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Risk-Based Decision Analysis SUMMARY Engineering is inherently based on a weighing of risks. Traditionally, this has been drawn to a large extent from judgment reinforced by experience. As techniques of risk analysis offered in the literature have become increas- ingly sophisticated, practical engineers and related professionals have pre- ferred to apply time-tested judgmental approaches rather than new tech- niques. Yet there is a need to improve methods of risk analysis in the engineering of dams and other structures whose safety is important to the public interest. This especially applies where funding for remedial work is limited and expenditures must be directed to achieve an optimum reduc- tion of risk. Those who advocate the use of advanced risk-based techniques must communicate, in understandable terms, the merits of their systems. Too often these have been presented on a general and overly technical statistical basis. There is a need to apply these numerical approaches to site specifics by merging theory with realistic appraisal of local conditions. Probability analysis is logically applied to natural events that affect projects, such as in calculation of the frequency and intensity of rainfall that may recharge the water in an incipient landslide or of an earthquake that may trigger move- ment of an earth or rock mass. These applications are well accepted, as are procedures for estimating floods. However, there is a largely unexplored potential for extension of risk analysis into other aspects of dam safety. The role of risk assessment is to provide a formal, consistent approach to evaluate the likelihood of occurrence of various adverse outcomes. In a de- cision analysis approach, actions are optimized in the face of uncertain ad- 41

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42 SAFETY OF EXISTING DAMS verse outcomes. Optimization could be to achieve minimum loss of life or property damage or to maximize risk reduction benefits at minimum cost. Contrary to the reasoning often given for the inadequacy or inappropriate- ness of risk analysis methods, uncertainty about events is the primary basis for using a formal probabilistic approach, not the reason to disavow its use- fuiness. This holds regardless of the sources of uncertainty, whether they are due to our limited modeling capabilities, scarcity of observational data, or the inherent randomness of the process. Another misconception is that the probabilistic risk analysis replaces engineering judgment and intuition. Far from being mutually exclusive, methods of risk analysis and engineer- ing judgment complement and strengthen each other. The accountability and consistency of judgmental procedures can be improved by risk-based procedures. Risk analysis helps decision makers summarize available information and quantify associated uncertainties of the available information. These procedures in themselves do not make decisions. Needless to say, when there is clear evidence of unsafe conditions at a dam, it is better to initiate remedial action (if possible) than to initiate extensive engineering studies, including formal risk analysis. In prioritizing dams for safety evaluation, it is appropriate to use an ap- proximate risk-based screening process. At this level of analysis, only rela- tive risk evaluation is needed. If information-gathering and -analysis pro- cedures are consistent for all the dams under investigation, the priorities obtained will be relatively insensitive to the decision criteria used for prioritizing. In risk analysis aimed at prioritizing dams, it is not necessary to do extensive probabilistic studies for hydrologic, geotechnical, or seismic aspects. In conducting a more detailed probabilistic risk assessment for a given dam, it is necessary to gather and analyze as complete a package of infor- mation as is economically and technically possible. It is also necessary to evaluate risk of failure due to all external and internal load conditions. Be- fore a decision is reached about the safety level of a dam, all economic, social, and political constraints should be incorporated. The most important recommendation to a new user of risk analysis pro- cedures is to overcome the reluctance to employ probabilistic procedures. It is true that more examples and case studies are needed, so that users can understand the simplicity and rationality of the available procedures. Groups that have developed the probabilistic risk-based studies should hold workshops and courses to apply the "academic" and "analytical" proce- dures to practical problem situations involving existing dams. The work done by the U.S. Bureau of Reclamation and by certain uni- versity groups on probabilistic risk analysis for dams should be made avail-

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R'sk-Based Decmon Analysts 43 able to the user community. This could provide further impetus to simplify and improve these methods. We believe that the limited acceptance of for- mal risk analysis comes more from lack of knowledge of the tools than from their complexity. Consistent and continuous use and improvements will in- crease acceptance in the long run. The methods will be adopted more widely as familiarity with them and appreciation of their value grow. INTRODUCTION The resolution of dam safety problems requires an understanding not only of technical questions but also of complex financial and institutional prob- lems. In the competition for limited public funds, a dam safety program is often seen as one of many worthwhile but expensive hazard mitigation pro- grams. In many cases the effective rehabilitation of an existing dam would im- pact severely on the financial resources of the dam owner. Increasingly, therefore, dam safety program managers, owners, and their technical staffs must be prepared to support and justify engineering decisions by the use of an analysis of the trade-off between cost and risk. For an owner of a large number of dams, such as a large utility, city, or water district, the problem may be to prioritize the dams for remedial measures and to budget appropriate funds in order to achieve the greatest safety for the least money. Methods of decision and risk analysis are helpful for making these decisions in as consistent a manner as possible. The methodology for risk assessment has to be evaluated in the context of specific decision situations. The owner of a single dam with multiple defi- ciencies has to decide what priority to assign to his work plan in order to accomplish his objective. Should he remedy a stability problem or increase the spillway capacity, or reduce seepage, or consider a combination of re- medial actions? An owner with several dams is confronted with similar de- cisions concerning the deficiencies of each dam. Each of the decision situations mentioned involves a fundamental trade- off between (certain) expenditures and (uncertain) future gains and losses. It is useful to identify one of the alternatives in a decision situation as the "reference alternative." In decision making about existing dams, the obvi- ous reference alternative is to "do nothing," i. e., to accept the risk and con- sequences associated with the status quo. Perhaps the most critical step in the decision analysis process is to con- ceive alternatives for providing added protection or for providing it more cheaply. For each alternative the engineer must evaluate the added cost in relation to the "do nothing" alternative as well as its effectiveness in reduc- ing the probability of failure or the consequences or both. Based on this

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44 SAFETY OF EXISTING DAMS evaluation and guided by appropriate decision criteria, the engineer must select the most favorable alternative or, when acting in an advisory capac- ity, present all the facts on cost and risk to the decision maker. There is no single best methodology of risk assessment and risk manage- ment for dams. Evidently, the amount and quality of information avail- able to the engineer will differ greatly depending on the nature of the deci- sion, the resources available to analyze existing information or to seek new information, and the time available to reach the decision. It is therefore appropriate to use different methodologies requiring different levels of so- phistication and different types of information about failure consequences and risk where the appropriate methodology is selected according to the decision situation. The sequential nature of engineering decisions has important implica- tions in risk assessment and management for dams. In general, assuming adequate records are kept, the amount and the quality of information about site conditions and structural properties increases with time. In this context it is useful to distinguish between decisions that have a "one-time" or "terminal" character (such as in design or rehabilitation) and those that do not (such as site exploration or dam inspection). Decisions in the latter category are expected to be followed either by other "nonterminal" deci- sions (more extensive exploration or inspections or by a "terminal" deci- sion. In the context of the U.S. Army Corps of Engineers' Dam Safety Pro- gram, decisions taken during "Phase I" dam inspection are nonterminal, while "Phase II" decisions involving repair and rehabilitation may be thought of as one-step or terminal decisions. The idea is that in analyzing a nonterminal decision it is necessary to consider follow-up actions, while one-step decisions can be analyzed in isolation. In the first step of a sequen- tial decision process the engineer is usually concerned about data acquisi- tion, while in the final step he seeks the actual realization of the benefits of proposed protective measures. It is also useful to categorize safety-related decisions involving dams ac- cording to the number and type of structures involved. The decision situa- tion may involve: a single dam, a group of dams in a given jurisdiction, a system of dams located in series on a waterway, a system of dams affecting a common area, or all dams of a certain type (e. g., concrete arch dams) affected by a par- ticular set of design criteria or regulatory requirements. Many considerations go into the formulation of the criteria for decisions affecting dam safety. It may be necessary to distinguish between the types

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R'sk-Based Decagon Analysis 45 of dams involved and their purpose (e.g., flood control vs. recreation), types of ownership (public vs. private), types of decisions (modification of operations vs. rehabilitation), and kinds of protective measures (structural vs. nonstructural). Lest the merits of methods of risk assessment and risk management be overstated, it should be mentioned that questions involving hazard mitiga- tion are often controversial. Different parties (owner, downstream resi- dent, builder) are affected differently by the outcome of the decision. EIence, they tend to assess costs and risks differently and may select differ- ent criteria upon which to base the decision. In light of these conflicts the main value of decision analysis methodology may be that it provides a framework for organizing factual information about costs and risk, for structuring the decision-making process, and for promoting and uplifting communication among the opposing parties (Vanmarcke 1974~. RISK ASSESSMENT: ALTERNATIVE METHODS The detail to which risk assessment is carried out depends on the intended application of its results. If comparisons are to be drawn among dams or among alternative treatments for a given dam, it is important that the as- sessment procedures be consistent. Three broad levels of risk assessment are currently in practice and may be categorized as subjective, index-based, and formal (quantitative). A subjective assessment is one in which all relevant factors are not sys- tematically accounted for. The engineer or owner considers those factors that appear most important to the case and uses this assessment to identify a solution to the problem. Such an assessment may often result in a good de- cision and may be all that is needed, but it will only rarely lead to an opti- mum solution, and it will be difficult either to document, respect, or fully account for. An index-based risk assessment is a systematic evaluation of the factors affecting dam safety that allows a ranking, rating, or scoring of a number of dams. It is more general and complete than a subjective assessment but does not permit numerical comparison of likelihood or expected cost. Spe- cific site conditions are often difficult to factor in, except subjectively. Sev- eral examples of such a qualitative risk assessment are presented later in this section. In a formal risk assessment one estimates occurrence frequencies, rela- tive likelihoods of different levels of response and damage, and the various components of cost and consequences. Although an actual value of risk cost is determined, this value often need not be considered in absolute terms but as a number suitable for comparison among alternative risk reduction

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46 SAFETY OF EXISTING DAMS measures. An integral part of a risk assessment is that one should vary as- sumptions about any of the study parameters to determine their effect on the risk cost and (when used on risk management) on the optimal choice. The most common format of a risk assessment involves the following steps: Identification of the events or sequences of events that can lead to dam failure and evaluation of their (relative) likelihood of occurrence. Identification of the potential modes of failure that might result from the adverse initiating events. Evaluation of the likelihood that a particular mode of dam failure will occur given a particular level of loading. Determination of the consequences of failure for each potential failure mode. Calculation of the risk costs, i.e., the summation of expected losses (economic and social) from potential dam failure. A more detailed discussion of these steps is given below. Step 1. Identify what loading conditions operate on the dam with the potential to cause a dam failure, and estimate the frequency of occurrence of these events. The loading conditions that usually need to be considered are static res- ervoir load, seismic load, and hydrologic (flood) load. However, for a spe- cific dam other loads (see next section) may need to be considered. In the course of the risk assessment, some loads may be ruled out as not having the potential for dam failure. It is recognized that the estimation of the fre- quency of hydrologic and seismic events with the potential to cause dam failure is difficult to make with confidence because of the lack of historic data. The evaluation of the likelihood of "internal" or "passive" initiating events (foundation instability due to strength deterioration or piping) is even more difficult. Nevertheless, such an estimate is a necessary part of any risk assessment. Step 2. Given the configuration, characteristics, and condition of the dam-foundation-spillway system and the loading conditions to which it will be exposed, identify the potential modes of failure that may result from the loading events. This is the first step in determining the response of the structure as well as the consequences of failure. The detail to which the modes need to be iden- tified is very much site- and problem-specific. In some cases the assessment of risk and consequences may be satisfactorily made by assuming a com- plete and instantaneous dam breach, while in other cases this assumption

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R'sk-Based Decision Analysis 47 would yield a very unrealistic estimate of damages (and hence the benefits of remedial measures). Step 3. Estimate the likelihood that a particular mode of dam failure will occur for a range of levels of potential adverse loadings. The third step is perhaps the most difficult in the risk assessment process. It is necessary to account for the entire range of loads through which it is exposed and for how a dam responds to these loads. An estimate of response is required for all types of loads over the entire damage potential range of loads such that the "unconditional" risk of failure may be realistically as- sessed. This step is one of the fundamental differences between a risk-based safety assessment and the "maximum event" analysis that is in common practice. Step 4. Determine the consequences of failure for each potential failure mode. Once a mode of failure has been defined, the flood caused by the dam break is routed through the flood plain. Inundation maps (and flow rates) are used to estimate the potential for loss of life, the level of property dam- age, and environmental impact. Uncertain factors such as season of year, time of day, reservoir elevation, and antecedent precipitation might have to be taken into account at this stage of the analysis. (These factors may also be important in identifying appropriate remedial measures.) Step 5. Determine the risk costs or "expected losses" associated with the existing dam in its present condition. The total economic risk cost is obtained by summing the product of the likelihood of the loading condition, the likelihood of dam failure in differ- ent modes given the loading condition, and the cost of the damages result- ing from that failure mode over the entire range of load levels and failure modes. Similar calculations can be made for the expected losses of life or the "social risk cost." These require expressing the life loss consequences for each potential failure mode in Step 4. Risk-Based Methods for Prioritizing Dams The Stanford risk-based screening procedure (McCann et al. 1983b,c) is divided into three phases. The objective in the first phase is to identify the expected losses given dam failure. The work involved includes tasks for gathering data, an evaluation of the likelihood of dam failure due to a number of initiating events, routing of a flood wave as a result of instanta- neous dam failure, and an estimate of the direct Tosses. The data collected

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48 SAFETY OF EXISTING DAMS will include information on the dam, the spillway, downstream topogra- phy and development, design criteria, inspection programs, etc. This cor- responds essentially to the Phase I inspection of the National Dam Safety Inspection Program. In the second phase the expected loss due to dam failure is determined. The probability of failure will be a function of the present structural capac- ity of the dam and the likelihood of occurrence of loading conditions that might induce failure. The objective in the third phase is to consider the mitigation alternatives that might be available, what their associated costs are, and the additional level of safety they would achieve. An analysis of this type will provide the decision maker with information on the cost-effectiveness of upgrading a dam. The actual tasks include identification of a mitigation program to upgrade the dam, determination of the cost of implementation, and a re- evaluation of the expected loss for the dam in an upgraded condition. The result of this phase is a ranking of the dams that can be based on a cost per unit of increased benefit. In several MIT Research Reports (1982) an analogous framework is pre- sented for decision analysis of hazard mitigation measures for existing dams. Several common decision situations are examined, including the problem of allocating limited funds for remedial work to a large number of dams. The proposed procedure is illustrated by means of a case study in- volving 16 actual dams located in rural Vermont. The basic sources of in- formation are the Inspection Reports issued under the National Dam In- spection Program, where it is shown how costs, risks, and consequences can be estimated for the status quo as well as under different alternatives for upgrading. A critical component in the analysis is of course the risk of dam failure, which is estimated by an updating procedure that permits combining dif- ferent sources of information. Based on general background information on the group of dams under study (type, age, location), a subjective prior risk is assigned. Using specific information on each dam (from the Inspec- tion Reports), the prior risk is then updated using Bayes's theorem. Empha- sis is on demonstrating the flexibility of the mode! as it includes carrying out a sensitivity analysis with respect to the decision criteria and the input data. As with all ranking and allocation procedures, an important step in the implementation of risk-based methods is the uniformity with which the method is applied. Consistency will be required in inspection reporting practice, interpretation of inspection reports (specific wording is useful), application of analysis procedures, etc. Regardless of the method adopted, whether probabilistic or deterministic, unless a degree of consistency in ap-

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R'sk-Based Decagon Aru~lys~s 49 plication can be ensured, achieving a reliable and consistent ranking will be jeopardized. Methods of Index-Based (Qualitative) Risk Assessment The development of a methodology to conduct a fast, reliable evaluation of the safety of dams in a jurisdiction has not been limited to formal risk-based procedures. In a preliminary risk assessment required to screen or prioritize a large number of dams for inspection or rehabilitation, it may be appro- priate to substitute an index-based procedure for formal quantitative risk analysis. Several organizations have developed such index-based proce- dures to provide a ranking or prioritizing of a system of dams, including the U.S. Bureau of Reclamation; the U.S. Army Corps of Engineers; and the states of Idaho, California, Pennsylvania, and North Carolina. Two of these methods are discussed below, in particular the procedure suggested by Hagen (1982) of the U.S. Army Corps of Engineers and the Safety Eval- uation of Existing Dams (SEED) program used by the U.S. Bureau of Rec- lamation. These procedures consider the same factors as does a quantita- tive risk analysis, but they are in terms of a set of ranking parameters that take integer values between 1 and 5. A score of 1 is most favorable, a score of 5 least favorable. According to Hagen?s method, the overall "relative risk" index for a dam equals the sum of an "overtopping failure score" and a "structural failure score," i.e., Rr = 0t + St, where 0~ = overtopping failure score = 0~ x O2 x O3 and So = struc- tural failure score = So X S2 X S3. The factors depend on the following considerations: Factor 0~: Number of homes endangered by failure. (Based on differ- ence in area inundated without failure and with failure, assuming water surface at the top of dam. Dam failure hydrograph superimposed on dis- charge prevailing at the time of failure.) Factor O2: Project flood capability in the percentage of current design flood standard. (Assuming the probable maximum flood is the current de- sign flood standard.) Factor O3: Project capability to resist failure by overtopping. (Based on inspection of the structure and review of design and construction records.) Factor So: Number of homes endangered by failure. (Area inundated is obtained from dam failure with water level at the top of flood control stor- age or normal maximum pool excluding surcharge used to pass design flood.)

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50 SAFETY OF EXISTING DAMS Factor S2: Evidence of structural distress. (Based on inspection of the structure and review of design and construction records.) Factor S3: Potential seismic activity. (Based on dam location on seismic zone map, knowledge of faults, recent earthquake epicenters, and dam de- sign procedures.) The maximum rating score for a dam by the selected rating scales would be 250 (i.e., 125 associated with "overtopping failure" ant] 125 with "struc- tural failure". A dam with a smaller score than some other dam should generally pose less of a risk. Safety Evaluation of Existing Dams (SEED) The U.S. Bureau of Reclamation has developed a program to evaluate the safety of existing dams. The evaluation process includes a review of avail- able data on a dam and a field inspection. The data review covers all as- pects of the dam from geologic and seismic conditions to a review of the construction experience and operations. A detailed evaluation report is pre- pared on each dam, and a site rating (SR), a numerical measure of the dam's condition and damage potential, is assigned. A score is given on a scale of 0 to 9 to various elements shown in Table 3-1. The SR is a sum of the element scores. During a field investigation a checklist of items is examined. For this purpose the Bureau has prepared a handbook to assist the examiner in iden- tifying areas of potential distress in the dam (SEED 1980~. On the basis of the site investigation, recommendations for upgrading are made, and their significance is measured by a weighting system that considers a categories' overall importance as well as its degree within each category. The sum of the weights for all recommendations is added to the SR to give a SEED value. The results for all dams are used to develop a SEED rank, where the highest SEED value has a rank of 1. Other features of the SEED program include information on estimates of costs to carry out the recommender] upgrades, scheduling information, sta- tus of different upgrades, and key personnel involved in the project. In ad- dition, the information is stored on a computer and is continually updated. METHOD OF RISK ASSESSMENT FOR SPECIFIC CONDITIONS It has been noted in previous discussions that an effective risk-based decision analysis must incorporate site-specific conditions related to the most likely fail- ure modes, hazard conditions, and possible remedial measures. The technical elements that are common to different procedures of risk-based dam safety as-

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R'sk-Based Decmon Analysis TABLE 3-1 Hazard Rating Criteria in Hagen s Procedure 51 Condition Age (years) Under 5 5-24 25-29 50- (0) (3) (4) (9) General condition Excellent Good Fair Poor (0) (3*) (6) (9) Seepage problems None Slighta Moderate High (0) (3) (6) (9) Structural behavior measurements current Yes Partial No end within acceptable (0) (6) (9) Damage Potential Low Moderate High Extreme Capacity (acre-feet) 0-999 1,000-49,999 50,000-499,999 500,000- (0) (3) (6) (9) Hydraulic height (feet) 0-39 40-99 100-299 300- (0) (3) (6) (9) Hazard potential (0) (4) (8) Hydrologic adequacy Yes No (O) (9) Seismic zone 0-1 2 3 (0) (3) (6) 4 (9) NOTE: Number in parenthesis is the weighting factor. aAssumed if not given. sessment are estimation of the frequency of occurrence of loading events, evalu- ation of the response of the structure to the loading, and prediction of damage downstream. The approach to the solution of these technical problems is best examined in the context of the major loading conditions to which the dam is exposed: static loading, hydrologic loading, and earthquake-induced dynamic loading. Risk of Dam Failure Due to Static Loading To determine the risk of dam failure due to static loading, each of the failure modes relevant to a particular dam needs to be identified. The items in the list must preferably be all-inclusive and mutually exclusive. If the likelihood of cer- tain failure modes is judged negligible compared with that of other modes, these may be omitted from formal consideration. Once the potential failure

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60 SAFETY OF EXISTING DAMS reduce the likelihood of failure; however, it can be effective in reducing the consequences of one. Flood Plain Management. A flood plain management program can be applied to all or only a portion of the area inundated by dam failure. Simi- larly, the program can be applied only to modification of uses of the flood plain or can be expanded to include existing uses. The preparation of inun- dation maps, as has been done in California, is a relatively conservative measure of modest cost. Such maps will not reduce the probability of fail- ure but will provide a basis for determining the impact of a flood, which enhances evacuation and reduces liability. Included are such measures as permanent relocation of downstream structures, change in existing land use, floodproofing of structures, instal- lation of individual or group levees to protect a damageable area from flooding, and purchase or other land-use controls to keep future develop- ment from being subjected to flooding. Since these alternatives do not af- fect the dam itself, there is no change in the likelihood of failure. The cost of this alternative can be quite high, depending on the nature of development or property values in the affected area. It should be noted that some measures, such as levees, may need to be higher (to contain flows from a breach) and therefore may be more expensive than they would if no dam existed. Social impacts could also be high, particularly in some areas involving relocation. EXAMPLES OF RISK ASSESSMENT AND DECISION ANALYSIS In this section a number of case studies involving the application of risk analysis to dams will be described. The emphasis in each write-up is on the problem formulation and the results. The risk assessment methodology is briefly summarized, but its details are not presented and may be found in the case study reports that are referenced. Case I: Jackson Lake Dam During the U.S. Bureau of Reclamation's review of its existing structures for adequacy of performance under current earthquake criteria, Jackson Lake Dam was identified as being located in an area with the potential for strong earthquake shaking. The fine-grained soils on which the embank- ment portion of the dam was founded and the hydraulic fill methods that were used to place a portion of the earth embankment presented the poten- tial for liquefaction at the site under strong earthquake loading. A drilling, sampling, and laboratory testing program was initiated to define the loca-

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R1sk-Based Decagon Analysts tion and physical properties of the various materials in the embankment and foundation. Once this information was obtained, a dynamic analysis of the dam with any proposed modifications or treatments could be carried out. Because it was anticipated that it would be several years for any perma- nent remedial measures to be completed, temporary restrictions on the wa- ter level at Jackson Lake were considered. A risk analysis was performed to assess the probability of an overtopping condition as a function of the re- striction level and to assess the level of downstream damage as a function of various modes of failure and restriction levels. The risk of overtopping was computed as a function of the probability of occurrence of various levels of earthquake, the probability of various structural responses due to these earthquakes, and the probability that the reservoir would be at an eleva- tion that would lead to overtopping. The analysis showed that at elevation 6756.5 the risk of overtopping due to the primary mode of failure under consideration (liquefaction at base level of 6750) was reduced by about 50 percent (see Figure 3-1~. Furthermore, it was seen by analysis of the out- flow hydrograph that even in the event of overtopping (from the primary mode of failure hypothesized) the flood produced with the water level re- stricted to this level would be greatly reduced (see Figure 3-2~. This level of reduction in risk appeared appropriate, but the magnitude of the benefits still needed to be incorporated into the decision analysis. The overtopping risk analysis for restricted elevations below 6760 as- sumed the reservoir would be maintained at the restricted elevation on a year-round basis. Actual operations could produce a variable water level at about the mean elevation and yet minimize impact on recreational inter- ests affected by the actual lake level as well as the timing and amount of releases. An operational plan that satisfied these objectives was developed by regional and project personnel. The plan called for water levels at eleva- tion 6760 for 1 month out of the year but below elevation 6755 for about 9 months. These criteria provide a lower risk of overtopping than a constant restriction level of 6756.5 but present the potential for larger floods during the 1-month period when elevations reach elevation 6760 if overtopping were to occur during this period; however, the total benefits of this operat- ing plan appeared to outweigh this short-term increased hazard. The question of a level of acceptable risk is brought to bear at Jackson Lake as the twin goals of maintaining dam safety and providing maximum benefits from the project are brought together. Responsible management of a public facility in such a case requires that an objective assessment be made of the hazard, the risk of failure, and the loss in benefits due to any restriction imposed. A decision analysis model was used to provide a con- venient format for presentation of all available information and to permit 61

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62 * .005 Z .004 cat o cr LL > .003 o 11 o J .002 m m o .001 _ / .000 ~ I 6740 6750 SAFETY OF EXISTING DAMS Calcu ration Points Primary Mode Failure Considering Constant Operation at Restricted \ Level if Restricted Level is Below 6760 _ Current Operating Criteria f - - y Probability of Overtopping / Under Proposed Operating / ~ Criteria, Equivalent to i' 57% Reduction in Primary r Mode Risk 6760 RESERVOIR ELEVATION (feet) 6769 FIGURE 3-1 Risk of overtopping versus reservoir elevation of Jackson Lake. (*From liquefac- tion failure due to earthquake plus effect of a seiche. Primary mode: liquefaction at base level of 6750.) an objective evaluation of the data. Although the data were limited, the risk analysis clearly showed a marked decrease in the risk of overtopping with decreasing reservoir elevation. Analysis of the flood hydrograph for the most likely hypothetical failure mode likewise showed a significant decrease in potential hazard with de- creasing reservoir elevation. Examination of these relationships and deter- mination of a reservoir operation procedure that minimizes adverse impact from a restricted reservoir level permitted establishment of a reservoir op- eration plan that provides for a meaningful reduction in risk to the public while maintaining the usefulness of the reservoir. Case II: Island Park Dam Island Park Dam is located on the Snake River in eastern Idaho. Its purpose is to provide storage and regulation of water for supplemental irrigation. There are some flood control benefits associated with the dam but only on

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R7sk-Based Decmon Analysis 63 an informal basis relying on forecasting techniques within the drainage ba- sin. The reservoir is popular as a recreation area and has an abundance of campsites as well as private homes along its shores. Island Park Dam is a zoned earthfill structure approximately 91 feet in height. The exterior slopes are 4: 1 upstream and 2: 1 downstream. The embankment materials consist of a 3-foot thickness of riprap on the up- stream face, an impervious central core flanked by shells of semipervious material, a rockfill section on the downstream side, ant] a zone of selected free-draining material at the downstream toe of the semipervious section. A long dike extends to the east of the dam. The dike is a homogeneous em- bankment with riprap on the upstream face. The structure height of the dike is generally less than 15 feet, and exterior slopes are 3: 1 upstream and 150,000 125,000 - ~n 'A 1 00,000 I 75,000 y LU 50,000 Flood Stays within Corps' Levees 25,000 1 , l \ 30,000 cf.s. ~ / by Flood Discharged / Cost / ~~ I I I o 6750 6760 6769 R ESE RVO I R E LEVATIO N (ft) 30 cat 25 - o o o . _ . _ - ~n LL 15 ~ cr: LL cat 10 0 Lo a: 5 ~- ~n o FIGURE 3-2 Jackson Lake flood and flood effects* versus reservoir restriction level. (*Given that overtopping occurs and that failure is in the primary mode with a 400-foot breach.)

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64 SAFETY OF EXISTING DAMS 2: 1 downstream. Crest length of the embankment is approximately 9,500 feet. Appurtenant structures are located on the right abutment and consist of a double-side channel concrete spillway inlet transitioning to a concrete- lined circular tunnel and a concrete-lined outlet works tunnel controlled by four 5 x 6-foot high-pressure gates. A U.S. Bureau of Reclamation technical memorandum presents the results of studies conducted to address the problem of providing adequate freeboard for Island Park Dam. This could be accomplished by various combinations of the actions mentioned in the next subsection. Additional factors complicated the issue considerably. These factors included the fol- lowing: An increase in the maximum discharge for the existing service spillway results in downstream property damage. An increase in reservoir elevation above 6305.0 may cause upstream property damages. Recent insect infestation of the surrounding forests raises the possibil- ity of significant debris accumulation in the reservoir. Concern has been expressed about the potential plugging of the existing spillway inlet struc- ture with debris. Alternatives to Be Examined The report examines the following alternatives to provide adequate free- board for Island Park Dam: 1. "Do nothing" alternative. a. Assume inadequate freeboard for the flood events (no plugging). b. Assume adequate freeboard for the flood events (no plugging). 2. Continue use of the existing structures and provide adequate free- board for the flood events and possible plugging of the existing service spill- way. 3. Raise the crest of the dam and dike to store the inflow design flood (IDE;) volume due to plugging of the spillway inlet and provide adequate freeboard. 4. Raise the crest of the dam and dike to control the inflow flood volume and provide adequate freeboard. Provide an emergency overflow area at the left dike to handle the volume of water due to plugging of the existing spillway. 5. Provide an auxiliary spillway to restrict the maximum water surface with or without regard for plugging of the existing service spillway. 6. Provide an auxiliary outlet works to restrict the maximum water sur- face with or without regard for plugging of the existing service spillway.

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R'sk-Based Decision Analysis Results of the Analysts With so many alternatives available as possible solutions to the problem of inadequate freeboard] at Island Park Dam, a framework for their examina- tion according to a common standard was required. The framework used was a risk-based decision analysis. The methodology operates on the fol- lowing basic concepts: 65 1. Cost is the common denominator by which various alternatives may be compared. 2. Two types of costs are determined: a. Costs due to construction, maintenance, etc., or capital invest- ment. These are direct costs. b. Costs due to damages incurred through the normal operation or failure of a structure during flood events. These are expected risk costs. The second types of costs have a probability of being incurred that must be factored into the calculation to allow comparison with direct costs. To- tal expected costs are then determined for the different alternatives. The results are tabulated below, with the component costs shown in the bar chart on Figure 3-3: Alternative No. 1A Alternative No. 1B Alternative No. 2 Alternative No. 3 Alternative No. 4 Alternative No. 5 Alternative No. 6 Sensitivity Analysis Before making any conclusions on the least-cost alternative, a sensitivity study was conducted to determine the impact of different probabilities of occurrence (for the flood events and spillway inlet flow restriction) on the computed risk costs. The probabilities are a reflection of engineering judg- ment, which is not constant from individual to individual. Therefore, three individuals from the field of dam and spillway design were polled for their response to the following question. Responses to the question are provided along with the judgment used by this study. What is the probability that a spillway inlet restriction (such as described in this study) will occur during the 100-year flood, 1,000-year flood, and IDFs? $ 1,790,000 970,000 1,410,000 3,620,000 2,460,000 11,480,000 7,000,000

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66 SAFETY OF EXISTING DAMS 11 10 9 8 7 6 5 4 3 2 o Total cost Construction cost r I C\\\1 Upstream risk cost Downstream risk cost Sensitivity point ,? , . .:t~l I ~1 r . ~ I, 1A 1B 2 3 4 5 I\ I \ ! r i.. ..-:~ ~ I 7.-- ... L l l l \ ..~::., ~ . ~ ' ...... '. ~ if Red .-... .. 1 ~R ~ / l \ .... ...... .-.-2. . .~ .... .... .~ .-.- ...... ..- . ..~ ..... _ 6 \ FIGURE 3-3 Costs for each alternative. The results of using the above probabilities in the analysis are plotted on Figure 3-3 as points next to the bars representing results from the original study. Note that the only significant impact on risk costs are on the down- stream risk costs. The upstream risk costs are virtually the same for each set of probability assumptions. Also, only alternatives 1A, 1B, and 2 are af- fected. (A second sensitivity analysis was made by assuming that the peak and volume IDFs have a recurrence interval of 1,000 years rather than 10,000 years.) Conclusions Notwithstanding the "other factors" presented for consideration by the de- cision maker, the results of the risk-based decision analysis for Island Park Dam (hydrologic aspects) are as follows: Alternatives 5 and 6 are not justified on the basis of risk. Modification of reservoir operation may essentially eliminate up- stream and downstream risk costs without any structural modification. Some combination of alternatives 1B, 2, and 4 should be required if formal modification of reservoir operation is not possible.

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Risk-Based Decagon Analysis 67 A decision is required as to the effectiveness of log booms in protecting against accumulation of debris at the spillway inlet causing flow restric- tion. The report makes it clear that this analysis is intended to provide input to the decision-making process and does not compromise the design process. There is no single exact solution to the problem. The effort is on presenting available data in a clear and concise manner. Conclusions and recommen- dations are made to give the decision maker insight to the reasoning. Case III: Willow Creek Dam Willow Creek Dam is located approximately 4 miles northwest of Augusta, Montana, in Lewis and Clark County. The reservoir stores and regulates irrigation water and has an active storage capacity of approximately 32,400 acre-feet at a normal water surface elevation of 4142.0 feet. Ap- proximately 2,600 acre-feet are available for flood storage to the crest of the existing spillway at elevation 4144.0. The main embankment, a homogeneous earthfil1 structure, was con- structed on Willow Creek about 1-1/2 miles upstream of the confluence with the Sun River by the U.S. Bureau of Reclamation between 1907 and 1911. The dam was raised in 1917 and again in 1941 with five dikes placed in low saddles in the northern shoreline. The existing embankment is 93 feet high and 650 feet long with a crest elevation of 4154.0 feet. A grass- lined, uncontrolled, open-channel emergency spillway is located about 3,600 feet north of the dam. The spillway crest consists of a 700-foot-long, 6-foot-deep buried concrete cutoff wall protected by riprap on both up- stream and downstream sides. A flood in 1964 caused a small flow, approximately 30 cubic feet/second, through the grass-lined natural-channel emergency spillway at Willow Creek Reservoir and resulted in an erosion phenomenon known as headout- ting. This occurrence for a minimum flow caused concern that spillway flows expected from the PMFs could result in erosion cutting back to and failing the spillway crest wall, releasing the reservoir into the Sun River Valley. The Decision Problem Examination of the situation at Willow Creek showed the basic elements to be as follows: The existing emergency spillway was hydraulically capable of passing the revised PMF.

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68 SAFETY 0F EXISTING DAMS A real but uncertain potential existed for erosion to occur to an extent great enough to cause loss of the reservoir through the spillway for dis- charges ranging from those with a reasonable probability of occurrence to those with a highly remote probability of occurrence. Loss of the reservoir through the spillway appeared to constitute a low hazard considering the remoteness of the site, the time factors associated with failure development, the interrelationship of the flood on the Sun River to the discharge from Willow Creek, and the incremental nature of property damages that would result from a postulated failure. It was determined that consideration should be given to providing for a flood less than the PMF and at the same time increase confidence in the capability of the spillway to pass the more probable lesser magnitude flows without experiencing serious headoutting problems. To determine the cost-effectiveness of these options, the costs of provid- ing for the PMF were compared with the costs of providing for a lesser flood plus the inherent risk costs associated with providing for less than the PMF. The final decision between designing for the PMF and a lesser event would consider the cost comparison between the two schemes as well as other factors that are not incorporated into the cost analysis (agency credi- bility, funding, public acceptability, etc.~. Risk Assessment The decision analysis study for Willow Creek spillway modification alter- natives requires as input the risk cost associated with alternatives that pro- vide for an IDF' less than the PMF. The risk cost is not an actual expenditure but rather the cost put "at risk" by providing for a specified design level of event. The annual risk cost is computed by multiplying the damages and losses resulting from a failure event times the annual probability of the event occurring. The total risk cost includes this product for all potential events exceeding the specified design level event integrated over the design life of the project. Damage costs are determined by appraising the consequences of struc- ture behavior for various conditions. Secondary damage costs such as loss of employment and water and power supplies are not addressed. The only primary cost considered is the direct cost due to inundation. This damage cost may be estimated from that experienced during previous floods' as was done for the initial assessment for the cost analysis. A preferred method employs current aerial photographs of the affected area since this includes

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R'sk-Based Decmon Analysis TABLE 3-2 Cost Analysis of Design Alternatives 69 Spillway Discharge (ft3/s) Recurrence Interval, I (years) Probability of Construction Exceedance, Costs, Risk Cost, P (percent) C (dollars) C (dollars) Total Expected Cost, C (dollars) 500 1,000 5,500 10,000 PMF 235 434 4,000 12,600 92,000 34.7 20.6 2.5 0.8 0.1 6,030,000 6,030,000 380,000 360,000 740,000 2,500,000 10,900 2,511,000 any construction that may have taken place since the last flood and may permit categorizing the damage as to building type or use. Several design alternatives capable of controlling the PMF were devel- oped, the least costly of which was estimated at a total cost of $2.5 million. It was found that a design protecting the existing emergency spillway for flows less than those of the PMF would be more cost-effective ($0.74 mil- lion versus $2.51 million). The different cost components are presented in Table 3-2 for the different alternatives. REFERENCES Bohnenblust, H., and Vanmarcke, E. H. (1982) "Decision Analysis for Prioritizing Dams for Remedial Measures: A Case Study," MIT Department of Civil Engineering Research Re- port R82-12. Hagen, V. K. (1982) "Re-evaluation of Design Floods and Dam Safety," Transactions of 14th International Congress on Large Dams, Vol. 1, Rio De Janeiro, Brazil, pp. 475-491. Langseth, D. (1982) "Spillway Evaluation in Dam Safety Analysis," MIT Ph.D. thesis. Lin, J. S. (1982) Probabilistic Evaluation of the Seismically Induced Permanent Displace- ments in Earth Dams, MIT Ph.D. thesis, Report No. R82-21. McCann, M. W., Jr., Franzini, J. B., and Shah, H. C. (1983a) Preliminary Safety Evaluation of Existing DamsVolume I, Department of Civil Engineering, Stanford University, Stan- ford, California. McCann, M. W., Jr., Franzini, J. B., and Shah, H. C. (1983b), Preliminary Safety Evaluation of Existing DamsVolume II, A User Manual, Department of Civil Engineering, Stanford University, Stanford, California. U.S. Bureau of Reclamation (1980) Safety Evaluation of Existing Dams (SEED), Government Printing Office, Washington, D.C. Vanmarcke, E. H. (1974) "Decision Analysis in Dam Safety Monitoring" in Proceedings Engi- neering Foundation Conference on the Safety of Dams, Henniker, New Hampshire, pub- lished by ASCE, pp. 127-148. Vanmarcke, E. H., and Bohnenblust, H. (1982) Risk-Based Decision Analysisfor Dam Safety, MIT Department of Civil Engineering Research Report R82-11.

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70 RECOMMENDED READING SAFETY OF EXISTING DAMS Germond, J. P. (1977) "Insuring Dam Risks," Water Popover and Dam Construction, June, pp. 36-39. Gruner, E. (1975) "Discussion of ICOLD's 'Lessons from Dam Incidents'," Schweizerische Banzeitung, No. 5, p. 174. Howell, J. C., Bowles, D. S., Anderson, L. R., Canfield, R. V. (1980) Risk Analysis of Earth Dams, Department of Civil and Environmental Engineering, Utah State University, Lo- gan. Mark, R. K., and Stuart-Alexander, D. E. (1977) "Disasters as a Necessary Part of Benefit- Cost Analysis," Science, 197 (September), pp. 1160-1162. McCann, M. W., Jr., Shah, H. C., and Franzini, J. B. (1983), Application of Risk Analysis to the Assessment of Dam Safety, Department of Civil Engineering, Stanford University, Stan- ford, Calif. Pate, M.-E. (1981) Risk-Benefit Analysis for Construction of New Dams: Sensitivity Study and Real Case Applications, MIT Department of Civil Engineering Research Report No. R81-26. Schnitter, N. (1976) "Statistische Sicherheit der Talsperren," Wasser, Energie, Left, 68 (5), pp. 126-129. Shah, H. C., and McCann, M. W., Jr. (1982) Risk AnalysisIt May Not Be Hazardous to Your Judgment, paper presented as a keynote lecture at the Dam Safety Research Coordina- tion Conference, Denver, Colorado.