Environmental Engineering Reference
In-Depth Information
12.2.6 Procedures for Calculation of Unsaturated Soil
Shear Strength Functions
The computations associated with the estimation of the shear
strength for an unsaturated soil are not complex. The proce-
dures described for the estimation of unsaturated soil shear
strength involve the substitution of parameters from the
SWCC into the shear strength equation.
The following steps are suggested for the estimation of the
unsaturated soil shear strength envelope. The saturated soil
shear strength parameters must be known (i.e.,
c
and
φ
):
strength (i.e., D.G. Fredlund et al., 1996; Vanapalli et al.,
1996b; Oberg and Sallfors, 1997; Goh et al., 2010) or the
shear strength information could be input as a table of val-
ues. In the latter case, an interpolation technique would need
to be used to get the desired shear strength. Some computer
codes can accept unsaturated soil shear strength equations.
12.2.7 Linearization of Unsaturated Soil Shear
Strength
There are situations where it may be sufficient to describe
the shear strength of an unsaturated soil in terms of a con-
stant
φ
b
value. The nonlinear shear strength envelope would
be approximated as linear segments along the shear strength
envelope. Following is an example to illustrate the estima-
tion of the unsaturated shear strength envelope for an unsat-
urated soil. In this case the SWCCs were generated from
grain-size distribution curves and are shown in Fig. 12.33.
The dry density of the soil samples was estimated to be
1550 kg/m
3
. These dry densities correspond to an initial
void ratio of 0.774 or an initial saturated porosity of 43.6%.
The specific gravity of the soil,
G
s
,
was assumed to be 2.75.
Each SWCC starts with a suction approaching zero and ends
with a suction of 10
6
kPa. The air-entry value for the soils
appears to be around 20 kPa.
The D.G. Fredlund et al., (1996) procedure is used to
calculate the unsaturated soil shear strength envelope. The
effective cohesion for the soils used in this study was esti-
mated to be 5.0 kPa. The effective angle of internal friction
wasassumedtobe27
◦
. The plasticity index was 22 and
this value corresponds to a
κ
factor of 2.4, according to the
correlation by Garven and Vanapalli (2006b).
Figures 12.34 and 12.35 show the computed unsaturated
soil shear strength envelopes for two soils. The shear strength
envelopes are clearly nonlinear in shape. It is now possible
to select a slope on the shear strength envelope that best rep-
resents the suction range of interest in the field. A line can
1. Information must be available on the SWCC. This
information might be in the form of experimental data
or best-fit parameters for an equation such as the Fred-
lund and Xing (1994) equation that can best fit the
experimental data.
2. Select a series of matric suctions (e.g., 12 values) that
reflect the range over which the unsaturated soil shear
strength envelope is to be defined.
3. When using the D.G. Fredlund et al., (1996) shear
strength estimation equation, it is necessary to select
a
κ
value that is dependent upon the plasticity of the
soil under consideration. When using the Vanapalli et
al., (1996b) equation, it is necessary to determine the
residual suction of the soil and then calculate the nor-
malized water content versus soil suction. There are
correlations with controlling parameters related to the
SWCC that must be selected when using the Goh et al.,
(2010) shear strength equation.
4. Substitute the selected matric suction values into the
respective estimation shear strength equations and cal-
culate a series of unsaturated soil shear strengths.
The calculated shear strength values can be used in com-
puter codes in one of several ways. For example, the unsat-
urated shear strength envelope could be defined using the
same equations as were used for the calculation of shear
50
45
40
35
30
25
20
15
10
SA1
SA2
5
0
10
6
0.1
1
10
100
1000
10,000
100,000
Soil suction, kPa
Figure 12.33
SWCCs estimated from grain-size distribution curves.
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