Geoscience Reference
In-Depth Information
S
1
/
2
0
n
−
1
, so that
with the Gauckler-Manning formula (5.41), one has
a
=
2
/
3 and
K
r
=
Equation (6.20) can be written as
(
n
0
.
60
P
−
0
.
40
)
L
S
1
/
0
0
.
60
t
c
=
/
(12.22)
It is remarkable that the powers of
L
and
S
0
are not very different from those in the
strictly empirical formula (12.21). Note, however, the different conceptual origins of
Equations (12.21) and (12.22); the former refers to the time required by the fluid particles
to travel the length of the drainage area, whereas the latter refers to a wave motion,
that is the time for the steady state signal to cover that same distance. Recall also that
on the basis of experimental data on
t
c
reported in the literature, McCuen
an
d Spiess
(1995) recommended that Equation (12.22) should not be used when (
nL
/
√
S
0
) exceeds
30 m.
Next, a decision must be made regarding the return period of the event
T
r
. This is
usually taken as the expected lifetime of the structure. To give an idea, ASCE and WPCF
(1982) suggest, depending on the economic justification, typical values of 5 y for storm
sewers in residential areas, 20 y in commercial and high value districts, and 50 y or more
for flood protection works.
Finally, with the duration of the rainfall event, i.e.
D
, and the return period of the
design storm, i.e.
T
r
, both decided upon, the intensity
P
can be determined from the
available intensity-frequency-duration data for the site. Figure 3.16 shows an example
of such data. If deemed necessary, the rainfall intensity at the point can be converted to
an area value by such means as illustrated in Figure 3.14.
The justification for equating the time of concentration with the duration of the selected
design rainfall event is illustrated in Figure 12.9. This shows that, if it is assumed that
D
t
c
, only part of the drainage area can contribute to the outflow. On the other hand,
if one assumes that
D
<
t
c
, the intensity
P
obtained for this longer duration, would be
too small; indeed, as illustrated in Figure 3.16, for a given return period
T
r
, the rainfall
rate
P
decreases with increasing duration
D
. Thus to allow the entire drainage area to
contribute to the outflow rate, and to obtain the maximal intensity for the selected return
period, it is reasonable to put
D
>
t
c
.
The Rational Method with Equation (12.21) (or (12.22)) and most of its subsequent
variations in the engineering literature are based on the notion that storm runoff consists
primarily of overland flow. As discussed in Chapter 11, on hillslopes with permeable
soils, this is often a tenuous assumption, as most of the runoff takes place through
subsurface flow paths. If for such situations Darcy's law is valid, the kinematic flow
speed (10.151) yields the following time of concentration
=
n
e
B
x
k
0
sin
t
c
=
(12.23)
α
in which
B
x
is the hillslope length (see Figure 10.26), and
n
e
,
are effective values
of the drainable porosity, the hydraulic conductivity and the slope angle, respectively.
k
0
and
α
