GRAIN-SCALE STRESSES IN A TWO-PHASE GRANULAR SYSTEM: A NUMERICAL MODEL

Many models of the deformation behavior of natural rocks assume that rocks are homogeneous materials. Yet, rocks often consist of two or more minerals with different grain sizes, shapes, and material properties. The deformation behavior of the bulk rock may be influenced by variables both intrinsic to the rock (grain size, shape and strength, and percentage and spatial distribution of each phase) as well as extrinsic to the rock (T, P, stress, strain-rate.) Because of the large number of variables, it is difficult to determine the effects of individual variables or interactions between variables.

We have developed a grain-scale numerical model to explore the effects of some of these variables on the bulk mechanical behavior of rocks. As bulk mechanical behavior arises from local grain contact forces, we examine the range of grain-scale stress networks that can develop in multi-phase assemblages. The model is based on the discrete element method (modified from Aharonov and Sparks, 1999), in which grains are approximated by circular disks which interact through elastic and frictional contact forces. We define sets of grains (500-5000) which consist of two populations with different grain size distributions and/or rheological properties. The shear and normal forces are calculated on each grain contact, and therefore the stress state of each grain can be calculated. Rigid boundaries apply a variety of macroscopic stress states. Due to heterogeneity in grain size, force is transmitted via a network of force chains, sets of grain contacts that can carry up to ten times the average applied confining stress.

We are systematically exploring a range of two-phase systems. Our initial models focus on two distributions of phases that have identical mechanical properties, but different mean diameters. The majority of grains with high internal differential stresses are from the smaller phase, an effect that is enhanced by increasing the proportion of small grains and increasing the size contrast between the phases. In systems with a low proportion of small grains, not unexpectedly, the force chains are mostly contacts between large grains, while the small grains are typically in low-stress areas between chains. However, with a high proportion of small grains, the few large grains are typically still in force chains, implying that they may still affect the bulk strength of the material.