Influence of packing density and stress on the dynamic response of granular materials
Granular Matter
Influence of packing density and stress on the dynamic response of granular materials
Masahide Otsubo 0 1
Catherine O'Sullivan 0 1
Kevin J. Hanley 0 1
Way Way Sim 0 1
0 Atkins , The Hub, 500 Park Avenue, Aztec West, Almondsbury, Bristol BS32 4RZ , UK
1 Department of Civil and Environmental Engineering, Imperial College London , London SW7 2AZ , UK
Laboratory geophysics tests including bender elements and acoustic emission measure the speed of propagation of stress or sound waves in granular materials to derive elastic stiffness parameters. This contribution builds on earlier studies to assess whether the received signal characteristics can provide additional information about either the material's behaviour or the nature of the material itself. Specifically it considers the maximum frequency that the material can transmit; it also assesses whether there is a simple link between the spectrum of the received signal and the natural frequencies of the sample. Discrete element method (DEM) simulations of planar compression wave propagation were performed to generate the data for the study. Restricting consideration to uniform (monodisperse) spheres, the material fabric was varied by considering face-centred cubic lattice packings as well as random configurations with different packing densities. Supplemental analyses, in addition to the DEM simulations, were used to develop a more comprehensive understanding of the system dynamics. The assembly stiffness and mass matrices were extracted from the DEM model and these data were used in an eigenmode analysis that provided significant insight into the observed overall dynamic response. The close agreement of the wave velocities estimated using eigenmode analysis with the DEM results confirms that DEM wave propagation simulations can
Discrete-element modelling; Dynamics; Elasticity; Waves; Filtering; Eigenmode analysis
-
2 Institute for Infrastructure and Environment, School of
Engineering, The University of Edinburgh, Edinburgh
EH9 3JL, UK
reliably be used to extract material stiffness data. The data
show that increasing either stress or density allows higher
frequencies to propagate through the media, but the low-pass
wavelength is a function of packing density rather than stress
level. Prior research which had hypothesised that there is a
simple link between the spectrum of the received signal and
the natural sample frequencies was not substantiated.
1 Introduction
Investigations of the nature of wave propagation through
granular materials provide essential material properties and
are often conducted for engineering applications. For
example, the velocity of the propagating wave can be related to the
small-strain stiffness of granular materials and is important
in geophysics, geotechnical engineering and fundamental
research into granular materials [
1–3
]. In these dynamic
geophysics tests, the wave velocity can be obtained using either
time domain techniques (e.g. [
4,5
]) or frequency domain
techniques (e.g. [
6–9
]). This paper explores whether
additional information, i.e. in addition to the elastic stiffness
parameters, can be obtained about the tested samples by
relatively simple analyses of the received signal. A testing
scenario is considered which involves a controlled
disturbance to generate an inserted signal at one sample boundary
and monitoring of the received signal at another sample
boundary.
Two research questions are considered here:
1. Granular materials act as a low-pass filter to seismic
(stress) or acoustic waves. Santamarina and Aloufi [
10
]
and Santamarina et al. [
11
] related the maximum
transmitted frequency ( flow− pass ) and the associated
wavelength (λlow− pass ) to particle size, while Mouraille and
Luding [
12
] related λlow− pass to the layer spacing. In
their analysis of bender element tests and simulations,
O’Donovan et al. [
13
] found that the relationship between
particle size and flow− pass differs from that proposed
by Santamarina and Aloufi [
10
] and Santamarina et
al. [
11
]. Data presented in O’Donovan [
14
] indicates that
flow− pass varies with confining pressure in randomly
packed monodisperse materials. Lawney and Luding [
15
]
examined a 1-D chain of spheres and observed that a
narrower band of frequencies is transmitted when there is
a variation in the sphere masses, in comparison with the
case of perfectly uniform spheres. At a given stress and
void ratio, the contact model also alters the frequency
limit [
16
]. A better understanding of the material
characteristics that determine flow− pass would enable us to
assess whether measurement of flow− pass in laboratory
seismic tests can provide useful information about how
to characterise the material. In addressing these issues
here, the influence of confining stress and void ratio on
flow− pass and λlow− pass are discussed.
2. The study also examines whether comparison of inserted
and received signals in the frequency (...truncated)