very sensitive to the choice of breach parameters
used in breach-inundation modeling. Therefore, it is important to consider the uncertainty
associated with breach-inundation modeling.
Breach size and time depend on the type of dam, the geometry of the dam, the
topography of the foundation and surrounding area, the properties of the materials making up
the dam, and the reservoir head and volume at the time of failure. Defining breach parameters
for dam break studies, therefore, is a process, which necessitates combining information from
available empirical relationships, historical experience and the exercise of professional
judgment.
The paper begins with some comments on empirical models and agency guidelines for
estimating breach parameters and empirical approaches for estimating peak breach flows. A
case study is presented to illustrate the inconsistency in peak breach flows obtained from
using breach parameters estimated from empirical models in the NWS DAMBRK model (Fread
1984), versus peak breach flows estimated based on historical dam failures. Some
suggestions are made for selecting more reasonable breach parameter estimates for use in
breach modeling.
1
Research Assistant Professor of Civil and Environmental Engineering, Institute for Dam Safety Risk
Management, Utah Water Research Laboratory, Utah State University, Logan, Utah 84322-8200; and Senior
Engineer, RAC Engineers & Economists, 1520 Canyon Road, Providence, Utah 84332-9431; 435.797.3202;
[email protected].
2
Professor of Civil and Environmental Engineering and Director, Institute for Dam Safety Risk Management,
Utah Water Research Laboratory, Utah State University, Logan, Utah 84322-8200; and Principal, RAC Engineers
& Economists, 1520 Canyon Road, Providence, Utah 84332-9431; 435.797.4010; [email protected].
3
Professor and Head, Department of Civil and Environmental Engineering, Utah State University, Logan, Utah
84322-4110 and Principal, RAC Engineers and Economists, 1520 Canyon Road, Providence, Utah 84332-9431;
435.797.2932; [email protected].
2.0
Breach Parameter and Peak Breach Flow Estimation Techniques
The available breach parameter and peak breach flow estimation techniques can be
classified into three categories, as follows: Agency guidelines, Regression-based methods
based on data collected from actual dam failures, and Physically-based simulation models. A
summary of the available methods is provided by Wahl (1998) and in ICOLD (1998). Breach
parameters typically include breach geometry (the maximum breach width, breach height, and
the breach side slopes), and the breach formation time.
Agency guidelines are generally in the form of suggested ranges (FERC 1987) or
conservative upper bound estimates (USBR 1988). Therefore, they do not appear to be
intended for obtaining accurate breach flow estimates.
The physically-based embankment dam breach models, such as BREACH (Fread
1988) and BEED (Singh and Scarlatos 1985) rely on bed-load type erosion formulas, which
may be appropriate for some stages of the breach process, but are not consistent with the
mechanics of much of the breaching process as observed in the field or laboratory (Wahl
1988). Therefore, in practice, most widely used methods for predicting breach parameters are
based on regression analyses of data collected from dam failures. However, some significant
research efforts are underway to better understand and model the physical breach
mechanisms by the ARS (2004), CADAM (Concerted Action on Dam-Break Modeling)
sponsored by the European Union (Morris 2000), and Wang and Bowles (2004).
Regression-based methods for predicting breach parameters, although widely used,
also suffer from some limitations. Firstly, the database of dam failures used to develop these
relationships is relatively lacking in data from the failure of large dams, with about 75 percent
of the cases having a height of less than 15 meters, or 50 ft (Wahl 1998). Therefore, these
relationships may not be representative of large dams. Moreover, many historic dam failure
cases are poorly documented, which limits the number of independent variables that can be
considered in developing regression relationships and thus the extent to which different
physical characteristics of the dam, the reservoir and the failure-initiating event can be
accounted for. The small numbers of cases with adequate information limits the degrees of
freedom for estimation of regression relationships.
For Dam Safety Risk Assessment, breach scenarios under all type of loadings (flood,
earthquake, and normal operating conditions), and under a full range of loading, which could
lead to failure, are considered. However, the present regression-based techniques of breach
parameter estimation do not distinguish between the different failure modes, although
Froehlich (1995a) considers overtopping failure modes separately from other modes. Also, it
is questionable whether the relationships based on historic data, which contain data for
relatively full reservoirs4, can be applied to estimate breach parameters for piping failure
scenarios at low pool elevations.
Additional problems arise when the breach parameters obtained from the regressionbased techniques are used in dam breach models such as DAMBRK or FLDWAV (Fread
4
None of the dams higher than 15 meters in the Froehlich (1995a) data set was less than about 60% full,
based on height of water above breach bottom, at the time of failure.
1993) to estimate a breach hydrograph. The historic dam failure data are the “Final” or
ultimate breach dimensions, which are the result of passing the complete breach hydrograph,
including the falling limb, through the breach section. Observations of actual dam failures and
model studies show that breaches continue to grow during the falling limb of the hydrograph.
Thus, the peak breach flow rate would not be expected to occur when the breach size is at its
maximum. However, breach development in DAMBRK “is not simulated in any physical sense,
but rather it is idealized as a parametric process” (Wahl 2001). The breach formation in
DAMBRK is triggered at an elevation specified by the user, the breach continues to grow to its
final shape over the breach formation time and stops growing after that irrespective of the
falling limb of the breach hydrograph still passing through the breach section. Thus, when
using the DAMBRK breach model, the timing of the peak breach flow rate will usually coincide
with the maximum breach size, unless the supply of water from the reservoir is sufficiently
limited to result in a peak breach flow prior to the maximum breach size. Therefore, it is
common for the use of breach parameters from regression analysis to lead to significant
overestimates of peak breach flow rates, at least for dams with large reservoirs. This bias is
expected to occur for all empirical breach parameter estimation approaches that use the final
breach width and final breach formation time. It is demonstrated in the case study presented
in Section 3.0, although we have seen this overestimation problem on many other dams.
3.0
3.1
Case Study
Background
To illustrate the inconsistency between the peak breach flow rates obtained from the
empirical methods, and peak breach flow rates obtained from the DAMBRK model using
empirical-estimates of breach parameters, a case study is presented. The study dam is an
approximately 150 ft high earthfill dam with approximately 82,000 acft of storage at full pool at
elevation 652.5 ft msl). It is a flood control structure with the dam crest at elevation 691.5 ft
msl. The NWS DAMBRK model was used to estimate the breach hydrographs based on
empirically-estimated breach parameters.
These breach analyses were conducted for use in a risk assessment in which only “best
estimates” were considered and no uncertainty analysis was performed. Therefore, the
objective was to obtain “reasonably realistic” estimates of breach parameters rather than
“conservative” estimates as is often the case for EAPs.
The following earthquake-induced failures by seepage erosion through cracks (SEC)
were considered at the following seven pool levels5: Full Pool (El. 652.5) – E.FP, El. 640 –
E.640, El. 630 – E.630, El. 620 – E.620, El. 610 – E.610, El. 600 – E.600, and El. 590 – E.590.
The following two empirical approaches were used to estimate breach flows:
1) Froehlich (1995a) for estimating breach parameters that were used in the DAMBRK
model to obtain a breach hydrograph
2) Froehlich (1995b) for estimating peak breach flow rate
5
Each pool elevation is followed by a run code, such as “E.640”, which refers to the “Earthquake” failure mode
and pool elevation of “640” ft msl.
The Froehlich (1995a) procedure for estimating average breach width, B, side slope ratio z,
and breach formation time, T, uses the following relationships for non-overtopping failures,
such as piping:
B
z
T
=
=
=
15 Vw 0.32 H 0.19
0.9
3.84Vw 0.53 H - 0.90
=
=
reservoir volume at the time of failure, in million cubic meters
height of the final breach, in meters.
(1)
(2)
(3)
in which:
Vw
H
This empirical procedure was developed using data from 63 dam failures including
several in the range of the height and capacity of the case study dam.
The Froehlich (1995b) procedure for estimating peak breach flow rates is based on the
breach height and reservoir capacity above the breach bottom elevation using the following
relationship:
Qp
=
0.607 Vw 0.295 Hw 1.24
=
=
reservoir volume at the time of failure, in cubic meters
height of water in the reservoir at the time of failure above the final bottom
elevation of the breach, in meters.
(4)
in which:
Vw
Hw
This empirical procedure was developed using data from 22 dam failures including
several in the range of the height and capacity of the case study dam.
Both of the above relations were developed in SI units but results were converted to US
customary units in this paper. The two approaches by Froehlich were selected mainly
because, unlike some other relations, which are based on just the height of the dam or the
height of the breach, Froehlich’s relations also take into account the reservoir volume. In
addition, Wahl (2001) found that both of Froehlich’s relations gave the smallest mean
prediction error and the narrowest prediction interval for peak breach flow out of the four
breach parameter estimation and ten peak breach flow estimation techniques that he applied
to the Jamestown Dam case study.
3.2
Comparisons and Sensitivity of Peak Breach Flow Estimates
Columns 5 and 6 of Table 1 contain the Froehlich (1995a) estimates of breach bottom
width, B, and breach formation time, T, respectively, for each of the seven failure scenarios
listed in Section 3.1. All breaches were assumed to be trapezoidal in shape with side slopes of
0.9 horizontal to 1.0 vertical. At full pool (FP), the estimated breach bottom width is 313 ft and
the estimated breach formation time is about 1.5 hours.
Columns 7 and 8 of Table 1 contain estimated peak breach flow rates for all seven
failure scenarios based on the Froehlich (1995a) breach parameters used in the DAMBRK
model, and the Froehlich (1995b) peak breach flow rate estimates, respectively.
Table 1. Estimates of breach parameters and comparison of peak breach flows
Embankment/Reservoir
Froehlich (1995a) Breach
Peak Breach Flow
Parameters
Parameters
Using
Reservoir
Froehlich
Failure
Breach
Pool
Froehlich
Volume
Average
Breach
(1995b)
Scenario Elevation at between pool
Bottom
(1995a)
Breach
Time
Predicted
Width
the time of elevation and
Breach
Width
(T)
Peak Breach
(B)
breach
Parameters in
bottom of
Outflow
DAMBRK
breach
ft msl
acft
ft
ft
hours
cfs
cfs
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
E.FP
652.5
82,300
443
313
1.5
784,029
366,974
E. 640
640.0
56,500
393
263
1.2
596,938
281,108
E.630
630.0
41,000
355
224
1.0
467,560
222,267
E.620
620.0
29,000
318
187
0.8
349,036
171,323
E.610
610.0
20,000
282
151
0.7
243,982
128,073
E.600
600.0
13,000
246
115
0.6
153,038
91,198
E.590
590.0
8,000
210
80
0.4
79,893
61,144
Following parameters were constant for the above listed seven failure scenarios:
Dam Crest Elevation = 691.5 ft msl
Breach Bottom Elevation = 546.5 ft msl
Breach Height = 145 ft
ko = 1
Side Slope of Breach, z (h:v) = 0.9
For the seven earthquake-induced SEC failure scenarios, a piping-type breach was
assumed to initiate at an elevation half-way between the pool level at the time of failure and
the bottom elevation. In the DAMBRK model, this type of breach is first treated as a pipe
assuming orifice flow and then as a broad crested weir when the reservoir elevation lowers
sufficiently and/or the pipe enlarges sufficiently such that the reservoir elevation is less than
[3*(piping centerline elevation) - 2*(current breach bottom elevation)] (Maeder 2003).
A comparison between the peak breach flow rates of columns 7 and 8 in Figure 1
shows that at the higher pool elevations using Froehlich’s breach parameters in DAMBRK
results in peak breach flow rates that are more than twice those obtained from using his
empirical equation for the peak breach flow rate, but that the difference narrows at lower pool
elevations. These differences occur because empirical methods for estimating breach
parameters, such as Froehlich (1995a), predict the ultimate breach width and the breach time
for achieving the ultimate breach width; whereas, in practice, the peak flow would generally
occur prior to development of the ultimate breach width and the breach development would
continue during the recession limb of the breach hydrograph. Thus, these empirical estimates
of breach parameters typically lead to overestimates of peak breach flows when used as inputs
in DAMBRK.
900,000
800,000
700,000
Peak Outflow (cfs)
600,000
500,000
400,000
300,000
200,000
100,000
0
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
Reservoir Volume (acre-ft)
Froehlich (1995b) Peak Breach Flow Estimate
Peak flow from DAMBRK using Froehlich (1995a) Breach Parameters
Figure 1. Comparison of peak breach flow rates for failure scenarios
The DAMBRK model typically predicts the occurrence of the peak breach flow rate at
the breach formation time when ultimate breach width specified by the user occurs. When the
ultimate breach width and breach formation time are specified as inputs, this would be
expected to lead to overestimates of the peak flow rate and the time to peak for the reasons
stated in the previous paragraph. In some cases DAMBRK predicts the occurrence of the
peak breach flow before the ultimate breach width is reached. These cases occur when the
reservoir level is reduced at a relatively rapid rate by a relatively wide breach or when the
breach time is relatively long (Full Pool: 2*B, T and Full Pool: B, 2*T cases on Figure 2).
Figure 2 contains plots of various estimates of the breach hydrographs and peak flow
rates for the seven failure scenarios listed in Section 3.1. The following hydrographs and peak
flow estimates are included in Figure 2, with the descriptions of the legend shown in italics:
a) Breach hydrographs based on the Froehlich (1995a) breach parameter estimates
run in the DAMBRK model for Full Pool: Froehlich Parameters and a line joining the
peak flows for the seven scenarios mentioned in Section 3.1: Froehlich Parameter
Peaks.
b) Breach peak flows estimated using the Froehlich (1995b) method for all seven
failure scenarios plotted as horizontal lines between the Breach Flow axis and the time
of the peak flow for the corresponding failure scenario in a): Full Pool: Froehlich Peak;
El.640: Froehlich Peak; El.630: Froehlich Peak; El.620: Froehlich Peak; El.610:
Froehlich Peak; El.600: Froehlich Peak; and El.590: Froehlich Peak.
c) Full pool sensitivity cases for varying breach width obtained from Froehlich
(1995a):
i) A line joining the peak flows for the Full Pool: 0.5*B, T; and Full Pool: 0.5*B, 0.5*T
sensitivity cases: 0.5*B Sensitivity Peaks.
ii) A line joining the peak flows for the Full Pool: B, 2*T; Full Pool: B, 0.5*T; and Full
Pool: Froehlich Parameters sensitivity cases: B Sensitivity Peaks.
iii) A line joining the peak flows for the Full Pool: 2*B, 0.5*T; and Full Pool: 2*B, T
sensitivity cases: 2*B Sensitivity Peaks.
d) Full pool sensitivity cases for varying breach formation time obtained from
Froehlich (1995a):
i) A line joining the peak flows for the Full Pool: 0.5*B, 0.5*T; Full Pool: B, 0.5*T; and
Full Pool: 2*B, 0.5*T sensitivity cases: 0.5*T Sensitivity Peaks.
ii) A line joining the peak flows for the Full Pool: 0.5*B, T; Full Pool: Froehlich
Parameters, which is for B and T, and Full Pool: 2*B, T sensitivity cases: T
Sensitivity Peaks.
The following observations are made based on Figure 2:
1) Peak breach flows estimated directly using Froehlich (1995b) [i.e. plotted as horizontal
lines and listed under b) above] are approximately half the magnitude of peak flows
estimated using DAMBRK based on Froehlich (1995a) [i.e. under a) above] (see also
Figure 1).
2) The time of the peak breach flow is not predicted by Froehlich (1995b). The Froehlich
(1995b) peak breach flows are therefore plotted as horizontal lines from the time of
failure (i.e. time = zero) to the breach formation time, estimated from Froehlich (1995a),
which is considered herein as an upper bound for the time of the peak breach flow.
3) Higher pool levels at the time of failure lead to higher breach flows [compare cases
listed under a) or b) above]
4) Halving the breach width obtained from Froehlich (1995a) for the full pool case leads to
lower peak breach flows even when the breach formation time is halved [i.e. compare
the plots listed under c) i) and c) ii) above].
5) Doubling the breach width obtained from Froehlich (1995a) for the full pool case leads
to higher peak breach flows [i.e. compare the plots listed under c) ii) and c) iii) above].
6) Halving the breach formation time obtained from Froehlich (1995a) for the full pool case
leads to higher peak breach flows [i.e. compare the plots listed under d) i) and d) ii)
above].
7) Doubling the breach formation time obtained from Froehlich (1995a) for the full pool
case leads to a lower peak breach flow [i.e. compare the plots listed under d) ii) and c)
ii) above].
1,600,000
1,600,000
1,400,000
1,400,000
1,200,000
Breach Flow (cfs)
Breach Flow (cfs)
1,200,000
1,000,000
800,000
1,000,000
800,000
600,000
600,000
400,000
400,000
200,000
200,000
0
0
0.5
1
1.5
0
0
0.5
1
1.5
2
2.5
3
3.5
Time (hrs)
Full Pool: Froehlich Parameters
Froehlich Parameter Peaks
1,600,000
1,600,000
1,400,000
1,400,000
1,200,000
1,200,000
1,000,000
1,000,000
800,000
600,000
200,000
200,000
0.5
1
1.5
2
2.5
3
3.5
4
Full Pool: Froehlich Parameters
Full Pool: Froehlich Peak
El.640: Froehlich Peak
El.630: Froehlich Peak
El.620: Froehlich Peak
El.610: Froehlich Peak
El.600: Froehlich Peak
El.590: Froehlich Peak
2*B Sensitivity Peaks
4
0
0
0.5
Time (hrs)
Full Pool: Froehlich Parameters
3.5
600,000
400,000
0
3
800,000
400,000
0
2.5
b) Breach peak flows using Froehlich (1995b)
Breach Flow (cfs)
Breach Flow (cfs)
a) Breach hydrographs based on Froehlich (1995a)
2
Time (hrs)
4
1
1.5
2
2.5
3
3.5
4
Time (hrs)
B Sensitivity Peaks
c) Breach width sensitivity
0.5*B Sensitivity Peaks
Full Pool: Froehlich Parameters
Full Pool: 0.5*B, 0.5*T, Linear
T Sensitivity Peaks
0.5*T Sensitivity Peaks
d) Breach formation time sensitivity
Figure 2. Estimated breach hydrographs and peak flow rates for failure scenarios
8) Peak breach flow rates occur at approximately the specified breach formation time
except when the reservoir level is reduced at a relatively rapid rate by a relatively wide
breach [i.e. about 1.2 hours instead of about 1.5 hours for Full Pool: 2*B, T] or when the
breach time is relatively long [i.e. about 2.3 hours instead of about 3.0 hours for Full
Pool: B, 2*T] or when both these conditions pertain [i.e. about 0.7 hours instead of
about 0.75 hours for Full Pool: 2*B, 0.5*T]
9) A steeper segment is evident on the rising limb of all hydrographs plotted in Figure 2.
This is associated with the transition from orifice flow through a pipe to broad crested
weir flow.
The above observations are consistent with what would be expected from the
discussion of the empirical approaches in Section 2.0.
3.3
Statistical Analyses on data set used in Froehlich (1995b)
The data used by Froehlich (1995b) to develop the regression relationship for predicting
peak breach flow rate (Qp) is plotted in Figure 36. The log-transformed multiple linear
regression equation by Froehlich (1995b) is specified as7:
ln Qp = - 0.499 + 0.295 ln Vw + 1.24 ln Hw
(5)
95% confidence intervals, (L, U), on the individual predicted values of Qp can be
computed using the following relationships (Haan 1994):
L = X h βˆ − t1−α / 2,n− p (σ 2 (1+ X h (X' X)−1 X h '))
(6)
U = X h βˆ + t1−α / 2,n− p (σ 2 (1+ X h (X' X)−1 X h '))
(7)
in which:
6
Yh
Yˆh
βˆ
=
=
=
X
=
n
X-1
X'
=
=
=
ln Qp, =
Xh β
an estimate of Y at the point Xh (a 1 x p vector) in p dimensional space.
a p x 1 vector consisting of the estimates of β, the coefficients of the
regression equation in Equation (5)
the p x n matrix of observed values of the independent variables in
Equation (5)
the number of historic dam failures used to estimate Equation (5)
the inverse of the matrix X
the transpose of the matrix X
Figure 3 in this paper is a reproduction of Figure 3 from Froehlich (1995b) in U.S. customary units
In order to match the coefficients of this equation the peak outflow rates for Puddingstone, Calif. and South
Fork, Penn. in the Froehlich (1995b) dataset were changed from 480, and 8,500 m3/s to 280, and 7,100 m3/s,
respectively. This change was needed to make these points plot at the correct positions as shown in Figure 3 of
Froehlich (1995b).
7
10,000,000
Measured Peak Breach Flows (cfs)
1,000,000
100,000
10,000
1,000
1,000
10,000
100,000
1,000,000
10,000,000
Computed Peak Breach Flows (cfs)
Line of perfect agreement
95% Confidence Intervals
Figure 3. 95% confidence intervals on predicted peak breach flows for the dams in
Froehlich (1995b) data set
As can be seen from the Figure 3, the width of the confidence interval increases
significantly for higher predicted flows when they are transformed from log space, in which the
Froehlich (1995b) was developed. The width of the 95% confidence interval at the lower end
of the historic breach flows (2,507 cfs) is 6,264 cfs, and at the upper end of the historic breach
flows (2,299,680 cfs), it is 3,474,288 cfs wide, with a coefficient of variation of approximately
0.6 in the untransformed space for both the cases.
Based on Equation 7, non-exceedance percentiles, α, for the peak breach flows using
Froehlich (1995a) breach parameter estimate in DAMBRK (column 7 of Table 1) were
computed in log space and are presented in Table 2. These were obtained by calculating the
one-sided t-distribution statistic for 19 degrees of freedom, with the standard error of the
Froehlich (1995b) regression model, σ = 0.42 in log-transformed space. Non-exceedance
percentiles were also computed for the peak breach flows from DAMBRK using 0.5*B, 0.5*T
[half of breach width and breach formation time, respectively obtained from Froehlich (1995a)
breach parameter estimates] for the E.FP, E.630, E.610, and E.590 failure scenarios.
Table 2. Non-exceedance percentiles for peak breach flows based on Froehlich (1995a)
breach parameter estimates and 0.5*B, 0.5*T estimates
Peak Breach Flows and Percentiles
Failure
Scenario
Using Froehlich (1995a)
Breach Parameters in
DAMBRK
cfs
(1)
E.FP
E. 640
E.630
E.620
E.610
E.600
E.590
(2)
784,029
596,938
467,560
349,036
243,982
153,038
79,893
Percentile
(3)
95%
95%
95%
94%
92%
88%
73%
Using Froehlich (1995a)
(0.5*B, 0.5*T) Breach
Parameters in DAMBRK
cfs
(4)
684,805
Percentile
(5)
91%
362,481
86%
175,663
77%
60,466
50%
Froehlich
(1995b)
Predicted
Peak Breach
Outflow
cfs
(6)
366,974
281,108
222,267
171,323
128,073
91,198
61,144
The Froehlich (1995b) peak breach flow estimates and their 95% confidence intervals
for the study dam are plotted against the reservoir volume at the time of breach in Figure 4.
Peak breach flows obtained from DAMBRK using Froehlich (1995a) breach parameters, and
the (0.5*B, 0.5*T) estimates are also shown in Figure 4.
From Table 2 and Figure 4 it can be seen that using the breach parameters obtained
from Froehlich (1995a) in DAMBRK resulted in significant overestimation of the peak breach
flows. For the high pool elevation failure scenarios (E.FP, E.640, and E.630), the peak flows
obtained from DAMBRK were approximately the 95th percentile. For the lowest pool elevation
scenario (E.590), the peak breach flow obtained from DAMBRK is at 73rd percentile. By using
half of the breach width and time to failure (0.5*B, 0.5*T) in DAMBRK, the peak flows (column
4) are still larger than those obtained from Froehlich (1995b) (column 6), but are more
reasonable than using the full breach parameter values in DAMBRK.
4.0
Some Suggestions for Developing Breach Flow Hydrographs
Some suggestions are made for selection of breach parameters based on consideration of
the following:
a) the limitations in the empirical procedures for estimating breach parameters that are
discussed in Section 2.0;
b) the comparisons and sensitivity studies presented in Section 3.2; and
c) the goal, stated in Section 1.0, of obtaining “reasonably realistic” estimates of breach
parameters rather than “conservative” estimates.
1,000,000
900,000
800,000
Peak Outflow (cfs)
700,000
600,000
500,000
400,000
300,000
200,000
100,000
0
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
Reservoir Volume (acre-ft)
Froehlich (1995b) Peak Breach Flow Estimate
95% Confidence Intervals
Peak flow from DAMBRK using Froehlich (1995a) Breach Parameters
Peak flow from DAMBRK using Froehlich (1995a) Breach Parameters (0.5*B, 0.5*T)
Figure 4. Predicted peak breach flows for the case study dam
We propose that breach widths and breach formation times be specified as fractions of
those estimated from the Froehlich (1995a) approach. The fractions, α and β, applied to B and
T, respectively, can be selected by comparing the peak breach flow rates obtained from
DAMBRK through some sensitivity studies with a range of values for α and β, with those
obtained from the Froehlich (1995b) approach. This approach should only be used when the
relevant characteristics of the study reservoir and dam fall within the range represented in the
data sets used by the Froehlich (1995a and b).
The justification for these adjustments is as follows:
a) The results of the statistical analyses given in the Section 3.3 shows that the peak
breach flows are consistent with upper bound estimates obtained using Froehlich
(1995b).
b) The peak breach flows would be modeled to occur at a time and breach width that are
less than the ultimate breach time and width estimated from Froehlich (1995a), which is
consistent with reality.
In selecting α and β consideration should be given to the confidence bounds on the
Froehlich (1995b) estimates of peak breach flows to obtain estimates with given nonexceedance percentiles, such as a) 50% for a “best estimate”, b) a higher value for an
estimate with a degree of conservatism, or c) a range of estimates at various percentile levels
to represent the range of uncertainty. Case b) might be applied when inundation results are to
be used for emergency response planning. Case a) might be useful when a single “best
estimate” of inundation characteristic is needed for a risk assessment although one must
remember that “best estimates” of breach parameters will not necessarily lead to best
estimates of dam failure consequences due to the nonlinear nature of relationships between
breach parameters and consequences (Chauhan and Bowles 2003). Case c) might apply
when it is desired to characterize the uncertainty in consequences estimates associated with
uncertainties in dam breach-inundation modeling, and hence address the nonlinear
interrelationships.
By matching “best estimates” of peak breach flows from the Froehlich (1995b)
approach, one would be emphasizing the rising limb of hydrographs, which is most critical for
estimating consequences, especially life loss. It is expected that the recession limb of the
breach hydrographs may initially decrease more rapidly than expected in some cases because
the DAMBRK model will not continue breach development beyond the specified breach width
after the peak breach flow occurs at the specified breach formation time. However, this is not
considered to be a significant limitation for estimation of consequences, although it could
possibly have an impact on cascade dam failure of downstream dams.
5.0
Conclusions
Use of breach parameters estimated from empirical approaches such as (Froehlich
1995a) as inputs to DAMBRK typically results in significant overestimation of peak breach
flows. Although conservative inundation delineations are sometimes sought for emergency
planning purposes, the use of inundation modeling results from dam breach modeling in risk
assessment requires either “reasonably realistic” results or characterizations of the
uncertainties in those results.
The overestimation problem is demonstrated for a case study presented in Section 3.0,
at least for a dam with a large reservoir. We have seen this overestimation problem on many
dams with large reservoirs. In Section 4.0, we provide some suggestions for the selection of
breach parameters as inputs to the dam breach model.
There is large amount of uncertainty associated with the breach parameter and breach
flow estimation. It would be useful to explore the uncertainties associated with breach
parameter estimates in the Froehlich (1995a) approach and to obtain data sets that cover a
wider range of dam and reservoir characteristics as the basis for improved and more widely
applicable predictive relationships.
However, an underlying need exists for a better
understanding of the physical mechanisms associated with dam failure and breach
development that can provide the foundation for physically-based approaches to breach
hydrograph determination.
6.0
Acknowledgements
The authors acknowledge some helpful discussions with Robert E. Gergens, Hydraulic
Engineer, Reservoir Control Branch, U.S. Army Corps of Engineers, Fort Worth District.
7.0
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