Safety of Existing Dams: Evaluation and Improvement (1983)

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HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 71 4 Hydrologic and Hydraulic Considerations GENERAL APPROACH Purpose One aspect of the investigation of the overall safety of an existing dam is an assessment of the probable performance of the project during future extreme flood conditions. Because the actual timing and magnitude of future flood events are indeterminate, such assessments cannot be based on rigorous analyses but must be made by analyzing the probable function of the project during hypothetical design floods. Generally one such hypothetical flood, called the spillway design flood (SDF), is adopted as a tool for assessing the capability of a project to withstand extreme flood conditions. In general, there are no legal standards for the magnitude of the flood that a project must pass safely or the type of analyses to be used. Also, there are no procedures and criteria for such assessments that are universally accepted in the engineering profession. However, a number of state agencies have adopted procedures and criteria for hydrologic and hydraulic investigations that provide appropriate guidelines for assessments of dam safety where the governmental agency responsible for dam safety has not specified the bases to be used. The current procedures and criteria considered appropriate for general application are described in this chapter. It should be recognized that hydrologic and hydraulic analyses for dam safety assessments represent a very specialized and complex branch of engineering for dams. For any project where the consequence of dam failure 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 72 would be serious, these analyses should be directed by an engineer trained and experienced in this specialized field. Because this is a complex field, the coverage in this chapter is limited to some of the basic concepts involved, and the reader is directed to the references and recommended reading sections of this chapter for further development of subjects of special interest. Data Needs Before beginning any hydrologic or hydraulic analysis, a review should be made of any available design records for the dam and spillway. Information such as discharge rating curves or tables, storage capacity, and pertinent dimensions of spillways and outlets should be made available. The procedures used in the design of the spillway should be compared with currently accepted techniques and criteria. If it is evident that the original design bases gave results substantially in accord with current practices, further investigation may be limited to verifying that the existing project meets the adopted design objectives. If, however, the bases used, such as design storms, are considerably different from what would be acceptable today, then a revised flood study is required. The review of project design bases should consider data made available since project construction. For example, in recent years the National Weather Service (formerly the U.S. Weather Bureau) has updated almost all its storm estimates for the United States. Also, any available flood studies for areas within or near the watershed should be consulted. Sources of such information may be the U.S. Army Corps of Engineers, U.S. Bureau of Reclamation, Soil Conservation Service, the state dam safety agency, and other dam owners in the area. Hydrometeorologic characteristics of the watershed of the dam, such as the mean annual precipitation and mean annual flow, should be developed, and past storage fluctuations or reservoir seasonal operation records should be evaluated. Data on unusual hydrologic events, such as peak instantaneous flood flows and operation of gates to spill excess runoff, should be obtained. Such background information permits comparisons of recorded hydrologic events and computed hypothetical events that may be helpful in assessing project safety. Hydrologic and hydraulic analyses provide only part of the data needed for decisions on whether a dam will provide a reasonable level of safety during future floods. Data on probable effects of project operation during extreme floods or dam failure on developments around the reservoir shores and downstream from the dam are also needed. The impact of these effects on the public welfare and the dam owner's liability for damages must be considered. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 73 Simplified Procedures The amount and complexity of the hydrologic and hydraulic analyses appropriate for an assessment of dam safety depend on the importance of the project, the hazards involved, and the data available. For an important project or one presenting significant hazards to downstream areas, detailed development and routing of design floods, as discussed later in this chapter, beginning with the section Spillway Capacity Criteria, would be advisable. However, in some cases the safety investigation of an existing dam will not require such sophisticated analyses. As noted below, several simple techniques are available that may provide acceptable degrees of accuracy. These approximate procedures should be used with care and under the direction of an experienced hydraulic and/or hydrologic engineer. Comparisons with Historical Peak Discharges Evaluations of the relative magnitude and the credibility of flood peak discharge estimates can be obtained by comparison with known historical peak discharges in other watersheds. Also, such information about maximum floods of record in similar hydrologic regions can provide a basis for estimating flood potential at a given site. Data on streamflow and flood peaks are collected and published by the U.S. Geological Survey in its water supply papers, hydrologic investigation atlases, and circulars. Figure 4-1 shows a comparison of observed flood peaks in a region based on such data. In the past a number of empirical formulas have been advanced for describing the relationship between drainage area characteristics and maximum observed flood discharges. Figure 4-1 shows curves based on two such relationships that have been used extensively, the Myer and Creager formulas. The Creager formula is or its equivalent where Q is the total discharge in cubic feet per second, q is the unit discharge in cubic feet per second per square mile, A is the drainage in square miles, and C depends on the drainage basin characteristics. C is a coefficient dependent on many factors, such as the following: • Storm rainfall. Intensity, areal distribution, orientation, direction, trend of great storms, and effect of ocean and mountain ranges. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS Figure 4-1 Comparison of regional flood peaks. 74 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 75 • Infiltration. Character of the soil, antecedent moisture, frozen ground. • Geographical characteristics. Shape and slope of watershed. • Natural storage. Valley storage, tributaries, lakes, and swamps. • Artificial storage. Reservoirs, channel improvements. • Land coverage. Forested, cultivated, pasture, and barren areas. • Sudden releases of flow. Ice and log jams, debris jams against bridges, questionable safety of upstream dams, sudden snowmelt. A value of 100 for the coefficient C seems appropriate to compare with the most extreme event of the probable maximum flood. Intermediate values with C equal to 30 and 60 are also plotted on Figure 4-1 for comparison. The Creager enveloping curve provides an estimate of the maximum peak discharge that might be expected for drainage areas generally less than 1,000 square miles. There have been flood discharges that exceeded the limits indicated by the Creager enveloping curve in several basins greater than 1,000 square miles. The Modified Myer equation was introduced by C. S. Jarvis in 1926 and is shown in Figure 4-1 solely for the purpose of comparison with the Creager equation. Generalized Estimates of Probable Maximum Flood Peak Discharges A source of probable maximum flood (PMF) peak discharges is contained in the U.S. Nuclear Regulatory Commission's Regulatory Guide 1.59 (1977). In addition, enveloping curves for areas east of the 103rd meridian were developed by the U.S. Army Corps of Engineers, the U.S. Nuclear Regulatory Commission staff, and their consultants, Nunn, Snyder and Associates. The enveloping curves were found to parallel the Creager curve. Isoline maps showing the generalized PMF estimates as well as a discussion of the way they may be used are contained in Appendix 4A. Use of such generalized data should be confined to situations in which more specific PMF discharge estimates are not available and where it is not practicable to develop estimates specifically for the project. Dam Break Flood Flow Formulas In assessing the hazard involved in the potential failure of a dam, an estimate of the downstream flood that would be produced by such failure is needed. As discussed in the section Dam Break Analyses, rather complex techniques are available to compute the characteristics of the downstream flood wave following a dam failure. However, a number of simplified methods for making rough estimates of peak downstream flows from dam 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS Figure 4-2 . Estimated flood peaks from dam failures. Source: U.S. Bureau of Reclamation (1977) 76 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 77 failures are contained in the references to this chapter. Several empirical formulas of varying degrees of accuracy have been summarized by Cecilio and Strassburger (1974). These formulas apply to instantaneous failure events only. Erosion-type failure can also utilize the same formulas with certain modifications as discussed by Cecilio and Strassburger. Other simplified approaches are presented by Sakkas (1974) and the Soil Conservation Service (1979). Figure 4-2 shows estimated downstream flood peak flows for a number of dam failures and a curve presented by Kirkpatrick (1976) as a basis for estimating such flows. Figure 4-3 shows data developed by Vernon K. Hagen (1982) on maximum peak flows immediately downstream of darns after their failure. Hagen presents two equations based on experienced dam failures, primarily dam failures in the United States that relate peak flood flows following failure to reservoir levels and storage volumes. The equations are defined as follows (English units): and where Q is the peak flow in cubic feet per second immediately below the dam following its failure, and the DF is a dam factor obtained by multiplying height of water in reservoir above streambed H by the reservoir storage S (where H is vertical height measured in feet from the streambed at the downstream toe of the dam to the reservoir level at time of failure, and S is storage volume of water in acre-feet in reservoir at time of failure). As noted on Figure 4-3, the first equation envelopes all dam failures listed by Hagen, while the second equation envelopes all except the failure of the high arch Malpasset Dam in France. BASES FOR ASSESSING SPILLWAY CAPACITIES In most cases assessment of the safety of an existing dam will require that the SDF be routed through the reservoir and spillway and any other outlet structures for which availability to release water from the reservoir during extreme flood events can be assured. The geometry and location of these hydraulic structures determine the quantity of water that can be discharged at any point of time during the inflow of the design flood. Desirable objectives for spillway operation and bases for assessing spillway adequacy are discussed in this section. Development of SDFs and assumptions regarding project operation for routing studies are covered in subsequent * In the original paper the equation was written in metric units. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 78 sections. Discharge characteristics and criteria for various types of spillways and outlet works are presented in Chow (1959), Davis and Sorenson (1969), King and Brater (1963), U.S. Army Corps of Engineers (1963, 1965, 1968a), U.S. Bureau of Reclamation (1977). The bases for determining spillway capacities and freeboard allowances for dams are discussed in a report by the U.S. Army Corps of Engineers (1968b). Figure 4-3 Peak discharge from significant dam failures. Present General Situation The design capacities of spillways for many existing dams were chosen in a subjective manner based on the magnitude of property damage and probable loss of project investment and human life in the event of dam failure during a severe flood. Also, many dams in the United States were built before data were available to assess adequately the flood-producing potentials of their watersheds. As a consequence, many existing dams have inadequate spillway capacities based on currently accepted criteria. Analyses have shown that about one-third of recorded dam failures resulted from spillway inadequacy. Also, of approximately 9,000 nonfederal dams in the United States inspected recently, almost 25% were designated as unsafe because of inadequate spillway capacity. The risk of severe consequences associated with the failure of these dams should be reduced by mitigating measures, as discussed later in this chapter. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 79 Currently Accepted Practices In 1970 a working group of the United States Committee on Large Dams (designated the USCOLD Committee on Failures and Accidents to Large Dams) conducted a survey on criteria and practices used in the United States to determine required spillway capacities. A survey questionnaire was distributed, and 4 federal agencies, 2 state agencies, 2 investor-owned utility companies, and 13 private engineering firms responded. The results of the survey (USCOLD 1970), summarized below, constitute an authoritative statement of practices accepted and used by those engineers in the United States involved in the engineering of dams. Design Objectives The USCOLD committee recognized that the costs of dams and associated facilities are influenced substantially by the degree of security to be provided against possible failure of the dam from overtopping during floods and that two basic objectives of spillway and related safety provisions are to protect the owner's investment in the project and to avoid interruptions in the services afforded by the project. But the committee noted that an additional and usually overriding requirement for security is to protect downstream interests against hazards that might be caused by the sudden failure of the dam and any ensuing flood wave. The survey found it to be common practice that spillway capacities, in connection with other project features, should be adequate to: • ensure that flood hazards downstream will not be dangerously increased by malfunctioning or failure of the dam during severe floods; • ensure that services of and investment in the project will not be unduly impaired by malfunctioning, serious damage, or failure of the dam during floods; • regulate reservoir levels as needed to avoid unacceptable inundation of properties, highways, railroads, and other properties upstream from the dam during moderate and extreme floods; and • minimize overall project costs insofar as practicable within acceptable limits of safety. Functional Design Standards The USCOLD committee also noted that functional design standards necessary to meet minimum security requirements for downstream areas at minimum cost usually conform with one of the following alternatives, the selection being governed by circumstances associated with specific projects and downstream developments: 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 80 Standard 1. Design dams and spillways large enough to ensure that the dam will not be overtopped by floods up to probable maximum categories. Standard 2. Design the dam and appurtenances so that the structure can be overtopped without failing and, insofar as practicable, without suffering serious damage. Standard 3. Design the dam and appurtenances in such a manner as to ensure that breaching of the structure from overtopping would occur at a relatively gradual rate, such that the rate and magnitude of increase in flood stages downstream would be within acceptable limits, and such that damage to the dam itself would be located where it could be repaired most economically. Standard 4. Keep the dam low enough and storage impoundments small enough so that no serious hazard would exist downstream in the event of breaching and so that repairs to the dam would be relatively inexpensive and simple to accomplish. Policies Affecting Spillway Capacity Requirements The following general policies (based on the accepted practices found by the USCOLD committee) provide guidance for application of the four functional design standards. These should be helpful if combined with some of the procedures in Chapter 3 under the section Flood Risk Assessments. • When a high dam, capable of impounding large quantities of water, is constructed upstream of a populated community, a distinct hazard to that community from possible failure of the dam is created unless due care is exercised in every phase of engineering design, construction, and operation of the project to ensure complete safety. The prevention of overtopping such dams during extreme floods, including the probable maximum flood, is of such importance as to justify the additional costs for conservatively large spillways, notwithstanding the low probability of overtopping. The policy of deliberately accepting a recognizable major risk in the design of a high dam simply to reduce project cost has been generally discredited from the ethical and public welfare standpoint, if the results of a dam failure would imperil the lives and life savings of the populace of the downstream flood plain. Legal and financial capabilities to compensate for economic losses associated with major dam failures are generally considered as inadequate justification for accepting such risk, particularly when severe hazards to life are involved. Accordingly, high dams impounding large volumes of water, the sudden release of which would create major hazards to life and property damage, should be designed to conform with security Standard 1. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 81 • Application of Standard 2 should be confined principally to the design of run-of-river hydroelectric power and/or navigation dams, diversion dams, and similar structures where relatively small differentials between headwater and tailwater elevations prevail during major floods and where overtopping would not cause either dam failure or serious damage downstream. In such cases the design capacity of the spillway and related features may be based largely on economic considerations. • Application of Standard 3 should be limited to dams impounding a few thousand acre-feet or less, so designed as to ensure a relatively slow rate of failure if overtopped and located where hazard to life and property in the event of dam failure would clearly be within acceptable limits. The occurrence of overtopping floods must be relatively infrequent to make Standard 3 acceptable. A slow gradual rate of breaching can be accomplished by designing the dam to overtop where the breach of a large section of relatively erosion-resistant material would be involved, such as through a fiat abutment section. The control may be obtained, in some cases, by permitting more rapid erosion of a short section of embankment and less rapid lateral erosion of the remaining embankment. • Standard 4 is applicable to small recreational lakes and farm ponds. In such cases it is often preferable to keep freeboard allowances comparatively small to ensure that the volume of water impounded will never be large enough to release a damaging flood wave if the dam should fail due to overtopping. In some instances adoption of Standard 4 may be mandatory, despite the dam owner's desire to construct a higher dam, if a higher standard is not attainable. Unless appropriate safety of downstream interests can be ensured, a higher dam is not justified simply to reduce the frequency of damages to the project. SPILLWAY CAPACITY CRITERIA Recommended Spillway Capacities Pursuant to the National Dam Inspection Act (PL 92-367), enacted August 8, 1972, the U.S. Army Corps of Engineers issued Recommended Guidelines for Safety Inspection of Dams, which was made an Appendix D of the National Program of Inspection of Nonfederal Darns, ER 1110-2-106 (1982b). This was also issued as Title 33 in the Code of Federal Regulations, Part 222. These documents contain guidelines for determining spillway capacity requirements for low, intermediate, and high dams with low, significant, and high hazard classifications. Similar guidelines have been used by the U.S. Bureau of Reclamation and the Soil Conservation 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 82 Service. State and local agencies, private companies, and engineering design firms have generally adopted the guidelines of one of the federal agencies in determining spillway capacity requirements, although in many cases, particularly for low and intermediate height dams, no specific guidelines were followed. As the U.S. Bureau of Reclamation and the Soil Conservation Service guidelines for spillway capacity requirements are generally consistent with those developed by the Corps of Engineers, and the latter are more specific and inclusive, use of guidelines for spillway capacity requirements that were adopted for the National Program of Inspection of Nonfederal Dams is recommended. These guidelines are presented in Tables 4-1, 4-2, and 4-3. Alternative Guidelines for Spillway Capacity Requirements Dams being reevaluated for safety or being enlarged or improved may have spillways smaller than required to pass safely some floods, as indicated in Table 4-3. A smaller capacity spillway may be acceptable if it can be shown that when a specific dam fails due to overtopping by a flood that just exceeds the routing capacity of a reservoir the resulting dam break flood would not cause additional loss of life and/or a significant increase in damage to improved properties over that which would occur prior to the dam failure. In this case, however, the minimum-sized spillway should safely pass the 100-year flood. As previously noted, in some cases dam owners may not be willing or able to enlarge spillway capacities of existing dams in accordance with the guidelines presented in Table 4-3 because of financial constraints, or a dam may have been in existence for 25 to 50 or more years without any threat of being overtopped, which appears to support the owner's belief that the risk of dam failure and consequent damages is small. Such cases will present difficult problems to governmental agencies having regulatory responsibilities for dam safety. In each such case the agency and the dam owner should TABLE 4-1 Dam Size Classification Impoundment Category Storage (acre-feet) Height (feet) Small <1,000 and 50 <40 and 25 Intermediate 1,000 and <50,000 40 and <100 Large 50,000 100 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 83 seek to provide as a minimum those corrective and mitigating improvements that could be made to increase the spillway capacity within the owner's financial means. Any increase in spillway capacity, even though less than indicated by Table 4-3, would decrease the risk of dam failure. However, all parties involved should recognize that such partial steps will not meet the design objectives to protect their interests. TABLE 4-2 Hazard Potential Classification Category Urban Development Economic Loss Low No permanent structure for Minimal (undeveloped to human habitation occasional structures or agriculture) Significant No urban development and no Appreciable (notable agriculture, more than a small number of industry, or structures) habitable structuresa High Urban development with more Excessive (extensive than a small number of habitable community, industry, or structures a agriculture) a Because this definition does not cite a specific number of lives that could be lost, difficulty was experienced in determining whether dams should be categorized as having ''significant or high hazard potential.'' The issue was clarified by emphasizing that the hazard potential classification should be based on the density of downstream development containing habitable structures. For example, dams located upstream of isolated farmhouses would be classified as having significant hazard potential, and those located upstream of several houses or a residential development would be classified as having high hazard potential. SOURCE: U.S. Army Corps of Engineers (1982b). DESIGN FLOODS By definition, the SDF is the reservoir inflow-discharge hydrograph used to estimate the spillway discharge capacity requirements and corresponding maximum surcharge elevation in the reservoir. The surcharge elevation is obtained by routing the SDF through the reservoir and spillway. Practices in establishing SDFs in the United States have undergone continuous evolution through several periods. At the present time there are 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 84 four methods currently in significant use for the derivation of the SDF: (1) an envelope curve method that uses the actual recorded peak flows for the river of concern or for the general region; (2) frequency-based floods using standard statistical techniques that convert the historic peaks into a probability of occurrence curve; (3) the hydrometeorologic approach that maximizes the combination of all of the appropriate physical parameters involved in flood development on the particular drainage area in question; TABLE 4-3 Hydrologic Evaluation Guidelines: Recommended Spillway Design Floods Hazard Size Spillway Design Flood (SDF)a Low Small 50- to 100-year frequency Intermediate 100-year to 1/2 PMF Large 1/2 PMF to PMF Significant Small 100-year to 1/2 PMF Intermediate 1/2 PMF to PMF Large PMF High Small 1/2 PMF to PMF Intermediate PMF Large PMF a The recommended design floods in this column represent the magnitude of the spillway design flood (SDF), which is intended to represent the largest flood that need be considered in the evaluation of a given project, regardless of whether a spillway is provided; i.e., a given project should be capable of safely passing the appropriate SDF. Where a range of SDF is indicated, the magnitude that most closely relates to the involved risk should be selected. 100-year = 100-year exceedance interval. The flood magnitude expected to be exceeded, on the average, of once in 100 years. It may also be expressed as an exceedance frequency with a 1% chance of being exceeded in any given year. PMF = probable maximum flood. The flood that may be expected from the most severe combination of critical meteorologic and hydro-logic conditions that are reasonably possible in the region. The PMF is derived from the probable maximum precipitation (PMP), which information is generally available from the National Weather Service, NOAA. Most federal agencies apply reduction factors to the PMP when appropriate. Reductions may be applied because rainfall isohyetals are unlikely to conform to the exact shape of the drainage basin. In some cases local topography will cause changes from the generalized PMP values; therefore, it may be advisable to contact federal construction agencies to obtain the prevailing practice in specific areas. SOURCE: U.S. Army Corps of Engineers (1982b). 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 85 and (4) a site-specific determination of the maximum flood for which failure of the dam would significantly affect downstream losses. Envelope Method The envelope process has probably been in use the longest of the three methods. It consists of plotting all of the floods for the river in question or for the hydrologically similar region, against a physical parameter, such as drainage area. An envelope curve is then drawn, and the appropriate peak discharge can be picked off for use as a design parameter. Obviously, the confidence in the flood value thus selected will vary with the length of the data base used in the envelope curve delineation. This procedure is usually acceptable only for rough estimates. It should not be considered as an accurate method for establishing the full flood-producing potential of a basin for determining an SDF. As suggested in the section Simplified Procedures, this method is preferably used only for comparison. Frequency-Based Floods The second method, statistical manipulation of recorded flood peaks, either for the river in question or for hydrologically similar areas, to produce a return period curve gained great favor in the United States in the early 1940s. Much time and energy have been devoted to determine the statistical distribution that provides the "best fit" for the existing data and that can be extrapolated beyond the period of record with the most confidence. This basic method has severe limitations in that the data base, i.e., usually annual flood peaks, in the United States is of relatively short duration. Very few records go back 100 years, and the majority are less than 50, so that only limited confidence can be placed in use of an extrapolated curve to predict flood events expected to occur only once in one or two centuries on the average. This is not to say that the method is not a useful tool for the hydrologist, but it does have severe drawbacks for use in deriving the SDF. To achieve some consistency of approach within the federal agencies, the Hydrology Committee of the Water Resources Council issued Bulletin 15, A Uniform Technique for Determining Flood Flow Frequencies, in December 1967. This bulletin recommends use of the Pearson Type III distribution with log transformation of the data (log-Pearson Type III distribution) as a base method for flood-flow frequency studies. Bulletin No. 15 was subsequently extended and updated by Bulletin No. 17 (Bulletin No. 17B, U.S. Department of Interior, Interagency Committee on Water Data, 1982, is the current edition) and its subsequent revisions. This update provides a more complete guide for flood-flow frequency analysis, incorporating currently accepted technical methods with 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 86 sufficient detail to promote uniform application. This guide is limited to defining flood potentials in terms of peak discharge and exceedance probability at locations where a systematic record of peak flows is available. The U.S. Geological Survey publishes information on a regional basis for estimating discharge frequencies for ungaged areas. Such data are published in Water Supply Papers with the general title Magnitude and Frequency of Floods in the United States, subtitled with the name of the basin. These are presented in the form of regression equations or by use of the "index flood" method. Most applications of flood frequency analysis methods deal only with peak flood flows and do not produce hydrographs of flow that can be used for routing floods through a reservoir. If such routing is required, an auxiliary method of developing the hydrograph is necessary. Such a method is described in the U.S. Army Corps of Engineers' (1982a) document Hydrologic Analysis of Ungaged Watersheds Using HEC-1. Frequency-based flood analysis should be used only for small-sized and low-hazard or low-risk dams, where accepted practice allows use of design floods with average return periods of 50 to 100 years. Small dams affected by flows from upstream reservoirs should not be evaluated by the frequency type of analysis. For such situations sequential flood routing of flood discharges from the upstream reservoirs and intermediate areas should be used. Hydrometeorologic Approach In the 1940s the U.S. Army Corps of Engineers and the U.S. Weather Bureau (now the National Weather Service) embarked on a study to determine probable maximum precipitation (PMP) magnitudes based on the synoptic processes that generate such floods. In the present report, careful consideration is given to the meteorology of storms that produced major floods in various areas of the United States. The synoptic features of the storm, such as dew point temperatures and rainfall amounts, were cataloged, as were the depth-area- duration (D-A-D) values produced by these storms. It was then possible hypothetically to maximize these D-A-D rainfall amounts by increasing the storm dew point temperature and other factors affecting rainfall to the maximum appropriate values. Adjustments were made for the natural barrier effects on the D-A-D amounts for different areas in the appropriate storm trajectories. The end result of these studies was a series of generalized D-A-D isopleths for use in selecting the PMP meteorologically appropriate for an area. These generalized data are commonly used for design studies in broad level regions, such as the Central states. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 87 In mountainous regions precipitation clue to lifting of air by ground slopes, called orographic precipitation, is complemented by precipitation clue to meteorological processes that would be present were the mountains not there, called convergence precipitation. In estimating maximum rainfalls these two rain-producing processes are maximized and summed. To facilitate estimate of the PMP, separate isohyetal maps showing orographic and convergence indices are presented in National Weather Service reports. The National Weather Service has published data for estimating hypothetical storms ranging from the frequency-based storm to the PMP event. There are two major hydrometeorological reports (HMRs) that are applicable for areas east of the 105th meridian: U.S. Weather Bureau (1956) and U.S. Department of Commerce (1978). Before using either of these reports the user should consult with the regulatory agency or the National Weather Service on the appropriate report to use. A U.S. Department of Commerce (1978) report has an auxiliary report: National Weather Service (1982), which describes in detail the application of the report. The U.S. Department of Commerce (1980) HMR Report No. 53 provides estimates of the PMP for 10-square-mile areas. As indicated by the entries in the references for this chapter, the National Weather Service also has issued a considerable number of special reports on individual watersheds. Several hydrometeorological reports of varying degrees of application are available for areas west of the 105th meridian. These areas are shown in Figure 4-4. Ordinarily, an estimate of PMP developed specifically for an area in which a reservoir is situated should be used instead of generalized estimates. As an example, in the Tennessee area, specific hydrometeorological reports that address the orographic effects of the Appalachian Mountains should be used over generalized estimates that neglect such effects. In areas not covered by specific National Weather Service reports or where doubtful estimates are available, transposition and maximization of major historical storms, D-A-D studies, or storm sequence studies may be necessary. Procedures in determining the PMP are outlined in many of the hydrometeorological reports mentioned above. In some geographic areas the SDF may result from snowmelt runoff or from the combination of extreme rainfall and snowmelt. Pure snowmelt hydrographs tend to have characteristic shapes and usually result in floods of large volume. Methods have been developed for determining snowmelt hydrographs based on rates of solar radiation. However, historical snow-melt flood hydrographs from the study basin or similar basins are often the best guide to hydrograph shapes and can be adjusted on the basis of water equivalent at the beginning of the melt season. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 88 Figure 4-4 Probable maximum precipitation study regions. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 89 Site-Specific Determinations For many small reservoirs the failure of the dam during a flood of the magnitude of the PMF would not significantly affect damages in downstream areas because of the devastation that would be produced by the natural flood. Where the dam already exists, the available spillway capacity is not adequate to pass the PMF, and it would be difficult or excessively costly to provide such spillway capacity, a lesser spillway capacity may be justified. One procedure that has been used is to consider a number of major floods, less severe than the PMF, that would cause overtopping and failure of the dam and to determine, by analyses of flood waves that would result from the respective failures, the maximum general flood in which the dam failure produces significant additional losses downstream. Such a flood is then adopted as the design flood for spillway improvements. Of course, this selection of design flood is very much dependent on the level of existing developments in the area downstream that would be affected by dam failure. With further development downstream, a larger design flood may be indicated. For this reason, use of this method for selection of an SDF is not well adapted to the design of a new project. Credibility of Maximum Flood Estimates Usually, estimates of probable maximum rainfalls and the attendant PMFs far exceed any rainfalls and floods experienced in the areas involved. Such rainfalls and floods are in the class of natural events that are rarely experienced in a person's lifetime. Perhaps naturally, the adoption of such a standard for design or evaluation of a project can raise doubts as to the possibility that such rainfalls can occur or that the criteria are reasonable. Of course, there is no way to ascertain that probable maximum rainfalls will ever be experienced over a given area. However, as identified in Appendix 4B, records of major storm rainfalls in the United States show that literally dozens of storms have produced rainfalls exceeding 50% of PMP estimates and a considerable number have almost reached PMP magnitudes. These data (U.S. Army Corps of Engineers 1982b) show that enough near-PMP events occur each decade to make consideration of such rainfalls clearly reasonable. ANALYSIS TECHNIQUES Following selection of the basis for the SDF, a number of decisions must be made relative to the conditions of the reservoir and the drainage basin to 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 90 be assumed to exist antecedent to the design flood and to the methods to be used in developing the reservoir inflow hydrograph, routing the inflow hydrograph through the reservoir storage, and determining the capability of the project to withstand safely such a hydrologic event. As noted before, if the PMF is adopted as a design flood, such analyses usually must deal with phenomena well beyond the range of past experiences in the basin. Often, hydrologic relationships derived from past experience should be adjusted to reflect the rainfall and runoff conditions visualized in the PMF. The objective of the analyses should be to reflect reasonably the probable maximum flood- producing potential of the basin without illogical pyramiding of improbabilities. Guidance for some aspects of those analyses is presented below. Providing for Seasonal Variations Seasonal variations in such basin characteristics as dominant storm types, vegetative cover, ground moisture, and snowpack can often significantly affect the runoff-producing capability of a drainage area. Also, seasonal changes in reservoir operations plans may affect the ability of the project to withstand major floods. To determine the most critical PMF estimate for such conditions, the PMP estimate for the dominant storm type of each season should be used with the most critical basin and project conditions characteristic of the respective season. This may require consideration of small-area thunderstorm- type rainfalls as well as large-area cyclonic-type disturbances. Placement of PMP Storm Over a Basin An isohyetal map of PMP amounts may be shifted to any position over the basin not inconsistent with the meteorologic conditions on which it is based. Several storm centerings should be considered in order to determine the most critical condition. In areas where a specific oval-shaped isohyetal pattern is used to estimate the design storm, placing the storm center near the downstream end of the drainage area produces the most critical condition for peak inflow but not for maximum volume. Distribution of PMP to Basin Subareas For a number of reasons it is often desirable to subdivide large drainage areas in computing PMF hydrographs. Such subdivisions may be required because a number of reservoirs are operational in the basin or to secure 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 91 subareas adaptable to unit hydrograph application. Nonuniformity of physical or hydrologic conditions in the area also may make subdivision into areas of fairly uniform characteristics desirable. One method of distributing PMP values to subareas is to transpose a selected PMP isohyetal pattern to the drainage area and determine the depth-duration curves for each area. Another method is to place the most intense rainfall over the most critical portion of the basin and derive depth-duration curves for successively large areas. Precipitation curves are then calculated corresponding to adjacent and mutually exclusive subareas. Rainfall Time Distribution To compute the flood hydrograph for the PMP, it is necessary to specify the time sequence of the precipitation. Usually, the estimate of PMP is derived by 6-hour increments. These increments should be arranged in a sequence that will result in a reasonably critical flood hydrograph. Ideally, the PMP time sequence should be modeled after historically observed storms if such storms show that major storm rainfalls have a predominant pattern. When no predominant rainfall pattern is evident from past records or has not been developed, a number of guides are available for arranging the rainfall into patterns consistent with the meteorologic processes involved and that will produce reasonably critical hydrographs. One such guide is as follows: 1. Group the four heaviest 6-hour increments of the PMP in a 24-hour sequence, the next highest four increments in a 24-hour sequence, etc. 2. For the maximum 24-hour sequence, arrange the four 6-hour increments ranked 1, 2, 3, and 4 (maximum to minimum) in the order 4, 2, 1, 3. Other days may be arranged in similar order. 3. Arrange the 24-hour sequences such that the highest period is near the center of the storm and the second, third, etc., are distributed in a manner similar to step 2 above. 4. The 6-hour increments may be further subdivided into 1-hour increments by determining the incremental differences from a depth- duration plot (mass curve) of the total PMP storm. The six 1-hour increments ranked 1, 2, 3, 4, 5, and 6 (maximum to minimum) should be arranged in the order of 6, 4, 2, 1, 3, 5. Typical rainfall distribution patterns applicable in California and the northwest states are shown in Figure 4-5. In some other parts of the country the time distribution pattern suggested in the Standard Project Flood Determinations (U.S. Army Corps of Engineers, 1965a) is adopted. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS Figure 4-5 Sample probable maximum precipitation time sequences. Source: U.S. Weather Bureau (1969). 92 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 93 Antecedent Storms Studies of historical storms in certain regions indicate that it is possible to have significant rainfalls occurring before or after the major flood-producing storms. Such meteorological sequences should be considered in studies involving a PMF estimate in an area where several reservoirs exist. As a general rule, the critical PMP in a small basin results primarily from extremely intense small-area storms, whereas in large basins the critical PMP usually results from a series of less intense large-area storms. A number of National Weather Service studies cover the time sequencing of storms. For areas not covered by these studies, it is often considered that the PMF is preceded 3 to 5 days earlier by a flood that is 40 to 60% of the principal flood. Assumed antecedent conditions generally provide wet and saturated ground conditions prior to the occurrence of a PMP. Antecedent Snowpack and Snowmelt Floods Flood flows in many parts of the United States frequently depend on the rate and volume of melting from snow that has accumulated during the winter months. The volume of water available in such form for flood runoff depends on the depth, density, and area of snow accumulation. The rate of melt depends on meteorologic factors, such as temperature, cloudiness, wind movement, humidity, and on basin physiographic factors, such as elevation, shape, orientation, and type of vegetation. The months in which the greatest snowmelt occurs will vary from one locality to another and from one year to another, depending on the geographic location, the prevailing climate, and meteorologic variations of the season. However, in most western states, major floods resulting from snowmelt occur between April 1 and June 30. Estimates of PMF in areas subject to snow accumulation require the evaluation of snowmelt as added contributions to runoff. The initial snowpack condition is important both from the consideration of snowmelt and for the storage and delay of liquid water in the snowpack. For the PMP-plus-snow flood conditions, it may be assumed that sufficient water equivalent exists to provide snowmelt continuously through the storm period throughout the entire range of elevation. Also, it may be assumed that the preceding melt and rainfall have provided drainage channels through the snowpack and have conditioned it to provide runoff without significant delay; thus, water excesses from rain and snowmelt during the storm period are immediately available for runoff. To estimate the initial snowpack condition at the beginning of the PMP, records of snow accumulation and water content prior to historical floods should be investigated. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 94 Methods of estimating the probable maximum snowmelt flood, whether the flood is entirely from thermal action on snow or from a combination of snow-melt and rain, have been developed by the U.S. Army Corps of Engineers. Snowmelt evaluation for basins may be accomplished either through the use of simplified generalized equations, sometimes known as the energy-budget method, or indirectly through use of snowmelt indexes, also called the degree- day method. In basin applications for design floods, the former are more appropriately used because of the requirement for direct rational evaluation of all factors affecting snowmelt and extending them to the given design condition. This involves detailed computations of major scope, but they are justified for the design of major water control projects. For daily stream flow forecasting uses, however, a simple snowmelt index is usually adequate when considering the overall accuracy of forecasts and time limitations in their preparation. The detailed applications of these methods are described in U.S. Army Corps of Engineers (1956, 1960, 1962), U.S. Bureau of Reclamation (1966), and U.S. Weather Bureau (1966a). Loss Rates The absorption capability of a watershed depends on many factors, and its determination is subject to several uncertainties. However, reasonable estimates of loss rates can be based on detailed seasonal rainfall-runoff studies performed for past floods within the watershed. These studies should cover antecedent precipitation conditions, base flow, and the type of soils in the watershed. The selection of loss rates is a major consideration in deriving hypothetical floods because a major portion of the rainfall is lost to interception or localized ponding and infiltration. The degree of conservatism in the estimate of the peak design flow is subject to the degree of conservatism by which the loss rates are assumed or applied. The loss rate is often not as significant in determining the PMF as it is in determining the 100-year flood. Seasonal variation in minimum loss rates, which should be considered as representative of the most extreme conditions for the season for the hypothetical flood, should be applied. Typical values used throughout the United States are in the range of 0.10 to 1.0 inch initial loss followed by a uniform rate of 0.05 to 0.15 inch per hour. Runoff Models The hydrologic response characteristics of the watershed to precipitation are embodied in a mathematical model termed a runoff model. A runoff model translates precipitation excess over a watershed to its resulting flood hydrograph. A number of different types of runoff models have been used, 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 95 including computer-based mathematical models (as discussed under Dam Break Analyses later in this chapter). A model may be derived from rainfall and runoff data for historical floods or by use of so-called synthetic procedures based on generalized empirical relationships between a basin's physical characteristics and its hydrologic characteristics. When practicable, a runoff model should be verified by using it to reproduce one or more historical floods. It is often necessary to divide a watershed into subareas on the basis of size, drainage pattern, installed and proposed regulation facilities, vegetation, soil and cover type, and precipitation characteristics. Runoff models are often derived for each subarea, and these subarea models are connected and combined by channel routing. The unit hydrograph has been found to be a very powerful tool in watershed modeling. The unit hydrograph is defined as the hydrograph that represents a unit volume of runoff (customarily 1 inch) from the study basin generated during a finite rainfall excess period. Thus, a 1-hour unit graph is the hydrograph that would be produced by 1 inch of rainfall excess (runoff) generated in a 1-hour period. Unit hydrograph derivation is discussed in several hydrology textbooks and publications. Generally, its use should be limited to drainage areas not exceeding 2,000 square miles. Unit hydrographs are usually derived in one of two ways depending on the extent of the data available. In the case of gaged drainage basins, historical flood events are analyzed by separating out the base flow component and calculating the depicted surface runoff volume. The event ordinates are then proportionally reduced or increased as appropriate to give a hydrograph that represents 1 inch of runoff from the basin under the particular temporal and spatial distribution of the actual storm precipitation. In the ideal case, several floods resulting from the type of synoptic situation that has been adjudged the most critical for that particular basin, i.e., frontal rainfall, convective rainfall, snowmelt, or a mixed snow/rain event, are available for separation analysis. These separated hydrographs and the resulting derived unit hydrographs are then compared with the actual rainfall event to establish the time parameter of the appropriate unit hydro-graphs. An infiltration analysis of the rainfalls and runoff volumes for the historical floods will often aid in determining the lengths of periods of rainfall excess represented by the derived unit hydrographs. After selection of a unit hydrograph and its time parameters, methods are available to correct the unit hydrograph to a time basis that is relevant to the PMP increments and to the basin characteristics. In the case of ungaged basins the unit hydrograph can be derived from climatically and geomorphologically similar basins for which data are available or from various mathematical models. For similar basins the procedure is the same as that described above. For the situation where there 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 96 are no streamflow data and no appropriately similar basin available, the mathematical approach permits derivation of a synthetic unit hydrograph based on the physical aspects of the basin (U.S. Army Corps of Engineers 1959). Various adjustments have been made to runoff models derived as above in attempts to make the models more nearly fit the runoff conditions anticipated during a PMF. Such refinements have attempted to account for the expected increase in overland and channel flow velocities during periods of very high runoff rates, for rain falling directly on a large reservoir surface, and for the shortened flow distances in the watershed because of a large reservoir expanse above the dam. These adjustments result in making the unit hydrograph peak earlier and higher. By combining critically arranged PMP increments with the adopted runoff model (with appropriate allowances for base flow and the recession limbs of antecedent storm hydrographs), a PMF hydrograph for the basin is obtained. If the runoff model represents the entire watershed, this PMF hydrograph is considered the inflow hydrograph for the reservoir. If the watershed has been subdivided, subbasin PMF hydrographs are appropriately routed and combined to obtain such an inflow hydrograph. Base Flow The base flow in a river at the beginning of the main hypothetical flood should be equivalent to the receded flow of any antecedent flood assumed or considered in the study. In the absence of an assured antecedent flood, as may be the ease for small drainage basins, a reasonable base flow such as the mean annual flow should be added to the principal flood. Channel Routing Outflow hydrographs from each subarea in a watershed above a darn under investigation should be routed through the river channel up to a point where they can be combined with another subarea hydrograph. This routing and combining should proceed from the uppermost subarea to the most downstream area adjacent to the reservoir of the dam under investigation. This procedure is generally called channel or stream flow routing. For rainflood or snowmelt flood studies where the rate of flow is not rapid, hydrologic storage-routing techniques can be used. There are several generic names for channel routing, but the most commonly used techniques are the Muskingum method and the Modified-Puls storage-indication method (U.S. Army Corps of Engineers 1969), or the progressive averagelagg method (Straddle-Stagger). Both of these methods assume that the 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 97 outflow at the downstream end of a channel reach is a function of the storage between successive water surface profiles in the reach. To allow for the steeper water surface slopes in rapidly rising streams, the Muskingum method uses the concept of wedge storage in the reach. In applying the hydrologic method of routing, care should be taken in making assumptions for the coefficients used in a specific routing procedure. These assumptions can make a significant degree of change in the attenuation of the flood peak. If in doubt about the coefficients, it is suggested that these should be derived from historical floods recorded at streamflow gaging stations with proper allowance for extrapolating the data to greater floods. Antecedent Reservoir Level It is difficult in most cases to estimate the initial reservoir level that is likely to prevail at the beginning of a SDF, except when the storage space is so small as to assure frequent filling. If a long period of streamflow records is available, hypothetical routing studies will provide some index to reservoir elevation probabilities, but even these computed relations may be greatly altered in the future if changing conditions result in substantial alterations in the river or regulation plan. For projects where the flood control storage space is appreciable, it may be appropriate to select starting water surface elevations below the top of flood control storage for routings. The U.S. Army Corps of Engineers' practice is to assume that 50% of the available flood control storage is filled at the beginning of the SDF. Conservatively high starting levels should be estimated on the basis of hydrometeorological conditions reasonably characteristic for the region and flood release capability of the project. Necessary adjustments of reservoir storage capacity due to existing or future sediment or other encroachment may be approximated when accurate determination of deposition is not practical. In view of the uncertainties involved in estimating initial reservoir levels that might reasonably be expected to prevail at the beginning of an SDF, it is common practice, particularly for small and intermediate height dams with a single low-level outlet, to assume that the reservoir is initially filled to the ''normal full pool level.'' This reservoir level should be in accordance with the operational practice for the season of occurrence of the SDF. Use of Gated Spillways Spillway crest gates are frequently used to provide required spillway capacity and to control the release of spillway discharges. The gates are de 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 98 signed to operate under controlled conditions during the occurrence of major floods. Proper operation of spillway gates for flood control can prevent downstream flooding that might otherwise occur with a fixed crest spillway. Also, the gates must be operated properly to prevent the release of reservoir discharges larger than those of the natural flood. The gates should be maintained and tested on a regular basis to assure that they will be fully operational during the flood season. For some projects it may be unsafe to assume that regulating gates would be attended during the occurrence of the SDF. The lag time between intense rainfall and the occurrence of the peak reservoir level could be too short for the gate operator to operate the gates properly, especially if the storm occurs at night. In this case gates should be assumed to be in the open position if they are normally open during the flood season, or closed if they are normally closed. No credit should be taken for any gate operation in the SDF routing unless it can be assured that the gates would be operated properly. Some regulatory agencies require that spillway gates at remote clam sites be locked in open position during usual heavy precipitation seasons, particularly if heavy snowfalls may prohibit access. Use of Low-Level Outlets Current practice is to assume no credit for water releases through any low- level outlet in routing the SDF. It is normal practice to assume that these structures are either clogged or inoperable. Many existing dams, particularly those of low and intermediate heights, have single, relatively small, low-level outlets that are controlled in some cases by a single gate or valve that is not operated regularly. These outlets cannot be relied on to be fully operational during an SDF. Although in some cases flow releases through power penstocks and turbines have been assumed to occur in the spillway flood routing, in most cases the power plant is assumed to be inoperational. For existing dams, consideration may be given to taking credit for power releases within certain limitations and to full assurance that the power plant could be operated safely during an SDF. Reservoir Routing The computation by which the interrelated effects of the inflow hydro- graph, reservoir storage, and discharge from the reservoir are evaluated is called reservoir routing. Generally, such routings assume a level pool within the reservoir. However, for long, narrow reservoirs some adjustment for the so- called wedge storage during rapidly rising pool levels may be in order. The basic tools for such a routing are the reservoir elevation-storage 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 99 curve and the spillway rating curve. The elevation-storage curve is a plot or table showing accumulated storage volumes versus reservoir stages or water surface elevations. The spillway rating curve is a plot or table showing the discharge capability of the spillway facilities (i.e., outlets, uncontrolled spillway weirs, spillway gates, etc.) versus reservoir stages or water surface elevations. All reservoir routing procedures use variations of the volumetric conservation equation: where I is reservoir inflow, O is the outflow or discharge, and ∆S is the change of storage, all for the same time interval. Usually it is assumed that outflow will vary linearly through a short routing interval and the equation is written: where the subscripts designate instantaneous values of O and S at the beginning and end of the routing interval. At any point in a routing computation, the value of I will be available from the inflow hydrograph and values of S1, and the corresponding O1 will have been determined by the routing for the previous time interval. Thus the routing for an interval consists of finding the value of S2 and the corresponding O2 that will satisfy the above equation. This can be done by trial and error, but the solution is more direct if the equation is written: By developing curves or tabulations of values of the terms in parentheses, a routing can be speedily accomplished by either graphical or arithmetic means. The results of the routing procedure are a reservoir stage hydrograph and an outflow hydrograph representing the attenuation of the PMF inflow hydrograph by reservoir storage, spillway, and outlet facilities. Freeboard Allowance It is common practice to provide an extra height of dam over the computed maximum reservoir level for the design PMF. This added height, termed freeboard, is an allowance for waves, wave runup, and wind surge or pileup of water that could be caused by strong winds over the full reservoir 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 100 surface. The type of dam, its geographical location and directional orientation, and the synoptic situation producing the PMP are all factors to be considered in the determination of freeboard allowance. A major consideration, the synoptic situation, should deal with the timing of the maximum winds, their orientation and duration that accompany the study storm. For example, some types of storm systems, such as hurricanes, usually have the heavy rain-producing mechanism in the forefront, followed by the maximum winds. This scenario on certain watersheds could result in the maximum winds occurring after the PMF has filled the reservoir. For assessing freeboard requirements, estimates are needed for the velocities, directions, and durations of winds that reasonably could occur with the reservoir at or near full pool. The "fetch," or maximum over-water distance adjacent to the dam in the direction of the wind, and depths of the reservoir also are needed in estimating wind effects. A number of approaches to computing these wind effects are available in U.S. Army Corps of Engineers' reports (1968b, 1976). The results of such computations will give the wave height and setup and runup elevations for the selected conditions. Common practice for major dams is to add from 3 to 5 feet to the maximum computed water surface level, including wind effects, to establish top of dam. DAM BREAK ANALYSES Knowledge of the nature and extent of catastrophic flooding and resulting risk to downstream life and property following collapse of a dam is a critical step in assessing and improving the safety of existing dams. Disasters caused by past dam failures and results from the recent Corps of Engineers' dam inspection program, have focused the attention of the public and federal and state officials on finding mitigatory measures for unsafe dams, on emergency action planning and preparedness, and on means for assessing public safety and predicting probable damage in the event of failure of existing dams. To better assess the hazard potential of a dam in a systematic and equitable manner, an analytical approach called dam break analysis should be used. Dam break analysis serves two primary goals. First, it provides information to the engineer about classifying the potential hazard of a dam for determining recommended spillway capacity. Second, it predicts flood depths and wave arrival times and identifies areas that could be affected by flood water should a failure occur. Estimation of downstream flooding times and identification of flood inundation areas permit rational development and implementation of emergency preparedness, warning, and evac 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 101 uation plans. Such plans, coupled with frequent inspection and conscientious maintenance work, could minimize the loss of life resulting from a failure. Many types of dam break models exist. The objective of each is to simulate the failure of a dam (i.e., produce a dam failure hydrograph and/or route the hydrograph downstream). Some modeling procedures can be performed readily by hand, such as the Soil Conservation Service (SCS) TR #66 Simplified Dam Breach Model and the Uniform Dam Failure Hydro-graph procedure described by Hagen (1982), while others such as the National Weather Service Dam Break Flood Forecasting Computer Model and the Corps of Engineers HEC-1 Flood Hydrograph Computer Package are very complex and require computer analysis. In general, the handworked methods represent simplified approaches to a complex phenomenon. Generally, simplified methods should be applied only to small dams and in instances where other dams are not involved or where damage to downstream developments is not significant. Inventory of Dam Break Models Several methods and computer models for analyzing the likelihood of dam failure and its potential downstream flooding effect are detailed in the literature. The decision as to which method to use for a given situation ultimately depends on the judgment of a qualified engineer. However, the choice usually involves the following considerations: • General availability, acceptance, and documentation of a model or method. • Capability of the model or method to simulate the conditions, assumptions, and uniqueness of a given dam situation. • Resources available to the user in the way of data, finances, and computer facilities for applying the method or model. • Purpose to which the results of the dam break analysis would be applied. (For example, where approximate downstream impacts resulting from postulated single dam failures are needed for preliminary planning, simple handworked methods can be considered first. Conversely, in situations where detailed flood wave arrival times, depths, and accurate inundation mapping are required, or where complex situations arise from multiple dams, the user should consider the computer model approach.) Several factors usually have to be evaluated or assumed whenever dam failures are postulated. The type of dam failure and mechanism causing failure require careful consideration, if a realistic breach is to be assumed. Size and shape of breach, reservoir storage, height of overtopping, and tim 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 102 ing of breach formation are critical factors in the determination of the dam failure hydrograph. Although considerable investigation has been conducted on historical dam failures, there is not enough information to predict all of the critical parameters with accuracy and consistency. Appendix 4C sets out guidelines used by one organization for assumptions relating to the breaching of dams. For the areas downstream from small dams the length of time assumed for breach development after erosion action is under way will significantly affect the estimated flood heights. However, little data are available on which to base such assumptions. The material of which the dam is structured will influence the time for breach development and estimates of such times should take into account conditions specific to the site. The following list of dam break models and modeling procedures are available, are documented in the literature, and have been widely used and accepted by both federal and private sector users: • Soil Conservation Service (1979) TR #66 Simplified Dam Breach Model . A quick, handworked method for (1) estimating maximum dam breach discharge from an empirical curve or equation based on historical dam failure data for height of dam versus maximum discharge and (2) estimating maximum discharge and stage at selected downstream floodplain points, utilizing a simplified version of the simultaneous storage routing—Kinematic routing method (e.g., Attenuation-Kinematic, or Art-Kin model). • Uniform Procedure for Dam Failure Hydrographs (Hagen 1982). A simple, quick, handworked procedure developed by V. K. Hagen of the U.S. Army Corps of Engineers for computing the critical failure hydro- graph for all dams regardless of type and condition. This method uses an envelope curve or equation, based on historical dam failure data, to relate a "dam factor," the product of dam height and reservoir storage, to peak discharge from a postulated dam failure. Since this procedure produces only a dam failure discharge hydrograph, the user must apply his own channel routing techniques for determining downstream consequences. • National Weather Service (NWS) Dam Break Flood Forecasting Model (Fread 1982). A computer model analysis consisting of two parts: (1) simulation of outflow hydrograph due to instantaneous or time- dependent erosion-type of dam break through an assumed hydraulic weir opening or orifice breach, while simultaneously considering the effects of the reservoir storage depletion and the inflow hydrograph via either a storage or hydraulic routing technique and (2) routing the generated outflow hydrograph through the downstream valley by dynamic hydraulic method to give flow time and stage at user- specified cross-section points. This model allows the 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 103 user to specify an inflow design flood hydrograph, select a method of reservoir routing, specify geometry and time of breach, specify depth of reservoir at time of breach, and specify hydraulic characteristics of downstream channel. The National Weather Service model has the capability of handling reservoir rim slides, multiple dams (series), bridge effects, and other complex downstream channel geometry conditions. • U.S. Army Corps of Engineers HEC-1 Flood Hydrograph Computer Package . This computer model analysis consists of two parts: (1) evaluation of the overtopping potential of the dam, by simulation of outflow hydro-graph due to time-dependent, erosion-type of dam breach through an assumed hydraulic weir opening, while simultaneously considering the effects of the reservoir storage depletion and the inflow hydrograph via storage routing technique and (2) estimation of downstream hydraulic-hydrologic consequences resulting from the assumed failure of the dam. While the HEC-1 allows the user to specify similar breach and downstream conditions as in the NWS model, a major feature of this model allows the user either to specify an inflow' design flood hydrograph or to input design precipitation and watershed characteristics for automatically generating an inflow flood hydrograph. • Some Other Methods and Models. There are several other methods available for estimating peak discharge from a postulated dam failure, ranging from simple handworked methods to sophisticated two- dimensional computer models. Although a brief listing of some of these methods is provided below, the reader is encouraged to consult with federal agency experts, consulting engineers, state dam safety engineers, and the technical literature on the uniqueness, advantages, and limitations of each method before using any of them: (a) TAMS Model. Developed by Balloffet for describing the propagation of a dam collapse wave in a natural channel (1974). (b) TVA Dam Breaching Program developed by the TVA Flood Control Branch in 1973. Predicts if a flood overtopped earth embankment will fad and, if so, the time and rate of failure. (c) Two-dimensional dam breach wave model developed by Strelkoff in 1978. (d) U.S. Army Corps of Engineers' Hydrologic Engineering Center dimensionless depth and distance curves, based on Sakkas's work, in 1980. Estimates maximum flood depths at downstream points from an instantaneous and completely failed dam. (e) Classic dam break equations for instantaneous ("pull the plug") and complete or partial dam failures, developed by Keulegan in 1961. Uses simple equations and cross-sectional depth-discharge rating curves. User must 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 104 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 105 furnish channel routing system to provide data for assessing downstream food consequences. Assessment of Available Dam Break Models The selection of a method or model for analyzing a postulated dam break should depend on the type and quality of information that the user desires for a given dam failure situation. The user should consider the following three major parts of analyses associated with dam failure for comparing the relative merits and capabilities of the available procedures: 1. Type of reservoir routing desired for design flood hydrograph (may also include generation of inflow flood hydrograph). 2. Assumed mode of failure for generation of dam break hydrograph: instantaneous versus gradual failure; partial versus complete cross- section failure; orifice versus weir-type failure for embankment dams; type of breach geometry assumed (rectangular, triangular, trapezoidal); type of time-dependent erosion model used (for embankment dams) (When does erosion begin? How long does breach erosion take?). 3. Whether peak failure discharge or estimated failure hydrograph is needed and the need for and type of downstream channel routing of dam break hydrograph. Few comparative analyses of different available procedures and models have been made. One study conducted at the University of Tennessee compared peak dam failure discharges for two simple handworked methods (SCS and Classic Equations-Keulegan) and two computer models (NWS and HEC-1) for a single 36-foot-high embankment subjected to a PMF-level flood (Tschantz and Majib 1981). The computed peak glows from this study compared as follows: Procedure Peak Flow at Dam (cfs) SCS 71,335 Classic equations 76,000 NWS 85,950 HEC-1 87,000 It should be noted in comparing these results that the first two handworked methods assume instantaneous failure, while the two computer model applications assume gradual dam breach by erosion. The study also compared peak flows, stages, and time of peak flows at selected points downstream from the failed dams. The four methods demonstrated little (±8%) difference among flood profile depths. Table 4-4 compares important features and capabilities for seven selected dam break analysis methods. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 106 MITIGATING INADEQUATE HYDRAULIC CAPACITIES Earlier sections of this chapter are concerned primarily with one question: Do a dam and reservoir acting together have the hydraulic capacity to withstand the adopted design flood? This section considers some of the alternative actions available when the answer to that question is no. In Chapter 3 the general types of measures available to mitigate deficiencies of unsafe dams are discussed, and the impacts that may be expected from use of each type are set out. In other chapters remedial measures for various types of structural deficiencies are discussed. It is often said that a dam is unsafe because its spillway has inadequate capacity. What is usually meant is that the development must be considered unsafe because the reservoir and spillway acting together are not capable of controlling the adopted design flood to the extent needed to ensure the structural integrity of the dam, thus creating potential for dam failure with uncontrolled release of stored water and serious damages to persons and properties downstream. It is well to keep in mind that the spillway, the dam, the reservoir, and the uses being made of the downstream areas are all part of the danger scenario we usually contemplate when we speak of an inadequate spillway, for such an overall view of the situation will be helpful in deciding on the most feasible mitigation plan. Each dam with inadequate hydraulic capacity is very much a unique case. Hence, it is not feasible to set out a list of mitigating measures and state precisely under what circumstance each should be used. In a specific situation the feasibility of each type of measure would very much depend on such aspects as the nature of the site, the type and condition of the development, the benefits it produces, the mode of operation, and the technical and financial resources available to the dam owner. In addition, the policies of the state dam safety regulatory agency and the legal and moral responsibilities of the dam owner to those endangered by the project must be considered. Types of Mitigating Measures Since most projects with inadequate hydraulic capacities would be endangered only during very rare flood events, the most feasible mitigation measures may involve operations or losses that could not be tolerated on a more frequent basis. The approaches that have been used to meet such problems can be classed as follows: • Increases in discharge capacity. • Increases in reservoir storage capacity. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 107 • Diversions of runoff from the reservoir. • Modification of dams to permit overflow. • Modification of project operations. • Modifications of use of downstream areas. • Do nothing or perform minimal repairs. (The dam owner may choose to do a minimal amount to remedy an ''unsafe'' structure or "inadequate" spillway. The reasons for this could be lack of funds, lack of a practical method for correction due to space limitation, or a combination of many site-specific circumstances. In arriving at a decision the dam owner must consider the potential for liability from property damage upstream as well as downstream, the potential for loss of life, and the moral obligation to avoid unnecessary hazard to those who might be affected by dam failure. To make the "do nothing" or "minimal repairs" approach a possible viable alternative, it is very important that an effective plan be formulated for an early warning to all who may be affected by a sudden increase in water level to protect against or at least to minimize the possibility of loss of life (see the section Emergency Action Planning). The above could also be a deliberate or designed procedure once the dam owner has determined that the "failure" of a structure or portion of a structure at a development under a low flood level may have a minimal incremental effect downstream. On the other hand, should the owner partially correct a deficiency, he could compound potential problems downstream. Increasing Discharge Capacity This is the most direct approach to solving the problem of inadequate spillway capacity, if it is found feasible. Some approaches to providing more spillway capacity are as follows: • Increasing crest length of ungated spillways. • Lengthening and adding gates to gated spillways. • Lowering crest of existing spillway. If needed to maintain pools for project operation, flashboards or gates can be used on the lowered crest. • Constructing a new spillway. This could involve reconstruction of a section of dam to serve as an auxiliary or emergency spillway or locating a new spillway in an abutment area or remote from the dam in a low saddle at the reservoir rim. A new remote saddle spillway could introduce new problems if it would discharge flood flows into areas or into a stream of another drainage basin that would not have been affected by such flows without the new spillway. • Improving the hydraulic efficiency of the existing spillway. At some projects such measures as removal of land masses projecting into approach 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 108 or retreat channels, removal of debris and deposits from such channels, or provision of guide walls or improved pier noses will add significantly to the discharge capacity of the spillway. Often the last two or three spillway bays on each end of a spillway are less efficient or have less flow capacity than the other bays. Severe flow angle of approach can cause flow separations and flow drawdown along the piers of these spillway bays. In some cases the flow reductions are as much as 20% in each bay. With proper guide walls or with modified pier noses to guide the incoming flow, uniform flow distributions across the bay could be achieved. Another benefit could be the reduction of structural vibration and cavitation erosion. • Providing a fuse plug levee or dike with crest lower than top of main dam designed to wash out and provide emergency spillway capacity. Figure 4-6 shows a system proposed by Harza Engineering Company for providing a fuse plug in an existing dam embankment. Only locations where the emergency discharge would not endanger the main dam or other important facilities should be considered for fuse plugs. Stoplogs, flashboards, or needle beam closures for new spillway structures can provide the same type of emergency spillway capacity but with better control of the spillway operation. Increasing Reservoir Storage Capacities In some cases it may be feasible to alleviate a problem of inadequate spillway capacity at an existing dam by making substantially more reservoir Figure 4-6 Harza Engineering Co. scheme for constructing fuse plug spillways. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 109 storage available by raising the top of the nonoverflow section of the dam, thus providing storage above operating pool levels for a major part of the SDF and reducing spillway capacity requirements. Also, increasing the height of a dam can effectively increase the flow capacity not only for the spillway but also for the other flow conveyance structures. Before such measures can be adopted, it is necessary to check whether the structures and geology downstream can withstand the additional energy of discharge without detrimental erosion and whether increase in reservoir stages would give problems with stability of structures. Also, it is necessary to check whether raising the structure would increase or create a problem in upstream channels or around the reservoir due to the increased water level. Some means of increasing the effective height of dams are as follows: • Adding or increasing height of parapet walls on the upstream side of the dam. On a masonry dam the upstream handrail may be removed and replaced by a solid concrete parapet of the same height or slightly higher. On a fill dam a concrete or masonry parapet could be used. • For larger height increases, concrete mass may be required to be placed on top and on the downstream face of a masonry dam. For embankment sections fill may be required to be placed on top and downstream face of fill. To place new mass concrete against old mass concrete, very special care in design and in construction must be exercised. • The use of flashboards on top of concrete dam. Flashboards can be designed to fail when reservoir height rises to a certain level. • Install inflatable dam similar to the "Faber" type on top of dam. The Faber is to be inflated by pumping water to fill the Faber tubing under pressure. This was used effectively for Mangla diversion in Pakistan to temporarily increase diversion water level. • Increasing height of a concrete dam by adding a concrete cap on top and installing posttensioned cables, tying old and new structures to the foundation. • Steel sheet piles can be driven in certain types of fill dams to increase height. Diversions Upstream from Reservoir At some projects it may be feasible to direct runoff from the reservoir to mitigate a spillway capacity problem. Usually such opportunities will be found only at impoundments in relatively fiat terrain or at relatively small impoundments. The possible dangers to others and legal implications of diverting runoff from natural channels should be considered before such a plan is adopted. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 110 Modification of Dams to Permit Overflow As discussed in Chapters 6 and 7, dams can be constructed to withstand overflow. A masonry dam generally can withstand overflow if the added hydraulic loading does not endanger the stability of the structure and if the overflow will not erode the foundation at the toe of the dam or damage other downstream facilities, such as outlet valves and controls. For an earth or rockfill dam there is the added problem of erosion of the top and downstream face of the dam by the overflow. The ability of masonry dams to resist overturning and sliding forces resulting from high reservoir stages and overflow can be improved by installation of high-capacity, posttensioned ties through the dam into the foundation. Armoring the foundation area at the toe can improve erosion resistance at this important location. Considerable guidance is available on designing for overtopping of rockfill dams (Curtis and Lawson 1967, Gerodetti 1981, Leps 1973, Olivier 1967, Parlin et al. 1966, Sarkaria 1968, and Wilkins 1963). Generally, designing an earth dam to permit overtopping should be considered only where the dam is low and the depth of overtopping would be small and the duration short. The rate of erosion and subsequent breaching of an earth dam would very much depend on the depth of overtopping, the geometry of the top of the dam, and the erosive characteristics of the soil of which the dam is composed. Thus, the indicated shallow overtopping of an existing small dam composed of erosion- resistant materials during a short interval in the passage of an SDF hydrograph may not require remedial action. Modification of Project Operations In some instances it may be feasible to modify project operations to substantially increase the reservoir storage space that would be available to regulate the design flood. In considering such a plan the effect of the modified operations on project benefits, the effectiveness of the increased storage in mitigating spillway capacity problems, and the assurance that the storage would, in fact, be available when needed should be appraised. Modification of Uses of Downstream Areas Seldom will it be feasible for the owner of an unsafe dam to reduce the hazard of dam failure by changing the uses of downstream areas, but this situation might arise if the dam and the downstream areas have the same owner. Downstream damage potentials can often be greatly reduced by just a little forethought in developing the areas. A classic example of the lack of such forethought involved the building of a new hospital in a nar 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 111 row mountain valley subject to natural flooding from the river that ran through the valley. Areas flat enough and extensive enough for either the hospital or its accompanying parking lot were scarce, but two areas were available, each of which could accommodate either the hospital or the parking lot but not both. One was in the low, narrow flood plain of the river. The other was on a low bluff well above the flood plain. Unfortunately, the developers placed the hospital on the low area and the parking lot on the bluff. The folly of this selection has been amply demonstrated during subsequent floods. REFERENCES Balloffet, A. (1979) Dam Break Flood Routing, Two Cases, Columbia University, New York, N.Y. Balloffet, A., et al. (1974) "Dam Collapse Wave in a River," Hydraulics Journal, ASCE, Vol. 100, No. HY5 (May), Proceedings Paper 10523, pp. 645-665. Cecilio, C. B., and Strassburger, A. G. (1974) Downstream Hydrograph from Dam Failures, Proceedings, The Evaluation of Dam Safety, Engineering Foundation Conference, November 28-December 3, 1974, published by ASCE, 1977. Chow, V. T. (1959) Open Channel Hydraulics, McGraw-Hill, New York. Creager, W. P., and Justin, J. D. (1963) Hydroelectric Handbook, John Wiley & Sons, New York. Curtis, R. P., and Lawson, J. D. (1967) "Flow Over and Through Rockfill Dams," Journal of the Hydraulics Division, Proceedings of the ASCE, Vol. 93, No. HY5 (September), pp. 1-21. Davis, C. V., and Sorenson, K. E. (1969) Handbook of Applied Hydraulics , 3d ed., McGraw-Hill, New York. Fread, D. L. (1982) DAMBRK: The NWS Dam-Break Flood Forecasting Model , Hydrologic Research Laboratory, Office of Hydrology, National Weather Service, NOAA, Silver Spring, Md. Gerodetti, M. (1981) "Model Studies of an Overtopped Rockfill Dam," Water Power and Dam Construction, (September), pp. 25-31. Hagen, V. K. (1982) Reevaluation of Design Floods and Dam Safety, paper presented at 14th ICOLD Congress, Rio de Janeiro. Kevlegan, G. H. (1950) "Wave Motion," pp. 711-768 in Engineering Hydraulics, H. Rouse, ed., John Wiley & Sons, New York. King, H. W., and Brater, E. F. (1963) Handbook of Hydraulics, 5th ed., McGraw-Hill, New York. Kirkpatrick, G. W. (1976) Evaluation Guidelines for Spillway Adequacy , Proceedings of the Engineering Foundation Conference, The Evaluation of Dam Safety, Asilomar Conference Ground, Pacific Grove, Calif., November 28-December 3, 1976, published by ASCE, pp. 395-414. Leps, T. M. (1973) "Flow Through Rockfill," offprint from Embankment Engineering, Ronald Hirshfeld, ed., John Wiley & Sons, New York, pp. 87-107. National Weather Service (1975) Hydrometeorological Report No. 33, Washington, D.C. National Weather Service (1977) Hydrometeorological Report No. 49, Washington, D.C. National Weather Service (1978) Hydrometeorological Report No. 51, Washington, D.C. National Weather Service (1980) Hydrometeorological Report No. 53, Washington, D.C. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 112 National Weather Service (1982) "Application of Probable Maximum Precipitation Estimates— United States East of the 105th Meridian," Hydrometeorological Report No. 52, NOAA, Washington, D.C., August. Newton, D. W., and Cripe, M. W. (1973) Flood Studies for Safety of TVA Nuclear Plants— Hydrologic and Embankment Breaching Analysis , Flood Hydrology Section, TVA, Knoxville, Tenn. Olivier, H. (1967) Through and Overflow Rockfill Dams—New Design Techniques, Proceedings, Institution of Civil Engineers, Paper No. 7012, pp. 433-471. Parlin, A. K., Trollope, D. H., and Lawson, J. D. (1966) "Rockfill Structures Subject to Water Flow," Journal of the Soil Mechanics and Foundations Division, Proceedings of the ASCE, Vol. 92, No. SM6 (November), pp. 135-151. Sakkas, J. G. (1974) Dimensionless Graphs of Floods prom Ruptured Dams, Report prepared for the Hydrologic Engineering Center, Davis, Calif. Sarkaria, G. S., and Dworsky, B. H. (1968) "Model Studies of an Armoured Rockfill Overflow Dam," Water Power, November, pp. 445-462. Soft Conservation Service (1979) "Simplified Dam-Breach Routing Procedure," Technical Release No. 66, March. Strelkoff, A. K. (1978) "Computing Two-Dimensional Dam-Break Flood Waves," Hydraulics Journal, ASCE, September. Tennessee Valley Authority (1973) Dam Breaching Program, Knoxville, Tenn., November. Tschantz, B. A., and Mojib, R. M. (1981) Application of and Guidelines for Using Available Dam Break Models, Tennessee Water Resources Research Center, Report No. 83, University of Tennessee, Knoxville. U.S. Army Corps of Engineers (1956) "Snow Hydrology," Summary Report of Snow Investigations, North Pacific Division, Portland, Oreg., June. U.S. Army Corps of Engineers (1959) Flood Hydrograph Analyses and Computations, EM1110-2-1405, August 31. U.S. Army Corps of Engineers (1960) Runoff from Snowmelt, Engineering and Design Manual, EM1110-2-1406, Washington, D.C. U.S. Army Corps of Engineers (1962) Generalized Snowmelt Runoff Frequencies , Technical Bulletin No. 8, Sacramento District, September. U.S. Army Corps of Engineers (1963) Hydraulic Design of Reservoir Outlet Structures, EM1110 2-1602, Office of the Chief of Engineers, Washington, D.C., August 1. U.S. Army Corps of Engineers (1965a) Standard Project Flood Determinations , EM 1110-2-1411, Washington, D.C. U.S. Army Corps of Engineers (1965b) Hydraulic Design of Spillways , EM1110-2-1603, Office of the Chief of Engineers, Washington, D.C., March 31. U.S. Army Corps of Engineers (1968a) Policies and Procedures Pertaining to Determination of Spillway Capacities and Freeboard Allowances for Dams, EC 1110-2-27, Change 1, February, 19. U.S. Army Corps of Engineers (1968b) Hydraulic Design Criteria. U.S. Army Corps of Engineers (1969) Routing of Floods Through River Channels, EM 1110-2-1408, March 1. U.S. Army Corps of Engineers (1976) Wave Runup and Wind Setup on Reservoir Embankments, ETL 1110-2-221, November 29. U.S. Army Corps of Engineers (1980) Hydrologic Engineering Center Report No. 8, Dimensional Graphs of Floods From Ruptured Dams, Davis, Calif. (based on work developed by Sakkas 1974-1980). U.S. Army Corps of Engineers (1982a) Hydrologic Analysis of Ungaged Watersheds Using HEC-1, Training Document No. 15, The Hydrologic Engineering Center, Davis, Calif. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 113 U.S. Army Corps of Engineers (1982b) National Program of Inspection of Nonfederal Dams, Final Report to Congress (contains ER 1110-2-106, September 26, 1979). U.S. Bureau of Reclamation (1966) Effect of Snow Compaction From Rain on Snow Engineering Monograph No. 35. U.S. Bureau of Reclamation (1977) Design of Small Dams, Denver, Colo. U.S. Committee on Large Dams (1970) Survey: Criteria and Practices Utilized in Determining the Required Capacity of Spillways, USCOLD, Boston, Mass. U.S. Department of Commerce (1977) "Probable Maximum Precipitation Estimates, Colorado River and Great Basin Drainages," Hydrometeorological Report No. 49, NOAA, National Weather Service, Silver Spring, Md., September. U.S. Department of Commerce (1978) "Probable Maximum Precipitation Estimates, United States East of the 105th Meridian," Hydrometeorological Report No. 51, NOAA, National Weather Service, Washington, D.C., June. U.S. Department of Commerce (1980) "Seasonal Variation of 10-Square-Mile Probable Maximum Precipitation Estimates, United States East of the 105th Meridian," Hydrometeorological Report No. 53, NOAA, National Weather Service, Silver Spring, Md., April. U.S. Department of Interior, Bureau of Reclamation (1952) "Discharge Coefficients for Irregular Overfall Spillways," Engineering Monograph No. 9. U.S. Department of Interior (1982) "Guidelines for Determining Flood Flow Frequency," Bulletin No. 17B, Hydrology Subcommittee, Interagency Advisory Committee on Water Data. U.S. Nuclear Regulatory Commission (1977) "Design Basis Floods for Nuclear Power Plants," Regulatory Guide 1.59, Revision 2, August. U.S. Weather Bureau (1956) "Seasonal Variation of the Probable Maximum Precipitation East of the 105th Meridian," Hydrometeorological Report No. 33, Washington, D.C. U.S. Weather Bureau (1960) "Generalized Estimates of Probable Maximum Precipitation West of the 105th Meridian," Technical Paper No. 38, Washington, D.C. U.S. Weather Bureau (1961) "Generalized Estimates of Probable Maximum Precipitation and Rainfall-Frequency Data for Puerto Rico and Virgin Islands," Technical Paper No. 42, Washington, D.C. U.S. Weather Bureau (1961/1969) "Interim Report—Probable Maximum Precipitation in California," Hydrometeorological Report No. 36, Washington, D.C., October 1961, with revisions in October 1969. U.S. Weather Bureau (1963a) "Probable Maximum Precipitation in the Hawaiian Islands," Hydrometeorological Report No. 39, Washington, D.C. U.S. Weather Bureau (1963b) "Probable Maximum Precipitation Rainfall-Frequency Data for Alaska," Technical Paper No. 47, Washington, D.C. U.S. Weather Bureau (1966a) "Meteorological Conditions for the Probable Maximum Flood on the Yukon River above Rampart, Alaska," Hydrometeorological Report No. 42, Environmental Science Services Administration, Washington, D.C., May. U.S. Weather Bureau (1966b) "Probable Maximum Precipitation, Northwest States," Hydrometeorological Report No. 43, Washington, D.C. Wilkins, J. K. (1963) "The Stability of Overtopped Rockfill Dams," Proceedings Fourth Australia- New Zealand Conference on Soil Mechanics and Foundation Engineering. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 114 APPENDIX 4A Figures 4A-1 through 4A-6 present generalized estimates of probable maximum flood (PMF) peak discharges. The maps may be used to determine PMF peak discharge at a given site with a known drainage area as follows: 1. Locate the site on the 100-square-mile map, Figure 4A-1. 2. Read and record the 100-square-mile PMF peak discharge by straight- line interpolation between the isolines. 3. Repeat Steps 1 and 2 for 500, 1,000, 5,000, 10,000, and 20,000 square miles from Figures 4A-2 through 4A-6. 4. Plot the six PMF peak discharges so obtained on logarithmic paper against drainage area, as shown on Figure 4A-7. 5. Draw a curve through the points. Reasonable extrapolations above and below the defined curve may be made. 6. Read the PMF peak discharge at the site from the curve at the appropriate drainage area. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS Figure 4A-1 Probable maximum flood (enveloping PMF isolines) for 100 square miles. 115 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS Figure 4A-2 Probable maximum flood (enveloping PMF isolines) for 500 square miles. 116 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS Figure 4A-3 Probable maximum flood (enveloping PMF isolines) for 1,000 square miles. 117 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS Figure 4A-4 Probable maximum flood (enveloping PMF isolines) for 5,000 square miles. 118 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS Figure 4A-5 Probable maximum flood (enveloping PMF isolines) for 10,000 square miles. 119 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS Figure 4A-6 Probable maximum flood (enveloping PMF isolines) for 20,000 square miles. 120 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS Figure 4A-7 Examples of use of enveloping isolines. 121 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 122 APPENDIX 4B STORMS EXCEEDING 50% OF ESTIMATED PROBABLE MAXIMUM PRECIPITATION Figures 4B-1 through 4B-5 show locations of storms that have exceeded 50% of the estimated probable maximum precipitation (PMP) value for the indicated durations and sizes of drainage areas. The specific storms are identified in Tables 4B-1 and 4B-2. Figure 4B-1 Observed point rainfalls exceeding 50% of all-season PMP, United States east of 105th meridian for 10 square miles, 6 hours. (Large number is the percentage of the PMP, small number is storm index; see Table 4B-1.) Source: U.S. Army Corps of Engineers (1982b). 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 123 Figure 4B-2 Observed point rainfalls exceeding 50% of all-season PMP, east of 105th meridian for 200 square miles, 24 hours. (Large number is the percentage of the PMP, small number is storm index.) Source: U.S. Army Corps of Engineers (1982b). Figure 4B-3 Observed point rainfalls exceeding 50% of all-season PMP, east of 105th meridian for 1,000 square miles, 48 hours. (Large number is the percentage of the PMP, small number is storm index.) Source: U.S. Army Corps of Engineers (1982b). 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 124 Figure 4B-4 Observed point rainfalls exceeding 50% of all-season PMP, west of continental divide for 10 square miles, 6 hours. (Large number is the percentage of the PMP, small number is storm index.) Source: U.S. Army Corps of Engineers (1982b). Figure 4B-5 Observed point rainfalls exceeding 50% of all-season PMP, west of continental divide for 1,000 square miles and duration between 6 and 72 hours. (Large number is the percentage of the PMP, small number is storm index.) Source: U.S. Army Corps of Engineers (1982b). 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 125 TABLE 4B-1 Identification of Storms Exceeding 50% PMP, East of 105th Meridian Corps Storm Center Storm Date Index Assignment Town State Lat. Long. No. No. (if available) 7/26/1819 1 — Catskill NY 42° 73° 12' 53' 8/5/1843 2 — Concordville PA 39° 75° 53' 32' 9/10-13/1878 3 OR 9-19 Jefferson OH 41° 80° 45' 46' 9/20-24/1882 4 NA 1-3 Paterson NJ 40° 74° 55' 10' 6/13-17/1886 5 LMV 4-27 Alexandria LA 31° 92° 19' 33' 6/27-7/11/1899 6 GM 3-4 Turnersville TX 30° 96° 52' 32' 8/24-28/1903 7 MR 1-10 Woodburn IA 40° 93° 57' 35' 10/7-11/1903 8 GL 4-9 Paterson NJ 40° 74° 55' 10' 7/18-23/1909 9 UMV Ironwood MI 46° 90° 1-11B 27' 11' 7/18-23/1909 10 UMV Beaulieu MN 47° 95° 1-11A 21' 48' 7/22-23/1911 11 — Swede Home NB 40° 96° 22' 54' 7/19-24/1912 12 GL 2-29 Merrill WI 45° 89° 11' 41' 7/13-17/1916 13 SA 2-9 Altapass NC 35° 82° 33' 01' 9/8-10/1921 14 GM 4-12 Taylor TX 30° 97° 35' 18' 10/4-11/1924 15 SA 4-20 New Smyrna FL 29° 80° 07' 55' 9/17-19/1926 16 MR 4-24 Boyden IA 43° 96° 12' 00' 3/11-16/1929 17 UMV 2-20 Elba AL 31° 86° 25' 04' 6/30-7/2/1932 18 GM 5-1 State Fish TX 30° 99° Hatchery 01' 07' 9/16-17/1932 19 — Ripogenus ME 45° 69° Dam 53' 09' 7/22-27/1933 20 LMV 2-26 Logansport LA 31° 94° 58' 00' 4/3-4/1934 21 SW 2-11 Cheyenne OK 35° 99° 37' 40' 5/30-31/1935 22 MR 3-28A Cherry Creek CO 39° 104° 13' 32' 5/31/1935 23 GM 5-20 Woodward TX 29° 99° 20' 28' 7/6-10/1935 24 NA 1-27 Hector NY 42° 76° 30' 53' 9/2-6/1935 25 SA 1-26 Easton MD 38° 76° 46' 01' 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 126 Corps Storm Center Storm Date Index Assignment Town State Lat. Long. No. No. (if available) 9/14-18/1936 26 GM 5-7 Broome TX 31° 100° 47' 50' 6/19-20/1939 27 — Snyder TX 32° 100° 44' 55' 7/4-5/1939 28 — Simpson KY 38° 83°22' 13' 8/19/1939 29 NA 2-3 Manahawkin NJ 39° 74°16' 42' 6/3-4/1940 30 MR 4-5 Grant NB 42° 96°53' Township 01' 8/6-9/1940 31 LMV 4-24 Miller Island LA 29° 92°10' 45' 8/10-17/1940 32 SA 5-19A Keysville VA 37° 78°30 03' 9/1/1940 33 NA 2-4 Ewan NJ 39° 75°12' 42' 9/2-6/1940 34 SW 2-18 Hallct OK 36° 96°36' 15' 8/28-31/1941 35 UMV 1-22 Haywood WI 46° 91°28' 00' 10/17-22/1941 36 SA 5-6 Trenton FL 29° 82°57' 48' 7/17-18/1942 37 OR 9-23 Smethport PA 41° 78°25' 50' 10/11-17/1942 38 SA 1-28A Big VA 38° 78°26' Meadows 31' 5/6-12/1943 39 SW 2-20 Warner OK 35° 95°18' 29' 5/12-20/1943 40 SW 2-21 Nr. Mounds OK 35° 96°04' 52' 7/27-29/1943 41 GM 5-21 Devers TX 30° 94°35' 02' 8/4-5/1943 42 OR 3-30 Nr. Glenville WV 38° 80°50' 56' 6/10-13/1944 43 MR 6-15 Nr. Stanton NB 41° 97°03' 52' 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 127 Corps Storm Center Storm Date Index Assignment Town State Lat. Long. No. No. (if available) 8/12-15/1946 44 MR 7-2A Cole Camp MO 38° 93°13' 40' 8/12-16/1946 45 MR 7-2B Nr. IL 38° 89°59' Collinsville 40' 9/26-27/1946 46 GM 5-24 Nr. San TX 29° 98°29' Antonio 20' 6/23-24/1948 47 — Nr. Del Rio TX 29° 100° 22' 37' 9/3-7/1950 48 SA 5-8 Yankeetown FL 29° 82°42' 03' 6/23-28/1954 49 SW 3-22 Vie Pierce TX 30° 101° 22' 23' 8/17-20/1955 50 NA 2-22A Westfield MA 42° 72°45' 07' 5/15-16/1957 51 — Hennessey OK 36° 97°56' 02' 6/14-15/1957 52 — Nr. E. St. IL 38° 90°24' Louis 37' 6/23-24/1963 53 — David City NB 41° 97°05' 14' 6/13-20/1965 54 — Holly CO 37° 102° 43' 23' 6/24/1966 55 — Glenullin ND 47° 101° 21' 19' 8/12-13/1966 56 — Nr. Greely NB 41° 98°32' 33' 9/19-24/1967 57 SW 3-24 Falfurrias TX 27° 98°12' 16' 7/16-17/1968 58 — Waterloo IA 42° 92°19' 30' 7/4-5/1969 59 — Nr. Wooster OH 40° 82°00' 50' 8/19-20/1969 60 NA 2-3 Nr. Tyro VA 37° 79°00' 49' 6/9/1972 61 — Rapid City SD 44° 103° 12' 31' 6/19-23/1972 62 — Zerbe PA 40° 76°31' 37' 7/21-22/1972 63 — Nr. Cushing MN 46° 94°30' 10' 9/10-12/1972 64 — Harlan IA 41° 95°15' 43' 10/10-11/1973 65 — Enid OK 36° 97°52' 25' SOURCE: U.S. Army Corps of Engineers (1982b). 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 128 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 129 APPENDIX 4C GUIDELINES FOR BREACH ASSUMPTION Presented here are guidelines for formulating emergency action plans with no admission, written or implied, that the structures are a hazard. Additional criteria for dam break analysis are given for use in a specific computer model. These guidelines are representative of criteria developed by an investor-owned utility, which were submitted and accepted by a regulatory agency. Prior to any use of these criteria, however, they should be discussed with the specific regulatory agency with which the dam owner has to deal. 1. All dams upstream or downstream from a given dam under investigation should be evaluated. 2. If failure of an upstream dam is found to cause or compound the failure of the dam under consideration, an evaluation shall be made. 3. If the upstream dam belongs to a different owner, efforts should be made to obtain the necessary information to perform a dam break evaluation. 4. If the downstream dam is owned and operated by another regulatory agency, the upstream owner should inform the downstream owner of the result of the upstream dam break evaluation. 5. Evaluation of flood-prone areas resulting from dam breaks should be made using available U.S. Geological Survey 7.5-minute quadrangle topographic maps. Cross-section intervals should be limited to 1 mile and a maximum of 10 miles except within reservoirs. Cross sections should be taken at or near a development or populated area. 6. Inundation maps shall be prepared for areas where potential flooding from the hypothetical dam break could cause significant hazard to human habitation. 7. No stability analysis or any type of geologic investigation shall be performed in connection with the dam break studies. However, results of earlier studies to satisfy regulatory requirements as to safety of the dam or dams in question may be used as references. 8. For all dam break analyses where a storm is not in progress, all reservoirs shall be assumed to be at normal maximum operating water levels unless otherwise noted. In so doing, all flashboards shall be assumed installed and gates in position. 9. For river channel base flow, use mean annual flow. When using the National Weather Service (NWS) Dam Break Model, it is often necessary to increase the base flow to an exceedingly high value before the computer program can run. However, it has been shown that base flows are insignificant compared to the failure flood waves. 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 130 10. The most likely mode of dam failure need not be the most severe; only the most severe shall be assumed. Initial failure of gates or other appurtenant features other than the dam shall not be considered because they will not produce the most critical flows. 11. For dam break analysis with no concurrent storm in progress, no cause of failure shall be assumed. Dams are considered to fail only to prepare an emergency action plan. Results of the study should not reflect in any way on the structural integrity of the dam or dams and are not to be construed as such. All reports and/or inundation maps shall contain such a qualifying statement. 12. Simultaneous failure of two or more adjacent or in-tandem dams shall not be considered. However, successive or domino-type failures shall be considered. 13. When the upper dam fails, and the lower dam is earth or rock, consider the lower dam to fail if it overtops. When the lower dam is concrete and stability analyses indicate a low factor of safety for overturning or sliding, failure should be assumed, if significant overtopping would occur. 14. When a lower dam is overtopped from an upstream dam failure, all flashboards and gates shall be assumed to fail. 15. For concrete dams (gravity or arch), assume instantaneous failure. When using the NWS Dam Break Model, a time of failure equal to 0.15 hour would be equivalent to instantaneous failure. 16. The shape for an instantaneous failure is similar to the geometry of the channel at the center line of the dam. 17. Any partial width but full depth failure for concrete gravity dams may be considered. 18. Complete failure for concrete arch dams is considered. When using the NWS Dam Break Model, the parabolic shape of the failure breach should be transformed into an equivalent trapezoidal section. 19. For earth and rockfill dams, assume failure by erosion. The word erosion should not be construed as a cause of failure but as a rate of failure dependent on time. 20. The shape of failure breach may either be trapezoidal, parabolic, or rectangular. For partial instantaneous breach of concrete gravity dams, assume a rectangular shape. For erosion failure, assume a parabolic or trapezoidal shape. For complete instantaneous failure, assume a parabolic or trapezoidal shape. 21. For mixed dams (concrete and embankment), assume failure to produce the largest but reasonable flow. 22. Final breach shape of embankment dams should be trapezoidal when the maximum base is equal to the height of the dam. A proportion 

HYDROLOGIC AND HYDRAULIC CONSIDERATIONS 131 ately smaller base may be assumed if the geometry of the original river channel is small compared to the height of the dam. 23. The maximum width of breach may be estimated by dividing the area of the dam (measured along the axis) by the maximum height of the dam. It could also be considered equivalent to the most hydraulically efficient section. Dimensions for this efficient section are given in most textbooks on hydraulics (e.g., Chow's Open Channel Hydraulics ). 24. The failure outflow hydrograph may be estimated by flood routing (hydraulic or hydrologic method) or by the approximate triangle method supplemented by empirical formulas. 25. To arrive at reasonable dam break mechanics, postulated failures shall be compared with historical dam failures. 26. All flood routing shall be done with the most practical and economical procedures. Computer models that simulate the dynamic passage of a dam break flood through river channels should be used when practical. 27. All flood routing shall be continued downstream until attenuated to a peak equivalent to the recorded precipitation-caused flood peak. In certain cases where the historical precipitation-caused flood peaks have caused damage in the area, continued routing may be necessary until attenuation to a mean annual flood peak value. 28. All bridges along the pathway of a dam break flood may be assumed to have failed prior to the arrival of the flood peak if it is determined that they will be overtopped. The NWS Dam Break Model can be used to route through bridges. 29. Flood wave arrival times shall be indicated at points on inundation maps with significant population. 30. A report documenting all pertinent assumptions, evaluations, and scenarios in the dam failure analysis shall be prepared for each study.