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Fabric and critical state of granular materials
La structure et l’état critique des matériaux granulaires
Yan W.M., Zhang L.
The University of Hong Kong
ABSTRACT: Critical state of particulate materials traditionally refers to a state where the material undergoes continued distortion at
constant volume and constant stresses. By saying so the internal state of the material at the critical state is described solely by an
isotropic (scalar-valued) parameter
–
the void ratio. Advances in modern laboratory tests have initiated the discussion of the effect of
fabric on critical state and thus its uniqueness. More recently Li and Dafalias (2012) have shed light on the uniqueness of critical state
from a thermodynamics perspective. This study uses the discrete element approach to investigate the fabric evolution of idealized
two-dimensional assemblages having different initial fabrics subject to numerical biaxial shearing. The current paper focuses on the
orientation of particles and void spaces at very large strains. It is shown that a unique fabric of particle orientation and void space is
achieved at very large strains where the granular assemblage distorts continuously at constant density and stresses.
RÉSUMÉ :
L’état critique des matériaux particulaires réfèr
e normalement à un état où le matériau est soumis à un cisaillement
continu sous volume et contraintes constants. Cela signifie que l’état interne des matériaux a l’état critique est décrit seulement par un
paramètre (scalaire) isotrope
– l’indice des vide
s. Avec les avancées en essais en laboratoire modernes a commencé la discussion de
l’effet de la structure sur l’état critique et son unicité. Li & Dafalias (2012) ont étudié récemment l’unicité de l’état critique par la
thermodynamique. Cette étude utilis
e une approche aux éléments discrets pour examiner l’évolution de la structure d’assemblées
idéalisées en deux dimensions ayant des structures initiales différentes et soumises à un cisaillement bi-axial numé
rique. L’objet de
cet article est l’orientation des particules et espaces des vides aux grandes déformations. On montre qu’aux grandes déformations une
structure unique faite de l’orientation des particules et des vides est obtenue quand l’assemblée granulaire est cisaillée de façon
continue sous densité et contraintes constantes.
KEYWORDS: anisotropy; critical state; discrete element analysis, fabric; microstructure.
1 INTRODUCTION
The concept of critical state is important to soil mechanics. It
defines the existence of a unique state where the particulate
material exhibits constant volume shearing at constant effective
stresses under continuous distortion. The state is often obtained
phenomenlogically. Over decades many constitutive models are
formulated in accordance with this concept since the pioneering
work by Roscoe and Schofield (1963) and Roscoe and Burland
(1968). On the one hand, those models successfully capture the
key mechanical behavior of many geomaterials subject to
compression and shear. On the other hand, with the advances in
modern laboratory testing techniques the influence of initial
fabric on the material’s stress
-strain-strength responses have
received much attention and the uniqueness of critical state has
been great challenged (Vaid et al. 1985, Negussey and Islam
1994, Mooney et al. 1998, Finno and Rechenmacher 2003, etc).
Herein fabric is a collective term to describe the geometric
arrangement of grains and the associated voids, and the
distribution of inter-particle contact forces. Material anisotropy
has often believed to be the prime reason for the observation of
a non-unique critical state. The critical state is often represented
by two projection lines (critical state line, CSL) in the
q
-
p
’
and
e
-
p
’
(or
v
-
p
’
) plane, in which
3 : / 2
q
s s
,
'
tr ' / 3
p
σ
where
s
is the deviatoric part of the effective stress tensor '
σ
;
e
is the void ratio and 1
v
e
is the specific volume. Internal
state of the soil at the critical state is solely described by a scalar
quantity of density (
e
or
v
) which implicitly shows that any
anisotropic information of the material cannot be properly
addressed. However, one may doubt why the material state
remains (or becomes) isotropic at the critical state where the
imposed stress is anisotropic (
/ '
q p M
where
M
is the
critical stress ratio). Besides, while density and stress are
uniquely related, should there be a unique particulate fabric at
the critical state?
More recently, Li and Dafalias (2012) revisited the critical
state concept and proposed an anisotropic critical state theory
(ACST) by considering the role of the particulate fabric. From a
thermodynamics perspective and based on the Gibbs stability
requirement, uniqueness of the critical state line (CSL) has been
proved. Furthermore, they also concluded that a unique fabric as
a function of the loading direction must exist.
This paper investigates the evolution of the fabric of a two-
dimensional idealized granular assemblage subject to numerical
biaxial shearing. It aims to shed light on ACST proposed by Li
and Dafalias (2012) from a numerical perspective using the
discrete element approach.
2 NUMERICAL SPECIMEN AND TEST
Two-dimensional mono-sized non-crushable pill shape rigid
particles with length-to-width ratio of 1.5 (width = 1 mm) are
generated with the built-in clump function in PFC2D (Itasca
2008). The linear contact model between particles is adopted.
The particles are then rained into a model container under
gravity fields of different directions (see Figure 1). By doing so,
assemblages formed by particles having different average
