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5 Design Flood Estimates: Methods and Critique TYPES OF APPROACHES As indicated in Chapter 3, most current criteria for spillway adequacy can be placed in two general classes: (1) criteria baser] on probable maximum precipitation (PMP) estimates or probable maximum flood (PMF) estimates derived from PMP estimates ant] (2) criteria based on either floods or rain- falIs having specifier] probabilities or average return periods. A third ap- proach to sizing spillways by analysis of risks to downstream areas from dam failures has come into use, and a variation of this approach, involving eco- nomic analyses of risks and costs of prevention, is also in use. The PMF is considered to define the upper range of flood potential at a site. Because of the methods user] in developing safety evaluation flood estimates, the crite- ria based on PMP and PMF estimates are termec! the deterministic approach, while those based on rainfalls or floods of specified frequencies are labeler] the probabilistic approach. These approaches to establishing appropriate design flood estimates are discussed in this chapter, and further details rele- vant to the deterministic and probabilistic methods are presented in Appen- dixes C and D. Details of the risk analysis approach, along with examples of its use, are presented in Appendix E. DETERMINISTIC APPROACH Summary In estimating a PMF or any design flood by deterministic methods, several tools of meteorology, hydrology, and hydrologic engineering are employed 44

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Design Flood Estimates 45 to synthesize a hydrograph of inflow into the reservoir and to model or simulate the movement of the flood through the reservoir and past the dam. The various steps in such analysis, all of which have been discussed in the NRC's report, Safety of Existing Dams: Evaluation and Improvement, Chapter 4 (1983), are generally as follows: 1. dividing drainage area into subareas, if necessary; 2. deriving runoff model; 3. determining PMP using criteria contained in NOAA Hydrometeoro- logical Report series; 4. arranging PMP increments into logical storm rainfall pattern; 5. estimating for each time interval the losses from rainfall due to such actions as surface detention and infiltration within the watershed; 6. deducting losses from rainfall to estimate rainfall excess values for each time interval; 7. applying rainfall excess values to a runoff model of each subarea of the basin; 8. adding to storm runoff hydrograph allowances for base flow of stream, runoff from prior storms, etc., to obtain the synthesized flood hydro- graph for each subarea; 9. routing of flood for each subarea to point of interest; 10. routing the inflow through the reservoir storage, outlets, and spill- ways to obtain estimates of storage elevations, discharges at the dam, tailwa- ter elevations, etc., that describe the passage of the flood through the reservoir. (This is essentially a process of accounting for volumes of water in inflow, storage, and outflow through the flood period. If there are several reservoirs in the watershed, the reservoir routing is repeated from the upper- most to the most downstream reservoir, in turn.) If the routing shows that the dam would be overtopped and if it is assumed such overtopping will cause the dam to fail, the resulting flood wave may be routed through the downstream valley to give a basis for assessment of damages. Probable Maximum Precipitation (PMP) Evaluation Of the factors that have an influence on the magnitude of the probable maximum flood (PMF), the intensity and duration of rainfall are the most important; hence, considerable discussion of such rainfall estimates follows here and in Appendix C. The rainfall that produces the PMF is termed the probable maximum precipitation (PMP). Its definition (which goes back to the early 1950s) is "the theoretically greatest depth of precipitation for a

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46 SAFETY OF DAMS given duration that is physically possible over a given size storm area at a particular geographical location at a certain time of the year." Several other definitions have been given for PMP, but, in any case, PMP should be termed an estimate, as there are yet unknowns and unmeasured atmospheric pa- rameters that are important to extreme rain storms. In the literature prior to about 1950, the term maximum possible precipi- tation (MPP) was used for estimates of most extreme rainfall. This was changed to probable maximum precipitation because the latter term implies a somewhat less extreme and absolute estimate and reflects the uncertainties involved in estimating maximum precipitation potentials. In practice, both MPP and PMP have essentially the same meaning. PMP estimates usually greatly exceed the rainfall amounts most people experience. Table 5-1 lists current PMP estimates for the Washington, D.C., area as read from charts developed by Schreiner and Riedel (1978~. By contrast, the maximum 24-hour point rainfall that has been recorded in 114 years of record at Washington, D.C., is 7.13 inches. However, within 125 miles, near Tyro, Virginia, 27 inches of rain fell in 12 hours during a storm occurring august 19-20, 1969. In Chapter 4 a brief history is given of the development of the concepts involved in PMP determinations. Such determinations are described in some detail in Appendix C and summarized sequentially as follows: 1. Study major rain storms to determine maximum areal rainfalls and ascertain, as well as possible, the meteorological factors important to the rainfall. 2. Transpose the major storms within topographically and meteorologi- cally homogeneous regions. (Adjust the storm rainfall by multiplying it by the ratio of an index of maximum atmospheric moisture in transposed loca- tion to that where the storm occurred.) TABLE 5-1 PMP Estimates (to Nearest 0.5 Inch) for Vicinity of Washington, D.C. Area Time Duration (h) (sq mi) 6 12 24 48 72 10 27.5 32.S 36 40 42 200 19.5 23 27 31 32 1,000 14 18 22 25 26 5,000 8.5 12 15 19 19.5 10,000 6.5 9.5 12.5 15.5 17 SOURCE: Schreiner and Riedel (1978~.

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Design Floor! Estimates 3. Adjust the rainfall (for each transposed storm) by the ratio of maxi- mum atmospheric moisture in place of occurrence to that which existed cluring the storm. 4. Smoothly envelop the resulting rainfall values durationally, areally, and if generalized PMP is being developed, regionally. Explanations should be given for discontinuities. 47 The resulting rainfall values may be regarded as PMP if sufficient storms were available to justify the assumption that the maximum rainfall potential has, in fact, been assessed. Appendix C describes some procedures that give the user a fee} for how conservative the PMP is. One shows the ratios of PMP depths for a 10-square-mile area and 24-hour duration to the point rainfall depths for 100-year average return period and 24-hour duration at the same locations. These ratios range between 2 and 6 in the United States. Another study shows that 90 known experienced storm rainfall depths are equal to or greater than 50 percent of PMP, both rainfall categories being for 24 hours and 10 square miles. Many more storms exceed 50 percent PMP for several combinations of durations and area sizes (Riedel and Schreiner, 1980~. Fig- ure 5-1 shows a comparison of generalized PMP for 200 square miles and 24 hours determined in 1947 with that in 1978 for the same region (United States east of the 105th meridian). This comparison shows a general increase in PMP estimates over the 31-year period. About 65 percent of the region shows an increase between 10 and 30 percent. From such comparisons it can be concluded that the PMP estimates for the United States from generalized charts determined by the National Weather Service are most likely on the low side when evaluated with reference to the accepted definition of PMP and that future increases in PMP estimates are probable. However, such future increases in estimates are likely to be incrementally less, in general, than those of the past during the period that the science of hydrometeorology was rapidly developing and the data base on past extreme events was being accumulated. Also, studies to redetermine probable maximum precipitation estimates for areas in the Tennessee Valley made in 1978 resulted in some lower estimates than those developed for the same areas in 1968; then more intensive studies sometimes can result in lower estimates even if more data became available. PMP estimates developed as indicated have been widely (but not univer- sally) accepted as the appropriate basis for design of spillways for large dams where failure of the structure by overtopping cannot be tolerated. The increases noted in PMP have posed difficult questions as to what should be clone with spillways at existing dams or those already under construction, where the spillways were adequate under previous criteria but would not be adequate with the revised PMP estimates.

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48 SAFETY OF DAMS 1 In 1.30 1.00 4~r 1~- ~':~:C . . 1 / ( ~ ~ 1.30 _ ~__ ~ 1 --1 1'''' t: ~ ~ ~ ~ ~~ .30 .2~1 s7 \` ~ STATUTE MILES :s ~ 100 0 100 200 300 - 1 Do 0 1 00 200 300 400 KILOMETERS A- - -_1_~_: 'I FIGURE 5-1 Comparison of generalized PMP estimates for 24 hours and 200 square miles made in 1978 with those made in 1947. (Ratios shown are 1978 values/1947 values.) Sources: The IS78 data are from Schreiner and Riedel (1978). The 1947 data are from U.S. Weather Bureau (1947). Antecedent Conditions An important consideration in assessing the impact of any extreme flood on a project is the spectrum of antecedent conditions. These conditions include soil moisture, snowpack and water content where applicable, ex- pected reservoir levels, state of vegetation, intended use or uses of the proj- ect, probability of preceding and subsequent precipitation events, and ambient temperatures. It is generally recognized that even though a hypothetical flood, such as the PMF, is an extreme event to be adopted as a basis for design, it should be conceived in hydrologic and meteorological reasonableness. The antecedent conditions, such as expected reservoir levels, existing snowpack, and soil moisture, are considered in the context of the causative event of the primary flood. For example, if the extreme floods for moderate to large basins result

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Design Flood Estimates 49 from tropical storms that occur from late summer through fall and highest reservoir levels always result from spring snowmelt floods, the two events are not usually combined. In another instance, the test of reasonableness might indicate that in mountainous country, major floods for small basins could result from a heavy rain producing convective thunderstorms, but not of the PMP magnitude, that could occur concurrently with the seasonal snowmelt- generated peak runoff. Generally, it can be considered meteorologically unlikely for the maximum snowmelt runoff flood to occur in combination with any extreme precipitation event. In each situation, it is desirable to evaluate meteorologic reasonableness of the criteria rather than to apply arbitrary rules. Soil moisture and the state of the vegetation affect loss rates and basin runoff characteristics. These vary seasonally and should be evaluated to determine appropriate conditions for occurrence prior to the PMF. Anteced- ent (and subsequent) storm conditions can have an impact on the adequacy of any reservoir design. The effects of the antecedent (or subsequent) storm are related to storm magnitude, area covered, season of occurrence, dry interval between events, and geographic region of the primary rainfall event. It is not feasible to establish general criteria for such conditions. Each situation should be carefully evaluated to assure that assumed conditions are sufficiently con- servative but not atypical of the region. The basic purpose for which the project is designed governs the rules for reservoir operations. Customarily this rule curve is the end-product of study of annual inflow patterns, the schedule of need for releases, the use of these releases, and any site-specific restrictions imposed on reservoir discharges and reservoir levels by downstream channel capacities and riparian inter- ests. These are additional items that must be weighed in importance, and from this analysis is obtained a reservoir level to be used as the initial point in the routing of the design flood and the antecedent storm through the storage and spillway facilities of the site. Usually to avoid increasing downstream flood damages, any assumed reservoir operation plan should include the requirement that no operating procedure will increase the peak reservoir outflow over the peak natural inflow unless specific flood easements to accommodate excess flow downstream have been obtained. As an example, drawdown of reservoir storage in anticipation of a tropical event, which ultimately tracks away from the project catchment, could produce down- stream flows in excess of the inflow that did occur. If this excess flow ex- ceeded channel capacity, it could lead to downstream property damage and claims. Often, however, the orderly drawdown of reservoir storage in those climates where the annual flood event is a snowmelt case, is an accepted practice. This acceptance is based on the fact that the seasonal snowmelt

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50 SAFETY OF DAMS runoff volume may be closely estimated with present-day prediction tech- niques. Reservoir Routing The ability of any reservoir to release water downstream is determined by the project components. Usually these components are comprised of some combination of spillway gates, flashboards, stanchion bays, low-level out- lets, and turbines if the project generates power. In preparation for routing the design flood through the project storage and these facilities, rating curves of discharge versus head must be computed for each applicable component and for the proposed combination of discharge facilities to be used. As a case in point, generally a project designed for flood control will limit releases to the bankful channel capacity downstream up to the point where the inflow has occupied the allocated flood storage volume. From that point on, the typical emergency spillway operates so that the discharge is a func- tion of the head on the spillway, the incremental flood storage usually being fairly small. In those cases where flood control is not the primary purpose of a project, a gated spillway is usually operated when the inflows exceed the capacity of outlet works, including hydropower turbines. This gate operation is usually carried out so that the reservoir level remains constant, thus the outflow is matched with the inflow up to the point of maximum gate operation. Some regulatory bodies require a gate capacity such that a specific percentage of the PMF can be accommodated with one gate inoperable without the dam being overtopped. The routing of the PMF inflow hydrograph through the available reser- voir storage and the spillway facilities of the project utilizes some variation of the volumetric conservation equation: I - 0 = AS where I = reservoir inflow 0 = the outflow or discharge AS = change of storage in reservoir The mechanics of applying and solving this basic equation are given in the standard hydrologic texts and will not be described herein. The preceding discussion is a simplified explanation of what can be very complex operational studies of effect of extreme storm rainfall on a basin and a reservoir. In a typical safety evaluation, judgment is required on many

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Design Flood Estimates 51 factors. Experienced hydrologic engineers may differ to such an extent that their assessments of project safety will be affected. Some may tend to adopt the most critical value for each parameter involved and, thus, tend to make the PMF estimate and routing excessively improbable. Others may tend to regard each of the aspects as independent of the PMP and other factors and adopt average or medium values for each factor. Detailed studies of each situation may provide a guide to selection of the most logical array of choices for that project, but it is not practicable to attempt to formulate rules for such choices at all projects. THE PROBABILISTIC APPROACH As indicated in Chapter 3, safety evaluation floods for small dams, where no serious hazards would exist downstream in the event of breaching, are usually based on rainfall-runoff probability estimates. As discussed in Chap- ter 4, the occurrence of floods in some basins far larger than could have been predicted by probability studies of prior stream records has discouraged the use of probabilistic methods for estimating extremely rare floods. However, the state of California uses estimates of floods with average return periods of 1,000 years as minimum floods for evaluating safety of low-hazard dams. In contrast to practices in the United States, the criteria of the Institution of Civil Engineers call for use of estimates of floods with average return periods of 10,000 years in the British Isles. Past experience has indicated that esti- mates of magnitudes of very rare floods developed by probabilistic methods are even more likely to change as additional basic data become available than flood estimates developed by deterministic methods discussed earlier in this chapter. Some of the basic principles of probability studies are discussed in Appen- dix D. Flood-frequency analyses as discussed in Appendix D produce esti- mated instantaneous peak flows with no estimate of flood volume. A complete hydrograph is needed to perform a flood routing through the reservoir of a given dam. Such a flood hydrograph can be synthesized by utilizing an observed hydrograph from a major historical flood and increas- ing the ordinates of that hydrograph by the ratio of the peak flow determined by frequency analysis to the observed peak flow. Rainfall frequency data can provide another way of synthesizing a flood hydrograph with desired estimated frequency of occurrence. Such a hydro- graph can be developed utilizing an appropriate rainfall-runoff model and rainfall frequency data such as available from NOAA Atlas 2 (Miller et al., 1973). Once a hydrograph of inflow into the reservoir, representing the safety

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52 SAFETY OF DAMS evaluation flood, is obtained, the routing and analyses procedures are essen- tially as described for the deterministic approach. THE RISK ANALYSIS APPROACH Methods of evaluating dam safety by analysis of effects of hypothetical dam failures on downstream areas and on project benefits and costs have been advanced in recent years. These methods do not depend on adoption in advance of specific bases or criteria for dam safety evaluation floods but depend upon site-specific analyses to select the flood appropriate to the safety evaluation. Two types of analysis are in use: (1) those that evaluate only the hydraulic effects of dam failures and (2) those that go further and make an economic analysis to determine the design that has minimum total cost. Appendix E discusses and gives an example of the latter approach. Through computerized modeling of floods and dam break inundation mapping, the safety evaluation flood can be selected at the flood peak level where downstream flood damages would not be increased by the overtop- pingof the dam. In other words, through an iterative trial-and-error compu- tation process, the spillway is sized so that all significant downstream flood damages, from spillway releases and other sources, will have occurred be- fore the dam fails by overtopping. This approach is allowed, as an alterna- tive to selecting a design flood from a generalized chart, by the U.S. Bureau of Reclamation and by several state dam safety programs including Arizona, Colorado, Georgia, North Carolina, Pennsylvania, and South Carolina. Pacific Gas and Electric Company, a private utility firm, also uses this approach to evaluate existing dams. This alternative is also proposed in draft guidelines prepared by a working group of ICODS, the Interagency Com- mittee on Dam Safety (1983) . One of the limitations of this general approach of evaluating only hydraulic effects is the possibility that subsequent down- stream development will encroach on the dam-break inundation area and thus change the conditions which determine that dam failure would cause no further significant damages. Another limitation is that potential damage to project structures and the value of project services (e. g., water supply) are not reflected in the analysis. A more complex version of this approach is to estimate the dollar cost of damage, loss of services provided by the dam, and construction costs of several design alternatives; to estimate the probability of failure for each alternative; and to select the final design at the lowest risk-cost combination. No dollar value is assigned to human lives; in some cases, downstream warn- ing systems and evacuation plans have been relied on to avoid putting hu- man lives into the risk-cost analysis. The quantitative risk-cost analysis approach has been applied to very few

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Design Floorl Estimates dams and is such a recent development that it can barely be called "current practice." However, its use in selecting design standards can be expected to increase in coming years. Risk analysis procedures have been defined by the Bureau of Reclamation (1981a) for internal use. The Interagency Commit- tee on Dam Safety (1983) encourages site-specific breach-routing studies as part of the hazard assessment for proposed dams and suggests that risk-based analysis may be a basis for decision on selection of the safety evaluation flood at particular existing dams. 53 CRITIQUE Some of the deficiencies or limitations observed in currently used criteria and procedures relating to provisions for safety of dams from extreme floods are inherent to any attempt to deal with the random-chance nature of rare floods. This discussion is not intended necessarily as criticism of the criteria or procedures nor of those groups who use them. The comments herein are based on the array of criteria and practices in current use and may not always be applicable to the programs of the Corps of Engineers and the Bureau of Reclamation. The goal of dam safety is to limit the risks from dam failures to acceptable levels. Probability of failure is controlled partly by design standards and partly by quality of design, construction, inspection, operation, and mainte- nance. Ideally, hazard, failure probability, and acceptable damage would be quantified for the site-specific conditions of each individual existing or proposed dam in order to establish site-specific standards for achieving this goal. With few exceptions, current practices do not involve quantification of these three critical elements for each dam. Instead, the most widespread current practice is to classify dams in three broad, not well-defined, qualitative damage potential categories (i.e., high, intermediate, and low hazard) and to somewhat arbitrarily assign one of three or four grades or ranges of design standards to each dam depending on its height, storage capacity, and qualitative hazard rating. Current practice treats all of the elements needed for selecting design standards in a general- ized way; thus, the appropriateness of the design standards as applied to individual dams is generally unknown. In defense of this current general practice, it must be recognized that most of the scores of federal and state regulatory agencies each have hundreds to thousands of dams under their jurisdictions. Given their limited resources, as a practical matter, they must use a generalized system of assigning design standards according to generalized hazard and size classifications, at least as an interim step until more detailed site-specific studies can be made. How- ever, the wide range of hazard versus size versus design standards among the

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54 SAFETY OF DAMS various agencies (see Table 3-3 and Appendix A) reflects a lack of uniformity even within the generalized current practice. This lack of uniformity in dam classification and safety design standards appears to result from three main factors: (1) lack of interagency and inter- governmental communication, (2) variations in engineering judgment in selecting the generalized standards, and (3) variations in public policy atti- tudes at the times the standards were selected. In any case, a critique of present practices must point out that, though a generalized approach to selecting design standards is justified as a practical interim step, there is a need for more uniformity among the various federal and state agencies in establishing size and hazard definitions and correlative design standards. Dam Classification Systems Even if we recognize the need for generalized hazard versus size versus design criteria classifications, the almost universally used high-, intermedi- ate-, and low-hazard classes are not well defined. Qualitative definitions for these terms, such as those used by the Soil Conservation Service and Corps of Engineers, are followed by most federal and state agencies. Some examples of the lack of uniformity in defining "hazard" among the many regulatory agencies are as follows: One federal agency estimates damage potential (i.e., hazard class) as- suming "sunny day" failure, while another federal agency assumes failure only during "floods" as a basis for its hazard classification. In defining high-hazard dams, agencies use such terms as "probable" loss of life, "possible" loss of life, "rural" and "urban" houses downstream, and one agency says that more than 10 houses in a dam-break floodwave places the dam in a high-hazard category. One state agency says a dam is high hazard if there is potential "extensive" loss of life, significant hazard if the dam would endanger "few" lives; another defines a dam as high hazard if there would be "substantial" loss of life, intermediate hazard if a "few" lives would be lost. In contrast, some agencies consider the probable loss of one human life as a high-hazard condition. No agencies define the dollar value of "extensive," "significant," or "minor" economic losses in their hazard classes. An attempt to quantify these hazard definitions was made by the North Carolina Dam Safety Program in 1980 and 1982. Questionnaires asking respondents to quantify the minimum values for each hazard class were distributed among the program staff and among participants at a Southeast- ern Regional Dam Safety Conference. The results (heretofore unpublished)

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Design Flood Estimates TABLE 5-2 Boundaries for Hazard Classes 55 Mean Values of Opinions Hazard Probable Loss Classification of Life Economic Lossa Low 0 Oto $30,000 Significant 0 $30,000 to $200,000 High 1 ormoreb Greater than $200,000 aIncludes downstream damages, but not cost of dam or value of services provided by reservoir. bStrong consensus that loss of one life defines high hazard. reflect an extremely wide range of opinions but indicate the following me- dian opinions from the 46 individual respondents for quantifying the bound- aries on hazard classes (Table 5-2~. Undoubtedly, others will disagree with these evaluations, but such an effort toward more specific hazard definitions could be a step toward a more uniform approach to setting generalized standards. Another weakness in current practice is that, generally, downstream haz- ards are only roughly estimated through judgment based only on visual inspection. This practice is a reflection of limited resources rather than technology, however, and it is reasonable to believe that essentially all prac- titioners recognize the desirability of inundation mapping through breach- routing methods. Spillway Capacity Criteria As shown in Chapter 3, there has been general agreement, with some exceptions, that the spillways of large, high-hazard dams should be able to pass the probable maximum flood without the dam being overtopped. All federal agencies agree with this standard. Only a few states indicated that smaller floods are used as criteria for spillway capacity at such dams. One other type of exception sometimes encountered involves concrete dams on solid rock foundations. Indicated overtopping of such a dam during the probable maximum flood may be permitted by some agencies, if the rock at the toe of dam is judged able to withstand the hydraulic forces imposed and the stability of the dam would not be compromised otherwise. For smaller dams and those with lower hazard ratings, there is much greater divergence in views concerning appropriate spillway capacity requirements. As noted in Chapter 4, the rationale for some of the spillway capacity criteria in use seems questionable, particularly the criteria based on an arbitrary percent- age of the probable maximum flood or an arbitrary percentage of a flood of

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56 SAFETY OF DAMS specified probability or criteria that combine the probabilistic and determi- nistic approaches. The problem with such a criterion, based on an arbitrary percentage of a derived flood or on arbitrary combination of floods devel- oped from differing concepts, is that it permits no direct evaluation of the relative degree of safety provided. While regional differences in climate, geography, development, etc., could justify some of the differences in spillway capacity criteria, it appears that not all the criteria could be efficient in limiting risks of dam failures to acceptable limits or in protecting the public interest. Efforts to secure more uniform approaches to specifying spillway capacity should be encouraged, but such effort is considered beyond the scope of this report. The newly established Association of State Dam Safety Officials may wish to consider action toward such a goal. Some differences among agencies have been noted in practices followed in developing probable maximum flood estimates from probable maximum precipitation values. These differences relate to assumptions regarding ante- cedent rainfalls, initial reservoir levels, arrangement of precipitation values, runoff models, etc. The committee has found general agreement in the following observa- tions regarding current spillway capacity criteria: Interpretations of data from past storms and storm mode} concepts are required to make estimates of PMP. As shown by past experience, PMP estimates can change as more data become available; thus, the PMP estimate cannot be regarded as a fixed criterion, but confidence in the estimates should rise with successive PMP estimates for a given locality. The probability that rainfall will equal or exceed current PMP esti- mates is indeterminate but probably not uniform for projects in different parts of the country. In order that judgments can be made on appropriate allocation of resources, it would be desirable to be able to express spillway design flood criteria in terms of annual probabilities. As has been found previously, statistical studies of data from past floods may serve to indicate the minimum spillway capacities that should be con- sidered but generally do not provide reliable basis for spillway design if there are significant or high hazards downstream in the event of dam failure. As a dam owner or as a regulator of dams in the interest of public safety, a government agency should seek to achieve a proper balance between costs to improve dam safety and risks to the public. It is appropriate that dam safety criteria recognize differences in conse- quences of failure.

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Design Flood Estimates It is good public policy to require management plans (such as warning systems, evacuation plans, and operating rules) to reduce hazards (princi- pally to lives) of dam failures, but the long-term use of such plans should not be a substitute for work to remedy serious safety deficiencies. (The commit- tee notes that maintenance over long time periods of an effective emergency management system to avert loss of life from failure of a dam would require continuing cledicated efforts and support to maintain and operate hard- ware, to train and inform emergency action personnel and the public, to establish and maintain institutional arrangements, ant] to upgrade the sys- tem to meet changes in the area to be served.) Even though some problems with current PMP estimates have been noted, such estimates still offer the bases on which the engineering profession has the most confidence for sizing spillways of new, large dams in the high- hazard category. Each existing large, high-hazard dam having a spillway that fails to meet current PMF criteria should be considered separately. It does not seem appropriate to adopt fixer] rules for such situations. Each study should con- sider how deficient the project is under current criteria and the relationship of the allocated spillway capacity to other floor] criteria. If the deficiency relates to change in safety evaluation criteria (such as an increase in PMP estimates), the reasons for such change and their relationship to the project in question should be critically examined. 57 Risk-Cost Analyses As described earlier in this chapter, the risk analysis approach has pro- vided a significant trend toward improved assessments and toward selecting more rational, site-specific spillway evaluation standards within the last few years. Though risk-cost analyses may appear to represent the most desirable approach to the goal of dam safety (i.e., in quantifying hazard, failure probability, and acceptable damage) at this time, this method has certain important problem areas or limitations that the user needs to consider. An ICODS critique of the risk-cost analysis method mentions the following points. Estimates of the probability of exceedance of extreme hydrologic events are imprecise, whereas the total costs associated with different alternatives may be sensitive to these estimates. Those factors which cannot be measured in economic terms such as loss of human life, social losses, and environmental impacts are more difficult to reflect in the risk analysis but may be the most important in making deci- sions.

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58 SAFETY OF DAMS Results of a quantitative risk-based analysis reflect probable annual . . ~ . , . . , . . . ~ . . .. costs but a dam failure may result in a single catastrophic toss from wn~cn the owner and many others may not recover; thus the relevancy of the analysis to the interests of the parties involved may be questionable. Additional problem areas noted in risk-cost analyses are as follows: Future development below a dam is usually unpredictable and may invalidate the risk-cost determination and the safety evaluation flood se- lected for present (or inaccurately predicted future) conditions. There may be a tendency to rely on downstream warning systems to eliminate loss of human lives from the analyses and thus to determine the lowest risk-cost design standard. However, the real effectiveness of a down- stream warning system may be questionable and reliance on such systems may give a false sense of security to design engineers, dam owners, ant! residents below a dam. Risk analysis places heavy emphasis on hydraulic evaluations of un- usual situations at dams and downstream. However, the reliability of flood- and dam-break-routing models has not been sufficiently determined; the models have been checked against only a few actual dam-break floods. Yet the accuracy of modeling flood and dam-break inundation areas is often critical in a risk-based analysis. One unknown in even the best dam-break- routing models is the "rate of breach development" to assign during the modeled failure; the estimate of damages from relatively small reservoir dam failures is often extremely sensitive to rate of failure (rate of reservoir release), particularly for "sunny day" failure conditions. Also, in quantify- ing downstream damage predictions (hazard) in risk-based analyses, the water depth/velocity and debris load required to damage various structures are sometimes uncertain. This can have a critical effect on the accuracy of the computed lowest risk-cost. The depth and duration of overtopping that various dams can with- stand without failure are unknown. It may be desirable economically, and physically safe, to allow some overtopping of existing dams in a risk-based analysis, but there are no reliable data on tolerable limits. This has dramatic economic implications nationwide that will not be resolved by risk-based analyses. Although a risk-based analysis may not be expensive if compared to probable costs of remedial measures to improve dam safety, for some dam owners such an analysis may not appear to be economically feasible for smaller (though high- or intermediate-hazard) dams. Further, some regula- tory agencies may not have the financial and technical resources to conduct

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Design Flood Estimates risk-based analyses on tens of thousands of dams in order to set appropriate site-specific design standards. 59 The above-discussed areas of potential problems in application of risk analysis technique do not, necessarily, detract from the usefulness of this type approach, as long as they are recognized and provided for. In fact, it is expected that, with more experience and research, these limitations may be minimized. Other factors that make risk-based analysis an attractive tech- nique are as follows: Risk-based analyses, as presently performed, generally are not in- tended to replace appropriately conservative design standards. Rather, risk- based analyses provide additional information to decision makers to help them decide how limited funds can best be allocates] to reduce risks. Risk-based analyses are not intended to provide a sole basis for making decisions. They only provide a portion of the information needed. By performing sensitivity studies, many of the problems with perform- ing a risk-based analysis can be minimizer] and the results bounclecI. The process of performing a risk-based analysis often uncovers factors or sensitivity relationships that might otherwise not be identifiecI. Those factors that cannot be measured in economic terms, such as loss of human life, can be accounted for in separate risk-based analyses and given the appropriate weight (as implied in Appendix E). Overview This critique of current practices has focused on three levels of sophistica- tion in setting standards: (1) the widespread generalized approach, relying largely on judgment to assess hazard and selecting design standards based on loosely defined categories; (2) using site-specific dam-break-routing studies to better define hazard and to select a spillway design flood without quanti- fying risks and costs; and (3) risk-based analysis, which extends the second category by attempting to quantify all of the significant variables in selecting standards. Some of the main strengths and deficiencies associated with each of these three levels have been discussed. Two other deficiencies must be pointed out in a broad overview of current practice. First, about one-half of the states either have no standards for nonfederal dams or have seriously inadequate implementation of standards (Tschantz, 1983, 1984~. Since there are well over 60,000 nonfederal dams in this country, this current practice (really, lack of applying any standards) has serious national implica- tions regarding the achievement of safety goals for dams. Second, most

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60 SAFETY OF DAMS standard-setting efforts have been focused (as does this report) on large, high-hazard, federally owned dams where it is clear that very high standards must be applied and where public investment in the dams and their services is very important. However, smaller nonfederal dams (U.S. Army Corps of Engineers, 1982) pose the greatest aggregate of risks nationally, and their wide range of sizes and hazards requires a wide range of design standards. Focus on the various aspects of the PMP or PMF for large, high-hazard dams has tended to detract from the need for developing appropriate standards for tens of thousands of smaller, yet very important dams. In summary, design standards based on size ranges and general hazard classifications of dams are a necessary evil from a regulatory or administra- tive standpoint, but the diverse and ambiguous definitions within this pre- dominant current practice reflect a serious lack of uniformity among federal end state agencies in applying this approach. The generalized hazard defini- tions are vague, and the appropriateness of the design standards applied to the size/hazard ranges is generally unknown, leaving the appropriateness of the generalized standards at specific dams even more in doubt than they reasonably could be. Exceptions exist for very large, very high-hazard dams for which there is a clear consensus that something like the probable maxi- mum flood is the appropriate inflow design flood or is most likely the best of the available alternatives for such applications. However, this design flood is not necessarily appropriate for the thousands of existing smaller (yet high- hazard) dams. Where site-specific studies are economically feasible, selec- tion of the design standard] for each dam through dam-break routing studies without placing a dollar value on predicted damages is definitely a tempo- rary improvement over the generalized standards but is limited by the possi- bility of future downstream development. Finally, risk-based analysis, which attempts to quantitatively balance the total cost of alternative design standards against probability of failure, has its own limitations in its present state of development, but can provide information useful to decisions involv- ing making dams safe from extreme floods.