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HARSTAD ASSOCIATES INC Project P&q.Jscef 2
ENGINEERS • PLANNERS Subject By
lob No �04 Date
VOLICIF. OF STOR."1 WATER RETENTION BASINS
by
Chester J. Ordon F. ASCE
Processor of Civil Engineering
y Wayne State University
Detroit, MI 48202
Combined sanitary and storm water collection
systems are traditionally provided with regulating
chambers for the purpose of intercepting a certain
percentage of the flow and allowing all in excess
of this to overflow directly into a local waterway
Excess flows occur during periods of rainfall so
the overflow is a mixture of sanitary sewage and
storm water runoff.
j With ever improving standards for our water-
ways, this practice is becoming increasingly un-
acceptable to the regulating agencies charged with
safeguarding the quality of our lakes and streams.
Infact, in many instances, 1t is equally unaccept-
able to allow the runoff from separate storm water
collection system to discharge untreated into local
waterways. This has come about as a result of in-
creasing evidence that the discharge from separate
storm water collection systems is substantially as
polluted as that which comes from a combined system.
One method of alleviating this problem is to
install a storm water retention basin on the line
just ahead of the interceptor, the basin to accum-
ulate all discharges in excess of that which is
directed to the interceptor,at least until the
basin is full. Any additional excess will have to
'be discharged into the receiving waters but this
should be kept to a designed for minimum, accept-
able to the regulating agency. After the storm has
passed, the basin is emptied by discharge into the
interceptor at a rate which both the interceptor
and the treatment plant can handle. The necessary
volume of the basin is the purpose of the discus-
sion which follows.
Basins for this purpose have been and are
being designed regularly in the United States and
several are in use today. The design of some of
these basins has been based on :i procedures out-
lined in the "Urban Storm Drainage Criteria Manual"
(1) developed and supplied by the Denver Regional
Council of Governments. This procedure is some-
times referred to as the Colorado Itrhan Hydrograph
Procedure (CUHP) Storage Analysis. The procedure
as outlined in the manual calls for the use of a
simple table., The table is a manual method for
determining a maxima which can be determined con-
veniently by formulas developed with the use of
calculus (2). Such formulas have been developed
and are in use in some areas. However, after a
critical examination of the CUHP and formulas based
on that method, it is the conclusion of this author
that they are mathematically incorrect and can lead
to badly underdesigned basins.
The problem of the design of retention basins
was studied in considerable detail with the objec-
tive of conceiving a fundamentally correct proced-
ure followed by the development of a convenient and
workable technique for the execution of the pro-
cedure. After considerable experimentation, a
A3-1
fairly simple and rational procedure was developed.
The process begins with a rainfall intensity vs.
duration relationship such relationship being ex-
pressed either as a family of curves or equations.
Each curve in the family represents the relation-
ship between rainfall intensity vs. duration for a
storm with a particular frequency interval or re-
turn period. Typically, a combined system 1s de-
signed for the so-called 10 year storm. A curve
that represents such a relationship appears in
figure 1.
7
6
5
4
1 3
2
0
50 100 15 21, �0
D-Duration-Minutes
Rainfall Intensity vs. Duration
Figure 1
Numerous types of equations have been developed
to fit this type of curve, the simplest to use and
to derive being the reciprocal type. In subsequent
calculations, equation 1 will be used. .
f S '
175
b + D 25+D
1 - Average storm intensity in inches/hr.
(inches per hour x 2.54 - centimeters
per hour)
D - Duration in minutes over which the
average intensity 1 persisted
Data in columns (1) and (2) of Table 1 were
computed from equation 0). They could just as well
been read directly from the original graph from
which the equation was derived.
term.
d'l4,
Jr, 4
�Tif'lt'
•iAji.
It is important to remind practicing engineers
tthe time represented in figure 1 is a duration
not time chronological. It states that there
Ibe a period, somewhere in the storm, where a
en average intensity of rainfall will persist
the stated duration.
The next step in the process is to develop the
&fall intensity vs. time chronological curve as
resented by figure 2.
7
6
5
4
"/Hr. 3
2
1
Cross Hitched
_ n
A iD 2
\
n�
T
Time -Chronological
Rainfall Intensity vs. Time
Chronological
Figure 2
Recognizing that the values of D on the iD vs
D curye must represent the area under the iT vs T
`curve for the same duration D, we have a basis for
developing an equation for the curve of figure 2.
-Working only with the part of the curve of figure 2
to the right of the central peak the ordinate f(D)
is a function of D.
,T Then:
a D _ aD
�t A- iD D 2 b+D 2 2 b + 2 D
end
D
e. IO f(D)dD - 2ba+ 2D
from which f(D) must be solved for. It develops
that
e f(D) iT (b + T)A ab (2)
With this equation, T is measured from the
central peak. The left side of the curve is a mirror
image of the right side and, therefore, the entire
curve can he drawn.
It is a matter of convenience to compute T with
the origin at the left extreme of the graph as illu-
strated in figure 3.
With the reciprocal type of equation the iT
curvy oxtends to Infinity in both directions from
the ctntr.rl park. It Is necessary to choose an
arhrtr.iry cut off point and begin the zero reading
Al-'2
iT
"/Hr.
0T -j-120
Time Minutes
Rainfall Intensity vs. Time Chronological
Figure 3
of figure 3 at that point. The arbitrary cut off
point is designated by "j" and taken to be 120 min-
utes. One hundred and twenty minutes was chosen
because the storm intensity i at that time span
from the central peak is so low that no appreciable
runoff will occur.
Then the equation for the rising limb of
figure 3 becomes:
IT _ ab for 0 < T < j (3)
(b+2j-2T)2
The equation for the falling limb becomes
i - ab for j < T < m (4)
T (b- 2j+2T)2
I
It is convenient to write equation (3) as:
ab/4
_
iT ((b/2 + j)- T)2
and equation (4) as:
i ab/4
)- T ((b/2 - j)+ T)2
Equations(3) and (4) make one assumption that
need not hold in all cases and that is that the
storm intensity curve is symmetrically distributed
on each side of the central peak. The A.S.C.E.
Manual of Engineering Practice No. 37, "Design and
Construction of Sanitary and Storm Sewers" illu-
strates an advanced peak storm used by the City of
Chicago and demonstrates with examples how this
configuration conforms to historical records of
numerous major storms. The Chicago rainfall dis-
tribution moves the peak to the left such that the
values of T between the peak and the rising limb is
3/8 T while that from the peak to the falling limb
is 5/8 T. The curve of figures 2 and 3 could easily
be adjusted to accomplish the same results but it
Is d.rubtful if this would affect the results of the
is
FA
W A0 J p,
retention basin de:;ign as pro;• i herein so the
tiy-...metric.il storm pattern will -vied in subsequent
calculations.
At this point, it is worth, iii l.• to emphasize it
,requent area of confusion and .nit. of the fallacies
on which the CUHP and formula-: thrived from this
method are based. Shown on fienre 2 1s that dura-
tion of 30 minutes during: which Ii..• gre.itest average
intensity i.•111 occur. Tho r, . - . r tinfall inten-
sity for this period will be -012 inches per hour
(8.10 cm pe: hour) as compur. I by .griation (1). The
ictual rainfall intensity v:,ri,.l Iron 1.47 inches
por hour (1.74 cm per hour) 1: 11 — beginning and
end of the period to 7.00 inch,-, per hour (17.78 cm
per hour) at the middle of the period. The rational
formula for runoff presumer. that the peak runoff
Item an area with .i time of cone4 ni r..t ion of 30 min-
utes will occur at, or soon .ficr, the end of the
most intense 30 minute peri..l or 1', minutes after
the central peak on the graph. lint P-time duration,
and T-time chronological, arc li-tinctly different
and must not be confused. Untortunately, manv texts
and references use the letter T in equation (1)
thereby leading to the confu.ion. The CUHP uses T
for both time duration and time chronological and
interchanges the two .i, thoneh the, were one and the
S.ime.
The basic assumption mride in developing; the
runott hydrograph is Lhat the runoff it any point of
time in the storm is equ.il to 0 - c f a. The rain-
fall intensity i being the average for the time of
concentration, 30 minutes in this example, immedi-
ately preceding the time at which the runoff is
being computed. However, this procedure is carried
out only during the rising limb of the hydrograph.
Continuing this procedure beyond the perk of the dis-
charge curve would have produced a falling limb which
would be a mirror image of the rising limb. But this
would not be a true representation of an actual run-
off hydrograph. Numerous engineers and governmental
agencies with much experience in hydrological anal-
ysis have developed synthetic hydrographs designed
for application to any typical watershed. An exam-
ination of several of these synthesized hydrographs
reveals that, in all cases, the falling limb is
about twice as long as the rising limb. This is
accomplished in the following algorithm by adjusting
the times for the falling; limb as shown in column
(9). The increment of time for the falling limb were
simply doubled from the Limo of the Wak and there-
after and folded back so that the same runoff figures
could be used.
Table I is the algorithm which implements the
generation of the runoff hydrograph based on the
assumptions made above. The area drained is taken
to be 50 acres (20.2 hectare) and the coefficient of
runuff was taken to be 0.3.
Referring to table 1, the columns are identified
and computed as follows:
(1) Time from beginning of storm - minutes.
(2) 1T rainfall intensity in inches per
hour from equations (3) and (4).
(3) Column (3) accumulates the values from
column (2).
(4) Values from column (3) are displaced a
time equal to the time of concentration.
Aar-1
30 minutes in this case.
(5) Column (4) subtracted from column il)
(5) - (3) - (4).
(6) Vol.., s for this column are compi i.•d
fron the equation (5) wher-:
TC/_* T
(5) - values taken from column i
TC - time of concentration - 10
minutes in thi; case
'.T - time Increment from coltirn ( I ) -
5 minute!:
Thu, column (6) - (5) - (5) in ILi
C:1
i0/2.5 I:
Sf•.
The v.ilues represent the runoff in inches
per hour from the area being drain.-d.
(7) The rising limb of a runoff hydrog;r.,pl
Irom ri 5O acre (20.' hectare) .ire.i . il..
. r vaIlie of 0.3 is computed wish II..•
vxpression cagIn. This become, 1..10
50 x q30 in th s ca;c.
The computations were stopped in column (i)
when the rising: limb of the hydrograph reached its
peak value of 48.28 cfs (1370 L/S). At thi; point,
a convenient check can be conducted. The rational
formula is intended only for the determination of
the momentary peak flow through the storm dr.iinag;e
pipes. The values can be obtained by substitution
into the equation:
Q -c is Q-0.3x 3.18x50-47.7cfs
(1350 L/S)
Also this value should occur at the end of the
most intense 30 minutes of rainfall or 15 minutes
after the rainfall peak time. The table shows a
value of 48.28 cfs (1370 L/S) at this time. The
difference comes from assuming straight lines be-
tween points at 2.5 minute intervals. Using;
smaller time increments would reduce this difference
The value of the runoff coefficient deserves
some explanation. It 1s sometimes erroneously re-
ferred to as the percent of runoff expressed as a
fraction. This mistaken impression does no harm so
long as the peak runoff rate is what is being sought
and engineering experience in the area has taught
engineers which values must be used to get reason-
able results. In our current calculations, the
concern is for the complete discharge hydrograph
and the total volume of runoff water it represents.
In actuality, C from the rational formula, repre-
sents the ratio of the peak runoff to the average
rainfall intensity rate for a period equal to the
time of concentration.
Doubling the time increments for the falling
limb serves to double the volume that would have
been under that portion of the runoff hydrograph.
Or, the volume under the entire discharge hydrograph
will be three times that under the rising; limb.
With this assumption. the volume of runoff expressed
.is :i percentage from in .irea with it runoff eoeffl-
cici.t of 0.3, becomes 457', of the raintall during; the
1.D c
t
.CEjL'•t/T/r
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RUNOFF
COMPUTATIONS FROM A
50 ACRE (20.2
HECTARE) AREA WITH A
TIME OF
CONCENTRATION
OF 30 MINUTES
C-0.30 Q0-20cfs
TABLE 1
T
Minutes
�T
Inches/Hr
Ei T
y
EiT 30
(3)-(4)
930
Q H
QH 40
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
60
0.21
0.21
2.25
c
62.5
0.22
0.43
65 '
0.24
0.67
2.70
67.5
0.26
0.93
70
0.28
1.21
3.00
72.5
0.30
1.51
75
0.33
1.84
3.47
77.5
0.36
2.20
80
0.40
2.60
4.05
82.5
0.44
3.04
85
0.48
3.52
4.80 .
87.5
0.54
4.06
90
0.60
4.66
0.21
4.45
0.37
5.55
92.5
0.68
5.34
0.43
4.91
0.41
6.15
95
0.78
6.12
0.67
5.45
0.45
6.75
�(
97.5
0.90
7.02
0.93
6.09
0.51
7.65
100
1.04
8.06
1.2.1
6.85
0.57
8.55
4
102.5
1.21
9.27
1.51
7.76
0.65
9.75
105.0
1.45
10.72
1.84
8.88
0.74
11.10
107.5
1.75
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