353
Interpretation of stress-dependent mechanical behaviour of rockfill materials
Interprétation de stress-dépendante et comportement mécanique de matériaux enrochement
Jannati Aghdam R.
Senior Geotechnical Engineer, Tehran, Iran
Soroush A.
Amirkabir University of Technology, Tehran, Iran,
ABSTRACT: This paper studies thoroughly the mechanical behavior of thirty types of rockfill materials subjected to triaxial
compression shearing, each with three different confining stresses. The materials’ characteristics, including mineralogy, gradations
and shape of particles; and also the tests’ results have been collected from the literature. The Hyperbolic Model (Duncan and Chang
1970) is employed as a framework for interpreting the mechanical behavior of the materials. Features of the behavior of the rockfill
materials, as compared with that of soils, are highlighted through the exponent parameter (n) of the Hyperbolic Model. It is shown
that unlike for soils, the exponent number, n, is not constant for a given rockfill material, and that the n value depends on the
confining stress level; for the materials under high pressures, n can even takes a negative value, which is a sign of particle breakage of
the materials
.
Two correlations for estimating initial elasticity modulus (E
i
) and internal friction angle (φ) of these materials are
suggested.
RÉSUMÉ : Cet article étudie soigneusement le comportement mécanique de trente types de matériaux enrochement soumis à un
cisaillement triaxial chacun avec trois différentes contraintes de confinement. Les caractéristiques du matériau : minéralogie,
gradations et forme des particules et aussi les résultats du test ont été collectés à partir de la littérature. Le modèle hyperbolique
(Duncan et Chang 1970) est utilisé en tant que cadre pour l’interprétation du comportement mécanique des matériaux. Les
caractéristiques du comportement des matériaux en enrochement, par rapport à celles des sols, sont mises en évidence par le
paramètre d’exposant (n) du modèle hyperbolique. Il est montré que, contrairement aux sols, le nombre d’exposants, n, n'est pas
constant pour un matériau donné en enrochement et, en ce que la valeur de n dépend du niveau de contrainte de confinement ; pour les
matériaux à hautes pressions, n peut même prendre une valeur négative, ce qui est un signe de rupture des particules de matières.
Deux corrélations pour estimer le module d’élasticité initial (E
i
) et l’angle (φ) de frottement interne de ces matériaux sont proposées.
KEYWORDS: Rockfill Materials, Triaxial Compression Shearing, Hyperbolic Model, Initial Elasticity Modulus.
1 INTRODUCTION
Shear strength and deformation characteristics of rockfill
materials depend generally on different parameters, such as
mineralogy, grain size distribution, size of particles, stress level,
and particle breakage (if any). The importance of particle
breakage goes back to its capability of changing gradations of
granular materials.
This paper presents the results of a comprehensive study on
the mechanical behaviour of thirty rockfill materials under
medium and large scale triaxial testing. Data about the materials
and the tests are gathered from the literature. The Hyperbolic
Model (HM) is employed as an analytical and behavioural
framework for this study. The important parameters of the HM
for the rockfill materials are determined and compared with
similar parameters for typical loose and dense sands. Variations
of deformation and strength parameters (E
i
and φ) of the
materials with confining stress (σ
3
) are studied. On the basis of
this study, two relationships for estimating E
i
and φ of the
rockfill materials are proposed.
2 PROPERTIES OF ROCKFILL MATERIALS
Thirty types of rockfill materials, on which conventional triaxial
compression tests had been carried out, are used in this study.
The material characteristics, including mineralogy, uniformity
coefficient, shapes of particles and etc. for three types of these
materials are presented in Table 1. Because of conciseness the
presenting of the all of materials characteristics has been
neglected.
3 HYPERBOLIC MODEL AND ITS APPLICATION
3.1.
Theory of the model
The Hyperbolic Model (Duncan & Chang 1970) considers the
behavior of a soil specimen under compressive triaxial testing
as a hyperbola. According to the model, the gradient of the
tangent to the stress-strain relationship (q:ε
a
), namely as
tangential deformation modulus (E
t
), is defined as follows:
(1)
Where φ= internal friction angle; C= cohesion; K= modulus
number; n= exponent number, R
f
= failure ratio; and
P
a
= atmospheric pressure.
The above parameters for a given material can be obtained
by carrying out, usually, three triaxial tests on the soil’s
specimens.
Parameters K, n, and R
f
are usually determined from the
triaxial tests results and on the basis of a nonlinear stress- strain
behavior, which is assumed as a hyperbola (Konder 1963). The
Hyperbola equation is as follows:
(2)
Where σ
1
= maximum principal stress; σ
3
= minimum
principal stress; and ε
a
= axial strain in triaxial compressive
testing. Parameters a and b=the reverses of initial elasticity
modulus (E
i
) and ultimate deviatoric stress (σ
1
-σ
3
)
ult
,
respectively. These parameters can be determined by drawing a
Interpretation of stress-dependent echanical behaviour of rockfill aterials
Interprétation de stress-dépendante et co porte ent écanique de atériaux enroche ent
Jannati Aghda R.
Senior Geotechnical Engineer, Tehran, Iran
Soroush A.
Amirkabir University of Technology, Tehran, Iran,
ABSTRACT: This paper studies thoroughly the mechanical behavior of thirty types of rockfill materials subjected to triaxial
compression shearing, each with three different confining stresses. The materials’ characteristics, including mineralogy, gradations
and shape of particles; and also the tests’ results have been collected from the literature. The Hyperbolic odel (Duncan and Chang
1970) is employed as a framework for interpreting the mechanical behavior of the materials. Features of the behavior of the rockfill
materials, as compared with that of soils, are highlighted through the exponent parameter (n) of the Hyperbolic odel. It is shown
that unlike for soils, the exponent number, n, is not constant for a given rockfill material, and that the n value depends on the
confining stress level; for the materials under high pressures, n can even takes a negative value, which is a sign of particle breakage of
the materials
.
Two correlations for estimating initial elasticity modulus (E
i
) and internal friction angle (
φ
) of these materials are
suggested.
RÉSU É : Cet article étudie soigneusement le comportement mécanique de trente types de matériaux enrochement soumis à un
cisaillement triaxial chacun avec trois différentes contraintes de confinement. Les caractéristiques du matériau : minéralogie,
gradations et forme des particules et aussi les résultats du test ont été collectés à partir de la littérature. Le modèle hyperbolique
(Duncan et Chang 1970) est utilisé en tant que cadre pour l’interprétation du comportement mécanique des matériaux. Les
caractéristiques du comportement des matériaux en enrochement, par rapport à celles des sols, sont mises en évidence par le
paramètre d’exposant (n) du modèle hyperbolique. Il est montré que, contrairement aux sols, le nombre d’exposants, n, n'est pas
constant pour un matériau donné en enrochement et, en ce que la valeur de n dépend du niveau de contrainte de confinement ; pour les
matériaux à hautes pressions, n peut même prendre une valeur négative, ce qui est un signe de rupture des particules de matières.
Deux corrélations pour estimer le module d’élasticité initial (E
i
) et l’angle (
φ
) de frottement interne de ces matériaux sont proposées.
KEY ORDS: Rockfill aterials, Triaxial Compression Shearing, Hyperbolic odel, Initial Elasticity Modulus.
1 INTRODUCTION
Shear strength and deformation characteristics of rockfill
materials depend generally on different parameters, such as
mineralogy, grain size distribution, size of particles, stress level,
and particle breakage (if any). The importance of particle
breakage goes back to its capability of changing gradations of
granular materials.
This paper presents the results of a comprehensive study on
the mechanical behaviour of thirty rockfill materials under
medium and large scale triaxial testing. Data about the materials
and the tests are gathered from the literature. The Hyperbolic
odel (H ) is employed as an analytical and behavioural
framework for this study. The important parameters of the H
for the rockfill materials are determined and compared with
similar parameters for typical loose and dense sands. Variations
of deformation and strength parameters (E
i
and
φ
) of the
materials with confining stress (
σ
3
) are studied. On the basis of
this study, two relationships for estimating E
i
and
φ
of the
rockfill materials are proposed.
2 PROPERTIES OF ROCKFILL MATERIALS
Thirty types of rockfill materials, on which conventional triaxial
compression tests had been carried out, are used in this study.
The material characteristics, including mineralogy, uniformity
coefficient, shapes of particles and etc. for three types of these
materials are presented in Table 1. Because of conciseness the
presenting of the all of materials characteristics has been
neglected.
3 HYPERBOLIC ODEL AND ITS APPLICATION
3.1.
Theory of the model
The Hyperbolic odel (Duncan & Chang 1970) considers the
behavior of a soil specimen under compressive triaxial testing
as a hyperbola. According to the model, the gradient of the
tangent to the stress-strain relationship (q:
ε
a
), namely as
tangential deformation modulus (E
t
), is defined as follows:
=
1 −
1−sin
1
−
3
2 cos +2
3
sin
2
3
(1)
Where
φ
= internal friction angle; C= cohesion; K= modulus
number; n= exponent number, R
f
= failure ratio; and
P
a
= atmospheric pressure.
The above parameters for a given material can be obtained
by carrying out, usually, three triaxial tests on the soil’s
specimens.
Parameters K, n, and R
f
are usually determined from the
triaxial tests results and on the basis of a nonlinear stress- strain
behavior, which is assumed as a hyperbola (Konder 1963). The
Hyperbola equation is as follows:
1
−
3
= +
(2)
Where
σ
1
= maximum principal stress;
σ
3
= minimum
principal stress; and
ε
a
= axial strain in triaxial compressive
testing. Parameters a and b=the reverses of initial elasticity
modulus (E
i
) and ultimate deviatoric stress (
σ
1
-
σ
3
)
ult
,
respectively. These parameters can be determined by drawing a
fitting line to the tests results, as shown in Figure 1. R
f
is
defined as follows:
