Quasi-static mechanical testing of granular structures (representing rock) is simulated using a Generalized Interpolation Material Point method (GIMP). The numerical analysis is carried out by representing the rock as a dense packing of non-uniformly-sized particles that are cemented in the vicinity of points of contact. Mechanical behavior of the cement is imparted by cohesive zone elements. With progressively increasing application of far-field stresses, local stresses increase to the point where the cohesive zone elements lose load-bearing capacity. The sensitivity of this decohesion to the number of cohesive zone segments was investigated (i.e., the discretization of cemented zones into conjoined cohesive elements). A parametric study also varied the traction strengths for these cohesive features. Cementitious micro-properties were estimated to represent cohesive characteristics of typical porous rock materials and to result in representative peak-loading behavior for the aggregate sample. Uniaxial compression and Brazilian tests were numerically performed on granular assemblies with rock-like properties. INTRODUCTION
Experimental testing of rocks under various loading conditions has revealed numerous complex mechanisms occurring at macro- and microscopic levels. The results of these phenomena are manifested in an emerging mechanical response and ultimately failure of the rock [1-8]. This preliminary program has been carried out to develop a model that will simulate these micro- and/or macroscale events and replicate experimental results from laboratory testing of rock samples. In this investigation, a cohesive zone model in the Generalized Interpolation Material Point Method has been implemented to simulate representative laboratory loading protocols.
The behavior of granular materials has been extensively studied by various researchers. Cundall & Strack  performed numerical calculations for interparticle forces within assemblies of discs and spheres. Chang et.al  derived closed-form solution for random packing under low levels of deviatoric stress. Potyondy and Cundall  proposed the bonded-particle model for describing the mechanical behavior of packing of non-uniform sized circular or spherical particles. Particle-type models of rocks have been used to address various phenomenona in rock in geomechanics [12-13]. Numerical/analytical concepts of cohesion in granular situations are not new. Barenblatt  used the concept of equivalent traction on contacting surfaces to describe localized separation under progressive loading. A number of researchers have used the cohesive layer modeling approach to represent localized failures in concrete [15-18]. These models offer advantage of incorporating non-linear material properties with mesh independent post-localization behavior.
As is no surprise, the candidate samples are represented by an assemblage of grains immobilized by frictional resistance and by cementation at contact points (as well as any pore filling cement). In these demonstrations, the grains were treated as spherical or with realistic structure determined from appropriate tomography. Cementation between the grains was described by cohesive zone elements. These cohesive zone elements were characterized using published traction-displacement relationships with peak strength. Numerical simulations of uniaxial compressive testing and laboratory loading are shown to demonstrate deformation and strength of typical granular assemblies.
In this simulation exercise, porous rocks have been represented as cemented, granular media with following assumptions: