895
Variation of Friction Angle and Dilatancy For Anisotropic Cohesionless Soils
Variations de l’angle de Frottement et de la Dilatance pour les Sols Anisotropes Sans Cohésion
Cinicioglu O., Abadkon A., Altunbas A., Abzal M.
Bogazici University, Istanbul, Turkey
ABSTRACT: The goal of this paper is to investigate and quantify the variation of peak friction and dilatancy angles of anisotropic
cohesionless soils as functions of the in-situ state of the soil. In this context, in-situ state of the soil is used as a broad term that
encompasses the combined effects of the stress state, volumetric state, and stress history of the soil prior to any shearing. Accordingly,
the parameters that define the in-situ state of soil are in-situ confining pressure (p
′
i
), relative density (I
D
) and overconsolidation ratio
(OCR), respectively. In order to quantify the influences of these parameters on the peak friction angle and dilatancy angle, a special
testing program was designed that employs mainly CK
o
D triaxial tests. These tests were conducted on reconstituted sand samples at
different p
′
i
-I
D
-OCR combinations. Analyzing the obtained results, two new functions are proposed that allow the calculation of the
peak friction angle and dilatancy angle of anisotropic cohesionless soils. The greatest advantage of the proposed functions is that they
use directly measurable or calculable parameters as input. Finally, using similar test data collected from literature, the proposed
empirical equations are validated.
RÉSUMÉ : Le but de cette étude est de chercher et de quantifier les variations des angles de frottement maximum et de dilatance de
sols anisotropes sans cohésion comme des fonctions de l’état in-situ du sol. Dans ce contexte, l’état in-situ du sol est utilisé comme un
terme général qui entoure les effets combinés de l’état de contrainte, l’état volumétrique, et l’histoire des contraintes du sol avant tout
cisaillement. Par conséquent, les paramètres qui définissent l’état in-situ du sol sont la pression de confinement, la densité relative et
le taux de surconsolidation, respectivement. Afin de quantifier les influences de ces paramètres sur l’angle de frottement maximum et
l’angle de dilatance, un programme d’essai spécial a été conçu qui emploie principalement des essais triaxiaux. Ces essais ont été
effectués sur des échantillons de sable reconstituées selon différentes combinaisons. L’analyse des résultats obtenus conduit à deux
nouvelles fonctions qui permettent le calcul de l’angle de frottement maximum et de dilatance de sols anisotropiques sans cohésion.
KEYWORDS: dilatancy, friction angle, sand, K
o
-consolidation, granular material
1 INTRODUCTION
Dilatancy is a property that is unique to granular materials.
However, for soils, manifestations of dilatancy depends on grain
size and shape; In case of fine-grained soils, we can describe
dilatancy as latent dilatancy since dilatant behavior manifests
itself as a change in the pore water pressure. Though, in case of
coarse-grained soils, dilatancy is physically evident and can be
directly measured by conducting simple soil tests. Even though
for both fine and coarse-grained soils dilatancy influences
strength, only for coarse-grained soils it has an effect on the
formation of shear planes, thus controlling the geometry of
failure mechanisms. Due to this fact, dilatant behavior of
coarse-grained soils draws much attention from the academia
(Taylor 1948, Rowe 1962, De Josselin de Jong 1976, Bolton
1986, Schanz and Vermeer 1996, Chakraborty and Salgado
2010). Even in the face of this ever-continuing scientific interest
in dilatancy, a practical function that renders the quantification
of dilatant behavior is yet to emerge. There are milestone works
towards understanding dilatant behavior as listed in the
references; however the proposed functions are either
impractical or conceptual. For example, one of the well-known
functions for calculating dilatancy (
ψ
) was proposed by Bolton
(1986):
−
⁄
= 0.3
= 0.3
−
′ −
(1)
d
ε
v
and d
ε
1
in Eq. (1) corresponds to the increments of
volumetric strain and major principal strain, respectively. I
D
is
the relative density ranging from 0 to 1 and p
′
f
is the
corresponding mean effective stress at failure. Q and R are
empirical fitting parameters whose units are dependent on the
unit used for p
′
f
. Accordingly, I
R
is defined as the relative
density index which yields p
′
f
dependent magnitude of I
D
. Later
Schanz and Vermeer (1996), relying on experimental results,
improved Eq. 1:
= −0.3
2 + 0.3
⁄
=
6.7 +
⁄
(2)
Recently Chakraborty and Salgado (2010) studied the values
of the fitting parameters Q and R, especially for low
confinement conditions. However, it is clear that the variables
of Eq. 1 and Eq. 2 are defined for the moment of soil failure and
this approach significantly reduces the practicality of the
proposed equations. Hence, the goal of this study is to calculate
dilatancy angle using parameters that correspond to the in-situ
state of the soil. Previous studies have shown that dilatant
behavior is affected by the confinement and compactness of the
soil. Accordingly, confinement is defined by confining pressure
(p
′
) and compactness is defined by the relative density of the
soil (I
D
), as is the case in Eq. 1 and Eq. 2. In addition to the
confinement and relative density, Vaid and Sasitharan (1991)
showed that stress path affects the dilatant behavior. That is
why, in this research the most ubiquitous stress path in nature is
chosen for sample preparation which is the K
o
consolidation.
Even though stress path followed during sample preparation
stage is confined to K
o
consolidation, the influence of stress
history is investigated by considering the overconsolidation
ratio (OCR) as a third variable. Since all these can be achieved
during a triaxial test, the tests conducted were K
o
-consolidated
and drained triaxial tests (CK
o
D). In order to achieve different
OCRs, the samples were unloaded under K
o
conditions.
In the remainder of this paper, the results of the tests
conducted are presented followed by the construction of the
dilatancy equations. Following, the proposed equations are
validated using data collected from the literature.
2 EXPERIMENTAL STUDY
The experimental approach in this study is to conduct sufficient
number CK
o
D tests at different p
′
i
-I
D
combinations so that it would
be possible to define the p
′
i
-
ψ
relationship for every 5% change in
I
D
. This is achieved for an I
D
range within 0.35 to 0.95 by
