Safety of Dams Flood and Earthquake Criteria (1985) / Chapter Skim
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Appendix E: Risk Analysis Approach to Dam Safety Evaluations
Appendix E: Risk Analysis Approach to Dam Safety Evaluations
Pages 241-254
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From page 241... ...
EXTRAPOLATION OF FREQUENCY CURVES A complete risk-based analysis sometimes requires an extension of floodfrequency curves beyond the 50-, 100-, or 500-year return periods, which is usually considered as defining the outer limits of the ability to make credible frequency estimates. As discussed in Appendix D, this is generally unjustified from available systematic flood flow records and records of historical floods.
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From page 242... ...
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From page 243... ...
Ideally, these target values would be a function of the region of the country in which one was working, and the size of the river basin of concern for both of these factors should explain variations in the return periods of PMF estimates. There are several reasonable pathways of extending the empirical frequency curve from the 100-year flood to the PMF.
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From page 244... ...
of the frequency curve out through the PMF estimate, which is assigned a return period of 106 years, or the smaller and more conservative value of 104 years. By using alternative flood-frequency relationships that jointly span the reasonable range one can capture the sensitivity of the expected damage costs and, in particular, the ranking of the alternative projects, to our uncertainty as to the true flood-frequency relationship.
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From page 245... ...
Intentionally breaching or destroying a clam, or widening or lowering a spillway, can result in increased discharges for modest 50- to 200-year return period floods, thereby increasing downstream damage cost associated with relatively likely events even though such structural modifications allow passage of the relatively improbable PMF without structural failure. On the other hancl, given the size of near-PMF floods even without structural failure of the dam, sudden or progressive dam breach during a flood may have a 245 Flow Rate 10,000 (100-yr flood)
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From page 246... ...
The question is whether to stay with the current spillway with capacity of 50,000 cfs, to increase the capacity to 75,000 cfs for an annual cost of TABLE E-1 Design Options and Costs for Illustrative Example Design Flow Annual Cost Option (cfs)
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From page 247... ...
the higher the spillway design discharge, the larger the range over which dam failure is avoided and damages stay below the maximum, and (2) the fourth inexpensive option of lowering, or lengthening, the spillway results in larger damage costs.
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From page 248... ...
$200,000 range with possible but very unlikely damages in the $10,000,000$420,000,000 range. To trade off dam failure prevention costs with possible flood damage and dam failure costs, an extended flood-frequency curve was constructed.
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From page 249... ...
is very unattractive because of the larger downstream damages it causes at all inflow levels up to and including the PMF. This stands in contrast to case 3, which had relatively small downstream damage potential, making the low-cost, lower crest spillway more attractive on an indicated cost basis.
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From page 250... ...
T= 106 Case 1: M = $20 million, L = $20 million 1 130 70 130 70 2 75 50 155 130 3 55 50 255 250 4 94 90 214 210 Case 2: M = $20 million, L = $100 million 1 320 120 320 120 2 130 55 210 135 3 55 50 255 250 4 95 90 215 210 Case 3: M = $20 million, L = $400 million 1 1050 310 1050 310 2 340 75 420 155 3 55 50 255 250 4 95 90 215 210 Case 4: M = $100 million, L = $20 million 1 460 300 460 300 2 320 250 400 330 3 275 245 475 445 4 470 450 590 570 Case 5: M = $200 million, L = $20 million 1 640 280 640 280 2 310 170 390 250 3 185 160 385 360 4 300 260 420 380 NOTE: Minimum cost value is underlined for each case and value of T
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From page 251... ...
An even more philosophical question is whether expected loss of life and expected damages are appropriate metrics to describe possible catastrophic events that are unlikely to occur in contrast to construction costs, which definitely will be experienced. Few argue against the use of probabilities in the analysis of recurring events without catastrophic consequences; examples are the analysis of the cost and benefits associated with frequent floods, year-to-year hydropower operations, or recurring navigational issues on waterways.
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From page 252... ...
For example, a key feature of the matrix decision approach and expected cost analyses is that the selected design is not confined to a specified SEF. The analysis probably would include the PMF as one of the safety evaluation floods, but no single flood is specified as the unique inflow hydrograph against which a design should be tested.
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From page 253... ...
suggests that just"the concept of probable maximum flood diverts our attention toward the illusion of absolute safety and away from the hard necessity to accept risk and minimize it by balancing opposing risk." The matrix decision table may make these trade offs more apparent. Dams are major social investments, and their failures due to the occurrence of large floods is of much concern both because of the loss of the investment embodied by the dam and the likely loss of life and property such a dam failure might cause.
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From page 254... ...
Thus, government agencies should carefully determine if the marginal increments in damages that result from changes in operating rules, structural modifications, and dam failures on balance indicate that structural modification and operating rule changes for existing dams are both justified and well advised. The procedures discussed in this Appendix can facilitate such determinations.
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