Environmental Engineering Reference
In-Depth Information
0
0.4
Fine sand
Sand
2
0.3
4
Silt loam
0.2
6
Silt
0.1
8
0
10
0
0.5
1
1.5
2
0
0.1
0.2
0.3
0.4
Time of drainage (days)
Specific yield
Figure 6.6 Specific yield as a function of drainage time
as described by Equation ( 6.8 ) (Nachabe 2002 ) with Δ h =
0.25 m for the sand and silt in Table 6.2 .
Figure 6.5 Specific yield as a function of depth to water
table for a fine sand and a silt loam using Equation ( 6.5 ).
K
()
n
s
K
estimates of specific yield as calculated from
Equations ( 6.8 ) and ( 6.9 ) for generic soils.
The foregoing discussion illustrates how,
in theory, S y is affected by the depth to the
water table and time since water level rise or
fall, but the assumptions used in these ana-
lyses represent ideal conditions that may not
be typical of actual field conditions. Sediment
properties are seldom uniform. True steady-
state conditions probably never exist in the
real world and many years may be required
for some soils to fully drain. Water tables in
most aquifers exhibit daily, seasonal, or annual
fluctuations, so complete drainage of the sedi-
ments is unlikely. Similarly, water-table rises
and declines typically do not occur instantan-
eously. The following sections describe several
other methods that have been used for estimat-
ing specific yield.
(6.7)
where Θ is effective saturation, h is pres-
sure head, θ s is saturated water content, θ r is
residual water content, h b is the bubbling pres-
sure head, λ is pore-size distribution index,
K is hydraulic conductivity, K s is saturated
hydraulic conductivity, and n = (2 + 3λ) / λ.
Applying the method of characteristics to
solve the one-dimensional flow equation under
conditions of gravity drainage, Nachabe ( 2002 )
developed the following closed-form approxi-
mate solution for S y :
S K
= −
[
Θ Θ ∆∆
n
n
]
t
/
H
+− −
(
θθ
) /(1
Θ
)
(6.8)
y
s
b
sura
s
r
b
where
Θ∆
=
[
H
(
θθ
) /(
nK
1/(
t
)]
n
1)
(6.9)
b
s
r
s
Θ sura = ( h b /H d ) λ is the effective saturation at land
surface for a water-table depth of H d , and Δ t is
time since rise or fall of the water table. For
Equation ( 6.8 ), a negligible change in saturation
at land surface is assumed over the time inter-
val of interest; for cases where this assumption
is not valid, a more detailed equation was given
by Nachabe ( 2002 ). Figure 6.6 shows how S y
changes with time, according to Equations ( 6.8 )
and ( 6.9 ), following an instantaneous decline
in water table for two sediments. Table 6.2
(modified from Loheide et al . ( 2005 )) contains
Laboratory methods for estimating S y
In the laboratory, specific yield is usually
determined by measurement of porosity and
specific retention and application of Equation
( 6.4 ). Johnson et al . ( 1963 ) described a column-
drainage approach, whereby a column, filled
with undisturbed or repacked sediments,
is saturated with water and in turn allowed
to drain. As previously mentioned, the time
allowed for drainage can have a large effect
on the calculated values of specific retention
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