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AD-AI7 2 015 HYDROLOGIC ENGINEERING CENTER DAVIS CA F/S 6/8GUIDELINES FOR CALCULATING AND ROUTING A DAM-BREAK FLOOdUIJIAN 77 D L GUNOLACH, W A THOMAS
UNCLASSIFIED H EC-R N5 N
LEVEL- ""
RESEARCH NOTE NO.5
GUIDELINES FOR
CALCULATING AND ROUTING A DAM-BREAK FLOOD
JANUARY 1977 DTICS ELECTERS JUL 27 1981
D
DISTRFl1PIiON( ~Approved for jUi
~ THE HYDROLOGIC)I)21I ' ENGINEERING CENTER
*research-training
CORPS OF ENGINEERS applicationU.S. ARMY
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Research Note No. 54. TITLE (ind Subtitle), 5. TYPE OFAEPORT PERIOD WVERIO
GUIDELINES FOR CALCULATING AND ROUTING A __•________.
DAM-BREAK FLOOD r 4. PERFORMING ORG6. REPORT IUMOER
7. AUTHOR(&) S. CONTRACT OR GRANT NUMBER(s)
David L. .Gundlach and. William A. Thomas
9. PERFORMING ORGANIZATION NAME AND ADDRESS. t10. PItOGRAM ELEMENT. PROJECT, TASKAREA & WORK UNIT NUMBERS
U.S. Army Corps of EngineersThe Hydrologic Engineering Center' /609 Second Street, Davis. CA 95616
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January 197713. NUMBER OF PAGES
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Distribution of this publication is unlimited.
17. DISTRIBUTION STATEMENT (of the abstract entered In Block 20, If different from Report)
IS. SUPPLEMENTARY NOTES
19. KEY WORDS (Continue on reverse side it necessary and identify by block number)
Dam failure, Flood profiles, Model studies, Waves(Water), Open channelflow, Flood routing, Mathematical models, Analytical techniques, Analysis,Hydrographs, Hydrograph analysis, Water levels, Discharge(Water),Reservoirs, Peak discharge, Rupturing, Unsteady flow, Steady flow,Teton Dam.
20. ABSTRACT (Continue an reverse aide If necessary and Identify by block number)
This report described procedures necessary to calculate and routea dam-break flood using an existing generalized unsteady open channelflow model. The recent Teton Dam event was reconstituted to test themodel's performance on such a highly dynamic wave. The proceduresoutlined relate, primarily, to partial breaches. Some deficiencies inthe model were identified which will require some further (CONTINUED)
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research and programming to improve the applicability of the program todam-break flood events. The special project memo established fourobjectives for this study. The first two, (1) level of accuracy ofexisting techniques and (2) sensitivity of calculated 'results to n-valuesand breach size, were summarized and presented in detail in Appendix A.The third objective, (3) description of physical phenomena controllingdepth and travel time and a discussion of pertinent field data, waspresented in the body of this report. The fourth objective, (4) documentationof the methodology, was included in Appendix B. Computerprograms utilizedin the methodology may be obtained from The Hydrologic Engineering Center.The computer program was applied to the Teton Dam data set to demonstratethe level of accuracy one might expect in such analyses. The. resultswere shown and, in general, appear reasonable.
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Q fSEARCII MOTENn. S
~U1DEINESFOR ALCULATINr, AND Pf)IITIN(,A D _13REAK FLOOD -
by A,/7 (A
) ) DAV I, /CUDLACII' fl L LI KTHrMAS
Janur477
Accession ForVE YRLICNINRI CTFNTIST14 GRAI CROFn ENUNCER N C.S. TFP1
DTIC TAB L EODSREUnanustif i fltAVIS, CALIFRNIA 4.Justiric"Itic., 0)5f66198
F~cces n F- F~q [COUDSTREE
____ ~ fc2~A
FOREWORD
This Research Ilote reports the findings of The Hydroloqic Fnqineerinn
Center on appropriate methodologies for calculatinq and routing floods re-
sulting from suddenly-breached dams.
This study was prepared for the U.S. Army Engineer Waterways Experiment
Station, Vickshurn, Miss. with fundinn provided bv the Defense luclear
Aqency under subtask L19HAXSX337, '"Ahove Ground Structures," work unit 17,
"Damage of Dams," and by the Office, Chief of Engineers under nA project
4A76271nAT4O, task Al, work unit IM06.
The material contained herein is offered for information purposes only
and should not be construed as Corps of Engineers policy or as being re-
commended guidance for field offices of the Corps of Engineers.
GUIDELINES FOR
CALCULATING AND ROUTING A DAM-BREAK FLOOD
Table of Contents
Paragraph Page
1. Introduction 1
2. Summary 2
3. Physical Phenomena and Field Data 3
4. Energy Components and Peak Outflow from Complete,Instantaneous Breaches 5
5. Instantaneous, Partial Breaches 6
6. Attenuation of the Flood Wave 9
7. Proposed Analytical Technique 9
8. Program Limitations 10
9. Proposed Areas of Research 11
10. Alternate Analytical Procedures 11
11. References 1?
9 . . . |
LIST OF TABLES
Table Page
1 Sensitivity to Breach Size and Rate of Development 2
2 Relative Size of Energy Components in Partial WidthBreaches 8
I1
LIST OF FIGURES
Figure Page
1 Components of Specific Energy Head 6
NOW.i
APPENDICES
APPENDIX A
Unsteady Flow Analysis - Teton Dam Failure
Table of Contents
Paragraph Page
1. Introduction A-I
2. General Description A-1
3. Geometric Models A-2
4. Unsteady Flow Models A-5
5. Steady Flow Modei A-15
iv
LIST OF TABLES
Table Page
1 Estimated Times for Leading Edge of Flood Wave A- 3
2 Estimated Peak Discharges A- 4
3 Results of Unsteady Flow Analysis Using SimulatedDischarge Hydrograph for Observed Conditions A- 8
4 Computed and observed Times for Leading Edge ofFlood Wave A-10
5 Computed and Observed Peak Discharges A-l
6 Results of Unsteady Flow Analysis Using SimulatedDischarge Hydrograph for 40% Breach Size A-12
v
LIST OF PLATES
Plate Page
1 Teton Dam, Teton River, Idaho Location Map A-16
2 Teton Dam General Plan and Sections A-17
3 Teton Dam Embankment Details A-18
4 Teton Dam Reservoir Capacity A-i9
5 Teton Dam Elevation Hydrograph for Reservoir A-20
6 Teton Dam Discharge Hydrograph at Damsite A-21
7 Teton Dam initial Estimate of Partial Failure A-22
8 Teton Dam Estimate of Partial Failure A-23
9 Teton Dam Discharge Hydrographs at Damsite A-24
10 Teton Dam Flooded Area Map Including High Water Marks A-25
11 Teton Dam Maximum Computed Water Surface Elevationsfor June 5, 1976 Dam Failure A-26
12 Teton Dam Maximum Computed Water Surface Elevationsfor June 5, 1976 Dam Failure A-27
13 Teton Dam Maximum Computed Water Surface Elevations
for June 5, 1976 Dam Failure A-28
14 Teton Dam Computed Times for June 5, 1976 Dam Failure A-29
15 Teton Dam Maximum Computed Water Surface Elevationsfor June 5, 1976 Dam Failure A-30
16 Teton Dam Maximum Computed Water Surface Elevationsfor June 5, 1976 Dam Failure A-31
17 Teton Dam Maximum Computed Water Surface Elevationsfor June 5, 1976 Dam Failure A-32
vi
APPEN4DIX B
Guidelines for Analyzing a Dam Break Flood with the Computer Program"Gradually Varied Unsteady Flow Profiles"
Table of Contents
Paragraph Page
I. Data Requirements B-1
2. Assumptions B-1
3. General Procedure B-2
4. Calculation of Outflow Hydrograph Using the PartialBreach Approach B-2
t. Routing the Dam Break Flood B-3
vii
PFSFARCH NnTE"NO. 5
GUIDELINES FOR CALCIILATIrff ANfD ROUTI C A DAH-BP.EAK FLnOr
1. Introduction. Planning and design requirements for a wide range of pro-jects, such as emergency preparedness and siting of nuclear Dower plants,have generated widespread interest in dam break floods. Much academic re-search and some laboratory research have been accomplished on this topic.Generalized analytic techniiues for calculating and routina such floods,particularly in non-prispiatic valleys, have not been readily available.Furthermore, prototype verification data are almost non-existent. This re-port describes procedures necessary to calculate and route a dam break floodusinn an existing generalized unsteady open channel flow model. The recentTeton Dam event was reconstituted to test the model's performance on such ahighly dynamic wave. The procedures outlined herein relate, primarily, topartial breaches. Some deficiencies in the model were identified which willrequire some further research and pronramminq to improve the applicabilityof the pronram to dam break flood events.
2. Summary. The special projects memo cited as reference (a) establishedfour objectives for this study. The first two, a) level of accuracy ofexisting technioues and h) sensitivity of calculated results to n-values andbreach size, are summarized below and presented in detail in Appendix A. Thethird objective, c) description of nhysical phenomena controllinn depth andtravel time and a discussion of pertinent field data, is presented in thebody of this report. The fourth objective, d) documentation of the method-ology, is included in Appendix q. Computer programs utilized in the meth-odolony, references (,) and (c), rav he obtained from The lvdrolonicEngineerinn, Center.
The computer proqrai of reference (c) was applied to the Teton Dam data setto demonstrate the level of accuracy one miaht expect in such analyses.The results are shown on pages A-?F through A-28 of Appendix A and, ingeneral, appear reasonable. This test case demonstrates the usefulness ofa neneralized corputer program because the methods proposed in references(d) and (e) were not a'nlicable to the Teton data set for reasons (iven inl)ara(Iraph 10.
Reqardlng sensitivity to breach size, paqes A-22 and A-23 show the twobreach sizes considered. The breach that developed at Teton was estimated,by others, to be 40 percent of the dam embankment. Geometric data were notavailable to verify this, therefore, our best estimate of the final Tetonbreach geometry, page A-22, is based on photographs. The breach shown onpage A-23 has the same side slope as that on page A-22, 0.6 on I but ithas zero bottom width. This seemed a likely intermediate condition, butno field data were available at the time of this study to establish anobserved intermediate condition.
The calculated outflow is shown on page A-24. The hydrograph labeled"trapezoidal breach" assumed the 40 percent breach size, page A-22,developed instantaneously. The hydrograph labeled "triangular breach"was determined in a similar manner for the 3im breach size. The thirdhydrograph on page A-94 was calculated for the trapezoidal breach (labeled4n'/ breach size on page A-72), but an observed reservoir drawdown curveat the dam, page A-20, was used which implies a gradual development ofthe breach rather than instantaneous failure. Thp last approach was con-sidered best in estimatinq the discharge hydroqraphfrom Tetor reservoirgiven the data set and analytical technique- available to us.
The sensitivity of calculated outflows to breach size and rate of developmentis illustrated on page A-24. It is summarized in the following table togetherwith pertinent elevation data for an n value of 0.04.
Table 1: Sensitivity to Breach Size and Rate of Oevelopment
Final Breach Size Rate of Calculated Peak Calculated Peak Elevations% of Total Dam Development I-fater Discharqe _SL
at Dam Axis At Dam Axis Miles nownstream106 CFS (1) At Dam Axis
_______from Dam Axi s5 10(;) .8 (3i) 5,TT- 493
Ine - r51 15 4933instanta- 2.4 5151 5,5 4933
neous
40 instanta- 3.4 5179 5020 4935neous
(1) Multiply by r.,93? to get Cubic meters Per Second
(2) Actual rate of development was unknown so the observed reservoirdrawdown curve, paqe A-20, was used to approximate outflowconditions.
(3) The actual peak discharqe. as estimated by personnel of the Walla'Jalla District, Army Corps of Engineers from observed data in theTeton Canyon three miles downstream from the dam, was 2,300,000 cfs.
From these results it is apparent that neither the size of breachs testednor the rates of failure assumed were very significant in predicting peakelevations five miles downstream from the dam.
The calculated peak flood elevations, near the dam, were very sen;tiveto n-values. Increasing n from .03 to .06 raised the peak flood elevation25 feet at the dam, as illustrated on page A-8 Tahl- 1. At 9 milesdownstream the calculated difference was only 4 feet. Differences continuedto diminish with distance.
Calculated Travel Times are shown on page A-29. They correspond to thedischarge hydroqraph labeled "simulated from observed data" on paqe A-24and n-values of 0.04.
Searching for a simolified approach in place of references (d) and (e) led toa trial application of the Modified Puls routing technique. The hydroqraphlabeled "simulated from observed data" on pane A-24 was routed and a watersurface profile calculated for the resulting peak discharges. A comparisonof the results with the observed elevations and the peak elevations computedwith the full equations is shown on pages A-3n through A-32. Additionalinvestigation is needed to establish the range of applicability of this"method.
3. Physical Phenomena and Field D)ata. Analysis of the dam-break floodinvolves understanding the physical processes before aoplying analyticaltechniques which approximate those physical processes. Three distinctlydifferent processes are involved: the process of structural failurecausing the breach to develop; the process of setting water into motionin a reservoir; and the process of flood wave attenuation.
The size, shape and rate of breach development are primarily responsiblefor the pealrate of -outfTow- rom the reservoir. Yet, of the three physicalprocesses, this one is the most difficult to quantify. With the exceptionof man-made breaches, it is difficult to visualize the instantaneous develop-ment of a breach. Some have occurred, however. The St. Frances Dam, ahigh head concrete gravity structure, apparently suffered an abutmentfailure which resulted in virtually the instantaneous failure of the entirestructure. The Johnstown flood of 1889 was caused by the complete failureof an earth fill dam. Reports indicate that less than half an hour wasrequired for overtoppinq flow to hreach the structure. The recent Tetonfailure, a full depth-partial width breach of an earth fill dam, is estimatedto have developed in less than two hours. Since natural failure of a majorstructure is so improbable, establishing a mode of failure requires a policydecision rather than an analytical technique. In qeneral, instantaneousfailure of the entire structure produces the largest flood wave.
"" : . . .. I i " p '' " " - - ' "3
The second physical process results from the depth of water above the breachinvert. That is, a reservoir has a total energy head equal to the elevationofthe water surface. If the dam is breached, the force of qravity will setwater into motion. The effect will propogate, as a negative wave, to theupstream end of the reservoir at a velocity equal to Vg7 where g isacceleration of gravity and y -s water depth. Because of the great depthin a reservoir, very little frictional resistance is mobilized during thepassage of this negative wave. As a result, water gains specific energyrapidly as it moves toward the breach. In instantaneous breach development,the peak outflow will occur within a minute or two after breaching.
Whereas the total energy head setting the water into motion is the specificenergy (i.e., the initial water depth) above the breach invert, the energywhich must be dissipated in the downstream channel is equal to the specificenergy from the downstream channel invert to the initial pool elevation.The fact that the water surface elevation drops down rapidly at the damaxis does not reflect a corresponding loss in energy head. When flowbegins, that specific energy above the breach invert is transformed intothree components: a pressure head, a kinetic energy head and an inertiahead. (The relative size of each of these energy head components isdiscussed more fully in sections 4 and 5.) Friction loss is relativelysmall and may be neglected unless the reservoir bottom is extremely rough(more than 5'. or 10' of the water depth).
The third physical process, flood wave attenuation, involves energydissipation and valley storage. As the flood wave moves downstream, thepeak discharge tends to decrease, the base of the flood wave will becomelonger and the wave velocity will decrease. tlear the dam, energy dissipationis primarily responsible for behavior of the flood wave. However,vlystorage soon becomes the primary factor in flood wave attenuation. 'Tiekey to the transition from energy dissipation to valley storage control isthe rate at which the slope of the total energy gradient, a line which mustintersect the initial pool elevation at the dam, is reduced to that of amajor rainfall flood in the downstream valley. It seems ohvious that thetotal energy at any cross section in the valley should not exceed the initialreservoir elevation, and yet some analytical techniques occasionally violatethat constraint. It is good policy to always check the total energy, aswell as the water volume, in a calculated flood wave.
The rate of energy dissipation is qoverned primarily by friction loss.t4inor losses from bends and contractions-expansions are often included inthe n-values.
The volume of water in the reservoir is the final piece of field data required.This volume strongly influences the peak elevations at downstream points.
'11
4. Energy Components and Peak Outflow from Complete, Instantaneous Breaches.It is useful to develop the relative size for each energy component in theflow at the dam axis and to compare all of them to the more common case ofsteady state critical flow at a contraction.
By assuming a rectangular cross section, zero bottom slope and instantaneousremoval of the entire dam, Saint-Venant developed an analytical solution forthe elevation of the free surface, reference (f).page 755. Utilizing thatequation, the depth of flow at the dam axis was determined, by Saint-Venantand others, to be 4 Yo where Y0 is the original water depth at the dam .Also, the velocity corresponding to the peak outflow was shown to be VgY0oCombining these relationships leads to the equation for peak discharge
qmax 7 Y" (1)
Yo is the initial water depth at the dam
q is acceleration of gravity
qmax is peak aater discharge in cfs/ft
Since this equation was developed for a rectanqular section, the totaldischarqe may be calculated by multiplyingq max by the width.
Usinn the relationships referenced above, the velocity head (i.e., thekineti energy head component of the specific energy head) was calculatedto be VY. Since, in the absence of frictirn and other losses, inertiais the only remaining term in the basic, unsteady flow equations of Saint-Venant, it may be calculated as follows.
Y o h + 2 4 (2)hi = 0 Y
These components are shown in Figure I along with the energy componentsfor critical , steady state flow.
This figure shows that in the dam break flood analysis, as well as steadystate critical flow at a contraction, the velocity head is half the pressurehead. However, the inertia head comnonent is zero in Figure la because flowis steady state.
h=Y
(Pressure) j I Inesre)
V 9 0
X
(a)Critjcal flow at a contraction (h)Critical flow from a breached dam(steady flow conditions) Ii~ifna~'y '1n., nnditinns
Finure 1. Components of Specific Energy Head.
The drawdown in water surface elevation to 4rv 0 at the dam axis, Fiqure ib,
does not reflect a correspondinc enerqy loss. Experimental results obtainedby Schoklitsch, reproduced on page 755 of reference (f, show relatively
little friction loss in flow approaching the dam axis. As might be expected,
the model results showed friction to be very siqnificant downstream. Testsreported by ES in reference (g)showed no impact from friction loss at the
dam axis. Howvever, the WES flume sloped at 0.005 ft/ft, whereas the flumein Scho.litsch's experiment had zero bottom slope.
The significance of this point is that all three enery components, pressure
head, kinetic energy head and inertia head, are siqnificant in complete,
instantaneous breachines. Consequently, investiqators encouraqe the use of
the cofplete routing equations, often referred to as the Saint-Venant
equations. Simplifications of the complete equations, such as tuskingham,
Tatm, Straddle-Staqqer and dified Pls, are not recommended because the
emnirical coefficients ould invariably be developed from rainfall floods
and wnould reflect different values of enerqy components relative to p.
5. Instantaneous, Partial Breaches. Partial breaches are classified,according to hydraulic performance, as full depth-partial width, partial
depth-full width or partial depth-partial idth. A separate equation has
been developed for calculatinq the peak water discharqe for each class,
paqe 25 of reference (g).
Full Depth-Partial Width 18B 4
n~a =8 h •Yo B 4 g (3)
ma iswdtrf hnnlfe
B is width of channel, feetb is width of breach, feet
Partial Depth-Full Width 1
max " B y(L -)Vry (4)
y is depth of water above bottom of breach
Partial Depth-Partial Width 118a . b. . (B) (YoI ()
0~a B V (5),r
An enpirical equation for partial depth-partial width breaches was reportedin references (g) and (h).
y 0.28n max =0. 29 h Y 28 (6)
For breach sizes in the following range.
B 0.. .- ) < 20 (7)
Since the discharge equations for partial breaches are similar, in form,to that for a full breach (1), the total specific energy has the same threebasic components. However, their size, relative to initial water depth,is considerably different from that shown in Figure 1. There is no analyticalsolution for partial breaches, therefore, experimental results, presented inreference(g), were used to calculate the individual energy head components.The following table presents experimental results for full depth breachesranging in width from 10% to 100% of the flume width in columns 1, 2 and 3.Fractions of initial water depth, calculated with equation 3, are shown incolumns 4 and 5. A sample of the calculations is presented in the paragraphfollowing the table. This sample calculation utilizes equation 3 and a i0)"breach size (i.e., full breach) to demonstrate that the relative value of eachenergy component is the same as the respective value produced by equation 1,the analytical, full breach equation, when equation 3 is carried to itsupper limit.
7
Table 2: Relative Size of Enerqy Components in Partial Width Breaches(l)
Test Breach Pressure Velocity InertiaNo Size Head Head (2) Head (3)
of Y0 of Y0 of Y0
(1) (2) (3) (4) ( )
1.1 I ul 1 44 34
2.1 60 70 12 18
3.1 0 82 12 6
4.1 15 89 (4),
5.1 10 q4 (4)
Notes: 1. Values in columns I and 2 are from Table AI, paqe 8, reference(a)and values in column 3 are from experimental results fromTables 1 through 5, Station 200, reference (n).
2. Velocity head is calculated with equations q and 9, following.
3. Inertia head is Y. - (pressure head + velocity head).
4. Calculated values exceeded 100 percent of Yo, which probablyreflects scatter in experimental results.
0max max (9)
wh'-re:
v = depth of water at dam axis
h = breach width
0 from equation (3)
Vb - Y (gmax hy
For the full breach, b 1.08 and y 4
0
SI
1I
max 4
2
V2 (12)max = 4 gYo2g q
2 Y (13)
This agrees with section 4 and shows the nrocedure followed in completinqTable 2. The inertia head, column 5 in Table 2, was calculated assuming7ero energy loss upstream from the dam.
2 4
Yo hi + 2 Y + Y Yo (14)
i ( )
i f0
Because of the decrease in relative significance of inertia head and evenvelocity head, it is satisfactory to apply simplifications of the fullSaint-Venant equations to oartially breached dams.
6. Attenuation of the Flood Ilave. As a flood wave moves downstream,friction and other losses chanqe the relative size of the three energycomponents. Even floods from fully breached dams eventually take on thecharacteristics of i rainfall flood and may be routed with a simplifiedroutinq method such as Modified Puls. Major areas of uncertainty are 1)how much distance is required for this transition, 2) how does this distancevary w*hen considering partial breaches and 3) what is the maximum breachsize to consider as a partial breach.
7. Proposed Analytical Technique. The guidelines presented in Appendix13 of this report are developed for the computer program "Gradually VariedUnsteady Flow Profiles". It is a solution of the basic Saint-Venantequations for unsteady flow and may be used to calculate the outflowhydrograph through any size or shape of breach, as well as to route thathydroqraph downstream and provide water discharge and water surface elevation
9
hydroqraphs at any number of computation points up to 45. The maximumdischarge, maximum elevation and maximum flow velocity are summarized foreach computation point.
Sufficient information is printed out so the time of arrival, time of peakand duration of the flood may be plotted.
This computer program accounts for the movement of the negative wave throughthe reservoir, for the tailwater submergence at the dam, for the threecomponents of energy presented earlier, for friction loss and for storagein the reservoir and the downstream valley.
Cross sections need not be rectangular or orismatic. A companion program,""ienmetric Elements from Cross Section Coordinates", is available totrans0f-n complex cross sections into the required geometric data set forthe routinq proqram.
These computer programs are generalized. That is, they are sufficientlyflexible and adaptable to be used without code changes. They are portablefrom one computer to another and documentation is available, from TheHvdrnloaic Enqineerinq Center.
8. Program Limitations.
a. Routing with the Gradually Varied Unsteady Flow Profiles computerprogram requires a large high speed computer (50,on, 60-bit words) andpersonnel who are experienced in applying mathematical models.
b. Any breach size may bp modeled, but the program assumesinstantaneous development.
c. All channels must be wet initially. That is, computations cannothe made if any portion of the model is dry. This is overcome by prescribinga base flow; however, the computer program has difficulty in establishingthis profile.
d. "ovement of the negative wave through the reservoir causes nocomputational problem until it reaches the upstream end of the reservoir.Computation nodes tend to qo dry and abort the computer run.
e. The analysis of multiple failures would require manual interventionto stop and restart the calculation Process as each new structure is brouqhtinto the system.
f. The program assumes a horizontal water surface transverse to theflow, whereas a great deal of transverse slope can exist in the actualorotntype situation.
in
9. Proposeq Areas of Research. All of the program limitations werecircurmvented in analyzing the Teton Data Set. The trade-off, however, wasanalysis tire. Seven weeks were required to set up the data, debug it andperform the analysis. The two tasks requiring the most time, probably 75',were establishing initial base flow conditions for the model (8c) andstabilizing the computations when the negative surge reached the upstreamboundary (8d). Both of these problem areas can be overcome by additionalprogramming. The improvements would reduce analysis time to four orfive weeks.
Instantaneous breach development, 8b, could be replaced by equations whichlet progressive development take place. In the absence of a theory, the rateof development would have to be prescribed with input data.
Developing the capability to handle multiple dam failures (3e), especiallyin tandem, will he a major modification.
This analytical technique is a one-dimensional model and will always have arorizontal water surface transverse to the flow. At present, two-dimensionalmodeling is not feasible.
10. Alternate Analytical Procedures. Alternate analytical procedures wereproposed in references (d) arT-)-.-- leither were applicable to the TetonData Set.
The dimensionless curves were developed from numerical solution of the St.Venant equations and include special treatment of the wave front as it movesalong a dry channel. By knowing reservoir volume, valley cross section atthe dam, initial reservoir elevation, stream slope and stream roughness,the curves will proviue three properties of the flood wave:
1. Time of arrival at downstream points. Maximum depth profile in the downstream channel3. Time of maximum depth at downstream points.
The curves extend for distances ranging up to fifteen times the reservoirlength. The outflow nydrograph at the dam is not needed to use thesecurves. It was assumed, in developing the curves, that the entire damis breached instantaneously and that the valley is prismatic. Neitherconoition was satisfied by the Teton case.
Tie procedure in reference (e)was developed for smaller structures and theTeton Uata Set was completely beyond the range of nomographs and curvespresented there. In any case, the procedure does not route the flood wavedownstream. Only the outflow discharge hydrograph is calculated at theuan axis. The procedure can handle a wide range of breach sizes, but it
pI
11t
is designed with partial breaches in mind. It has the advantage of tailwater correction, which is essential when breaching of a low dam coincideswith a high flow condition in the stream. The procedure is well documentedand is easily applied.
A possible alternative approach for partial breaches is the Modified Pulsrouting technique. Preliminary work with this technique produced the re-sults shown on pages A-30 through A-32 for the Teton Data Set. A Manningn value of 0.04 was used; further details are given in Paragraph 5, AppendixA. The advantage of this technique is that readily available and easilyapplied computer programs (e.g., HEC-l and HEC-2) can be utilized; totalanalysis time would probably be reduced to two to three weeks.
The disadvantage is that the range of application is limited whereas thetechnique presented in Paragraph 7 is generally applicable.
Additional research is needed to define the range of applicability of theModified Puls technique. The present hypothesis is that the size of theinertia component, Table 2, would provide a suitable parameter for definingthat range.
This research would not require additional physical modeling. Studies re-ported in references (g) and (h) offer test data for numerical studies.Other numerical experiments could be performed by using results from anal-yzing variations of the Teton Data Set with the complete equations. Theseresults could be obtained while pursuing any of the areas of research pro-posed in Section 9.
Computer programs which utilize the Modified Puls routing technique areavailable and are presently developed to a higher degree of serviceabilitythan programs solving the full equations. Water surface profile computationswill be required in conjunction with the Modified Puls routing to produce awater surface profile. These computations are computerized also. No majorcomputer program development would be required. The appropriate existingcomputer programs, HEC-l and HEC-2, are well documented.
11. References.
a. Special Projects Memo No. 473 subject Calculating and Routing theFlood Resulting from a Suddenly Breached Dam, dated 26 August 1976.
b. "Geometric Elements from Cross Section Coordinates", The HydrologicEngineering Center, June 1976.
c. "Gradually Varied Unsteady Flow Profiles", The Hydrologic EngineeringCenter, June 1976.
d. "Dimensionless Graphs for Routing Floods from Ruptured Dams", byJohn Sakkas, dated January 1976, The Hydrologic Engineering Center.
12
e. "Computation of Outflow from Breached Dams", Defense Intell inenceArjency, June 1q63.
f . Keulegan, "Wave 'lotion", Ennineerin a !ydraulics, Fd. ,,y '!.
fouse, John )iley ? Sons, Inc., 'Iew York, New York, Fifth Printinn, Octoher7065.
9. "Flood Resulting From Suddenly Breached fams", Conditions ofMinimum Resistance, Hydraulic .Iodel Investiqation, '1iscellaneous Paper No.2-374, Report 1, U.S. Army Corps of rnqineers, Waterways Experiment Station,Vicksburg, Mississippi, February 1960.
h. "Floods Resultinq From Suddenly 5reached Dars", Conditions ofhigh Resistance, Hydraulic Model Investigation, NMiscpllaneous Paper No. 2-374, Report 2, U.S. Army Corps of Enqineers, W4aterways Experiment Station,Vicksburq, M'ississioDi, 'ovember In1l.
13
APPENDIX A
UNSTEADY FLOW ANALYSIS
TETON DAM FAILURE
1. INITRODUCTION
This phase of the study which calculates and routes the flood resultingfrom a suddenly breached dam, consists of a computer solution in conjunction
with the Teton Dam failure as defined in objectives a and b of SpecialProjects Memo No. 473. The analysis utilizes the unsteady flow computerprogram to determine water surface elevations resulting from various breachsizes and n values. The level of accuracy was determined by comparing avail-able flood data (particularly high water marks) from the June 5, 1976 damfailure with calculated results.
The analysis used data generally available to field personnelengaged in the study of the impact of a dam break flood such as topo-graphic maps, aerial photography, dam description, gaged stream flowsand reservoir elevation-capacity curves. The primary area of studyincluded about 30 miles of flood plain downstream of the dam.
2. GENERAL DESCRIPTION
The Teton Dam is located on the Teton River in southeastern Idahoapproximately 13 miles north and east of the city of Rexburg (see Plate I).The dam was designed as a zoned earthfill embankment with a crest elevationof 5,332 feet (mean sea level datum) and a maximum height of 305 feet(above riverbed). It would create a reservoir of 288,250 acre-feet whenfilled to an elevation of 5,320 feet. (Plan and sections of the dam are
shown in Plates 2 and 3.) The dam is located in a narrow steepwalledcanyon. The channel geometry is essentially the same for some 4 milesdownstream of the dam whereupon the Teton River enters upon a widerelatively flat flood plain.
The total reservoir storage just prior to failure on June 5 was about
251,300 acre-feet at an elevation of 5,301.5 feet. Measured inflow was
3,580 cubic feet per second and measured outflow before any leaks developedwas 940 cubic feet per second.
Although water stored upstream of the dam caused the flooding, othersources contributed significantly to the floodflow in the downstream reaches.
However, the complexity of major irrigation diversions and numerous returnflows precludes an accurate accounting of all sources. According to therecord obtained from the damaged recorder at the gaging station on HenrysFork near Rexburg (at Idaho State Highway 88), 3,460 cubic feet per second
A-l
were flowing in Henrys Fork at the time the leading edge of the floodwave arrived about 4:00 p.m. on June 5. The contribution of the SnakeRiver, just upstream of its confluence with Henrys Fork was estimatedat 5,600 cubic feet per second around 1:00 p.m. of the same day.
Table I presents a preliminary tabulation of available data pertainingto the leading edge of the flood wave generated by the dam failure.Distances shown are measured from the dam breach along the estimatedpath of the leading edge of the wave.
Instantaneous peak discharges were determined at two sites along thestudy reach (Table 2). Indirect measurements based on field surveys andempirical formulas were used to compute the peak discharges at the sites.The indirect methods for computing peak discharge were based on hydraulicequations relating discharge to the water-surface profile and the geometryof the channel.
3. GEOMETRIC MODELS
The channel configuration upstream ard downstream of the dam wasmodeled independently according to procedures contained in the usersmanual, generalized computer program (723-G2-L745B), Geometric ElementsFrom Cross Section Coordindtes (GEDA), Hydrologic Engineering Center, U.S.Army Corps of Engineers, June 1976.
The upstream geometric model (reservoir) was developed essentially fromtwo cross sections located at the damsite and at the estimated upstreamlimit of the reservoir (when filled to capacity). The cross section data atthe damsite were obtained for preproject conditions from topographic informa-tion shown on Plates 2 and 3. Information for the other section was obtainedfrom U.S. Geological Survey topographic maps (scale 1:24,000). Data werecoded in the standard HEC-21 format and input into the GEDA program. Computedresults were compared with respective values taken from the reservoir capacitycurve of Plate 2 and, where necessary, adjustments made to the upstream crosssection until computed volumes (at specified elevations) plotted reasonablyclose to the published curve (see Plate 4).
The downstream model (channel) was developed in a similar manner althougha more detailed definition of the channel configuration was necessary. Sincethe actual flooded area resultinq from the dam failure included severalmajor tributaries (the Snake River, Henrys Fork and the Teton River), therewas no readily available information on storage (volume) within the studyreach with which to calibrate the geometric model. Cross sections weretaken on the average every mile, and conveyance limits were designatedso as to effectively model conveyance for the large flows expected in thedam break analysis.
1HEC-2 Water Surface Profiles, Generalized Computer Program (723-02A),Hydrologic Engineerinq Center, U.S. Army Corps of Engineers, October 1973.
A-2
TABLE 1
ESTIMATED TIMESFOR LEADING EDGE OF FLOOD WAVE(BASED ON FIELD OBSERVATIONS)
ApproximateMilesa Arrival Elapsed time mean velocity
Location downstream Date time between sites between sitesfrom dam (month/day) (hours) (minutes) (ft/min)(mi/hr)
At damsite 0.0 6-5 1157 - - -
In Teton Canyon 3.0 6-5 1205 8 1,980 23
At Teton 8.8 6-5 1230 25 1,220 14
At Sugar City 12.3 6-5 1300 30 620 7
At Rexburgb 15.3 6-5 1340 40 400 5
Henrys Forknear U.S.G.S.gaging station,Henrys Fork nearRexburg 22.6 6-5 1530 110 350 4
Menan Bridge onthe Snake Riverimmediatelyupstream of theUnion Pacific 30.6 6-5 1800 150 280 3
aDistances measured along the estimated path of the leading edge of the flood wave.
bMaximum depths estimated at 6-8 feet within the city of Rexburg.
A-3
TABLE 2
ESTIMATED PEAK DISCHARGES(BASED ON FIELD OBSERVATIONS)
MilesaLocation downstream Date Time Discharge
from dam (month/day) (hours) (cubic feet per second)
In Teton Canyon 3.0 6-5 b 2,300,000
At Teton 8.8 6-5 c 1,060,000
aDistances measured along the estimated path of the leading edge of the flood wave.
bPeak probably occurred between 1230 and 1330 hours.
CPeak probably occurred between 1300 and 1400 hours.
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The area, hydraulic radius, top width and average n value werecalculated at each cross section in the goemetric models for the eleva-tions specified. By calculating length-weighted values, the precedingelements were modified such that they would apply to uniformly spacedcomputation points along the length of each model (reservoir and channel).
4. UNSTEADY FLOW MODELS
The unsteady flow data models of the reservoir and the channel weredeveloped according to procedures contained in the users manual, generalizedcomputer program (723-G2-L2450), Gradually Varied Unsteady Flow Profiles,Hydrologic Engineering Center, US. Army Corps of Engineers, January 1976.
Reservoir Model
In the case of the reservoir, tables of geometric elements were preparedat 21 uniformly spaced computation points (approximately 2,800 feet apart)and input into the unsteady flow program. Since inflow into the reservoirjust prior to failure was measured (approximately 3,600 cubic feet persecond), the upstream boundary condition was based on such. A normaldepth was determined for the measured discharge rate at the upstream crosssection. A steady flow condition was assumed, and a constant elevation(determined from the normal depth calculation) was specified as the boundarycondition. Initial values (discharge and elevation) were specified onlyat the most upstream and most downstream computation points (nodes) anda linear interpolation scheme within the program utilized to determinevalues at the remaining nodes. The values of discharge and elevation atthe upstream node are the same as those utilized in the computation of theelevation hydrograph at the upstream boundary. The elevation used at thedownstream node (damsite) was 5,301.5 feet (the observed reservoir watersurface elevation at time of failure) and the discharge was estimatedas 3,000 cubic feet per second. (Although the measured discharge was 940cubic feet per second before any leaks occurred, a higher discharge ratewas used because of significant seepage just prior to failure). In thereconstruction of the actual discharge hydrograph at the damsite, theobserved reservoir water surface elevations at particular points in time(after failure) were input initially for the downstream buundary condi-tion (see Plate 5 for a plot of the observed data). Since the observeddata were not adequate with respect to time to define a reasondble eleva-tion hydrograph, a greater number of coordinate points were coded in thefinal analysis (refer to Plate 5). The computed discharge hydrograph atthe damsite, based on the preceding conditions, is shown in Plate 6. (Notethat the computed maximum discharge is about 1,800,000 cubic feet persecond at about 2:00 p.m. of June 5.
When analyzing various breach sizes (partial failures), an elevationversus discharge curve was developed for the downstream boundary condition
A-5
(at the damsite). For the breach sizes shown in Plates 7 and 8 the dischargecorresponding to various critical depths was calculated according to
1
(b + z D 3/2
(b + 2z Dc) c
where
b = bottom width (in feet)
z = slope of the sides, horizontal divided by vertical
D = depth (in feet)c
g = acceleraticn due to gravity (in feet per second per second)
Q = discharge rate (in cubic feet per second)
After converting the various depths to elevations, the discharge ratingcurve corresponding to each breach size was input into the unsteady flowprogram. The computed discharge hydrographs are shown in Plate 9 andcompared with the simulated hydrograph for observed conditions.
Preliminary information received indicated that 40 percent of the damembankment was lost such that an initial estimate of the breach configura-tion (based on available photographs) is shown in Plate 7. The resultingdischarge hydrograph, Plate 9, represents an instantaneous failure of thesize depicted. (The same is true in the case of the triangular breach shownin Plate 8.) In the case of the discharge hydrograph computed for observedconditions, the downstream boundary condition corresponds to a gradual failureand results in significant differences in peak and in the time to peak.
In the unsteady flow analysis of the reservoir system, only the resultsfor n values of 0.04 are included. When n values were varied, there wasno significant difference in the computed discharge hydrographs at thedamsite.
Channel Model
In the case of the channel, tables of geometric elements were preparedat 37 uniformly spaced computation points along the study reach (approxi-mately 4,500 feet apart) and input into the unsteady flow program. The
'Handbook of Hydraulics, King and Brater, Fifth Ed., McGraw-HillBook Co., 1963, pp. 8-11.
A-6
upstream boundary conditions (at the damsite) are the various dischargehydrographs computed in the unsteady flow analysis of the reservoir.The downstream boundary conditions are discharge rating curves based onnormal depth calculations. The depth and corresponding discharge wasdetermined using Manning's equation
1 .49Q 1.4- A R2/3 S1/2
n
where
n = coefficient of roughness
A = area (in square feet)
R = hydraulic radius (in feet)
S = slope (in feet per foot)
The values for the geometric elements, A and R2 /3, for specified depths(elevations), were taken from GEDA output for the most downstream channelcross section. The slope was determined from available topographic maps.Values of n ranged from 0.03 to 0.07, and for each n value a dischargerating curve was developed as a downstream boundary condition.
In order to simulate the actual flow existing in the probable floodedarea downstream of the dam, the local inflow option of the unsteady flowprogram was utilized. Major inflow occurred where Henrys Fork and theSnake River entered the system. The estimated flows just prior to failurewere 3,500 and 5,600 cubic feet per second respectively.
In order to establish stable base flow conditions for each n valueprescribed, the model was run for a period of 24 hours with the estimatedinflows at the upstream boundary and local inflow points which existed justprior to failure. (The discharge and initial approximations of watersurface elevation at each node or computation point were input prior torunning. Since the discharge just prior to failure was estimated fromobserved conditions within the study reach, values were fixed, whereasinitial water surface elevations were manipulated until stable conditionsresulted.) Once stable base flow conditions were obtained, the variousboundary conditions (upstream and downstream) were input into the model.The model was then allowed to run until the peak of the flood hydrographpassed the downstream limit of study.
Results of the various runs are tabulated in Tables 3, 4, 5 and 6.Plate 10 is a Xerox reduction of the flooded area resulting from the June 5dam failure as published by the U.S. Geological Survey. The relative
A-7
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A-9
TABLE 4
COMPUTED AND OBSERVED TIMESa
FOR LEADING EDGE OF FLOOD WAVE
Observed Computed arrival timeMilesb Arrival n-values
Location downstream Time 0.03 0.04 0.05 0.06 0.07from dam (hours) (hours)
At damsite 0.0 - - - - - -
In Teton Canyon 3.0 1205 1206 1207 1208 1209 1210
At Teton 8.7 1230 1230 1230 1230 1240 1240
At Sugar City 12.9 1300 1340 1400 1420 1430 1440
At Rexburg 15.8 1340 1440 1500 1520 1530 1540
Henrys Forknear U.S.G.S.gaging station,Henrys Fork nearRexburg 21.1 1530 1540 1550 1650 1710 1740
Menan Bridge onthe Snake Riverimmediatelyupstream of theUnion Pacific 27.6 1800 1730 1750 1830 1920 2030
aTimes occurred on June 5, 1976.
b.Distances based on the unsteady flow data model.
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location of the odd numbered computation points and conveyance limitsare shown (a discussion of the conveyance limits is contained in theusers manual for the GEDA program). (It is apparent from Plate 10that the majority of high water mark observations are along the edgesof the flooded area.) Maximum water surface elevations are plotted inPlates 11, 12 and 13.
The observed high water marks (taken from Plate 10) were plotted inPlates 11, 12 and 13 and designated as left or right bank (looking down-stream). The ground profile shown reflects the minimum elevation in thevarious cross sections used in the geometric model. Horizontal distancesare measured along the most probable path of concentrated flow and notalong any particular tributary as shown in Plate 10. The spacing andlocation of the odd numbered nodes are also included in the profile plots.Maximum water surface elevations computed in the simulation of observeddata were plotted for the odd numbered nodes shown. Water surface profileswere then drawn for each n value used in the analysis.
If a number of cross sections are drawn on Plate 10 normal to estimatedflow lines, particularly in the area of Rexburg where floodwaters tendedto spread laterally, a significant variation in high water mark elevationsbetween the left and right banks of a given cross section is apparent. Insome instances, the difference is as much as 30 feet. This situation isalso apparent in Plates 11, 12 and 13. In general, where floodwaters wererelatively confined between the left and right banks, elevations of highwater marks on opposite sides are essentially the same.
A comparison of the observed and computed maximum water surface eleva-tions (Plates 11, 12 and 13) would seem to indicate the following:
(1) Floodwaters were probably concentrated in the center ofthe flooded area between the U.S.G.S. gaging station onthe Teton River and the downstream limits of Sugar City(see Plate 10).
(2) Floodwaters were probably concentrated in the vicinityof Rexburg.
It is difficult to analyze the accuracy of the computed results based onobserved high water marks. Any detailed analysis would definitely requirehigh water marks within the limits of flooding. If such could be obtaineda greater effort could be made in stipulating conveyance limits and in theactual calibration of an unsteady flow model.
Tables l and 4 compare the estimated (based on field observations) andcomputed arrival times of the leading edge of the flood wave, whereasTables 2 and 5 compare estimated (based on field observations) and computedmaximum discharges at particular locations within the study area. Plate 14gives an indication of the time required for passage of the flood wave(based on n=0.04).
A-14
In the unsteady flow model, determination of the arrival time of theleading edge of the flood wave depends on a noticeable difference in thecomputed water surface elevation occurring at a given node. Since minorfluctuations of the water surface were present in the base flow and sincethe printout interval was 10 minutes after 12:30 p.m., arrival times wereestimated (probably ± 30 minutes).
Computed peak discharges (Table 5) differ significantly from thoseestimated from observed data (Table 2). It is reasonable to assume thoughthat the discharges of Table 2 are only rough approximations.
In the development of the unsteady flow data model, there was no effortmade to locate computation points at those locations specified in Tables 1and 2. (Usually, computation points are located such that results are printedat desired locations.)
5. STEADY FLOW MODEL
The information originally coded in the HEC-2 format and utilized indevelopment of the channel geometric model, was used to determine the storage-outflow relationships for various reaches downstream of the dam. Multipleprofiles were run using HEC-2 and the volumes in a given reach, correspondingto a specified discharge, computed. (It should be noted that an n-value of0.04 was used in the multiple profile computations.)
The discharge hydrograph (see Plate 6) based on observed data, was routeddownstream with the storage-outflow relationships previously determined.Channel routing was accomplished with HEC-l'using modified Puls. The peakdischarges computed for each reach were subsequently input into the HEC-2data deck.
Before running, the HEC-2 deck was modified to reflect the conveyancelimits adopted in the unsteady flow analysis (see Plate 10). Encroachmentlimits were set with the X3 card as close as possible to the conveyancelimits previously designated (this was necessary since GR stations did notalways correspond to the conveyance limits specified in the geometric datamodel). The resulting water surface profile is shown in Plates 15, 16 and 17(superimposed for comparison).
The difference in the computed water surface profiles between the twomethods (the steady flow and the unsteady flow analysis) is due, in part, tothe difference in the computed discharges. Discharges computed using modifiedPuls were lower in the upstream channel reaches and higher in the lowerreaches. This is attributed to the significant effect of the inertia component(in the unsteady model) immediately downstream of the dam and in the waystorage is treated in the two methods.
1HEC-l Flood Hydrograph Package, Generalized Computer Program (723-010),Hydrologic Engineering Center, U.S. Army Corps of Engineers, January 1973.
A-15
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1 o , I 2 In~ tor f5 l
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[Irt In mit or meosred el~o
*"rr~a t~ 3 ?ltrtcta'd~~t ~ ~ ~TETON DAM
GENERAL PLAN AND SECTIONSMAXIMUM SECTION WITHOUT CAMBER
A-1 7 PLATE 2
CAholes ci dO'', lea
Jt' ~ o o
'~ I t'ps/e~i 'r.of
* I ~--Assursed f~rm
/ "VI I lie"'o~f r egul,f~ es u, formiofon surf,. ond
"''U CTOFF TRENCH
'I SCALE OF FEET
- --- Crest f, C AR7 k2-a $1LQ1F
Cr,Lf.~ Or ptnol grounsd sur face
f~ ~ ~ ~~SP tt' .o ,r -
,.Os'reoV or f e'*o ,'o~es j' ci$C'i 26,,s Asue'uraefr0fudt
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4'0O * C 11105 a, tel St ;3 o-i
r f qir5.' holes -ET got
' er Ott/ef II'I Assumied bottom of boL 1St'eo'I 1ld ulrwnstreom rows of rstholes of I~ !orrmtte
01,sren cop of, oroo holthle5esr6 to
fl OfI fou0,o hey ~ frenc '
I( cop
* rt'eo' >r.,-~ ~ 0IA soised top of formatc,,
DETAIL A ;;tsj , oro' opce ~e'lP . 011 0*0 1 'LtPi
Groot cop
- G(,oot holes
FOUNDATION KEY TRENCH
V ~ V 71 " *> ~ '-1 664 34?
OofJ ,~~rout cop asa fcondot,an key trench
A- ef r.i~freoIV' row of grout holes*~~~t -. * I\, - f ta0 row 0o' grout hole's
* -- .e
0 3
M rntor 531 Sood -~ t 19 .. 0?rNdrb '4
LI~~t 330-00,4.2
R~~STOF DAM -~~~~~~~-- .- MJ ows onfi grot holestoowstamo.erno othls
Blanket
grout holes as direc ted
Zil n90 1b( ,m0 ao tec A f Aolloty outlet works access shoft
Assumed bottom of basalt ~ --- :- :formation f A,,jottr Ot let wotks
solo 000 TAY 10-S
f oornstreom to. of gtout holesOof thyol~te fo 0o~
~f PBPrfef fo damt EDEAAIEL DEALembankmentn founoaoion etO1CLG* N tPA
V- ,ma, s d~ecte Ji 9# g! FO S P3901
CONCRETE GR~ouT CAPPLT 3
PL-T 18
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A-20 PLATE
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A2 PLATE.12A-27 PLATE 12
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A-28 PLATE. 13
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A-29
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A-30 PLATE 15
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4-3 PLATE 163SQaHj :uaiu
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A-32 PAE1
APPENDIX B
Guidelines for Analyzing a Dam Break Flood with the Computer Program"Gradually Varied Unsteady Flow Profiles"
1. Data Requirements
a. Topographic maps are required. The area of coverage should extendfrom the upper end of the reservoir in question to the most downstream pointof interest. The contour interval should be less than the level of accuracyexpected from the study.
b. Aerial or round photographs are desirable. These provide hydraulicengineers with a basis for estimating hydraulic roughness coefficients.Consequently, they are not needed for the reservoir area but for the channeland flood plain.
c. Reservoir capacity curves or tables are required and may becalculated from the topographic maps. These show the volume of water storedas reservoir depth increases.
d. Breach size and shape is required and may be estimated.
e. Reservoir level at breaching is required and may be estimated fromaerial photography if reservoir records are not available.
2. AssumDtions.
a. It is customary to assume that the breach is developed instantlyand completely to the desired size and shape. Otherwise, several instantaneousbreaches of different sizes may be postulated and the resulting floodscalculated.
b. Critical depth controls at all partial breaches. In view of thevalues presented in Table 2, main body of this report, inertia is not amajor consideration over a wide ranne of partial breach sizes.
c. The streambed and banks are fixed (i.e., do not erode) durlnqthe event.
d. Any bridge across the stream fails instantly upon impact of theflood wave. The resultinq enerqy loss is neqliqible.
p-
3. General Procedure. The general procedure depends somewhat upon thetype of breach postulated. That is, if the entire structure is removed,the final step of the analysis will calculate the outflow hydroqraph fromthe reservoir plus route that outflow hydrograph to all downstream pointsof interest in a single operation.
If only a partial breach is postulated, the outflow hydronraph is calculatedfirst and the routing to domnstream points is accomplished in a separateoperation. The same analytic technique is used for both.
The obvious advantage of the first approach is a savings in the timerequired for performing the analysis. A morp significant advantage isthat the method includes any submergence effects due to the rise intailwater elevation at the dam. This submergence effect can he suffi-ciently large to change the shape of the outflow hydroqraph from thereservoir.
Oartial breaches cannot be analyzed using the first approach because theexisting computer program '.ill not accommodate a hydraulic jump. On theother hand, the rise in tailwater elevation is usually small enough sothat no submergence effect develops. Therefore, the second anoroach isadequate.
4. Calculation of Outflow Hydrograph llsing the Partial Rreach Approach.The details which follow present the partial breach approach. The firststep in the calculation will determine the outflow hydroqraph, paragraphsa-f. Routing the flood hydrograph to downstream points is presented inparagraph 8.
a. Calibration of rfross Sectional Data to Reservoir Volume. Locatecross sections on the topographic map so reservoir volume may be calculatedusing the average end area technique. Include all major tributary arms inthe reservoir. Code this data for the computer program "Geometric Elementsfrom Cross Section Co-ordinates" (GEDA) and calculate the reservoir volumefor the range of elevations up to full pool. This result should agree withthe reservoir capacity curve. If it differs, ( + 5'), cross sections whichare more representative should be developed. Usually, this means recodingsome of the tributary arms.
h. Geometric flodel for Reservoir. Select a distance between computationnodes that comolies with criteria in the routing program, "Oradually VariedUnsteady Flow Profiles" (IISTrLn). Values typically ranqe between t-mile(409 m) and S miles (15,000 m). Execute GEDA to produce the required tablesof geometric properties and n-values at each computation node. The mostdownstream section should be at the dam axis and include the breach thatwas postulated.
B-?
c. Downstream Roundary. Calculate a critical depth ratinn curvefor the breach size and shae postulated. Fach elevation selected ,4illestablish an area and top width for use in the followinq equation.
0cr =cr
whe re:Acr cross sec-tional area, square feet
Dcr A cr/RcrRcr= too widti, feet
n acceleraion of qravitv feet/second/second
d. Initial Conditions. Establish the initial water surface elpvationand discharge at each computation node in the reservoir. It is exoedient toalways select a hor'znntal water surface and zero discharqe. lthouqh, onemay postulate whatever conditions he desires hv startinq the comouter modelit the above conditions and simulatina inflow/outflow records u to the timewhen breaching is anticinated.
e. Upstream Poundary. Isually, the initial reservoir inflow isassuned to be zero. It may he other.jise if so desired. In either case,code thp inflow hydrograph as descrihd in the 1ISTFLO users manual.
f. Calculatirg the Outflow Hvdrograph. Select an interval betweenprintouts that is very short (a minute or less) durinn the early part ofthe hydroqraph (5 minutes or so). 'isually, the calculated peak will occurdurinq this interval and the time hPtieen printouts may he increased to l0or 15 minutes. In any case, oh,,tair i sufficient amount of orintnut todefine the entire outflow hydrooranh shape.
r Routinu the ran Rrpak Flood
,1. 1en-Mtric lcdol for routin.i 9)ownstroam. Locate cross sections tothe downstream points of interest us-in- inforriation oained from the reservnirW,.oel and followinq s t eps in the users manual . selec the distance between-.on-utation nodes. (This distance dos not have to he the sare as that usedin the reservoir when rnutinf with a two step process. However, use thesane genpral (iuidelines.) Code tho data and execute Ur,[A to produce the re-quired qeotetric data tahles.
B-3
b. Downstream Boundary. If possible, set the downstream boundarya couple of nodes beyond the noint of interest. Calculate a ratinq curveby slope-area or by extrapolating from observed values.
c. Upstream Boundary. The outflowv hydrograph calculated in paragraph4 hecome.s the upstream boundary for this step.
d. Initial Conditions. Establish initial conditions hy calculatinga base flow profile. (Zero or negative depth is not an acceptable initialcondition. ) It is expedient to prescribe a hank full water discharge, tolet the computer model stabilize by simulatinq the steady flow profile forthat discharge and finally to decrease the inflow, nradually, until thedesired base flow discharge is reached. Simulate the base flow conditionsfor a sufficiently lonq period of time to establish a steady flow profile.Code this profile (water surface elevation, discharge) to form the initialconditions for routing the dam break flood.
e. noutina the Flood. The computer )roqram referenced in suhparanraphlc produces both a discharge hydroqraph and a %,"ater surface elevation hydro-graph at every computation noda. A summary table gives maximum and minimumvalues for elevation, discharq, and vlocity.
P-4
List of Research Notes
1. Research Note No. 1. A Cumulus Convection Model Applied to ThunderstormRainfall in Arid Regions by D. L' Morgan, The Hydrologic EngineeringCenter, Davis, California, December 1970.
2. Research Note No. 2. An Investigation of the Determinants of ReservoirRecreation Use and Demand: The Effect of Water Surface Elevation byWilliam D. Carson, Jr., The Hydrologic Engineering Center, Davis,California, November 1972.
3. Research Note No. 4. An Assessment of Remote Sensing Applications inHydrologic Engineering by Robert H. Burgy and V. Ralph Algazi, TheHydrologic Engineering Center, Davis, California, September 1974.
4. Research Note No. 5. Guidelines for Calculating and Routing a Dam-Break Flood by David L. Gundlach and William A. Thomas, The HydrologicEngineering Center, Davis, California, January 1977.