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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 References ARS. 2004. Coordination and Cooperation with European Union on Embankment Failure Analysis. http://www.ars.usda.gov/research/projects/projects.htm. Chauhan, S.S., and D.S. Bowles. 2003, Dam Safety Risk Analysis with Uncertainty Analysis. Proceedings of the Australian Committee on Large Dams Risk Workshop, Launceston, Tasmania, Australia. 17 p. Federal Energy Regulatory Commission. 1987. Engineering guidelines for the evaluation of hydropower projects, FERC 0119-1, Office of Hydropower Licensing, Washington, D.C. July. 9 p. Fread, D.L. 1984. 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