Stress-Deformation Analysis for Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 692

of the constitutive surface cross section at a constant void ratio
when plotted using the arithmetic and logarithmic scales. An
essentially linear cross section on the arithmetic plot becomes
an asymptotic curve on the logarithmic plot.
The asymptotic cross-sectional curve illustrates the
logarithmic form of the void ratio constitutive surface in
Fig. 13.28a. Ho (1988) proposed an approximate form of
the void ratio constitutive surface, as shown in Fig. 13.28b.
The approximate surface consists of three planes, namely,
planes I, II, and III. The three planes converge at a void ratio
ordinate corresponding to nominal values of the stress state
variables [i.e., log σ − u a ≈ 0 and log u a − u w ≈

0].
Planes I and III are referred to as the orthogonal planes.

Plane I is perpendicular to the e -log σ − u a plane and
has a slope in which is represented by the C t index. Plane

III is perpendicular to the e -log u a − u w plane and has
a slope represented by the C m index. In other words,
only one index is required to describe void ratio changes
when the stress state variable changes occur within the

Figure 13.26 Typical SWCC plotted to semilogarithmic scale.

Remolded Madrid clay
Legend γ 0 (kN/m 3 )

w 0 (%) P s -max (kPa) w f (%) S f (%)

4.7
11.0
16.6

15.4
15.4
15.6

484
388
244

27.1
26.3
27.8

101.0
98.6
106.0

0

500

1000

0 1000 2000 3000

Matric suction, ( u a - u w ) (kPa)

(a)

1

10

100

1000

1 10 100 1000 10,000

Matric suction, ( u a - u w ) (kPa)

(b)

Figure 13.27 Cross section of void ratio surface plotted using arithmetic and logarithmic scales:
(a) cross section showing stress state changes across constant-void-ratio surfaces on arithmetic
scale; (b) cross section showing stress state changes across constant-void-ratio surfaces on loga-
rithmic scale (modified after Escario, 1969).