Nature and Phase Properties of Unsaturated Soil - Unsaturated Soil Mechanics in Engineering Practice - page 44

soil parameters which have physical meaning. The shrinkage
curve equation is meant for the simulation of the drying of
a soil.
The a sh parameter represents the minimum void ratio cor-
responding to the shrinkage limit of the soil. The relationship
between void ratio and gravimetric water content is linear if
the degree of saturation, S , remains constant during shrink-
age. The slope of the relationship between void ratio and
water content is related to the initial volume-mass proper-
ties. The slope of the line tangent to the initial portion of
the shrinkage curve is equal to a sh /b sh . The effect of varying
the a sh parameter can be seen in Fig. 2.22:

A

Δ V a = 0

Δ V a ≠ 0

B

D

C

Constant degree
of saturation, S

a sh
b sh =

G s
S

(2.8)

The influence of changing the b sh parameter is shown in
Fig. 2.23. The b sh parameter is equal to the slope of the degree
of saturation line on the shrinkage plot. Equation 2.8 shows
that once the minimum void ratio of a soil is known, the b sh
parameter can be calculated for a specific degree of saturation.
The c sh equation parameter controls the rate of curvature
of the shrinkage curve as the soil begins to desaturate, as
shown in Fig. 2.24. The parameter, c sh varies somewhat
depending on the soil type and the initial state of the soil.

Gravimetric water content (%)

Figure 2.19 Volume-mass shrinkage curve for initially unsatu-
rated soil specimen (from M.D. Fredlund et al., 2002a).

where:

2.2.4.2 Estimation of Shrinkage Curve
The volume change of a soil specimen is commonly not
measured when performing a laboratory test for the SWCC.
The basic experimental data from a SWCC test generally
consists of gravimetric water content versus soil suction. The
shrinkage curve can be used in conjunction with the SWCC
equation to compute the void ratio-soil suction relationship.
The ratio between the a sh and b sh shrinkage curve equation
parameters is fixed by the initial degree of saturation S and the
specific gravity G s . There are two additional parameters to
determine: a sh and c sh . Values for the curvature of the shrink-
age curve, c sh , can be estimated based on regression analyses

a sh = minimum void ratio, e min ,

b sh = slope of the line of tangency,

c sh = curvature of the shrinkage curve,

a sh /b sh = G s /S = constant for a specific soil, and

w = gravimetric water content.

A least-squares fitting algorithm can be used to fit the
shrinkage curve equation to various data sets. A typical fit of
the data for an initially saturated soil is shown in Fig. 2.21.
The proposed shrinkage curve equation can describe a wide
variety of shrinkage curves. The effects of soil structure and
initial degree of saturation can be accommodated through

2.2

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0 10 20 30 40 50 60 70 80

Gravimetric water content, %

Figure 2.20 Typical soil shrinkage data for variety of soils with different initial volume-mass

properties (from M.D. Fredlund, 2002a).