Solving Stress-Deformation Problems with Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 777

suction be computed. The matric suction equivalent can be
used in place of the actual in situ matric suctions when per-
forming the calculations. Consequently, the swelling index
on the total stress plane C ts is used instead of the swelling
index with respect to matric suction C m when performing
the comparative calculations.
The average of the initial and final stress states is used for
each increment when calculating the elastic modulus func-
tion. The initial void ratio was 1.0 and the swelling index C ts
was 0.1. A Poisson's ratio of 0.3 was selected. The matric
suction modulus equation can be written as follows for the
total stress plane:

decreased elastic modulus results in increased amounts of
heave being computed at extremely small stress levels.
Figure 14.62 shows that the total heave calculated increases
almost linearly with decreasing stress level steps. The total
heave predicted when using a stress level of 1 kPa (i.e.,
200 stress steps) is 117mm while the total heave predicted
when using a stress step level of 7.2 kPa (i.e., 25 stress
steps) is 115 mm. The error due to nonlinearity associated
with small stress steps appears to be on the order of 0.5%
from the correct solution. The change in the computed
results in going from using 25 stress steps to 200 stress
steps was about 2%.
The sensitivity of the analysis to stress step level is great-
est when the expansive clay exists to the ground surface and
an attempt is made to compute heave as the total stress (i.e.,
the overburden pressure) goes toward zero. It is clear that
the placement of a small amount of nonswelling material
(e.g., a gravel layer) on the surface of the clay layer makes
the solution less sensitive to the number of stress steps used
in the computations. Figure 14.63 illustrates how the finite
element solution converges onto the correct solution as the
analysis moves toward calculations for all stress increments.

n t σ y − u a ave

H = (14.85)

The total stress state is expressed as the sum of the over-
burden pressure and the matric suction equivalent, as shown
in Fig. 14.61. A constant swelling index from a semilog plot
produces a linear elastic modulus function. Consequently,
the analysis is nonlinear and the solution is a function of
the refinement of the layers used in solving the problem.
Figure 14.61 shows that the elastic modulus H decreases
with the decreasing stress level near ground surface. The

100

Example 1
e 0 = 1.0
C ts = 0.10
μ = 0.3

80

60

n ms = 85.52

40

20

0

0 200 400 600 800 1000

Stress state, kPa

Figure 14.61 Elastic modulus function H as function of stress state.

120

125 steps 0.6 mm or 0.5% total heave

25 steps

3.5 mm or 3% total heave

115

200 steps

10 steps

40 steps

20 steps

110

200 steps, total heave = 117 mm
25 steps, total heave = 115 mm

105

0 4 8 12 16 20

Size of stress step, kPa

Figure 14.62 Total heave versus size of each stress increment.