Evolution of force distribution in three-dimensional granular media

Abstract

Based on the discrete element method, the nature of normal contact force distribution and the effect of microstructure (contact fabric) on stresses in granular media sheared under constant mean stress condition is analyzed. The particles are tested in a periodic cell, having a nearly monodispersed system of spherical particles ("hard" and "soft"). The granular systems were initially isotropically compressed to have different solid fractions in order to obtain "dense" and "loose" samples. To study the nature of the force distribution, the granular medium was considered as both (i) noncohesive and (ii) with low values of interface energy. For the granular systems considered here, the nature of force distribution is shown to be dependent on shear history. The amount of interface energy introduced in the granular system does not seem to change the nature of normal force distribution significantly. However, it improves the postpeak stability in agreement with previous research [C. Thornton, Geotechnique 50, 43 (2000)]. The simulation of systems subjected to quasistatic shearing, in general, reveals that in a hard system (both dense and loose), the normal contact force distribution (i) at "peak" shear strength is purely an exponential decay throughout the entire range of force scale that is used, and (ii) at "isotropic" and "steady" states, the contact normal force distribution is bimodal with forces greater than average decaying exponentially at both the states, while the forces less than average tend to be half-Gaussian at the "isotropic" state and a second-order polynomial function at the "steady" state. For the soft (dense) system, the normal contact force distribution at "peak" shear strength is bimodal with forces greater than average decaying exponentially while the forces less than average tend to be a second-order polynomial function. However, for the soft system at both "isotropic" and "steady" states, the contact normal force distribution is half-Gaussian throughout the entire range of force scale that is used. It has been pointed out that in a granular system undergoing slow shearing, the shear strength of the system seems to depend on the ability of the material to form strong fabric anisotropy of contacts carrying strong (greater than average) force.