Solving Stress-Deformation Problems with Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 731

CHAPTER 14

Solving Stress-Deformation Problems with Unsaturated Soils

14.1 INTRODUCTION functions relevant to the calculation of volume-mass

changes. This chapter presents procedures and examples of
one-dimensional, two-dimensional, and three-dimensional
volume change calculations.

The constitutive equations and related soil properties for
volume change of unsaturated soils were presented in the
previous chapter. The constitutive equations were written
in three forms: the elasticity form, the compressibility form,
and the historical soil mechanics form. Tests that can be per-
formed in a soil mechanics laboratory for the measurement
of unsaturated soil properties were described. Emphasis was
placed on three main types of tests that could be performed:
(i) compression tests (i.e., one-dimensional tests and the
isotropic triaxial tests), (ii) pressure plate tests to obtain
SWCCs, and (iii) shrinkage curve tests. The data from these
three types of tests were analyzed to produce approximate
constitutive surfaces for an unsaturated soil. The constitu-
tive relationships form the extremities or “bounding” faces
of the three-dimensional volume-mass constitutive surfaces.
The Pham and Fredlund (2011a) volume-mass constitu-
tive model was also presented. The model provides a means
of estimating the volume-mass properties along any stress
path when the soil behavior can be traced back to initially
saturated slurry conditions.
Laboratory test data may need to be converted from one
format to another format that is more acceptable for perform-
ing numerical modeling solutions for practical engineering
problems. For example, it might be necessary to convert the
coefficient of volume change, m v or m 1 , into a nonlinear
function comprised of equivalent values of Young's modu-
lus E and Poisson's ratio μ . This chapter and Chapter 13 are
directed toward understanding the theory of volume change
for an unsaturated soil and the conversion of laboratory-
measured soil properties into parameters that can be used
in an engineering analysis. The procedures that can be used
for calculating volume change or heave in expansive soils
are also described. The interpretation of the stress history
of the soil from the laboratory test results is often required
for the interpretation of the initial stress state condition in
expansive soils.
Procedures have also been proposed for estimating
unsaturated soil properties and unsaturated soil property

14.2 ESTIMATION OF STRESS-DEFORMATION
PROPERTIES

Engineering analyses should start with relatively simple
engineering models and progress toward the consideration
of more rigorous and complex models that better describe
unsaturated soil behavior. A common starting point is to
assume that the material behaves in an isotropic and elastic
manner. The term “elastic” means that the material behaves
in a conservative manner in the sense that all work done
by external stresses is stored and is recoverable upon
unloading. An important simplifying feature associated with
isotropic and elastic materials is the decoupling of shear and
volumetric deformations.
The basic material properties commonly used for stress-
deformation analyses are the elastic parameters referred to
as Young's modulus E and Poisson's ratio μ . The actual
soil properties are generally nonlinear and as a result the
elastic soil parameters need to be viewed in an incremental
manner. In other words, the elastic properties are a function
of stress state.
Young's modulus E and Poisson's ratio μ are elastic
parameters defined on the basis of a particular laboratory
test, namely, a uniaxial compression (or extension) test with
radial stress held constant. Young's modulus for an unsatu-
rated soil is defined as

d(σ v − u a )

E = (14.1)

dε a

where:

σ v − u a = vertical net axial stress in a uniaxial compres-

sion (or extension) test and

ε a = axial (vertical) strain.