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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 ex- treme flood conditions. Because the actual timing and magnitude of future Hood events are indeterminate, such assessments cannot be based on rigor- ous 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 assess- ing 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 ac- cepted in the engineering profession. However, a number of state agencies have adopted procedures and criteria for hydrologic and hydraulic investi- gations that provide appropriate guidelines for assessments of dam safety where the governmental agency responsible for dam safety has not speci- fied 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 engi- neering for dams. For any project where the consequence of dam failure 71

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72 SAFETY OF EXISTING DAMS 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 sec- tions 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. Informa- tion such as discharge rating curves or tables, storage capacity, and perti- nent dimensions of spillways and outlets should be made available. The procedures used in the design of the spillway should be compared with cur- rently accepted techniques and criteria. If it is evident that the original design bases gave results substantially in accord with current practices, fur- ther 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 stud- ies 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 devel- oped, and past storage fluctuations or reservoir seasonal operation records should be evaluated. Data on unusual hydrologic events, such as peak in- stantaneous flood flows and operation of gates to spill excess runoff, should be obtained. Such background information permits comparisons of re- corded 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.

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Hydrologic and Hydraulic C(msideratKms Simplified Procedures 73 The amount and complexity of the hydrologic and hydraulic analyses ap- propriate 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 advis- able. 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 di- rection of an experienced hydraulic and/or hydrologic engineer. Comparisons with Historical Peak Discharges Evaluations of the relative magnitude and the credibility of flood peak dis- charge estimates can be obtained by comparison with known historical peak discharges in other watersheds. Also, such information about maxi- mum 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 de- scribing the relationship between drainage area characteristics and maxi- mum observed flood discharges. Figure 4-1 shows curves based on two such relationships that have been used extensively, the Myer and Creager for- mulas. The Creager formula is Q = 46CA(0 s94 A - 0 048) or its equivalent q = 46CA(0~894 A - 0 048 - I) where Q is the total discharge in cubic feet per second, q is the unit dis- charge 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 coeffi- cient 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.

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Hydrologic and Hydraulic Cor~iderat~ons 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 offlou'. 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 intro- duced by C. S. Jarvis in 1926 and is shown in Figure 4-1 solely for the pur- pose 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 Regula- tory Commission staff, and their consultants, Nunn, Snyder and Associ- ates. The enveloping curves were found to parallel the Creager curve. Iso- line maps showing the generalized PMEi estimates as well as a discussion of the way they may be used are contained in Appendix 4A. Use of such gener- alized data should be confined to situations in which more specific PMF discharge estimates are not available and where it is not practicable to de- velop estimates specifically for the project. Dam Break Flood Flow Formulas In assessing the hazard involved in the potential failure of a dam, an esti- mate 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

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Hydro7~g~c 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 sim- plified approaches are presented by Sakkas (1974) and the Soil Conserva- tion 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 maxi- mum peak flows immediately downstream of dams after their failure. Hagen presents two equations based on experienced dam failures, primar- ily 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): Q - 530 ~Dpy0.5* and Q = 370 (DF)° s, 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 multiply- ing 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 dis- charged at any point of time during the inflow of the design flood. Desir- able objectives for spillway operation and bases for assessing spillway ade- quacy 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.

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78 SAFETY OF EXISTING DAMS 107 ~ 106 - LL C: I Cat In - 105 DAM FACTOR (Ac.Ft.2) FIGURE 4-3 Peak discharge from significant dam failures. a. Teton, Idaho b. Malpasset, France c. Swift, Montana d. St. Francis, California e. Johnstown, Pennsylvania f. Schaeffer, Colorado 9. Buffalo Creek, West Virginia h. Laurel Run, Pennsylvania Q = 530[DF]0 5 ': a _ ~ ~^ - o7nrmclO.5 1 o4 ~ 3 10 . 1o6 107 1o8 sections. Discharge characteristics and criteria for various types of spill- ways 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 determin- ing spillway capacities and freeboard allowances for dams are discussed in a report by the U.S. Army Corps of Engineers (1968b). 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 proba- ble 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 be- fore data were available to assess adequately the flood-producing poten- tials of their watersheds. As a consequence, many existing dams have in- adequate 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.

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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 authori- tative 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 pro- vided 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 in- creased 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 nec- essary 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:

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80 SAFETY 0F EXISTING DAMS 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 suffer- ing 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 proce- dures 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 inade- quate justification for accepting such risk, particularly when severe haz- ard~s to life are involved. Accordingly, high dams impounding large vol- umes 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.

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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 down- stream. In such cases the design capacity of the spillway and related fea- tures 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 accom- plished 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 flat 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 clam should fail due to over- topping. In some instances adoption of Standard 4 may be mandatory, de- spite 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 loam Inspection Act (PL 92-367), enacted August 8, 1972, the U.S. Army Corps of Engineers issued Recommended Guide- linesfor Safety Inspection of Dams, which was macle an Appendix D of the National Program of Inspection of Nonfederal Dams, ER 1110-2-106 (1982b). This was also issued as Title 33 in the Code of Federal Regula- lions, Part 222. These documents contain guidelines for determining spill- way 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

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121 Cal Ul - '1: — I.U A: Ul of Ct x ·S.~O ONV3nOH '39~HOSlO Ed Coold WnWIXVW 319~90Ud

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122 SAFETY OF EXISTING DAMS APPENDIX 4B STORMS EXCEEDING 50% OF ESTIMATED PROBABLE MAXIMUM PRECIPITATION Figures 4B-1 through 4B-S 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. - 58 53 —- -—1 1 74 _ _ _ 1 74 ~ ~ '~ ~ 43 · ~ 30 · 1 53 —~52 T ~ ~ —~—~ it.,, l ~ ~449~4 j-~-J~ 4~ OCR for page 71
Hydrologm and Hydraulic Considerations ~ ,51. 22 51 59 123 151 ~ f~'9l~ - ~ r 1 3~ -—- -—~ ~ 35 1~2 tf~: ~ ~50> 1 57e ~ ~ ~ ~ ~ >_ 1 52 ~ ~ ~' 28 , ?—r 60 _—- 2; 54' —61 ~ ·—~———? ' ~13 'I 1 21 \53 ~ ~ ~ \ `x I <~-~ 51 ~,:_ /' ~ \ ~ i: i 63 `~ 60 ,) ~ ~ ,4~ ~77.26 70 B.2 ~ , 5 ~ ah, >,~x 47~ ~ FIGURE 4B-2 Observed point rainfalls exceeding 50 % of all-season PMP, east of 105th merid- ian 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). 151 \ _ ~ - _____ - 57 ~63 ~ ;~--~` 53~- 51 - 53 1 44 45 1-~ - 32 _—J-13 ~ _ 54~ 55—~ ~ -—~ 34 63 \ ~ If 39 ~ / -7 ~ ~~_~~n ~ ~ 1 5 ~ _ ~ _ _ _ , W~y,842664 7~27~6 W17: ~ 63)~ 48 ~ ~ FIGURE 4B-3 Observed point rainfalls exceeding 50 % of all-season PMP, east of 105th merid- ian for 1,000 square miles, 48 hours. (Large number is the percentage of the PMP, small num- ber is storm index.) SOURCE: U.s. Army Corps of Engineers (1982b).

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24 SAFETY OF EXISTING DAMS 62 _~ ~ l_____N ~ / , ~ , W ~——_ / I 62 ~ I 25 TO 1__ i85 ;26 - _, 74~\ 55 61 ~ ,61 85 1 _ 1 21< —- 26 A 1 9 66 1 5 2 1 llll F__ —- - 1 =__ 'T1 at_ 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 num- ber is storm index.) SOURCE: U.S. Army Corps of Engineers (1982b). ~ 76- _ ~ _ __ _ _ ~ ·) i__ / ,' ha_ ' L ~ i/ ~ rid ~ _ 1 8t ~ 53 11 ~ 3. ( 55 \ ~ 58 ~ 37! ll '~t'59/ 29 ~ I ~ A _ _ _ _ _ _ T 1 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).

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28 TABLE 4B-2 Storms with Rainfall Exceeding 50 % of PMP, West of Continental Divide Storm Center Duration Index for Storm Date No. Town State Lat. Long. 1000 mi2 8/11/1890 1 Palmetto NV 37°27 117°42 8/12/1891 2 Campo CA 32°36 116°28 8/28/1898 3 Ft. Mohave AZ 35°03 114°36 10/4-6/1911 4 Gladstone CO 37°53 107°39 12/29/1913- 1/3/1914 5 — CA 39°55 121°25 2/17-22/1914 6 Colby Ranch CA 34°18 118°07 2/20-25/1917 7 — CA 37°35 119°36 9/13/1918 8 Red Bluff CA 40°10 122°14 2126-31411938 9 CA 34°14 117°11 3130-4/2/1931 10 — ID 46°30 114°50 24 2/26/1932 11 Big Four WA 48°05 121°30 11/21/1933 12 Tatoosh Island WA 48°23 124°44 1/20-25/1935 13 — WA 47°30 123°30 6 1/20-25/1935 14 — WA 47°00 122°00 72 214-811937 15 Cyamaca Dam CA 33°00 116°35 12/9-12/1937 16 — CA 38°51 122°43 2127-31411938 17 — AZ 34°57 111°44 12 1/19-24/1943 18 — CA 37°35 119°25 18 1/19-24/1943 19 Hoogee's Camp CA 34°13 118°02 1/30-21311945 20 — CA 37°35 119°30 12/27/1945 21 Mt. Tamalpias CA 37°54 122°34 11/13-21/1950 22 — CA 36°30 118°30 24 8/25-30/1951 23 — AZ 34°07 112°21 72 7/19/1955 24 Chiatovich Flat CA 37°44 118°15 8/16/1958 25 Morgan UT 41°03 111°38 9/18/1959 26 Newton CA 40°22 122°12 617-811964 27 Nyack Ck. MT 48°30 113°38 12 9/3-7/1970 28 — UT 37°38 109°04 6 9/3-711970 29 — AZ 33°49 110°56 6 6/7/1972 30 Bakersfield CA 35°25 119°03 12/9-12/1973 31 — CA 39°45 121°30 48 SOURCE: U.S. Army Corps of Engineers (1982b).

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Hydrologic and Hydraulic Considerations APPENDIX 4C GUIDELINES FOR BREACH ASSUMPTION 129 Presented here are guidelines for formulating emergency action plans with no admission, written or implied, that the structures are a hazard. Addi- tional criteria for dam break analysis are given for use in a specific com- puter model. These guidelines are representative of criteria developed by an investor-owned utility, which were submitted and accepted by a regula- tory 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 investi- gation 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 evalua- tion. 4. If the downstream dam is owned and operated by another regula- tory 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 flood- ing from the hypothetical dam break could cause significant hazard to hu- man 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 reser- voirs shall be assumed to be at normal maximum operating water levels unless otherwise noted. In so doing, all flashboards shall be assumed in- stalled 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 insignifi- cant compared to the failure flood waves.

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130 SAFETY OF EXISTING DAMS 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 ap- purtenant 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 fad! only to pre- pare 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, con- sider 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 slid- ing, failure should be assumed, if significant overtopping would occur. 14. When a lower dam is overtopped from an upstream dam failure, all Dashboards 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, as- sume a rectangular shape. For erosion failure, assume a parabolic or trape- zoidal shape. For complete instantaneous failure, assume a parabolic or trapezoidal shape. 21. For mixed dams (concrete and embankment), assume failure to pro- duce the largest but reasonable flow. 22. Final breach shape of embankment dams should be trapezoiclal when the maximum base is equal to the height of the dam. A proportion-

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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 effi- cient section. Dimensions for this efficient section are given in most text- books 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 economi- cal 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 cer- tain cases where the historical precipitation-caused flood peaks have caused damage in the area, continued routing may be necessary until atten- uation 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.