FLOW THROUGH A BREACHED DAM

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• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 81
• Document Creation Date: December 27, 2016
• Document Release Date: October 25, 2013
• Sequence Number: 2
• Publication Date: June 1, 1957
• Content Type: REPORT

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FLOW THROUGH A BREACHED DAM
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MILITARY HYDROLOGY BULLETIN 9
JUNE 1957
A
CORPS OF ENGINEERS
RESEARCH AND DEVELOPMENT REPORT
PREPARED UNDER DIRECTION OF
CHIEF OF ENGINEERS
BY
MILITARY HYDROLOGY R & D BRANCH
U. S. ARMY ENGINEER DISTRICT, WASHINGTON
STAT
STAT
STAT
1
?-?
201548
?
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Military Hydrology R&D Branch, U. S. Army Engineer
District, Washington, D.C.
FLOW THROUGH A BREACHED DAM.
June 1957,51 pp.
(Military Hydrology Bulletin 9)
DA R&D Project 8-97-10-003
Unclassified Report
This bulletin gives method of computation of the
outflow hydrograph from a dam under the following
conditions of breaching: (1) Relatively small
breaches of various shapes and (2) relatively
large breaches with rectangular shape in which
frictional resistance of flow through reservoir
becomes an important factor.
UNCLASSIPIRD
1. Hydrology
2. Dam breach hydrographs
I. U.S. Army Engineer
District Washington,
Military Hydrology
Bulletin 9
Military Hydrology R&D Branch, U. S. Army Ingimeor
District, Washington, D. C.
FLOW THROUGH A BREACHED 'DAM.
June 1957, 51 pp.
(Military Hydrology Bulletin 9)
DA R&D Project 8-97-10-003
Unclassified Report
UNCLASSIYIND
1. Hydrology
2. Dem breach hydrographs
I. U. S. Army Ingiseer
District Washington,
Military Hydrology
Bulletin 9
This bulletin gives method of computation of the
outflow hydrograph from a dam under the following
conditions of breaching: (1) Relatively small
breaches of various shapes and (2) relatively
large breaches with rectangular shape in which
frictional resistance of flow through reservoir
becomes an important factor.
Military Hydrology R&D Branch, U. S. Army Engineer
District, Washington, D. C.
FLOW THROUGH A INIACHED DAM.
June 1957, 51 pp.
(Military Hydrology Bulletin 9)
DA R&D Project 8-97-10-003
Unclassified Report
This bulletin gives method of computation of the
outflow hydrograph from a dam under the following
conditions of breaching: (1) Relatively small
breaches of various shapes and (2) relatively
large breaches with rectangular shape in which
frictional resistance of flow through reservoir
becomes an important factor.
UNCLASSIFIED
1. Hydrology
2s Dam breach hydrographs
I. U. S. Army Engineer
District Washington,
Military Hydrology
Bulletin 9
Military Hydrology R&D Branch, U. S. Army Engineer
District, Washington, D. C.
FLOW THROUGH A BREACHED DAM.
June 1957, 51 PP.
(Military Hydrology Bulletin 9)
DA R&D Project 8-97-10-003
Unclassified Report
UNCLASSIFIED
1. Hydrology
2. Dam breach hydrographs
I. U. S. Army Engineer
District Washington,
Military Hydrology
Bulletin 9
This bulletin gives method of computation of the
outflow hydrograph from a dam under the following
conditions of breaching: (1) Relatively small
breaches of various shapes and (2) relatively
large breaches with rectangular shape in which
frictional resistance of flow through reservoir
becomes an important factor.
-
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Military Hydrology R&D Branch, U. S. Army Engineer
UNCLASSIFIED
Military Hydrology R&D Branch, U. S. Army Engineer
UNCLASSIFIED
District, Washington, D.C.
1.
Hydrology
District, Washington, D: C.
1.
Hydrology
FLOW THROUGH A BREACHED DAM.
2.
Dam breach hydrographs
FLOW THROUGH A BREACHED DAM.
2.
Dam breach hydrographs
June 1957,51 pp.
June 1957, 51 pp.
(Military Hydrology Bulletin 9)
I.
U.S. Army Engineer
(Military Hydrology Bulletin 9)
I.
U. S. Army Engineer
DA R&D Project 8-97-10-003
District Washington,
Military Hydrology
DA R&D Project 8-97-10-003
District Washington,
Military Hydrology
Unclassified Report
Bulletin 9
Unclassified Report
Bulletin 9
This bulletin gives method of computation of the
outflow hydrograph from a dam under the following
conditions of breaching: (1) Relatively small
breaches of various shapes and (2) relatively
large breaches with rectangular shape in which
frictional resistance of flow through reservoir
becomes an important factor.
Military Hydrology R&D Branch, U. S. Army Engineer
District, Washington, D. C.
FLOW THROUGH A BREACHED DAM.
June 1957, 51 pp.
(Military Hydrology Bulletin 9)
DA R&D Project 8-97-10-003
Unclassified Report
This bulletin gives method of computation of the
outflow hydrograph from a dam under the following
conditions of breaching: (1) Relatively small
breaches of various shapes and (2) relatively
large breaches with rectangular shape in which
frictional resistance of flow through reservoir
becomes an important factor.
UNCLASSIFIED
1. Hydrology
21 Dam breach hydrographs
I. U. S. Army Engineer
District Washington,
Military Hydrology
Bulletin 9
This bulletin gives method of computation of the
outflow hydrograph from a dam under the following
conditions of breaching: (1) Relatively small
breaches of various shapes and (2) relatively
large breaches with rectangular shape in which
frictional resistance of flow through reservoir
becomes an important factor.
Military Hydrology R&D Branch, U. S. Army Engineer
District, Washington, D. C.
FLOW THROUGH A BREACHED DAM.
June 1957, 51 pp.
(Military Hydrology Bulletin 9)
DA R&D Project 8-97-10-003
Unclassified Report
This bulletin gives method of computation of the
outflow hydrograph from a dam under the following
conditions of breaching: (1) Relatively small
breaches of various shapes and (2) relatively
large breaches with rectangular shape in which
frictional resistance of flow through reservoir
becomes an important factor.
UNCLASSIFIED
1. Hydrology
2. Dam breach hydrographs
I. U. S. Army Engineer
District Washington,
Military Hydrology
Bulletin 9
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MILITARY HYDROLOGY BULLETIN 9
FIAW THROUGH A BREAC,:TED 1)A1
PREPARED IN CONNECTION WITH
RESEARCH AND DEVELOPMENT PROJECT NO. 8-97-10-003
FOR
ENGINEER RESEARCH & DEVELOPMENT DIVISION
OFFICE, CHIEF OF ENGINEERS
MILITARY HYDROLOGY R&D BRANCH
U.S. ANY ENGINEER DISTRICT, WASHINGTON
CORPS OF ENGINEERS
JUNE 1957
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1
PREFACE
This Bulletin is the ninth of a series of papers dealing with the
various aspects of hydrology involved in military operations and with the
hydrologic techniques and methods of analysis which are considered most
suitable for army use. A number of these techniques were developed in the
course of Research and Development Project No. 8-97-10-003, assigned to
the Army Engineer District, Washington, on 14 March, 1951 by the Office,
Chief of Engineers. Printing of this bulletin was authorized by the Office,
Chief of Engineers on 9 May 1957.
Mr. A. L. Cochran of the Office, Chief of Engineers, formulated
the objectives and scope of this bulletin. Messrs. W. B. Craig and
H. E. Ernst of the Military Hydrology Branch, Washington District, assembled
the material and prepared the text of the Bulletin, under the supervision
of Mr. R. L. Irwin.
iii
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PREFACE
SUMMARY
Paragraph
CONTENTS
Page
iii
vii
CHAPTER I: INTRODUCTION
1 Purpose and Scope
2 Discussion of Problem,........
3 Abbreviations and Nomenclature
4 Related References
CHAPTER II: SMALL BREACHES
1
1
2
3
5 Fundamental Considerations
5
6 Assumptions
5
7 Breach Shape
5
8 Breach Discharge - Weir
5
9 Breach Discharge - Orifice
7
10 Reservoir Storage
7
11 Breach Discharge Hydrograph-Weirs
8
12 Breach Discharge Hydrograph - Orifice
9
13 Sample Computations
9
14 Conclusions
17
CHAPTER III: LARGE BREACHES
15 Fundamental Considerations
19
16 Reservoirs
19
1
17 Effective Width
20
18 Average Reservoir Bottom Slope
20
19 Roughness Coefficient
20
20 Dam Completely Removed
20
21 Half Depth-Full Width Breach
21
22 Full Depth-Partial Width Breach
22
23 Basis of Computations
23
Routing Procedures
23
25 Outflow Hydrographs
25
26 Method of Computation
26
27 Sample Computations
27
28 Units
29
29 Summary and Conclusions
29
LIST OF SYMBOLS
30
REFERENCES
32
TAW OF EQUIVALENT ENGLISH-METRIC UNITS
35
LIST OF PLATES
37
APPENDIX
39
APPENDIX PLATES
51
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SUMMARY
The failure or demolition of high dams, impounding large volumes
of water, may release large flood waves capable of seriously damaging
downstream military or civilian installations or disrupting river
crossings or other military operations. The outflow through a breached
dam is influenced by the dimensions of the breach, the volume and shape
of the reservoir, the inflow into the reservoir, the tailwater condi-
tions, and other variables. The theoretical and experimental equations
are very complex and are too cumbersome for military use. Simplified
solutions for determining the flow through a breach were developed in
this bulletin to permit fairly rapid prediction of the breach outflow
with a degree of accuracy acceptable for military situations. Com-
putation procedures were developed both for relatively small breaches
(where the opening itself is the controlling factor) and for relatively
large breaches (where frictional resistance to flow through the reser-
voir becomes a critical factor).
vii
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Par. 1
CHAPTER I
INTRODUCTION
1. Purpose and Scope. a. The amount of damage resulting from a
major flood wave is proportional to the height, duration, and speed of
propagation of the wave. These factors vary with the river channel
characteristics and rate of flow from a breached dam. An estimate of
the situation requires then, among other factors, a reliable estimate
of the rate of flow that can be expected from a breached dam under
various possible circumstances; therefore, this manual was prepared to
provide methods whereby the rate of flow from a breached dam can be
readily estimated with a degree of accuracy that is adequate for mili-
tary plans and operations.
b. The methods presented herein require a minimum of basic data
and the solutions are presented in a dimensionless graphical form when-
ever practicable.
c. The breaches are classified according to size as follows:
(1) Small breach openings; those less than one-sixth the
area of the average reservoir cross-sectional area, and which may be
created by use of conventional weapons.
(2) Large breach openings; those more than one-sixth the
area of the average reservoir cross-sectional area, and which may be
created by use of nuclear weapons.
2. Discussion of Problems. a. Many of the rivers of the world
have been developed for hydro-electric power, flood control, irriga-
tion, navigation, and other purposes. High dams, impounding large vol-
umes of water, have been constructed in connection with many of these
developments. The failure or deliberate demolition of high dams, such
that large quantities of water are suddenly released, may create major
flood waves capable of causing disastrous damage to downstream military
and civilian installations. Major flood waves may seriously damage or
destroy power plants, industrial plants, and bridges, and disrupt ir-
rigation and navigation. These damages, accompanied by loss of life,
could constitute a national disaster and adversely affect a nation's
economy and war effort. Military operations against dams in the in-
terior zones could be carried out by either aerial attack or sabotage.
River crossing operations in the combat zone may be prevented or de-
layed by a major flood wave created by the breaching of a dam. The mere
existence of a large dam in the headwaters, under the control of the
opposing force, could act as a deterrent to a river crossing operation.
b. The hydraulic characteristics of a surge released from a
breached dam are a function of the size, shape, and position of the
breach; the volume of the water stored behind the dam; the height,
width, and length ratios of the reservoir; and the reservoir inflow
and tailwater conditions at the time of breaching. The partial dif-
ferential equations expressing the laws of unsteady flow for these var-
iables are very complex; and at the present time a general solution of
practical value has not been developed.
c. The advent of the atomic era with its thermonuclear weapons
has introduced a new concept of military capabilities with respect to
military hydrology. Establishment of a basic policy for the use of
1
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Par. lc
atomic weapons in any major war, and the concurrent developments of
various types and sizes of atomic weapons, have required a revaluation
of the methods of computing the effects of dam breaching operations.
d. The surge from a dam that has been partially or completely
removed from a reservoir presents phenomena of which little is known,.
The shape of the reservoir water surface profiles, and their change in
shape with respect to time have not been definitely determined. The
hydraulics of unsteady, open-channel flow requires an idealized flow
picture to give equations that can be integrated by the method of
characteristics. The procedure, using the method of characteristics,
is laborious and a number of authorities on hydraulics have raised
questions to its accuracy. Military hydrology units would probably
require the use of a "Univac" or some similar electronic computer to
solve the above problem in the field within the permissible time for
appraisal. Since it is not practical to provide electronic equipment
at this time, some method should be devised that would be simple and
yet give answers that are adequate for field conditions.
e. Several theoretical and experimental studies have been made
in the past pertaining to sudden releases of impounded water in spe-
cial situations and under idealized conditions. The discharge and
general profiles of a surge have been theoretically determined by
St. Venant (Ref. 36) and experimentally checked by Schoklitsch for a
long horizontal channel of rectangular cross section (Ref. 33); how-
ever, since the results of these experiments could not be directly
applied to the problem of dam-breaching, this bulletin attempts to
analyze the different theories and develop a simple procedure to de-
termine the breach outflow hydrograph.
f. A comparison of discharge values obtained from the St.
Venant equation as modified by Schoklitsch, for openings of partial
width extending to full depth, with those from flat pool reservoir
routing which employs the formulas for steady flow over weirs, indicates
that the latter departs from peak discharge values based upon the re-
sults obtained by Schoklitschts model studies when the ratio of width
of reservoir (B) to the width of the opening (b) becomes less than 11.4.
However, since by Schoklitsch the divergence in peak discharges is a
function of the one-fourth power of the ratio B/b, the maximum devia-
tion in discharge by the method of flat pool routing for a rectangular
reservoir cross section of uniform width will be less than twenty per-
cent from the more exact methods when Bib is greater than 6. This dis-
crepancy in peak discharge is considered within the probable limits of
accuracy of basic data which will be employed in the solution of a
problem. This parameter, therefore, is used for the classification of
breaches as "small" or "large" presented in paragraph lc and discussed
in Chapters II and III, respectively.
3. Abbreviations and Nomenclature. a. The following abbreviations
are used in the bulletin:
cfs
ft
ft2
ft3
hr
cubic feet per second
feet
square feet
cubic feet
hour
2
km
km2
In
m3
m3/sec
ms1
kilometers
square kilometurs
meters
cubic meters
cubic meters per second
mean sea level
Par. 3a
b. A tabulation of the symbols used in the formulas appears on
pages 30 and 31. Those symbols which are from quoted material have
been modified to conform to this list. A definition sketch of small
breaches is included as Plate'No. 1.
c. Conversion factors for the English and Metric systems are
presented for convenience in tabular form on page 35.
4. Related References. All references cited in this manual and other
selected references to technical literature that pertain to the breaching
of dams are listed on pages 32 through 34 . Material that is classified
for security reasons has been omitted.
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11
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Par. 5
CHAPTER II
SALL BREACHES
5. Fundamental Considerations. a. For purpOes of this study, a
"small" breach opening is defined as one whose azea is less than one-
sixth that of the average reservoir cross-sectional area. For this con-
dition, the opening itself is the controlling fanor and flat-pool
reservoir routing methods employina the formulas for steady flow over
weirs will give acceptable results, as explained in paragraph 2f. In
this chapter, there are developed simplified methods which will permit
a rapid solution of the outflow from a small breach opening with a de-
gree of accurac3 acceptable for military situations.
b. The rate at which water is released from a reservoir through
a breached dam is graphically represented by a discharge hydrograph.
This breach discharge hydrograph shows the volume rate of flow during
successive time intervals beginning with the time of breaching. It is
constructed by plotting time as abscissa and discharge as ordinate. In
order to compute the breach hydrograph, it is necessary to determine
the breach discharge rating curve, as well as the capacity and certain
shape characteristics of the reservoir. Computation procedures are
presented in subsequent paragraphs of this chapter.
C. A detailed exposition of the derivation of the equations and
graphs presented in this chapter for determining the breach discharge,
reservoir storage, and breach hydrograph, is given in the Appendix.
6. Assumptions. a. There is either no inflow into the reservoir
or the inflow is small relative to the volume of storage in the reser-
voir.
b. Less than eighty percent of the flow depth through the
breach is submerged by tailwater due to channel conditions below the
dam. The amount of submergence is dependent on the relative sizes of
the breach and channel, the channel slope, and the position of the bot-
tom of the breach above the river bed. Tailwater conditions should be
investigated in all cases to determine whether or not the computation
procedures are applicable to a particular problem. If excessive sub-
mergence exists, conventional methods of reservoir routing should be used,
7. 18E22.21221.222. (see Plate 1) a. Weir type breach openings:
those that extend to the top of the dam. A regular shape breach of this
type approximates one of the following geometric patterns: parabola,
triangle, rectangle or a trapezoid. An irregular shape breach of this
type does not approximate one of the geometric patterns listed above.
b. Orifice type breach openings: those that result from
puncturing an opening through the structure below the top of the dam
(d is greater than 1.5D)
8. Breach Discharge, Weir. The top width, depth and shape cf the
breach and also the pool level must be given, or assumed in order to com-
pute the breach discharge.
a. The rectangular breach shape is further defined for use in
this bulletin by the shape coefficient which is deternined by the fol-
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W.?
V*
Par. 8a
lowing equation:
bt
Cr =
(1)
where bt is the breach width at the initial reservoir elevation and d is
the depth of breach from the initial reservoir elevation (see definition
sketch, Plate 1). The initial discharge (Qmax) is then computed by means
of the curves on Plates 2 and 3 on which maximum discharge values (Qmax)
are plotted as functions of shape coefficient values ranging from 0 to 5.
Plates 2 and 3 are for the English and Metric systems, respectively.
The discharge for any pool elevation less than the initial is computed by
means of the appropriate curve on Plate L. The ratio of the instan-
taneous discharge to the maximum discharge (Q/Qmax) is plotted as a
function of the ratio of the corresponding head of water on the breach
to the initial depth of water on the breach (h/d).
b. The triangular breach shape coefficient equation is
bt
Ct (2)
2d
The initial discharge (Qmax) at the initial reservoir elevation, and
the discharge (Q) for any pool elevation less than the initial are com-
puted by the same procedure as outlined for the rectangular breach.
c. The initial trapezoidal breach discharge (Qmax) is equal to
the sum of the discharges of the triangle and rectangle which are the
component parts of the trapezoid; however, for discharge (Q) for any
pool elevation less than the initial the parabolic carve on Plate 4 is used.
d. The parabolic breach shape coefficient equation is
Cn (3)
x- 1;2d
The initial discharge (Qm,,x.) at the initial reservoir elevation and the
discharge (Q) for any pooI-elevation less than the initial are computed
by the same procedure as outlined for the rectangular breach. The
curves on Plate 5 may be used to aid the plotting of a parabolic breach
profile. Values of the ratio of the X coordinate to the breach depth
d(x/d) are given for values of CD ranging from 0 to 5 with the ratio of
the y coordinate to breach depth- d(y/d) as parameter.
e. In the case of the irregular shaped breaches the initial dis-
charge is determined by application of the formula
Q2 = A3
bw
(4)
in the following manner:
Planimeter the cross sectional area of the breach below elevation 0.75d
and scale the water surface width bw at elevation 0.75d.
Then
where
h = 0.75d+
A
2bw
h = head of water on breach crest
6
(5)
Par. 8e
A = area of breach below elevation 0.75d
bw = water surface width at elevation 0.75d.
If h is not equal to d, then an adjusted discharge is obtained by use of
Plate L. Entering the curve for a parabola with the value of h/d, the
discharge ratio Q/Qmax is obtained. The assumed discharge Q divided
by this discharge ratio then equals the adjusted maximum discharge.
Successive trials are then made for each new discharge until the ratios
h/d and Q/Qmax approach unity. Two trials will usually be sufficient.
9. Breach Discharge-Orifice. Assuming or given the breach dimensions,
the cross-sectional area of the orifice is determined. Knowing the
cross-sectional area A and d (the depth of water from the initial reser-
voir surface elevation to the centroid of A), the curves on Plate 6 are
entered with the ratio A/d2 to obtain the maximum discharge. To deter-
mine the discharge for any depth h, other than maximum, the curve for the
orifice on Plate 4 is used.
10. Reservoir Storage. a. For purpose of this report, reservoir sto-
rage is represented by The equation
s = kylm (6)
where
Yi
storage at the corresponding depth yl
depth of reservoir at the dam
a constant
in
a constant
The initial reservoir storage S is then
S = kPm
(7)
where P = initial depth of reservoir at the dam.
It is necessary to evaluate SI P, and m in equation (7). The constant
k can be determined but it is not required. Methods of computing P
and m in decreasing order of given data are presented in the following
paragraphs?
b. Given: Two or Yore Points on Storage Curve and Initial
Reservoir Depth. Plot the given points on logarithmic paper with storage
as abscissa and reservoir depth as ordinate; then in equals the reciprocal
of the slope of the straight line drawn through the given points, and
the maximum storage equals that value corresponding to the maximum depth.
c. Given: Storage, Depth, and Reservoir Surface Area at
Initial Pool Elevation. The constant in is determined by the equation
-(8)
where A is the reservoir surface area. The storage curve is con-
structed by drawing a straight line through the point (P.S) plotted on
logarithmic paper (as in par. 10b) with a slope equal to the reciprocal of in.
7
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Par. 10d
d. Given: Topographic Maps, Initial Depth. Construct the sto-
rage curve by planhnetering areas for selected contours up to the initial
reservoir elevation. Multiply the average area between adjacent contours
by the contour interval and accumulate the products. Plot the accumulated
storage against the countour elevation. S and in are determined as dis-
cussed in paragraph b above. If the initial storage is given, then it
is only necessary to planimeter the area at the initial contour eleva-
tion and determine in according to equation (8).
e. Given: Initial Depth, Initial Storage, Terrain Characteris-
tics. The value of in for a reservoir of known terrain characteristics
is selected from the following table of empirical values:
Reservoir Type
Lake
Flood plain and foothill
Hill
Gorge
In
1.0 to 1.5
1.5 to 2.5
2.5 to 3.5
3.5 to 4.5
11. Breach Discharge Hydrograph-Weirs. a. The breach discharge
hydrograph for a parabolic, rectangular or triangular shaped breach
at initial pool elevation is constructed by means of Plates 7 to 10.
The time factor t/tk is shown as abscissa and 'al (ratio of depth of
water in reservoir below bottom of breach to depth of water below initial
reservoir elevation) is given as ordinate for values of discharge (Q/Qmax)
with in as parameter. For each value of Q/Qmax enter the curves with the
known laIl m, and breach shape and read the corresponding values of
(t/tk). The term tk is defined as follows:
tk = S
@max
Knowing the initial conditions,
corresponding Q then, is:
t S
tk Qmax
where
or
S =
Qmax=
S=
Qmax=
storage
maximum
storage
maximum
(9a)
S and Qmax, the time in seconds for the
in m3 and
discharge in m3/sec;
in ft3 and
discharge in cfs.
(9b)
(The discharge hydrograph curves are usually constructed so that the
time is expressed in hours.) The breach discharge hydrograph is then
plotted with t as abscissa and Q as ordinate.
b. The breach discharge hydrograph for a parabolic, rectangular,
or triangular shaped breach or for pool elevations less than initial is
constructed by means of Plate 4. The ratio Q/qmax for initial outflow
is determined for the corresponding value of h/d. Entering the appro-
priate hydrograph curves (Plates 7 to 10), the corresponding value of t
is determined. The origin of the coordinates of the breach hydrograph
8
Par. llb
is then moved t units to the right and the hydrograph determined as out-
lined in a, above.
c. A close approximation of the breach discharge hydrograph for
an irregular or a trapezoidal shaped breach at initial pool elevation
and at pool elevations less than initial can be determined
by substituting a parabolic shape breach of equivalent Q and d (as
outlined in paragraphs 8c to 8e, inclusive) and applying the methods for
determination of the discharge hydrograph outlined in paragraphs ha and
b above, using the curves for a parabolic breach.
12. Breach Discharge Hydrograph-Orifice. The breach hydrograph for
the orifice type of breach is obtained in the same manner as for the
weir type, using the curves on Plate 10. The discharge is obtained as
discussed in paragraph 9 and the storage is computed according to para-
graph 10.
13. Sample Computations. Four examples are presented in this sec-
tion and exhibited on Plate Nos. 11 to 15. The problems are repre-
sentative of the various initial conditions and given basic data that
might be available for the determination of the breach hydrographs.
The problems are discussed in the following order: an arch dam with
parabolic weir and orifice breaches, a gravity dam with a trapezoidal
breach, a buttress dam with a rectangular breach, and a breached dam
with flood inflow into the reservoir at the time of breaching. Solu-
tions of these problems follow:
a. Arch Dam: Parabolic Weir and Orifice Breaches (Plate No 11)
(1) Situation: It is known that the enemy is preparing
for an assault crossing of a certain river defended by our troops. The
river is of such width and depth that amphibious equipment will be re-
quired. At the headwaters of the river is a high power dam under our
control. It is planned to prevent the enemy crossing the river by des-
troying his floating bridge equipment by means of flood waves released
from the dam.
(2) Known Data: Construction drawings furnish the following
information on the dam and reservoir (see fig. 1, Plate No 11):
type of construction
crest length
maximum reservoir depth
width (crest)
width (base)
maximum pool elevation
minimum power pool
maximum storage
storage available for power
concrete arch
140 m
120 in
3.5 in
13.5 in
980 in above ms1
905 in above ms1
72.8(106) m3
70.0(106) m3
(3) Assumptions: It is assumed that the following breaches
in the dam could be created by demolition:
(a) Parabolic breach in top of dam having a top width
of 71 in and a depth of 25m.
(b) Circular orifice breach near bottom of dam having
a diameter of 30 in at elevation 920.
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Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/25: CIA-RDP81-01043R002300060002-4
Par. 13a
The reservoir is now at maximum elevation and it is estimated that if cy-
clic waves are first released through the regulation conduits the reser-
voir will be drawn down 10 in at the time of breaching.
(4) Required: The breach discharge hydrographs for:
(a) Parabolic breach with pool at elevations 980
(b) Orifice breach with pool at elevations 980
(5) Parabolic Breach Computations:
From equation (3)
(712 2.0
2 x 25)
and 970.
and 970.
C =
For Clo = 2, the following .coordinates of the breach profile are
from Plate No. 5:
'ILI 25(Y/d)
25(x/d)
1.0 1.42 25.0
35.5
.8 1.27 20.0
31.8
.6 1.09 15.0
27.2
.4 .89 10.0
22.2
.2 .63 5.0
15.8
Entering the curve for a parabola on Plate 3 with C
=
2,
then
By definition,
Qmax =2.7
d2?5
Qmax . 2.7( 25)2.5 .
a . 120 - 25 = 0.79
120
8500 m3/sec
obtained
The constant in is computed as follows: the storage curve is plotted,
(Plate 11), from the 2 points given,
total storage (S) = 72.8(10)L6 at elev. 980
power storage 70.0(10)'
then
storage = 2.8(10)6 at elev. 905
. 7.1" . 3.4
2.1"
The following coordinates of the breach hydrograph (fig. 2) are obtained
by entering the curves on Plates 7a and 7b with !al equal to 0.79 and in
equal to 3.4, where according to equation (9a)
10
^.
Par. 13a
8500
tk _ 72,8(10)6 . 8.57(10)3
PARABOLIC BREACH DISCHARGE HYDROGRAPHS
Q
_1(10)-5
tk
Pool Elev. 980
Pool Elev. 970
t
hours
,)Q
m-5/sec
t
hours
,Q
m-5/sec
Q max
1.00
0.0
0.00
85oo
.80
2.3
0.20
6800
.60
5.4
0.46
5100
.40
10.2
0.87
3400
.36
-
1.00
3060
0.0
3060
.30
14.2
1.22
2550
0.22
2550
.20
20.2
1.73
1700
0.73
1700
.15
25.8
2.21
1275
1.21
1275
.10
33.8
2.90
850
1.90
850
4
The discharge hydrograph for the condition where the reservoir surface is
at elevation 970 at the time of breaching is obtained as follows:
entering the curve for a parabola on Plate No. 4 with
h = 15 = 0.60
-23
= 0.36 is obtained, and the new maximum
Qmax
discharge equals 0.36 x 8500 = 3060 m3/sec
Inspection of the hydrograph for the parabolic breach at pool elevation
980 (fig. 2) shows that a discharge of 3060 m3/sec occurs at time 1.0
hours (nearest 0.1 hr). The origin of the hydrograph, therefore, is
moved 1.0 hour to the right.
(6) Orifice Breach Computations: The cross-sectional area
of the breach is
A =m( l5)2 = 707 m2
and the maximum head of water on the breach is
d = 980 - 920 = 60m
11
11
j
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r.
Par. 13a
then
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A 707
-2 = 77677 m
0.196
d 0)
Entering the curve for metric units on Plate No. 6, with
then
By definition,
A/d2
Qmax
= 0.196
= 0:52
= 0.52(60)2?5 = 14,500 1u3/sec
a z . 0.50
P 120
Values of the breach hydrograph (tabulated below and plotted on fig. 2
Plate 11) are obtained by entering the curves on Plates 10a and 10b with
fat equal to 0.50 and in equal to 3.4,
tk . 72.8(10)6
14500
where
- 5.01(10)3
ORIFICE BREACH DISCHARGE HYDROGRAPHS
Q
TII(10)-5
ic
,
Pool Elev. 980
Pool Elev. 970
t
hours
,Q
m)/sec
t
hours
Q
m3/sec
Qmax
1.00
0.0
0.00
14,500
.91
0.40
13,200
0.00
13,200
.80
14.8
0.74
11,600
0.34
11,600
.60
24.2
1.21
8,700
0.81
8,700:-.1,
.40
3o.4
1.52
5,800
1.12
5,800
.30
32.8
1.64
4,350
1.24
4,35o
.20
34.6
1.73
2,900
1.33
2,900
.15
35.7
1.79
2,180
1.39
2,180
.10
36.5
1.83
1,450
1.43
11450
When the pool is at elevation 970 at time of breaching
and
38 970 - 920 = Son
-0.83
60
Entering the curve for the orifice on Plate No. 4 with h/d equal to 0.83,
.2 . 0.91 is obtained, and the new
Qmax
12
maximum discharge equals
0.91 x 14,500 = 13,200 m3/sec
Inspection of the breach hydrograph for the orifice when the reservoir is
at elevation 980 (fig. 2) shows that the discharge of 13,200 m3/sec occurs
at time 0.40 hours. The origin of the coordinates therefore is moved 0.40
hours to the right.
b. Gravity Dam: Trapezoidal Weir Breach (Plate No. 12)
(1) Situation: A large reservoir located in the enemy's zone
of interior is an important source of water for the heavy industries lo-
cated in the valley downstream. In addition to supplying water for indus-
trial use, the dam generates power, benefits navigation, and controls
floods. The loss of this strategic source of water by destruction of the
dam would seriously cripple the enemy's war effort. It is desired to
evaluate the effects of the flood wave released by breaching the dam, upon
industrial plants and military airfields situated in the flood plain be-
low the dam.
(2) Given Data: The dam is a rubble masonry gravity struc-
ture, 400 in long with a maximum reservoir depth of 38m (see fig, 1
Plate No. 12). The reservoir has a maximum capacity of 200(10)0 m3 and
the storage curve is given in fig. 3.
(3) Assumptions: It is assumed that the dam can be breached
by aerial attack or by sabotage. The breach is trapezoidal in shape and
has a top width of 65 in, a bottom width of 20 m and a depth of 20 m be-
low maximum pool elevation. It is planned to breach the dam when the
reservoir is filled; however, the reservoir may be drawn down 5 in below
maximum elevation at the time of attack.
(4) Required: The breach discharge hydrographs when the
reservoir is at elevations 245 and 240 in above msl at the time of
breaching.
(5) Computations:
Separate the trapezoidal breach into its component parts; a triangle
(45x20m) and rectangle (20x20m); then according to equations (1) and (2);
Par. 13a
and
Ct
Cr
=
45
=
1.13
o.50
2 x 20
20
2 x 20
Ehtering the curves on Plate 3 with 1.13 and Cr = 0.50, then for the tri-
angle;
Qmax
1
d2.5
Qmax =
and for the rectangle:
Qmax_
d2?5
0)4
1.4(20)2.5 = 2500 m3/sec
1.7
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13
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/25: CIA-RDP81-01043R002300060002-4
13b
and
Qmax
then for the trapezoid;
Qmax '
1.7(20)2?S = 3050 m3/sec
2500 + 3050 = 5550 m3/sec
The constant in equals the reciprocal of the slope of the storage curve
plotted on logarithmic paper (fig. 3),
.61
in 2.0
311
by definition, a
38 - 20 . 0.47
38
Values of the breach hydrograph, tabulated below
are obtained by entering the curves on Plates 7a
with 'a' equal to 0.47 and in equal to 2.0, where
200(10)6
tk ' 3.6(10)4
5550
and plotted on fig. 2,
and 7h (parabolic breach)
according to equation (9a)
TRAPEZOIDAL BREACH DISCHARGE HYDROGRAPHS
Q.t
7 (l0)5:
-uk :
:
Pool Elev, 245
Pool Elev. 240
Qmax
t
hours
Q
m3/sec
t
hours
' Q
m3/sec
1.00
0.0
0.0
5550
.80
3.4
1.2
4Y10
.60
8.0
2.9
3330
.58
-
3.0
3200
0.0
3200
.40
15.0
5.4
2220
2.4
2220
.30
20.5
7.4
166o
4.4
1660
.20
29.5
10.6
1110
7.6
1110
.15
37.0
13.3
830
10.3
830
.10
48.0
17.3
560
14.3
560
The discharge hydrograph for the condition where the pool is 5 m below
the maximum elevation at time of breaching, is obtained as follows:
Entering the curves on Plate 4 with h/d equal to 15/20, then for the
triangle;
and
Q =0.49
Qmax
Q = 0.49(2500) = 1200 m3/sec
and for the rectangle;
and
Q = 0.65
Qmax
Q = 0.65(3050 - 2000 m3/sec
114
Par. 13b
then the new maximum discharge of the trapezoid is
Q = 1200 + 2000 = 3200 m3/sec
Inspection of the hydrograph for the trapezoidal breach at pool elevation
245 (fig. 2, Plate 12) shows that the discharge of 3200 m3/sec occurs at
time 3.0 hours. The origin of the coordinates therefore is moved 3.0 hours
to the right. Values of the hydrograph for pool elevation 240 at the time
of breaching are tabulated above and plotted on fig. 2, Plate 12.
c. Buttress Dam: Rectangular Weir Breach (Plate No. 13)
(1) Situation: An "Ambursen" type of buttress dam producing
hydroelectric power is vulnerable to enemy attack. In the event the dam
is breached, hydroelectric power not only will be lost, but important
military bridging downstream will be endangered.
(2) klown Data: The following information is known (fig. 1,
Plate 13);
type of construction slab and buttress
crest length 900 ft
maximum reservoir depth 100 ft
buttresses 18 ft on centers
normal operating pool 8110 ft above msl
normal operating capacity 50,000 acre-ft
normal reservoir surface area 1,500 acres
(3) Assumptions: A rectangular breach 50 ft below normal
operation and 140 ft long is assumed by the destruction of eight slabs
and seven buttresses down to elevation 790. At the time of attack the
reservoir may be at any elevation between 817 ft above msl and the nor-
mal elevation 840 ft above msl.
(4) Required: The breach discharge hydrographs for eleva-
tions of 840 and 817.
(5) Computations: According to equation (1)
cr 140 =1.140
2 x 50
Entering the curve on Plate 2 with Cr = 1.40
Qmax = 8.7
d2.5
Qmax = 8.7(50)2.5 =
and 153,800 cfs
According to equation (8)
100 x 1500
in == 3.0
50,000
By definition,a - = 100 5? = 0.50
100
Values of the breach hydrograph, tabulated below and plotted in fig. 2,
are obtained by entering the curves on Plates 8a and 8b (rectangular
breach) with lat equal to 0.50 and in = 3.0, where according to equation (9a)
15
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Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/25: CIA-RDP81-01043R002300060002-4
f
Par. 13c
tk
= 5(10)4 4.36(10)4 . 1.42(10)4
1.538(10)5
RECTANGULAR BREACH DISCHARGE H/DROGRAPHS
Q
_
t -5
ilic
Pool Elev, 840
Pool Elev 817
Qmax
t
hours
Q
cfs
t
hours
Q
lfs
1.00
0.0.
0.00
153,800
.80
5.9
0.84 '
123,000
.60
13.0
1.85
92,300
.40
22.2
3.16
61,5oo
o.00
61,500
.30
28.8
4.09
46,200
0.93
46,200
.20
37.5
5.32
30,800
2.16
301800
.15
44.8
6.35
23,100
3.19
23,100
.10
52.5
7.46
15,400
4.30
15,400
The discharge hydrograph for the condition when initially the reservoir is
23 ft below normal is obtained as follows:
Enter1 rig the curve for a rectangle on Plate No. 4
with
h . 27 . 0.54
d 50
0.140 is obtained and the new maximum discharge is
Qmax
0.40 x 153,800 . 61,500 cfs
Inspection of the above tabulation when the reservoir is at elevation 840
at the time of breaching indicates that the discharge 61,500 cfs occurs
at 3.16 hours. The origin of the coordinates of the hydrograph are there-
fore moved 3.16 hours to the right.
d. Reservoir Inflow: Conventional Routing (Plate Nos. 14, 15)
(1) Situation: The reservoir of the arch dam (see par. 13b
and Plate 11) is at spillway level, discharging 20 m3/sec. It is pro-
posed that another dam, situated upstream from the arch dam be breached in
order that the resulting flood wave will bring the reservoir of the arch
dam to the maximum elevation before breaching.
(2) Initial Conditions: The following information is known
in addition to the data given in par. 13b(2). The spillway is a gated
structure discharging into a side-channel and then into a tunnel driven
through rock around the right abutment. The spillway crest is at eleva-
tion 974 and is discharging 20 m3/s. It is assumed that all the spillway
gates are open and can not be closed. The spillway rating curve is ahowil
in figure 1, Plate No. 14. The parabolic breach (fig. 1, Plate No. 11)
is assumed at the time the reservoir reaches the maximum elevation. The
breach discharge hydrograph from the dam upstream has been routed down
16
^
Par. 13d
to the reservoir of the arch dam by the methods described in M. H. Bulletin
No. 10 and is shown as the inflow hydrograph in figure 2, Plate No. 14.
(3) Required: The time of breaching of the arch dam to pro-
duce the highest stages downstream and the breach discharge hydrograph.
(4) each Rating Curve Computations: The maximum discharge
for the parabolic breach was computed in paragraph 13b(4) and is equal to
8500 m3/sec when the reservoir water surface is at elevation 980 in.
Assuming various reservoir elevations, the parabolic curve on Plate No. 4
is entered with the various h/d values to obtain Q/Qmax. The values of Q,
thus obtained, are tabulated below and plotted as the breach discharge
curve in figure 1, Plate No. 14.
BREACH RATING CURVE
Res. Elev.
m above ms1
h
m
h/d
Q/Qmax
m3/sQ
980
25
1.00
1.00
8500
978
23
.92
.85
7220
976
21
.84
.705
6000
974
19
.76
.57
4850
972
17
.68
.46
3910
970
15
.60
.36
3060
968
13
.52
.27
2290
966
11
.44
.195
166o
964
9
.36
.13
1100
962
7
.28
.08
68o
960
5
.20
.04
340
955
o
.00
.00
o
(5) Storage Curve Computations: The reservoir storage
plotted logarithmically in figure 3, Plate No. 11 is replotted on
Cartesian coordinates in figure 1, Plate No. 14.
(6) Outflow Hydrograph Computations: The discharge hydrograph
is obtained by the conventional level pool reservoir routing method which
is based upon the premise that inflow volume minus outflow volume equals
the change in the volume of storage. The procedure and computations are
shown on Plate No, 15. The discharge hydrograph is shown as the outflow
curve in figure 2, Plate No. 14. Upon obtaining a reservoir elevation
979.7 the inflow becomes less than the outflow and the pool level starts
to fall. At that time (2.4 hours after inflow rate started to increase)
the arch dam was breached producing a flow of 8320 m3/sec through the
breach and 920 m3/sec over the spillway. The combined spillway and breach
discharge vs elevation curve was used for the initial routings to obtain
the recession side of the breach hydrograph.
14. Conclusions. a. The amount of storage in the reservoir and the
depth of the breach have the greatest effect on the discharge hydrograph.
The breach shape has a lesser effect. If a parabolic weir breach is
assumed, regardless of the actual breach shape, the error in discharge at
any time will not exceed 8 percent of the maximum discharge.
17
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Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/25: CIA-RDP81-01043R002300060002-4
Par. 14a
b. The methods presented in this chapter do not apply if eighty
percent or more of the breach is submerged. In each problem then, tail-
water conditions should be investigated. Also, if the inflow into the
reservoir is relatively high, compared to the volume of storage, the meth-
ods are not applicable. In these cases, the flow should be routed through
the reservoir and breach by conventional methods.
18
Par, 15
CHAPTER III
LARGE BREACHES
15. Fundamental Considerations. a. For purposes of this study, a
"large" breach is defined as one whose area is greater than one-sixth that
of the average reservoir cross-sectional area. For this condition, fric-
tional resistance of flow through the reservoir becomes an important factor,
and the procedures developed in Chapter II for small breaches will not give
acceptably accurate results, as explained in paragraph 2f. Therefore, in
this chapter, there are presented the basic theory, assumptions, and com-
putation procedures for outflow through a large breach opening with the
objective of developing a rapid procedure which will be sufficiently accu-
rate for solution of most military problems of this nature.
b. Experiments indicate that there are primarily three regimes
of flow from a reservoir when a dam is breached. The first regime is of
short duration, and is controlled by potential flow theory in which only
laminar-viscous effects are significant. The second regime of flow is a
transitional phase in which the flow is changing from potential to turbu-
lent flow conditions. This regime has not been analyzed mathematically
at this time, since there is no known method for computing the flow which
is governed by a changing frictional effect. The first and second re-
gimes of flow occur in such a short time interval that they are of little
practical significance to military hydrology. The third regime of flow
occurs when the effect of turbulence is fully developed and frictional
effects become appreciable.
c. Model studies have been made representing a rectangular
reservoir with a horizontal bottom and of infinite length, while reser-
voirs normally encountered in the field by military hydrologists have
varying bottom slopes. Model studies have been conducted at hydraulic
laboratories in Russia, Yugoslavia, France and other countries; however,
data are usually for specific problems and limited in application.
d. The basic theory and assumptions used in deriving the dimen-
sionless outflow hydrographs for the three following conditions of
breaching are considered for a dam impounding a reservoir of uniform width
and constant bottom slope:
(1) The dam suddenly and completely removed;
(2) The top half of the dam removed for its entire width
(3) The dam partially breached by a rectangular section
extending from the top of the dam to the reservoir bottom.
16. Reservoirs. Large earth dams on alluvial streams normally have
a large length to height ratio. The cross-sectional area of the broad
flood plain is usually many times greater than the area of the channel
cross section. The land also normally rises sharply at the extreme width
of the river valley. Reservoirs with these characteristics were assumed,
for purpose of this study, to have a rectangular valley cross section nor-
mal to the direction of flow. The river channel and flood plain slopes of
a long reservoir can often be considered equal and constant throughout
their lengths. The initial reservoir longitudinal cross section, parallel
to the direction of flow, was therefore assumed to be a triangle with the
height equal to the height of the dam and the length equal to the length
19
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Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/25: CIA-RDP81-01043R002300060002-4
Par. 16
of the reservoir. The reservoir width was assumed to be equal to the
flood plain width, and the reservoir depth equal to the depth of pool
over the flood plain. This latter assumption neglects the river-channel
area below the elevation of the flood plain, as it was considered negligible
in comparison with the area above the wide flood plain. The flood plain
was considered of such width that an analysis based on the unit width of
reservoir was sufficiently accurate for military hydrology purposes.
17. Effective Width. The effective width of a reservoir is defined as
a width equivalent to the uniform width of an idealized prismatic reservoir,
with triangular longitudinal profile, wherein the length, depth, and stor-
age capacity are identical to the given reservoir. The effective width of
a reservoir was determined as follows:
a. In the cases of the Complete breach and the Vertical-partial
width breach:
B = 2 Jrzjlih (1)
where B = effective reservoir width
= initial storage above the breach lip
L = length of reservoir
h = depth from the initial water surface to
the bottom of the breach
b. In the case of the half depth-full width
B = 1.33 VAL
where all terms are defined above.
breach:
(2)
18. Average Reservoir Bott2111222. The average bottom
reservoir was computed as the initial depth of water at the
the reservoir length.
So = Ho/L
where
So = average reservoir bottom slope
Ho = specific head (initial depth of reservoir
at dam)
slope of the
dam divided by
(3)
19. Roughness Coefficient. The standing timber and willows in a re-
servoir basin are usually removed prior to filling. Due to the clearing
of the river overbank areas, and the depths of flow in the reservoir com-
pared to the normal flood depths, the value of the coefficient of rough-
ness was assumed to be constant throughout the given problem and related
to the initial depth of flow at the dam. The outflow hydrographs were
computed with a coefficient of roughness of 0.030, when the initial pool
depth was taken as 50 meters.
20. Dam Completely Removed. The various assumptions, used in deter-
mining the outflow hydrograph fr9m a relatively long, narrow reservoir
when the dam is suddenly and completely removed, are as follows:
a. The initial discharge and depth of the surge was determined
by the equations of St. Venant:
Y = (4/9)H0
20
(4)
where
Rmax
Y
Qmax =
H0=
B =
g
(8/27)13(g)0.51101.5
depth of flow at the dam
initial discharge through the breach
specific head (initial depth of reservoir
at dam)
effective reservoir width
gravitational constant
(5)
Par. 20a
The above equations are applicable in both the English and metric system
of units.
b. The characteristics of the outflow from a breached dam change
with time. The initial outflow was assumed to be equal to the theoretical
discharge computed by Equation 5 of subparagraph Han above and to remain
constant until the critical profile for maximum flow was obtained. A
water surface profile for the lower limit of maximum discharge was com-
puted by the general method of steady, gradually-varied flow. The compu-
tation procedure was modified slightly to adjust for the unsteady nature
of the flow in the reservoir. It was assumed that the discharge de-
creased between the dam and the head of the negative wave in proportion
to the distance upstream from the dam. Since the entire length of the pro-
file was not initially known, the length of each reach of the backwater
curve was assumed and adjusted by trial after the entire preliminary pro-
file was computed. The starting elevation of the profile was assumed to
be one-half the initial depth of the reservoir in accordance with experi-
mental tests and also in reasonable agreement with the theory of St. Venant.
The outflow was assumed to remain constant until the volume of released
storage equaled the storage over the water surface profile described above.
The fluid upstream of the negative wave was assumed to be at rest and to
have no effect on the outflow. Profiles with discharges less than the
initial discharge were computed in the same manner as described above and
are shown on Plate 16. The limit of this regime of flow was assumed to
have been reached when the discharge at the dam equalled that computed by
Manningls equation with a slope equal to the ratio of one-half the depth
below the initial pool elevation to the reservoir length as shown by the
profile for 90 m3/sec on Plate 16. The peak stage of the flood wave was
assumed to move downstream from the dam when the discharge equalled the
normal discharge at one-half the initial depth of the reservoir. Following
this time this water surface profile in the reservoir was assumed to be
nearly a straight line which pivoted about the upper end of the reservoir.
The discharge at the dam for the remainder of the outflow was computed by
Manningvs equation with a slope equal to the ratio of the depth below the
Initial pool to the reservoir length. A coefficient of roughness of 0.030
and an initial depth of approximately 50 meters were used for all computa-
tions.
21. Half Depth-Full Width Breach. The assumptions described in Par. 16
to 20 for the reservoir shape and with the dam completely removed, are
generally applicable to the condition in which the top half of the dam is
removed for its entire width. The total storage released was the volume
above the breach lip for all computations. The additional assumptions used
21
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Par,, 21
in determining the outflow hydrograph are as follows:
a. The initial peak discharge over the breach lip was computed by
a modified St. Venant's equation:
Qmax = (8/27)B(Ho/h) 0.33(g)0.5h1.5 (6)
h = depth from the initial water level in the
reservoir to the bottom of breach. The
ratio of the term (110/h) should not ex-
ceed 6. Other terms are defined in Par.20.
b. The outflow characteristics over the breach lip were assumed
to be similar to the flow conditions over a broad crested weir. The
peak outflow from the opening was assumed to be equal to the theoretical
discharge computed by the modified St. Venant equation given in sub-
paragraph "a" above abd to remain constant until the critical profile
for maximum flow was obtained. The discharge over a broad crested weir
at the time and following conditions of the critical profile is based on
the theory of critical flow at critical depth under steady flow conditions.
The initial surge from a dam breached to one half depth is unsteady flow,
according to the theory of St. Venant, and equals about 70 percent of
the critical discharge of a broad crested weir. The controlling water
surface profile for the maximum discharge was computed in the same manner
as described in paragraph 20b. The starting elevation, however, was
assumed to be equal to the sum of the critical depth above the weir and
the velocity head a short distance upstream from the opening for the
peak discharge. The initial discharge was assumed to remain constant un-
til the volume of released storage equaled the storage over the critical
water surface profile for maximum discharge. Profiles with discharges
less than the initial discharge were computed as described above. The
limit of this regime of flow occurs when the reservoir is emptied to the
elevation of the breach lip. A coefficient of roughness of 0.030 was used
for all computations. The local phenomenon of drawdown at the breach was
neglected as the storage immediately over the drawdown profile was con-
sidered small in comparison to the storage above the entire water surface
profile in the reservoir.
22. Full Depth-Partial Width Breach. The assumptions described for
the complete breach (Par. 16 to 20) are generally applicable to a verti-
cal breach extending from the top of the dam to the bottom of the reser-
voir and with a breach width less than the effective reservoir width.
The assumptions as to reservoir shape, effective reservoir width, co-
efficient of roughness and storage indication are the same as for the
complete breach. Outflow hydrographs were computed to compare the effects
of various breach widths for a given size reservoir and with a fixed
bottom slope. The breach widths varied from a very small opening, in
which friction was not a predominant factor, B/b >12, to a breach of
full reservoir width in which friction was of considerable importance.
The values for the extreme conditions were taken from Chapter II and Plate
18 of this manual respectively. Various bottom slopes were selected for
purposes of computation. The additional assumptions made for a vertical
breach of partial widths are as follows:
22
II
Par. 22
a. The initial peak discharge was computed by the St. Venant e-
quation as modified by Schoklitsch.
Qmax
(8/27)b( Bib)0025( g) 005H0105
where b = breach width
Other terms are defined in Par. 20
b. The characteristics of the outflow from a breach of full depth
and partial width may affected by the tailwater conditions below the
dam. This is particularly true for lesser discharges when the tailwater
depth is relatively high with respect to the headwater. A tailwater rating
curve was computed with an assumed downstream channel, equal to the reser-
voir cross sectional areas and with the channel bottom slope assumed equal
to the average reservoir bottom slope.
(1) Several tailwater discharge rating curves were computed
for the breach condition. One such discharge rating curve was computed by
use of the submerged weir equation derived in "Submerged-.Weir Discharge
Studies", by James R. Villemonte, ENR 25 Dec. 1947. Also a discharge rating
curve was computed by the Francis weir equation with the discharge coeffi-
cient and the submergence coefficient derived from the Guntersville Dam
Study for TVA as given in ASCE Separate No. 626, Feb. 1955. The two
rating curves were compared with the discharges computed by equation (7)
and found to be within reasonable agreement. The discharge rating curves
used on this study for breaches of full depth and partial widths were
computed by equation (7), and established the starting elevations for the
water surface profiles.
(2) Water surface profiles were computed through the reservoir
in the same general manner as described for the complete breach (Par. 20).
The starting elevations of the water surface profiles were determined from
the discharge rating curve for the assumed breach discharges. The unit
width discharges used for the computation of the water surface profiles,
however, were less than the unit width breach discharge because of the
change in flow areas. The reservoir cross sectional area being larger than
the breach area, the breach discharge was reduced proportional to the
ratio b/B. The discharges in the reservoir were also assumed to decrease
in proportion to the distance upstream from the dam as for the other
breach conditions.
23. Basis of Computations. Outflow hydrographs were computed as a
function of the reservoir bottom slope for the conditions of a complete
breach and a breach of half depth and full width. The range of bottom
slopes selected was from 0.0001 to 0.003 which was assumed to be repre-
sentative of those slopes usually encountered in field operations. The
outflow hydrographs from a vertical breach of partial widths were computed
with the same range of bottom slopes as given above, but with varying
breach width ratios. Each of the reservoir routings were computed by a
storage method of flood routing as described in the following paragraph.
24. Routing Procedure. a. The storage method of flood routing, as
developed by "Pills", was used in determining the outflow hydrograph for
this study. This method of reservoir routing is a conventional storage
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Par. 24a
method of routing based on the law of continuity, and is
At(I-0) = AS
expressed as follows:
(8)
which states that inflow minus outflow equals the change in storage. Equa-
tion 8 was rewritten in terms of inflow, outflow and storage at the begin-
ning and end of the routing step as follows:
where
11+12 01 02
t + S1 9 t S2 2 t
2
is the rate of inflow
0 is the rate of outflow
S is the storage
t is a selected interval of time
(9)
Subscripts 1 and 2 refer to the beginning and end of time t.
The second and third terms of equation 9 are known as the storage indica-
tion values at the beginning and end of the routing period. Storage indi-
cation curves were developed as follows:
(1) The volume of storage was computed under each of the
instantaneous water surface profiles described in Par. 20 to 22.
(2) The product of one half the profile discharge at the
breach and a routing time increment was computed for time increments of
1 min,, 15 min., 1 hour, 4 hours and 24 hours.
(3) The storage indication values were determined as the sum
of steps (1) and (2) for each selected time increment, and the storage in-
dication curves were plotted with discharge (0) as ordinate against the
corresponding storage indication value (S + Ot/2) as abscissa. Smooth
curves were drawn connecting the points of equal time values.
(4) In equation 9 all known terms are on the left and all un-
knowns on the right. Routing is accomplished by solving for the right 'land
term (S2 +__4200
t) of the equation. The value of 02 is computed from the
2
02
relation between 02 and (S2 +7 t) which was described above as the
storage-indication curve. Each term of equation 9 represents a volume.
If 11, 12, OD and 02 are expressed in units of cubic feet per second and
Si and S2 are expressed in units of cubic feet, it follows that "t" must
be expressed in units of seconds. Assuming no inflow into the reservoir
equation 9, becomes:
01 ,
Si u
2
02
= S2 +_.__t
t
(10)
b. With the aid of the storage indication curves the solution of
equation 10 was effected as follows: for the initial routing period, the
storage indication corresponding to the maximum discharge (OD was
2)4
Par. 24b
determined from the storage indication curve. The volume of storage re-
leased in the routing step was determined as the product of the discharge
at the beginning of the step (01) and the time increment of the step (t).
The value of the released storage (Olt) was subtracted from the storage
indication described above, and is represented by:
01 01
Si + t - Olt = Si - t (11)
2 2
The right hand term of equation 11 is equal to S2 + (02/2)t as determined
by equation 10. The discharge at the end of the step (02) was determined
from the storage indication curve as the discharge corresponding to the
storage indication value of equation 11. This discharge then became the
beginning discharge for the next routing step. The reservoir outflow was
routed with small time increments (1 min. to 1/)4 hour - varying for dif-
ferent bottom slopes) for the first portion of the routings. The time in-
crements were then increased when the change in the discharge rate for
each routing step became reasonably small. The value (Olt) should be a
reasonable approximation to the storage released during the routing step.
The routing proceeded in the above manner until the entire storage above
the breach was released from the reservoir.
25. Outflow Hydrographs. a. Each of the outflow hydrographs deter-
mined by the routing procedure of Par. 24 was converted to a dimensionless
hydrograph for general application. The dimensional hydrographs were
transformed by dividing the instantaneous discharge by the maximum dis-
charge, and the time by a dimensional time factor. The dimensional time
factor was determined as the ratio of the initial reservoir storage to the
maximum discharge. The dimensionless outflow hydrographs for the dams
completely removed from the reservoirs are shown on Plate 17. The
dimensionless outflow hydrographs for the other breach conditions were
computed in a similar manner as for the complete breach but are not
shown. The outflow hydrographs for a vertical breach with partial
widths were computed as a function of the ratio of breach width to ef-
fective reservoir width.
b. The dimensionless outflow hydrographs then were cross plotted
as a function of the bottom slope for four breach conditions:
(1) Complete breach
(2) Half width-full depth breach
(3) One fifth width-full depth breach
(4) Full width - one half depth breach
The hydrographs were plotted as bottom slope (ordinate) and dimensionless
time (abscissa) with the ratios of discharges (QAmax) as the parameter
and are shown on Plates 18, 19, 20 and 21, respectively.
c. The dimensionless outflow hydrographs from the vertical
breach with partial widths may, by use of Plates 18, 19 and 20, be cross-
plotted as a function of the breach width ratios. Plate 22 is given as
an example to illustrate the process. The breach width ratios (breach
width/effective reservoir width) were plotted against the dimensionless
time factor (abscissa) with the ratios of the discharges plotted as the
parameter.
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Par. 26
26. Method of Computation. a. The breach outflow hydrograph from
a dam that has been completely removed from the reservoir is computed as
follows:
(1) From the basic data of the problemIdetermine the effective
reservoir width and average bottom slope of the reservoir by equations
(1) and (3) respectively.
(2) Enter Plate 18 with the average reservoir bottom slope
(ordinate) and determine the dimensionless time factor (abscissa) for each
ratio of Q/Qmax.
(3)
Compute the initial peak discharge by equation (5),
Par. 20a
(4) Compute the dimensional time factor as the ratio of the
initial reservoir storage to the initial total peak discharge.
(5) The outflow breach hydrograph is determined as:
(a) the product of the dimensionless time factors of
step (2) and the dimensional time factor of step (4) and plotted as the
abscissa;
(b) the product of the ratios Q/Qmax and the initial
peak discharge of step (3) are plotted as ordinate for the corresponding
values of time.
b. The outflow hydrograph from a dam that has had the top half
removed for its entire width is computed in the same general manner as
described in sub-paragraph (a) above:
(1) The effective reservoir width is computed by equation (2);
and the average bottom slope is computed by equation (3).
(2) The dimensionless time factor for each ratio of Q/Qmax
is determined from Plate No. 21;
(3) The initial peak discharge is computed by equation (6);
(4) The outflow breach hydrograph is determined as described
in steps (4) and (5) in subparagraph (a) above.
c. The outflow hydrograph from a vertical opening with various
width ratios for an average bottom slope of 0.00019 is computed as follows:
(1) Determine the effective reservoir width in the same
manner as described in subparagraph (a) above.
(2) Compute the ratio of the breach width to the effective
reservoir width.
(3) Enter Plate 22 with the breach width ratios of step (2)
and determine the dimensionless time factor for each ratio of 00max.
(4) The outflow breach hydrograph is then determined in the
same manner as described in steps (4) and (5) of subparagraph (a) above.
d. The outflow hydrograph from a vertical opening with various
width ratios for any average bottom slope is computed as follows:
(1) From Plates 18, 19 and 20 read the dimensionless time
ratio for each parameter at the selected bottom slope. From Plate 22 read
the dimensionless time ratio for each parameter at breach width ratio of
.083 (B/b -.