Solving Stress-Deformation Problems with Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 756

Figure 14.34 Location of unloading surface (i.e., curve 1) obtained from oedometer test results.

A stress reversal associated with going from loading to
unloading conditions results in a slight curvature near the
start of the rebound curve. As a result, the first portion of
the rebound curve is generally omitted when determining the
slope of the rebound curve, C s . The slope of the rebound
curve is referred to as the swelling index C s .
The slope of a line through the points of free swell from
various surcharge pressures is referred to using the variable
C ts (see Figs. 14.23 and 14.34). The C ts index will be slightly
larger but quite similar in magnitude to the C s index.
The swelling index C s has been shown to typically
range between 10 and 20% of the compressive index C c .

Figure 14.35 shows approximate swelling index values
which have been correlated with the liquid limit and the
rebound void ratio of the soil (NAVFAC, 1971). The
correlation of C s versus the index properties shows that the
swelling index decreases with an increase in the void ratio
from which swelling occurs for a particular soil. The plot
is useful for obtaining an estimate of the swelling index C s
of an expansive soil.

14.5 ONE-DIMENSIONAL FORMULATIONS FOR
DEFORMATION ANALYSIS FOR UNSATURATED
SOIL

The analysis of one-dimensional heave can be numerically
modeled using the conversion of matric suctions onto the
total stress plane. The calculations for a one-dimensional
heave analysis can be performed either longhand or with
assistance from numerical modeling software. Both types of
one-dimensional solutions will be shown in this chapter. The
final pore-water pressure conditions are assumed, and as a
result it is necessary to simply solve the stress-deformation
equation for the y- direction. Transient solutions with
changes in pore-water pressure conditions with time (i.e.,
water flow partial differential equation) are solved in con-
junction with a stress-deformation analysis (see Chapter 16).
Two approaches are presented for the calculation of one-
dimensional heave in an expansive soil. First, it is possi-
ble to linearize the void ratio-stress state relationship on
a semilogarithm plot and perform a summation-type long-
hand analysis for the calculation of total heave. Second,

Figure 14.35 Approximate correlation of swelling index C s with
plasticity of soil and rebound void ratio (after NAVFAC, 1971).