1031
Discrete Element Method Study of Shear Wave Propagation in Granular Soil
Étude de la propagation des ondes de cisaillement dans un sol granuleux par la méthode des
éléments discrets
Ning Z.
Department of Civil, Construction, and Environmental Engineering, North Carolina State University, Raleigh, NC, USA
Evans T.M.
School of Civil & Construction Engineering, Oregon State University, Corvallis, OR, USA
ABSTRACT: Shear wave velocity is a fundamental parameter for describing the small-strain response of soil and is a critical input for
multiple constitutive models used to describe the static and dynamic behavior of granular materials. Shear wave velocity is understood
to be a function of particle parameters (shape, elastic properties, gradation) and state (void ratio, boundary stress), but the exact effects
of these parameters are difficult to measure using laboratory results alone. This paper presents results of a study of shear wave
propagation in granular soil using the discrete element method (DEM). In this study, cylindrical assemblies of particles were
subjected to shear wave excitation at one end and axial propagation velocities were measured. The effects of excitation frequency,
particle size, and confining stress were investigated. Micromechanical observation of the specimen is presented and analyzed in terms
of particle velocity vectors.
RÉSUMÉ : La célérité de l’onde de cisaillement est un paramètre fondamental pour décrire le modèle constitutif du sol. Plusieurs
modèles utilisent ce paramètre pour décrire le comportement statique et dynamique de matériaux granuleux. La vitesse de l’onde de
cisaillement est fonction des paramètres des particules (la forme, les propriétés élastiques, la granularité) et de leur état (indice des
vides, contrainte aux limites). Par contre, il est difficile de mesurer l’effet exact de ces paramètres en utilisant des résultats
expérimentaux. Cet article présente les résultats de l’étude de la propagation de l’onde de cisaillement dans un sol granuleux en
utilisant la méthode des éléments discrets. Les particules, groupées en cylindre, sont excitées par des ondes de cisaillement à un bout
du cylindre. Les vitesses de propagation sont ensuite mesurées. Les effets de la fréquence d’excitation, de la taille des particules et de
la contrainte de confinement sont étudiés. Les observations du spécimen sont présentées et analysées en termes de vecteurs de célérité
des particules.
KEYWORDS: small strain, shear wave velocity, discrete element method.
1 INTRODUCTION
Shear (S-) wave velocity is a fundamental parameter for
describing the small-strain response of soil and is a critical input
for multiple constitutive models used to describe the static and
dynamic behavior of granular materials (Santamarina 2001). S-
wave velocity is understood to be a function of particle
parameters (e.g. shape, elastic properties, gradation) (Patel et al.
2009) and state (e.g. void ratio, boundary stress) (Hardin and
Richart 1963). Many of these properties can be measured (or
observed) as specimen-averaged quantities, but in some cases,
the parameter of interest is not directly observable using
standard laboratory practices. For example, Agnolin and Roux
(2007) have shown that shear wave velocity is a function of
both void ratio (packing fraction) and coordination number (i.e.,
specimens with identical void ratios but different coordination
numbers exhibit different wave propagation speeds). This
complex behavior implies a need for investigation of wave
propagation in particulate assemblies that goes beyond
traditional specimen-averaged approaches.
Discrete element method (DEM) simulations are a useful tool
for investigating the complex behavior of particulate materials
in conjunction with laboratory tests. In terms of wave
propagation, 2D DEM simulations have been conducted to
study the general relationships between wave propagation
variables and soil fabric (Sadd et al. 1993). In a DEM study of
the acoustic properties of weakly cemented sandstone by Li and
Holt (2002), a logic similar to S-wave generation and
measurement in laboratory tests was applied. O’Donovan et al.
(2012) recently used 2D DEM models to simulate bender
element tests on an idealized granular material.
In the current study, 3D DEM simulations were used to simulate
S-wave propagation in a granular material. The effects of
excitation frequency, particle size and confining stress are
investigated and compared to published trends of small-strain
response for granular materials. Micromechanical observation
of the specimen is presented in terms of particle velocity
vectors.
2 SIMULATION OF SHEAR WAVE PROPAGATION
2.1
Generation of DEM assembly and shear waves
Cylindrical DEM specimens were generated with the following
properties: G
s
=2.7, D
50
=2.0 mm, C
u
=1.2, G
g
=2.9 GPa, ν
g
=0.31,
and μ=0.31 (note that G
g
, ν
g
, and μ are grain, not specimen,
parameters). Two planar rigid walls defined the top and bottom
boundaries of the specimen and were used to control the applied
vertical stress. Radial confinement was supplied by stacked
cylindrical walls (Zhao and Evans, 2009) to simulate a flexible
membrane, which can help to minimize the wave reflection
from the lateral boundaries (O’Donovan et al. 2012).
S-waves were generated by applying a horizontal excitation to a
thin layer of particles at one end of the specimen using a
sinusoidal pulse. Compared to the S-wave generation method
used in the bender element test, in which the wave source is a
point and the wave propagation front is spherical, the S-wave
generation method in the current study can help to reduce the
compression (P) wave interference effect (Lee and Santamarina
