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2 Extreme Floods and Earthquakes The Nature of the Problem Other chapters of this report describe the technical methods that have evolved to estimate the magnitude of extreme floods and earthquakes, the limitations of the methods, and some possible improvements in the methods. In this chapter an attempt is made to take a broader look at the problems of coping with extreme floods and earthquakes at dams from the viewpoint of society as a whole. In so doing, it will be shown why there are no absolute solutions to these types of problems. DESIGN OBJECTIVES Dams are designed and constructed to withstand various natural forces and events that have occurred in the past or may be expected to occur in the future. A vital part of the process of designing these structures, which gener- ally are expected to serve society for 100 years or more, is to anticipate the future vagaries of nature that may result in floods or earthquakes that would cause the dam to fail (i.e., be breached or collapse). Some people have the mistaken impression that dams, especially govern- ment-built flood control dams, are designed and operated to protect prop- erty and residents downstream against all floods that could conceivably occur. This is not usually true. Extreme events could overwhelm the flood storage capacity of even large reservoirs. When such extreme floods occur, spillways pass on the large inflows, possibly leading to downstream flood- ing. To set this matter in perspective, it is important to understand that the primary purpose of a dam spillway is to protect the dam itself from failing 8

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Extreme Floods and Earthquakes 9 due to breaching or overtopping. A properly functioning spillway protects the dam by passing excess flood waters downstream, thereby limiting the amount of water held behind the dam. Thus an extraordinarily large flood may pass over the spillway and cause damages downstream possibly ap- proaching those that would have occurred if the dam had not been built. However, the failure of the dam could produce flood rates and damages greater than would have been experienced if the dam had not been built. While either exceptionally severe earthquakes or extremely large floods could cause a clam to fail, in this chapter the main attention is devoted to floods. The reason for this is simply that essentially al' dams are exposed to the threat (and reality) of floods, whereas a much smaller fraction of existing dams may be subjected to significant earthquake forces (i.e., those located in active seismic zones). Also, the structural characteristics of many clams pro- vide them with an inherent capacity to withstand earthquake forces, while protecting a clam against failure from overtopping can only be achieved in most cases by providing specific flood handling facilities (i.e., spillways). Experience indicates that rare and large-magnitude precipitation events can produce flows of water with which most clam structures cannot cope except to pass them downstream. When considering such floods, it would be very desirable to be able to predict how frequently extreme events of specific magnitude might be expected to occur. Some argue that only after develop- ing a satisfactory response to this problem can one rationally determine the degree of protection from floods that should be provider! in dam structures. Surprising as it may seem to some, uncler criteria in current use to deter- mine capacity built into dam structures to withstand or pass floods, it is possible for a flood event to exceed the clam's capacity to resist it. While terms such as unlikely, rare, or low probability are used to describe these kinds of events, it should be understood that what is being described is an event that can occur. The problemfaced by designers of dams and members of the body politic who use, pay for, or are affected by these structures is to determine "how much protection should be provided for the dam," considering these events can but may not occur during the life of the dam. It is not possible to provide absolute safety against all hazards and especially from events pro- duced by "mother nature." The objective should be to balance the benefits of making dams safer against the cost of the increased safety and to reduce any risks to acceptable proportions. Objectives for either design or safety evaluations of clams relating to ex- treme floods ant] earthquakes can be considered in two broad categories, namely, (1) those relating to economic efficiency and (2) those relating to equity. The economic efficiency objectives encourage maximizing the excess of project benefits over project costs. Equity objectives seek appropriate balance between competing interests of such parties as the dam owner, those

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10 SAFETY OF DAMS who benefit from the dam, and those who would be harmed if the dam were to fail. Since the magnitude and timing of future floods and earthquakes are indeterminate, direct determination of optimum measures to attain the economic objectives is not possible. For the same reason, simple answers to problems of equity among those affected by a dam are not available. The probable maximum flood (PMF) has become a standard design crite- rion for flood protection of major dams over the past decades. The concept that equity requires that a dam impose no additional potential for damage or loss of life in downstream areas if such addition can be avoider! is usually cited as the reason for this use of the PMF. Economic efficiency is not usually cited as a basis for such choice, although for large, high-hazard dams, eco- nomic considerations, if properly evaluated, possibly could lead to use of the PMF. The PMF is first of all a hypothetical flood based upon a set of assump- tions that attempt to define the maximum flood potential for the particular site. The calculation of the PMF is based on a combination of facts, theory, and professional judgments. The methods user] to calculate a PMF are not standardized, at least not to the extent that a set of indivicluals with the knowledge and expertise to make such calculations would independently arrive at identical evaluations. The discrepancies arise primarily from the technical, scientific, and moral issues underlying the professional judgments of the estimators as well as the lack of a quantitative definition of exactly what a PMF represents. Moral issues are involved because a dam owner may make economic decisions involving risks to others without the input or con- sideration of those at risk. While it may be unsettling to accept the fact that one's ability to make estimates of the PMF is less than one might like, it would be remiss to suggest otherwise. In attempts to reassure the body politic that the level of flood for which the dam is designed is reasonable, there may have been erroneously perpetuated a myth of absolute safety by describing the PMF as one ". . . where its magnitude is such that there is virtually no chance of its being exceeded" (Bureau of Reclamation, 1981a,b), or ". . . (a flood that) . . . would have a return period approaching infinity and a probability of occur- rence in any particular year, approaching zero" (Wall, 1974~. Such state- ments suggest that the ability to predict future extreme floods is greater than that which actually exists and leads to unrealistic expectations on the part of the public. In adjudicating disputes involving claims of liability for flood damages, the courts have relied on criteria like "foreseeability" and the "appearance of certainty" to reach results that fall within the mainstream of legal analysis. However, from the perspective of the engineering profession, such concepts are of questionable merit since they do not necessarily comport with modern interpretations of probabilistic and statistical relationships. No universal answers are available to questions on the degree of protection

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Extreme Floods and Earthquakes that should be provided for a new dam if the PMF is not the appropriate estimate of the worst possible flood that may occur, or on the actions that should be undertaken at an existing dam if new information suggests that the PMF for that structure was underestimated. 11 WHAT SHOULD SAFETY COST? The responsibility for the general welfare requires that when government considers a level of protection (or safety) for its facilities, it must simultane- ously consider the cost of providing that level of safety. It is faced with choosing whether an additional investment in reducing the risk to those who would be directly affected is of greater benefit to society than would be obtained by expending those funds for some other activity. In theory, it would be possible to provide extraordinarily safe dams, e.g., by providing spillway capacities equal to five or more times the PMF. Most would agree that such gross conservatism is unwarranted. Although not directly compa- rable, few of us would accept the Plea of buying or operating automobiles that were built like army tanks even though such machines would reduce the likelihood of beinginjurec] or killed in an auto accident. For most individuals the cost and inconvenience of such protection would be viewed as excessive. We recognize differences in personal reactions to an imposed risk (e.g., the risk arising from a dam upstream from our residence) and a voluntary risk, as that imposed by our ownership of an automobile. The way society approaches the question of risk has been dominated by feasible or practical concerns. Government by its own actions and by using its authority to regulate the behavior of inclivicluals has generally satisfied the public desire for increased safety. It has not, however, provided explicit target levels for acceptable risk as matters of public policy. It is obvious that these questions can only be resolved through the political process. What inclividuals or groups ought to demand in terms of "safety" is not entirely a technical or scientific issue. On the one hand, individuals make judgments about their participation in "voluntary" risks and may influence the riskiness of various goods and services by their willingness to pay for more (or less) safety. On the other hand, society is called upon to provide various goods and services for collections of individuals where, acting as the agent for these collective interests, government has the obligation to decide what level of risk to accept for these ("involuntary" risk) situations. In its struggles to resolve these dilemmas, government is required to consider, evaluate, and then choose among alternative courses of action that satisfy its responsibility to individuals directly affected and simultaneously the "general welfare" of society. It is unlikely that government can develop an ubiquitous risk policy with respect to all activities, because the character and consequences of the

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12 SAFETY OF DAMS risks imposed are so different. In this sense, government cannot be expected to behave differently than individuals. Devising appropriate policies for assessment and management of risk has become a dominant dilemma of this decade. REASONABLE CARE AND PRUDENCE IN DAM DESIGN For the reasons discussed above, selecting the amount of protection from floods or earthquake resistance that should be included in the design of a clam is in the final analysis a matter of judgment. In order to determine whether such judgments reflect reasonable care and prudence (i.e., the exercise of good judgment ant] common sense) depends upon an understand- ing of what these criteria mean. The floods consiclered here result from natural precipitation without hu- man influence or intervention. Thus, an important premise is that certain floods are ". . . so extraordinary and devoid of human agency that reason- able care would not avoid the consequences . . ." and are sometimes re- ferred to as an act of God (New Columbia Encyclopedia, 1975~. While the phrase, act of God, may imply to some the idea of divine intervention, it also conveys important secular concepts. First, it suggests that certain natural forces may result in events of such enormous force or consequence that no reasonable persons would plan or conduct their lives in ways that anticipate such events. Second, such acts or events occur only rarely so infrequently that one intuitively assumes that the risk of such an event has little if anything to do with the reality of day-to-day affairs. The understancling of nature has improved and expanded through the sciences, and engineers have been successful in applying this knowledge to the construction of facilities that provide society with some degree of protec- tion from natural events. Thus, the hydrological, meteorological, and geo- logical sciences have improved our understanding of extreme floods and earthquakes and provided some tools that enable us to predict limiting mag- nitudes for such events. The tools for predicting floods are based upon two different scientific principles: historical observation and causality. An historical record of pre- cipitation and runoff events (if sufficiently long) permits the use of the laws of probability and statistics to estimate the risk of floods of various magni- tudes. Regardless of the accuracy of these predictive tools, they do not offer any guidance on the level of floor! risk that is appropriate for any dam. That is, even if accurate predictions of the probabilities of all sizes of floods were possible, it still would be necessary to decide whether spillways of dams should be built to withstand the flood that arises once in a thousand years, in ten thousand years, in a million years, etc.

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Extreme Floods and Earthquakes 13 Another method of defining the flood potential at a site involves construct- ing a hypothetical but plausible storm (probable maximum precipitation) that is assumed to occur over a particular drainage basin where a dam exists or is contemplated. From the present knowledge of the meteorology of such storms, the geological and hydrological characteristics of the drainage ba- sin, and their interrelations, it is possible to estimate a flood (probable maxi- mum flood- PMF) resulting from this storm. This method of flood estimation, which is in general use, also presents a number of difficulties. First, inasmuch as the method is hypothetical, it is difficult to estimate the risk or probability of such a flood actually occurring. Second, if larger storms are observed sometime in the future (i.e., larger than the estimated probable maximum precipitation (PMP) used to calculate the PMF), these will in turn result in a bigger estimate of the probable maximum flood. (Flood estimates based on probability studies also tend to increase as more streamflow data become available.) Such an increase in probable maximum flood estimate challenges the adequacy of the existing spillway. Since this method does not provide an estimate of the risk for the original PMF, it cannot be used to determine how much additional protection would be obtained from ex- panding the spillways to handle a larger PMF. Obviously, the risk of dam failure due to floods will be reducer] by a design that permits larger floods to pass, but such decisions must also meet the test of reasonable care and prudence. What constitutes reasonable care and prudence in selecting the magni- tude of a flood for which a dam should be designed? There appears to be no completely satisfactory answer to this question leastwise one that would satisfy everyone. Those who would be directly affected by the possibility of a dam failure would surely choose to make the dam as floodproof as possible. Yet it is doubtful whether these individuals would be willing to pay the costs required to decrease the risk of the dam failing if the risk of failure were already relatively low (Thaler and Gould, 1982~. The current procedures used for selecting the spillway design flood (SDF) attempt to delimit reasonable care by acknowledging that the level of pro- tection provided should reflect consideration of the hazard potential of the dam (viz., loss of human life, property damage, dam services, opportunity costs) . The PMF, in spite of the fact that it is a hypothetical event of unknown risk or probability, appears to meet a standard of reasonable care, as demon- strated by the performance of dams over the past five decades. On the other hand, since the spillways of many existing dams are inadequate by PMF standards but have survived in spite of this inadequacy, it is legitimate to question whether this standard is higher than may be required. It is axio- matic that excess protection, i.e., that capacity provided at oftentimes con- siderable cost but that is never used is rarely challenged as unreasonable.

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14 SAFETY OF DAMS However, if a dam should fail, one can be assured that a careful inquiry will be made to determine whether the designers used reasonable care in select- ing a design flood. While accountability for dam designers is essential, it is obvious that the ambiguity imbedded in the requirement to exercise reason- able care leads designers to act more conservatively in selecting a spillway design flood. While balancing risks and costs is the ideal, this balancing cannot be accomplished with confidence at this time. In particular, the probability or average recurrence intervals of extreme floods and earthquakes can only be estimated approximately. While moving toward the ideal of balancing, some recommendations are needed to answer current concerns for the design of new dams and the retrofitting of existing dams. The PMF is a concept that has prevented dam failures throughout the world. To a lesser extent perhaps, the similar concept of a limiting earth- quake magnitude (the maximum credible earthquake MCE) has provided a basis for preventing dam failures resulting from seismic events. To date, these notions have proven highly conservative, since few natural events have challenged them. The concepts have great usefulness in the design of new high-hazard dams. Even here, once the PMF and MCE have been estimated and' the dam designed, there ought to be exploration of the cost of meeting somewhat different design levels. For example, if only a tiny addition to the cost of building the dam would be required to design to a higher standard, this greater standard makes sense. Similarly, if the cost of designing to the PMF and MCE are very large in relation to a slightly less stringent design, careful consideration must be given to whether the more stringent design is needed. For dams that pose no threat to life, a balancing of the risks of property damage and loss of dam services against the costs of greater dam safety is appropriate. Such balancing is reasonable, since the relevant floods would be sufficiently frequent that their probabilities could be estimated with confidence. For dams that involve a small risk to life, balancing is similarly appropri- ate, although the risk to even a small number of people should call forth somewhat greater safety than the case of only-risk to property. Such low- hazard dams provide opportunities for research on balancing and also pro- vide test cases for implementing the technique of balancing. The methods developed for these cases may help bring the technique of balancing into the design of high-hazard dams.