1207
Critical State for Unsaturated Soils and Steady State of Thermodynamic Process
Etat critique de s sols non saturés et état stable thermodynamique
Zhao C.G., Li J., Cai G.Q., Liu Y.
School of Civil Engineering, Beijing Jiaotong University, China
ABSTRACT: Critical state is an important concept in modern soil mechanics. It was developed by Roscoe, Schofield and Wroth
(1958) and Schofield and Wroth (1968) for saturated soils. Currently, the critical state for unsaturated soils has not been clearly
defined and the necessary conditions and constraints to attain to critical state for unsaturated soils have not been definitely developed.
More studies on critical state of unsaturated soils are required. Based on theory of thermodynamics, the conditions and constraints to
attain to steady state of thermodynamic process for unsaturated soils are proposed in this paper. This paper points out that the steady
state of a deformation process of unsaturated soils is the ultimate state of the deformation process and it is, by concept, the critical
state of unsaturated soils. The conditions and constraints for critical state of unsaturated soils presented in the paper are more general
and complete, and are based on more rigorous thermodynamic theory instead of only being based on the laboratory test results of
particular unsaturated soil samples.
RÉSUMÉ :
Le concept d’état critique est un concept important en mécanique des sols. Il a été développé pour les sols saturés par Roscoe et al ;
(1958), et Schofield et Worth (1968). En revanche, ce concept n’est pas encore clairement décrit pour les sols non saturés. Il est donc
nécessaire de mettre en place des études plus approfondies dans ce sens. Dans cet article, en se basant sur la théorie de la
thermodynamique, les conditions et les limites pour atteindre l’état critique dans les sols non saturés sont exposées. Ici on considère
que l’état permanent de la déformation dans les sols non saturés est l’état ultime du processus de déformation, il peut donc être
considéré comme étant l’état critique. Les conditions et les limites pour l’état critique des sols non saturés présenté dans cet article
sont plus générales et complète , car elles sont basées sur la théorie de la thermodynamique au lieu d’être issues des essais de
laboratoire sur des échantillons de sols non saturés.
KEYWORDS: unsaturated soils; critical state; steady state of thermodynamic process
1 INTRODUCTION
Critical state is an important concept in modern soil
mechanics. It acts as the cornerstone of critical state soil
mechanics since it gives the final point of a soil deformation
process, which is necessary for establishing soil constitutive
models. Without the concept of critical state, it would not be
able to know which direction a soil deformation process
evolves, and where and when the deformation process ends. If
the end point of a deformation process is not defined, significant
deviations might occur in constructing soil constitutive models.
Once the initial state and the end point (the critical state) of a
deformation process are defined, relatively more accurate
models can be established by taking advantage of interpolations
between the initial state and the critical state, rather than only
using one-sided extrapolation from the initial state (without
critical state). Therefore critical state is a fundamental concept
that most constitutive models for soils are based on.
The critical-state concept was proposed by Roscoe,
Schofield and Wroth (1958), and Schofield and Wroth (1968),
and is defined as the end or ultimate state of a deformation
process for saturated soils, in which soil keeps shear deforming
with constant stress and volume in large strains. In three-
dimensional axisymmetric space (i.e. in triaxial stress state),
when a soil deformation process evolves to a critical state, the
stress and strain should satisfy the following necessary
conditions and constraints:
0;
0;
0;
0
s
p
q
(1)
The critical state can be expressed in
q p
space and
ln
e p
space by the following two equations, respectively:
( / )
;
ln( )
c
c
q p M
p
(2)
where
p
is the mean effective stress of saturated soils,
q
is
the deviator stress,
is the specific volume,
s
is the deviator
strain,
M
is the slope of the critical state line in
q p
space,
and
are the intercept (at
) and the slope of the
critical state line, respectively, in
space.
1kPa
p
ln
e
p
Previous and current studies of critical state have been
conducted mainly on saturated soils. Although the constitutive
models for unsaturated soils within the framework of critical
state soil mechanics have been developed by Alonso, Gens and
Josa (1990), Gens and Alonso (1992), Wheeler and Sivakumar
(1995), Wheeler, Sharma and Buisson (2003), Sheng, Sloan and
Gens (2004), Li (2007), Sun, Sheng, Cui and Sloan (2007) to
mention only a few from the existing literature, the definition
and the necessary conditions and constraints for critical state of
unsaturated soils have not been provided explicitly and clearly.
So it is affected to determine the value of critical state for
unsaturated soils correctly and accurately.
The engineering properties and behaviors of unsaturated
soils are much more complicated than those of saturated soils
because of the existence of air in unsaturated soils. Comparing
