Environmental Engineering Reference
In-Depth Information
100
90
Best-fit curve
Experimental data
80
70
60
50
40
30
20
10
0
0.0001
0.001
0.01
0.1
1
10
100
Particle size, mm
(a)
40
Predicted from grain size
Experimental data
35
30
25
20
15
10
5
0
0.1
1
10
100
1,000
10,000
100,000 1,000,000
Soil suction, kPa
(b)
Figure 2.5
Comparison between experimental and predicted SWCCs for sand (from M.D.
Fredlund, 2000). (a) Grain-size distribution curve for sand. (b) Measured and predicted SWCC
for sand.
There are three general categories of grain-size distribu-
tions (Holtz and Kovacs, 1981):
well-graded
soils,
uniform
soils, and
gap-graded
soils. Well-graded and uniform soils are
unimodal in character while gap-graded soils are bimodal.
proposed a four-parameter equation that provided a reason-
able fit over the entire soil suction range. The similarity in
shape between the SWCC and the grain-size distribution curve
suggests that the SWCC equation (Fredlund and Xing, 1994)
could be used to describe the grain-size distribution curve.
The Fredlund and Xing (1994) equation allows for inde-
pendent control of the shape of the lower end of the grain-
size distribution curve (i.e., the fine particle size range). The
reversed grain-size distribution scale requires that the original
Fredlund and Xing (1994) SWCC equation be modified as
2.2.2.1 Unimodal Equation for Grain-Size Distribution
Grain-size distribution curves have shapes that appear to be
similar to SWCCs when plotted using a semilog scale. The
similarity in shape is anticipated since the SWCC provides
a representation of the void distribution in a soil while the
grain-size distribution curve represents the distribution of
the solid particles. The solid particles plus the voids add
up to the total soil volume. It would be anticipated that
the distribution of the soil particles (i.e., represented by the
grain-size distribution) would bear an inverse relationship
to the distribution of voids (i.e., represented by the SWCC)
(M.D. Fredlund, 2000).
There are several empirical equations that have been pro-
posed to represent the SWCC. Fredlund and Xing (1994)
1
P
p
(d)
=
ln
exp
(
1
)
a
gr
d
n
gr
m
gr
+
⎧
⎨
7
⎫
⎬
ln
1
⎡
⎤
d
r
d
+
⎣
⎦
×
1
−
ln
1
(2.1)
⎩
d
r
d
m
⎭
+
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