National Academies Press: OpenBook

Safety of Existing Dams: Evaluation and Improvement (1983)

Chapter: 3 Risk-Based Decision Analysis

« Previous: 2 The Safety of Dams
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 41
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 42
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 43
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 44
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 45
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 46
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 47
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 48
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 49
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 50
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 51
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 52
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 53
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 54
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 55
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 56
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 57
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 58
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 59
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 60
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 61
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 62
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 63
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 64
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 65
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 66
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 67
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 68
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 69
Suggested Citation:"3 Risk-Based Decision Analysis." National Research Council. 1983. Safety of Existing Dams: Evaluation and Improvement. Washington, DC: The National Academies Press. doi: 10.17226/289.
×
Page 70

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

RISK-BASED DECISION ANALYSIS 41 3 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 increasingly sophisticated, practical engineers and related professionals have preferred to apply time-tested judgmental approaches rather than new techniques. 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 reduction 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 specifies 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 movement 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 decision analysis approach, actions are optimized in the face of uncertain ad

RISK-BASED DECISION ANALYSIS 42 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 inappropriateness of risk analysis methods, uncertainty about events is the primary basis for using a formal probabilistic approach, not the reason to disavow its usefulness. 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 engineering 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 approximate risk-based screening process. At this level of analysis, only relative risk evaluation is needed. If information-gathering and-analysis procedures 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 information as is economically and technically possible. It is also necessary to evaluate risk of failure due to all external and internal load conditions. Before 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 procedures 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" procedures to practical problem situations involving existing dams. The work done by the U.S. Bureau of Reclamation and by certain university groups on probabilistic risk analysis for dams should be made avail

RISK-BASED DECISION ANALYSIS 43 able to the user community. This could provide further impetus to simplify and improve these methods. We believe that the limited acceptance of formal risk analysis comes more from lack of knowledge of the tools than from their complexity. Consistent and continuous use and improvements will increase 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 problems. In the competition for limited public funds, a dam safety program is often seen as one of many worthwhile but expensive hazard mitigation programs. In many cases the effective rehabilitation of an existing dam would impact 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 deficiencies 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 remedial actions? An owner with several dams is confronted with similar decisions concerning the deficiencies of each dam. Each of the decision situations mentioned involves a fundamental tradeoff 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 obvious reference alternative is to "do nothing," i.e., to accept the risk and consequences associated with the status quo. Perhaps the most critical step in the decision analysis process is to conceive 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 reducing the probability of failure or the consequences or both. Based on this

RISK-BASED DECISION ANALYSIS 44 evaluation and guided by appropriate decision criteria, the engineer must select the most favorable alternative or, when acting in an advisory capacity, present all the facts on cost and risk to the decision maker. There is no single best methodology of risk assessment and risk management for dams. Evidently, the amount and quality of information available to the engineer will differ greatly depending on the nature of the decision, 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 sophistication 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 implications 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" decisions (more extensive exploration or inspection) or by a "terminal" decision. In the context of the U.S. Army Corps of Engineers' Dam Safety Program, 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 sequential decision process the engineer is usually concerned about data acquisition, 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 according to the number and type of structures involved. The decision situation 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 particular 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

RISK-BASED DECISION 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 mitigation are often controversial. Different parties (owner, downstream resident, builder) are affected differently by the outcome of the decision. Hence, they tend to assess costs and risks differently and may select different 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 assessment 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 systematically 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 decision and may be all that is needed, but it will only rarely lead to an optimum 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. Specific site conditions are often difficult to factor in, except subjectively. Several examples of such a qualitative risk assessment are presented later in this section. In a formal risk assessment one estimates occurrence frequencies, relative 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

RISK-BASED DECISION ANALYSIS 46 measures. An integral part of a risk assessment is that one should vary assumptions 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 reservoir load, seismic load, and hydrologic (flood) load. However, for a specific 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 frequency 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 identified is very much site-and problem-specific. In some cases the assessment of risk and consequences may be satisfactorily made by assuming a complete and instantaneous dam breach, while in other eases this assumption

RISK-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 assessed. 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 damage, 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 different modes given the loading condition, and the cost of the damages resulting 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 instantaneous dam failure, and an estimate of the direct losses. The data collected

RISK-BASED DECISION ANALYSIS 48 will include information on the dam, the spillway, downstream topography and development, design criteria, inspection programs, etc. This corresponds 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 capacity 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 reevaluation 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 presented 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 involving 16 actual dams located in rural Vermont. The basic sources of information are the Inspection Reports issued under the National Dam Inspection 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 different 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 Inspection Reports), the prior risk is then updated using Bayes's theorem. Emphasis is on demonstrating the flexibility of the model 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

RISK-BASED DECISION ANALYSIS 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 appropriate to substitute an index-based procedure for formal quantitative risk analysis. Several organizations have developed such index-based procedures 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 Evaluation of Existing Dams (SEED) program used by the U.S. Bureau of Reclamation. These procedures consider the same factors as does a quantitative 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., where Ot = overtopping failure score = O1 × O2 × O3 and St = structural failure score = S1 × S2 × S3. The factors depend on the following considerations: Factor O1: Number of homes endangered by failure. (Based on difference in area inundated without failure and with failure, assuming water surface at the top of dam. Dam failure hydrograph superimposed on discharge 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 design 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 S1: Number of homes endangered by failure. (Area inundated is obtained from dam failure with water level at the top of flood control storage or normal maximum pool excluding surcharge used to pass design flood.)

RISK-BASED DECISION ANALYSIS 50 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 design procedures.) The maximum rating score for a dam by the selected rating scales would be 250 (i.e., 125 associated with "overtopping failure" and 125 with "structural 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 available data on a dam and a field inspection. The data review covers all aspects of the dam from geologic and seismic conditions to a review of the construction experience and operations. A detailed evaluation report is prepared 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 identifying 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 recommended upgrades, scheduling information, status of different upgrades, and key personnel involved in the project. In addition, 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 failure modes, hazard conditions, and possible remedial measures. The technical elements that are common to different procedures of risk-based dam safety as

RISK-BASED DECISION ANALYSIS 51 sessment are estimation of the frequency of occurrence of loading events, evaluation of the response of the structure to the loading, and prediction of damage downstream. TABLE 3-1 Hazard Bating Criteria in Hagen's Procedure 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 Yes — Partial No measurements current (0) (6) (9) and within acceptable 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 (0) (9) Seismic zone 0-1 2 3 4 (0) (3) (6) (9) NOTE: Number in parenthesis is the weighting factor. a Assumed if not given. 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 certain failure modes is judged negligible compared with that of other modes, these may be omitted from formal consideration. Once the potential failure

RISK-BASED DECISION ANALYSIS 52 modes have been identified, there are three basic approaches for estimating the corresponding failure probabilities. 1. Analytical (probability) approach. In a common version of this method a factor of safety is computed for the condition. The uncertainty in the calculation is quantified by examination of the ranges and the variation of the individual input parameters to the analysis. Based on this uncertainty analysis the probability that the factor of safety will fall below 1 is determined. 2. Empirical (historical frequency) approach. In this method the number of failures for similar dams for the same failure condition is determined and divided by the total number of dam-years of operation for dams of this type as a crude estimate of the probability of failure. The obvious limitation of the approach is the scarcity of information in each narrowly defined category of dam type, age, loading type, failure mode, etc. 3. Judgmental approach. In this method the investigator attempts to quantify his judgment based on all available information. The judgmental statement may be made directly in terms of annual probability of failure of the dam due to a particular condition (e.g., probability of failure due to internal erosion = 1 × 10-3 annually), in terms of the chance of failure over a specified remaining operational life of the dam, or as a fraction of the probability associated with other modes (e.g., about twice the risk attributable to flooding and overtop- ping). The analytical-probabilistic approach is the most elegant of these methods; however, adequate data to support or justify such studies are often not available. Some important potential failure modes do not lend themselves to a factor of safety formulation as is common in stability analysis. Also, the calculated probability of failure is very sensitive to the tails of probability functions describing the various parameters, and these are not well known at all. Therefore, it is not yet practical to incorporate these approaches in a comprehensive program of assignment of risks to a number of potential failure mechanisms from static loading. A combination of the empirical and judgmental approaches appears to be most practical at the present time. Historical failure probabilities can be obtained for specific conditions and types of structures, but they need to be adjusted based on the conditions at a particular dam. This adjustment is based on the inspection, analysis, and judgment of the engineers performing the safety evaluation of the dam. The two estimates may be combined by means of a Bayesian updating procedure in which a weight is assigned to the relative confidence in each of the estimates (historical and engineer's judgment). Such a procedure is easily understandable, consistent with the level of data available, and practical to implement.

RISK-BASED DECISION ANALYSIS 53 Flood Risk Assessment Flood risk assessment has been practiced for many years in the study of water resources. Procedures used have been reviewed, evaluated, criticized, and extolled by experts in probability theory, hydrology, meteorology, mathematics, and other disciplines. Because of lack of agreement on the most appropriate methodology for estimating flood probabilities, the U.S. Water Resources Council recently directed the Interagency Hydrology Committee, under the council's auspices, to select a unique technique for computing flood probability for gaged locations. The committee responded by declaring that a unique technique does not exist that will provide the best answer for all locations and conditions. Nevertheless, the committee recommended that the Pearson Type III distribution with log transformation of the flood data be used as an uniform technique. The most recent publication describing the results of the Hydrology Committee's effort is Bulletin 17B. No similar publication has been developed for ungaged locations. This does not mean that adequate methods are not available but only that experts cannot agree on a single best method for every condition. The procedure recommended by Bulletin 17B covers flood events with return periods of 1:500 years only. Extrapolation to extreme rare events is not covered. Traditionally, flood probability has been expressed in terms of annual exceedance probability. This means that specific flood magnitudes have an assigned probability of being exceeded during any given year. The use of exceedance probability for conveying the risk of the design flood being exceeded during the useful life of a project is extremely important in judging inflow design floods for sizing spillways and establishing crest elevations. For example, if a designer expects to establish an inflow design flood that would have a .01 probability (1% chance) of being exceeded during a 200-year useful life, a flood event with an annual exceedance probability of .00005 would need to be selected. This corresponds to an average exceedance interval (AEI) of 20,000 years and would be near the magnitude of a probable maximum flood. While analytical procedures (such as the binomial distribution) can be used to estimate such an event, the historical record is rather short, and such extreme extrapolations are difficult. Extrapolation becomes increasingly uncertain the further it is carried beyond the length of the period of record. Historical records of flood events are rather limited in the United States; therefore, in general, extrapolations beyond an annual exceedance probability of .01 (100 years AEI) will have a limited degree of reliability. In any ease the analyst should quantify the uncertainty in the estimated exceedance probabilities.

RISK-BASED DECISION ANALYSIS 54 There has been much debate regarding the wisdom of attempting to find an acceptable means for estimating the probability of extreme flood events. Mathematical formulas recommended for this purpose are always suspect because of the data sample available. Regional processing of data is used to improve the reliability of results. Historical records are searched to obtain evidence regarding past occurrences of large floods. Because of better data on historical storms, precipitation data are converted to runoff and probability of floods estimated from the larger data samples. Tree rings, sun spots, and other indicators of significant climate changes have also been proposed for estimating the probability of extreme floods. Stochastic hydrology uses random number generators to simulate long periods of flood record of any length desired. However, the generated floods are constrained by the statistical parameters of the relatively short actual data sample used to derive the parameters. For the probable maximum flood (PMF) the best approach for purposes of conducting a risk-based decision analysis may be to extend peak flow-probability relationships to conventionally derived values of PMFs by some reasonable mechanism. A PMF is defined as the largest flood considered reasonably possible for a specific location and its probability of exceedance should be close to zero. The function describing annual exceedance probability could be extended in a smooth curve from the limit of the relation obtained by historical records of flood events until the curve becomes asymptotic to the PMF value. The extended curve can then be varied in sensitivity studies accompanying the risk-based decision analysis. Earthquake Risk Assessment Earthquakes pose a multitude of hazards to dams, either by direct loading of the structure or by initiating a sequence of events that may lead to dam failure. For example, strong ground shaking or fault offset at the dam foundation are direct loads on the structure, while an upstream dam failure, seiche, or landslide into the reservoir are earthquake-generated events that can lead to overtopping and failure. A comprehensive probabilistic seismic risk assessment involves these two steps: (1) evaluation of the likelihood of occurrence of levels of seismic loading at the dam site (seismic hazard analysis) and (2) evaluation of the conditional probability of the different modes of dam failure given the occurrence of seismic loads (conditional reliability analysis). Overall seismic safety assessment requires combining the information generated in these two steps. The hazards typically associated with earthquakes are ground shaking, faulting, seiche, landslide into the reservoir, and upstream dam failure.

RISK-BASED DECISION ANALYSIS 55 It is the job of the risk analyst to identify those failure scenarios that are the most significant contributors to the chance of an earthquake-induced dam failure. For example, slope instability of the upstream face of an earth embankment and liquefaction of the foundation may be postulated as potential failure modes when the dam is subjected to strong earthquake ground shaking. Once the hazards and corresponding modes of dam failure have been identified in a preliminary way, the risk analysis proceeds to the evaluation of the probabilities in each step of load-response-failure sequence. In the case of ground shaking and faulting the techniques available to evaluate occurrence probabilities are well established. However, the comment made in reference to the evaluation of the risk of extreme hydro-logic events also applies here. The uncertainty in key input parameters leads to considerable variability in the estimates of probability of occurrence of earthquakes that have the potential of causing dam failure. It is therefore necessary to quantify the uncertainty in estimated seismic hazard. A variety of opportunities are available to conduct probabilistic analyses, the number depending on the failure under consideration. As an example, various approaches exist to perform probabilistic slope stability analyses. The result of the probabilistic analysis expresses the chance of failure as a function of load level. These conditional probabilities usually increase monotonically from 0 to 1 as loading increases. Among the sources of uncertainty are the variability of material properties in the dam, the response prediction for known values of the input parameters, and in defining the failure state. CONSIDERATION OF REMEDIAL ACTIONS The dam owner and engineering staff should become aware of and evaluate remedial measures that are available either to reduce the likelihood of dam failure or to reduce its consequences. These remedial measures can be structural or nonstructural. They are available individually or in combination with other remedial measures. The structural measures generally obtain their effectiveness from reducing the likelihood of the dam failure, whereas nonstructural measures may either reduce the likelihood of failure or reduce the consequences. The value of remedial measures is measured by the benefits obtained, the costs associated with the measure, and the adverse effects of implementation of the measure. Benefits may involve reduction in the number of lives lost, reduced damages, improved project outputs, compliance with regulatory or design requirements, etc. Costs should include future expenditures as well as the initial expenses required to make the measure effective. Indirect costs may be involved in some of

RISK-BASED DECISION ANALYSIS 56 the measures. The action may require a party other than the owner to spend money. Discussed below are the most common alternatives available to an engineer or owner facing the decision of how to remedy problems with existing dams. The emphasis in the discussion of each alternative is on its impact on failure risk and consequences. Of course, in a formal risk assessment this qualitative evaluation is quantified in terms of fractional risk reduction and reduced losses in the event of a failure. A number of examples are presented in the section Examples of Risk Assessment and Decision Analysis. The Status Quo Alternative Do Nothing. This is the reference alternative to which other measures are compared. If it is selected, there will obviously be no change in the consequences or the likelihood of failure. Structural Measures Structural remedial measures can usually be classified as modifications of the dam, modifications to the spillway, corrective maintenance, or construction of new facilities, as follows: Modifications of the Dam. A dam may be modified to reduce consequences of failure, to reduce the likelihood of overtopping, to enhance the structural integrity, or to resist erosion and external damage. In each case these improvements act to reduce the likelihood of dam failure. The measurement of change in the likelihood of dam failure is often difficult; however, it is usually accomplished by describing the effectiveness in reaching design standards. The cost of improvements to comply fully with design standards is often prohibitive. Therefore, evaluation of many alternative measures may be needed to determine which measures are the most cost-effective in reducing the risk of dam failure. Reservoirs may be lowered or dams removed to reduce or eliminate the consequences of their failure. Such measures are not attractive to dam owners because the benefits from the dam are diminished or eliminated. Similarly, an owner's liability from the consequences of dam failure is also reduced or eliminated. These measures generally involve high costs and can have large adverse effects. Sediment accumulated in the reservoir area will be subject to transport downstream if the dam is removed. The environmental aspects of the reservoir area are also difficult to resolve when a dam is removed. Removal of a dam can affect those secondary users who have become accustomed to its presence and have learned to rely on it.

RISK-BASED DECISION ANALYSIS 57 Increasing the height of a dam to reduce the likelihood of overtopping is most effective when it will fully accommodate the requirements for the inflow design flood. The increased dam height will result in increasing the consequences of its failure when full. It will also increase the potential level of the reservoir and flood lands previously unaffected by the project. Thus, this measure is not usually a viable alternative when there is concentrated development around the reservoir rim. When raising the top elevation of the dam, care must be taken to ensure that the foundation is capable of supporting the additional load. The cost associated with this measure may be high. However, when only a few feet of height are needed to comply with design standards, a wall or dike possibly may be constructed along the top of the dam within cost constraints. Modification of the Spillway. Spillway modifications may be needed to enhance its ability to pass greater floods or improve its ability to resist erosive action during higher velocity flow. Greater capacity will reduce the likelihood of failure by larger floods, while better erosion resistance will reduce the likelihood of failure during the passage of the spillway's current capacity. It is a possibility that enlarging a spillway may increase the rate of discharge for more frequent storms and cause downstream flooding to increase in frequency. Spillways may be widened or their crests lowered to increase flow capability. Additional spillways may also be provided to obtain greater flow capacity. These types of improvements can vary from a quick fix with a bulldozer to an elaborate new gated facility. If the crest is lowered without the addition of gates, the ability of the project to perform its intended functions may be seriously compromised. Also, new lands may be needed to accommodate the additional flow downstream from the spillway. Emergency spillways or fuse plug type spillways may be considered as an economical means of avoiding dam failure and reducing risk. In some eases there is serious concern about an unlined spillway's ability to pass intended flows without rapid erosion followed by sudden discharge of the reservoir, which would be tantamount to a dam failure. In dam safety the objective is to avoid the sudden release of the reservoir. Damage to the spillway and to the dam are usually anticipated during the inflow design flood; however, maintenance of spillway crest is necessary to reduce the likelihood of sudden release of water. Types of protection may range from grass cover to an expensive concrete lining. Adverse effects are normally not severe. Construction of Upstream Facilities. Reduction of the magnitude of flow reaching a dam of concern can be accomplished by construction of an up-

RISK-BASED DECISION ANALYSIS 58 stream dam or diversion facility. Depending on the nature of the facility, the likelihood of dam failure by overtopping may be slightly reduced or essentially eliminated. The failure consequences would also be reduced. Generally, costs associated with these measures are large. Adverse effects may also tend to discourage their implementation. Corrective Maintenance. Whenever apparent deficiences are observed at a dam, measures can be taken to reduce or eliminate the source of deficiency. The types of deficiency can be associated with internal or external features of the dam, or they can be associated with the stability of the spillway. Some of these methods include replacing concrete, bringing the top of the embankment up to grade, outlet repairs, replacing riprap, etc. These methods may become expensive but are normally not when taken care of in a timely manner. The effect of performing this maintenance is largely beneficial. Leveling the Top of an Earth Embankment. This may be an applicable measure in eases where an allowance for settlement was made but has not taken place as anticipated (and is not expected to), resulting in a ''crown" effect. Because earthfills and their foundations are expected to consolidate and settle over time, it is common practice to camber or overfill earth embankments. Although reasonable allowances for this settlement are made, it is impossible to predict accurately the amount of settlement that will occur. The result is that in many cases, after essentially all settlement has occurred, the crest of the dam is not level, thus leaving an opportunity for concentration of flow if overtopping were to occur. This can be especially critical for dams not capable of withstanding floods as large as the PMF (e. g., low hazard dams). This concentrated [low has been specifically cited as a major contribution to some severe damage in actual overtoppings. Implementation of this remedial measure would involve "shaving" off the camber and providing a level weir. For example, this could provide overtopping the entire length of dam by 1.5 feet instead of a concentrated flow at the abutments of perhaps twice that amount. Cost would be in the moderate range in this ease, and the procedure would reduce the likelihood of failure due to overtopping. It is recognized that overtopping flows will concentrate in groins and, therefore, that special erosion protection would be needed there. Other Remedial Measures. The above listing gives some common possible remedial measures. However, remedial actions are often quite site-specific and relate to the particular modes of failure (seepage, piping, liquefaction, deformation, etc.) that may be most relevant to a specific dam. Repair or

RISK-BASED DECISION ANALYSIS 59 strengthening of a parapet wall, plugging an access opening in a parapet wall, constructing a small dike downstream of the existing dam, relocating the dam to a new site, densification of the foundation, installation of relief wells downstream of the dam, and construction of stability berms are some examples of constructed or proposed remedial structural measures that can be implemented at a specific site or in a specific problem situation. Nonstructural Remedial Measures Nonstructural remedial measures, such as those listed below, can be used to reduce the likelihood of dam failure and the consequences of dam failure. Intensive Surveillance. This can be done to monitor dams with suspected or known problems. Depending on the specific site, various features may need inspection surveillance at different frequencies. Special inspections may be called for during or immediately following significant natural events, such as large floods or earthquakes. This alternative measure would usually need to be coupled with other structural or nonstructural measures, such as a lower operating pool, or may be used temporarily until positive measures are taken. Inspections themselves neither reduce the likelihood nor the consequences of dam failure; however, they can be effective in reducing risk if appropriate follow-up action is taken. Reservoir Regulation. This provides a means to reduce the likelihood of failure. This may be a reduced likelihood of overtopping through lowering a reservoir to provide additional storage capacity for floods or it may be related to increased upstream slope stability through reducing the rate of drawdown. Reservoir restriction may be permanent, seasonal, or based on flood forecasting. The latter regulation can greatly reduce the probability of failure, but it may have no effect on the consequences of failure. Reservoir restriction by which the maximum reservoir elevation is limited year-round below the design level can reduce both the probability of failure and the consequences of failure. A case history of an example of the use of risk-based decision making to reduce risk by reservoir restriction is presented in the section Examples of Risk Assessment and Decision Analysis. The cost of this alternative is generally low. However, other impacts can be significant by reducing benefits of the project and also by adverse environmental and economic effects in and around the reservoir area of the dam. Emergency Action Plans. An emergency action plan (see Chapter 2) is a nonstructural measure that can be used as a temporary alternative until more positive remedial measures can be implemented. Such a plan does not

RISK-BASED DECISION ANALYSIS 60 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. Similarly, 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 inundation maps, as has been done in California, is a relatively conservative measure of modest cost. Such maps will not reduce the probability of failure 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, flood proofing of structures, installation of individual or group levees to protect a damageable area from flooding, and purchase or other land-use controls to keep future development from being subjected to flooding. Since these alternatives do not affect 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 ease 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 embankment portion of the dam was founded and the hydraulic fill methods that were used to place a portion of the earth embankment presented the potential for liquefaction at the site under strong earthquake loading. A drilling, sampling, and laboratory testing program was initiated to define the loca

RISK-BASED DECISION ANALYSIS 61 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 permanent remedial measures to be completed, temporary restrictions on the water level at Jackson Lake were considered. A risk analysis was performed to assess the probability of an overtopping condition as a function of the restriction 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 elevation 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 outflow hydrograph that even in the event of overtopping (from the primary mode of failure hypothesized) the flood produced with the water level restricted 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 assumed 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 interests 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 elevation 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 operating 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 ease 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 convenient format for presentation of all available information and to permit

RISK-BASED DECISION ANALYSIS 62 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. Figure 3-1 Risk of overtopping versus reservoir elevation of Jackson Lake. (*From liquefaction failure due to earthquake plus effect of a seiche. Primary mode: liquefaction at base level of 6750.) Analysis of the flood hydrograph for the most likely hypothetical failure mode likewise showed a significant decrease in potential hazard with decreasing reservoir elevation. Examination of these relationships and determination of a reservoir operation procedure that minimizes adverse impact from a restricted reservoir level permitted establishment of a reservoir operation 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

RISK-BASED DECISION ANALYSIS 63 an informal basis relying on forecasting techniques within the drainage basin. 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 upstream face, an impervious central core flanked by shells of semipervious material, a rockfill section on the downstream side, and 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 embankment 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 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.)

RISK-BASED DECISION ANALYSIS 64 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 × 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 following: • 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 possibility of significant debris accumulation in the reservoir. Concern has been expressed about the potential plugging of the existing spillway inlet structure 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 spillway. 3. Raise the crest of the dam and dike to store the inflow design flood (IDF) 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 surface with or without regard for plugging of the existing service spillway.

RISK-BASED DECISION ANALYSIS 65 Results of the Analysis With so many alternatives available as possible solutions to the problem of inadequate freeboard at Island Park Dam, a framework for their examination according to a common standard was required. The framework used was a risk- based decision analysis. The methodology operates on the following basic concepts: 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 investment. 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. Total 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 $ 1,790,000 Alternative No. 1B 970,000 Alternative No. 2 1,410,000 Alternative No. 3 3,620,000 Alternative No. 4 2,460,000 Alternative No. 5 11,480,000 Alternative No. 6 7,000,000 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 judgment, 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?

RISK-BASED DECISION ANALYSIS 66 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 downstream risk costs. The upstream risk costs are virtually the same for each set of probability assumptions. Also, only alternatives 1A, 1B, and 2 are affected. (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 decision 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 upstream 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.

RISK-BASED DECISION 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 restriction. 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 recommendations 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. Approximately 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 earthfill structure, was constructed 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 upstream 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 headcutting. 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.

RISK-BASED DECISION ANALYSIS 68 • 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 discharges 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 headcutting problems. To determine the cost-effectiveness of these options, the costs of providing 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 credibility, funding, public acceptability, etc.). Risk Assessment The decision analysis study for Willow Creek spillway modification alternatives requires as input the risk cost associated with alternatives that provide 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 structure 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

RISK-BASED DECISION ANALYSIS 69 any construction that may have taken place since the last flood and may permit categorizing the damage as to building type or use. TABLE 3-2 Cost Analysis of Design Alternatives Spillway Recurrence Probability, Construction Risk Total Discharge Interval, I of Costs, C Cost, C Expected (ft3/s) (years) Exceedance, (dollars) (dollars) Cost, C P (percent) (dollars) 500 235 34.7 — 6,030,000 6,030,000 1,000 434 20.6 — — — 5,500 4,000 2.5 380,000 360,000 740,000 10,000 12,600 0.8 — — — PMF 92,000 0.1 2,500,000 10,900 2,511,000 Several design alternatives capable of controlling the PMF were developed, 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 million 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 Report R82-12. Hagen, V. K. (1982) "Reevaluation 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 Displacements 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 Dams—Volume I, Department of Civil Engineering, Stanford University, Stanford, California. McCann, M. W., Jr., Franzini, J. B., and Shah, H. C. (1983b), Preliminary Safety Evaluation of Existing Dams—Volume 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 Engineering Foundation Conference on the Safety of Dams, Henniker, New Hampshire, published by ASCE, pp. 127-148. Vanmarcke, E. H., and Bohnenblust, H. (1982) Risk-Based Decision Analysis for Dam Safety, MIT Department of Civil Engineering Research Report R82-11.

RISK-BASED DECISION ANALYSIS 70 Recommended Reading Germond, J. P. (1977) "Insuring Dam Risks," Water Power and Dam Construction , June, pp. 36-39. Gruner, E. (1975) "Discussion of ICOLD's 'Lessons from Dam Incidents'," Schweizerische Bauzeitung, 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, Logan. 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, Stanford, 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, Luft, 68 (5), pp. 126-129. Shah, H. C., and McCann, M. W., Jr. (1982) Risk Analysis—It May Not Be Hazardous to Your Judgment, paper presented as a keynote lecture at the Dam Safety Research Coordination Conference, Denver, Colorado.

Next: 4 Hydrologic and Hydraulic Considerations »
Safety of Existing Dams: Evaluation and Improvement Get This Book
×
Buy Paperback | $100.00
MyNAP members save 10% online.
Login or Register to save!
Download Free PDF

Written by civil engineers, dam safety officials, dam owners, geologists, hydraulic engineers, and risk analysts, this handbook is the first cooperative attempt to provide practical solutions to dam problems within the financial constraints faced by dam owners. It provides hands-on information for identifying and remedying common defects in concrete and masonry dams, embankment dams, reservoirs, and related structures. It also includes procedures for monitoring dams and collecting and analyzing data. Case histories demonstrate economical solutions to specific problems.

  1. ×

    Welcome to OpenBook!

    You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

    Do you want to take a quick tour of the OpenBook's features?

    No Thanks Take a Tour »
  2. ×

    Show this book's table of contents, where you can jump to any chapter by name.

    « Back Next »
  3. ×

    ...or use these buttons to go back to the previous chapter or skip to the next one.

    « Back Next »
  4. ×

    Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

    « Back Next »
  5. ×

    To search the entire text of this book, type in your search term here and press Enter.

    « Back Next »
  6. ×

    Share a link to this book page on your preferred social network or via email.

    « Back Next »
  7. ×

    View our suggested citation for this chapter.

    « Back Next »
  8. ×

    Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

    « Back Next »
Stay Connected!