Environmental Engineering Reference
In-Depth Information
Table 6.1 Statistics on specific yield from 17 studies compiled by Johnson ( 1967 ).
Tex tur e
Average specific
yield
Coefficient of
variation (%)
Minimum
Maximum
Number of
determinations
Clay
0.02
59
0.0
0.05
15
Silt
0.08
60
0.03
0.19
16
Sandy clay
0.07
44
0.03
0.12
12
Fine sand
0. 21
32
0.10
0.28
17
Medium sand
0.26
18
0.15
0.32
17
Coarse sand
0.27
18
0.20
0.35
17
Gravelly sand
0.25
21
0.20
0.35
15
Fine gravel
0.25
18
0. 21
0.35
17
Medium gravel
0.23
14
0 .13
0.26
14
Coarse gravel
0.22
20
0.12
0.26
13
unit volume of rock). Specific yield is treated
as a storage term, independent of time, that
accounts for the instantaneous change in water
storage upon a change in total head. In real-
ity, the release of water is not instantaneous.
Rather, the release can take an exceptionally
long time, especially for fine-grained sedi-
ments. King ( 1899 ) determined S y to be 0.20 for
a fine sand; however, it took two and a half
years of drainage to obtain that value. The wide
range of values that has been reported for S y in
the literature is attributed to natural heteroge-
neity in geologic materials, different methods
used for determining S y , and, in large part, to
the amount of time allotted to the determina-
tion (Prill et al ., 1965 ). Johnson ( 1967 ) compiled
values of S y from 17 studies ( Table 6.1 ). As shown
in the table, S y tends to increase with increasing
sediment grain size. The variability within each
textural class (based on the coefficient of vari-
ation) tends to decrease with increasing grain
size. Coarser sediments drain more quickly
and, hence, S y for these sediments shows less
time dependency.
Specific yield varies with depth to the water
table, decreasing as that depth decreases. As the
water table approaches land surface, the sedi-
ments above the water table are unable to fully
drain to S r . The interested reader is referred to
the analysis of Childs ( 1960 ) for further insight
into this phenomenon. The extreme case occurs
when depth to the water table is less than the
height of the capillary fringe; here, no water
is released when water levels change. This
phenomenon is sometimes referred to as the
reverse Wieringermeer effect and is reflected
by a nearly instantaneous rise in water level
in response to only a small amount of infiltra-
tion (Gillham, 1984 ). Dos Santos Jr. and Youngs
( 1969 ) and Duke ( 1972 ) suggested the following
expression for specific yield:
S
=− d
ϕθ
(
H
)
(6.5)
y
where H d is depth to water table and θ is volu-
metric water content. θ ( H d ) can be determined
from measured water-retention curves or esti-
mated on the basis of texture from published
tables of soil properties ( Section 5.2.3 ). The
effect of depth to water table on S y , as described
in Equation ( 6.5 ), is shown in Figure 6.5 for two
soils described by Duke ( 1972 ).
Specific yield also varies with time follow-
ing a change in water-table height. Nachabe
( 2002 ) developed a formula for determining S y
as a function of depth to water table and time
following an instantaneous change in water-ta-
ble elevation. It was assumed, as in the analysis
of Childs ( 1960 ), that the material was uniform
and a static equilibrium pressure head profile
initially existed above the water table. Water-
retention and hydraulic conductivity curves
were represented by slight rearrangements of
the Brooks and Corey ( 1964 ) formulas given in
Section 5.2.3 :
Θ
= − −=
r
( ( )
θ θθθ
h
) /(
)
(
hh λ
/
)
(6.6)
s
r
b
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