Stress-Deformation Analysis for Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 691

Constant - water content
stress path

b ms

D ms

b ts

D ts

w 0

w 0

D m

b m

D t

b t

( u a - u w )

log ( u a - u w )

Legend
Water content increase
Water content decrease

(a) (b)

Figure 13.24 Water content constitutive surfaces for unsaturated soil: (a) arithmetic plot of stress
state variables versus water content; (b) semilogarithmic plot of stress state variables versus water
content.

Figure 13.26 illustrates a typical SWCC plotted on a
semilogarithmic scale. A reasonably linear curve is obtained
over a wide stress change in comparison to the arithmetic
plot in Fig. 13.19. The slope of the SWCC is equal to the
D m index. The C m index can then be computed from the
C m /D m ratio obtained from the slope of the shrinkage curve
(Fig. 13.20).
Using a conversion between a semilogarithm scale and an
arithmetic scale (Lambe and Whitman, 1979), the C t , C m ,
D t , and D m indices can be written in terms of the a t , a m ,
b t , and b m coefficients:

e 0

C t

a t σ − u a ave
0 . 435

C t = (13.79)

a m u a − u w ave
0 . 435

C ts

C m = (13.80)

b t σ − u a ave
0 . 435

D t = (13.81)

b m u a − u w ave
0 . 435

Net normal stress ( - u a )

σ

D m =

(13.82)

Figure 13.25 Typical compression curve for compacted soil plot-
ted to semilogarithmic scale.

where:

(σ − u a ) ave = average of the initial and final net normal

stresses for an increment and

Figure 13.25 shows a typical compression curve for an
unsaturated, compacted soil. The results show that the void
ratio versus net normal stress curve can be largely linearized
when a logarithmic scale is used for the stress state variable.
The compressive index C t can be computed from Fig. 13.25
and is commonly referred to as the compression index C c
for the saturated soil. The D t

(u a − u w ) ave = average of the initial and final matric suc-

tions for an increment.

The 0.435 constant arises from the logarithm of the natural
log base taken to the base 10 (i.e., log 10 2 . 718). Even though
the extreme planes take on a linear relationship, the cross
section of the constitutive surface on the logarithmic, the

index is related to C t on the

saturation plane:

log σ − u a and log u a − u w plane is no longer a series

of straight lines as observed on the arithmetic σ − u a

and u a − u w plane. Figure 13.27 shows a comparison

C t = D t G s (13.78)