The Concept of Effective Stress in Unsaturated Soils - Multiscale Geomechanics: From Soil to Engineering Projects - page 152

and the capillary pressure p c were kept constant during the test, even though σ, p a
and p w varied. However, [JEN 62] questioned the validity of the effective stress
principle in unsaturated soils because it could not explain the phenomenon of
collapse observed during wetting tests under constant total stress.

In recent years, a number of researchers have shown that irreversible strains,
such as those in collapse, could be correctly described by a generalized effective
stress concept associated with an elasto-plastic law that integrated a yield surface
function of capillary pressure [BOL 96; DAN 02; KHA 01; KHA 04; KOH 63;
LOR 00; MOD 94].

These studies have shown that the effective stress concept, extended to
unsaturated soils, remains an efficient means by which to qualitatively and
quantitatively describe the unified mechanical behavior of soils passing from
saturated to unsaturated domains and vice versa.

Table 6.1 summarizes the expressions of χ proposed by several researchers.

Today, different approaches are used to characterize the behavior of polyphasic
granular media (Figure 6.1). We can mention, as an example, the macroscopic
phenomenological, homogenization, and discrete elements methods (DEM).

The extension of the effective stress tensor concept to unsaturated soils, under
the hypothesis that the unsaturated soil is a poro-elastic material, in other words,
when the solid constituent has a reversible elastic behavior, is presented as

σ ' = σ + π

[6.6]

ij ij ij

i π : isotropic tensor, ij

π =

ij

The micro-macro approach of the unsaturated porous media has led some
investigators to generalize the Hill's lemma [CHA 95].

This approach, based only on mechanical considerations of statics, gives an
expression of π as

π = Sp + Sp − U

[6.7]

gg ll