Granular Matter (2014) 16:69–78
DOI 10.1007/s10035-013-0455-3
ORIGINAL PAPER
Strong force networks in granular mixtures
N. H. Minh · Y. P. Cheng · C. Thornton
Received: 21 January 2013 / Published online: 27 October 2013
© Springer-Verlag Berlin Heidelberg 2013
Abstract Using the results of 3D discrete element method
simulations we study the force transmission through binary
mixtures of sand and silt sized spheres under one-dimensional
compression. Three types of contact are categorized depend-
ing on the size of the two spheres in contact. The contributions
of each contact type to the deviator stress are dependent on
the proportion of silt sized spheres. We demonstrate that the
magnitude of the deviator stress is solely due to the normal
and tangential forces at contacts transmitting normal forces
greater than a characteristic normal force, which is generally
slightly greater than the average normal force. The maxi-
mum packing efficiency was obtained with the mixture of
30 % silt sized spheres and this mixture corresponds to a
transition point when there are enough silt sized particles to
start to separate the sand sized particles from each other and
establish contacts between silt sized spheres that contribute
to the deviator stress.
Keywords Granular mixtures · Discrete element · Strong
force transmission · Characteristic force · Force distribution ·
One dimensional compression
N. H. Minh (B )
School of Engineering, Nazarbayev University, Astana 010000,
Republic of Kazakhstan
e-mail: minh.nguyen@nu.edu.kz
N. H. Minh· Y. P. Cheng
Department of Civil, Environmental and Geomatic Engineering,
University College London, Gower Street, London WC1E 6BT, UK
C. Thornton
School of Chemical Engineering, University of Birmingham,
Edgbaston, Birmingham B15 2TT, UK
1 Introduction
The behaviour of granular systems is highly dependent on
the size distribution of the constituent particles. Force trans-
mission through assemblies of discrete particles of different
sizes can be characterized by a high degree of force inhomo-
geneity. This happens when a small number of contacts in the
system transmit forces of significantly higher magnitude than
the other contacts. The force transmission can be represented
by two distinct classes called the strong force and the weak
force contact networks [1, 2]. The strong forces were defined
as contact forces contributing primarily to the macroscopic
deviator stress and hence they determine the shear strength of
the sample. Column-like structures [3] carrying strong forces
were observed inside granular systems, and the buckling of
these structures (i.e. the strong force chains) leads to the
development of shear bands [4]. The contacts transmitting
weak forces, on the other hand, tend to be oriented perpen-
dicular to the loading direction and support the stability of
the strong force chains. The weak forces only contribute to
the isotropic stress component or have a negligible contribu-
tion to the deviator stress. For slightly polydisperse systems
[1, 2], the characteristic force that divides the strong forces
and the weak forces is approximately the mean normal con-
tact force of the whole system. The relative proportion of the
strong contacts in a three dimensional system [2] is about one
third of the total number of contacts. These characteristics of
the contact force network are important features of granular
media that reflect the high level of redundancy in the system
in which only some of the contacts are required to resist the
overall applied deformation.
In this study, we investigate the effect of particle size dis-
tribution on the compression behaviour of imperfect binary
mixtures of a polydisperse sand-sized material and a finer
uniform silt-sized material; the maximum size ratio in the
123