Non-uniformity of stress and deformation in axisymmetric finite element models of Tennessee marble

An impediment to accurate numerical simulation of the inelastic behavior of rocks has been the difficulty of obtaining detailed constitutive information. Here we present results of finite element simulations using a constitutive model for Tennessee marble developed from a suite of axisymmetric compression tests. The model includes dependence of the dilation factor, friction factor, and plastic hardening modulus on mean stress and accumulated inelastic shear strain. Although the development of the constitutive model assumed uniform deformation in the samples, here we use the numerical simulations to study the evolution of inhomo-geneities due to realistic boundary conditions Thai simulate those in laboratory experiments. Even when in-homogeneities do not affect the overall stress-strain behavior they can be significant in initiating the failure process and in determining whether a description of failure as a bifurcation from homogeneous deformation (as in the Rudnicki-Rice theory) is appropriate. Our finite element models involve three distinct configurations for axisymmetric test pieces. The first is for homogeneous deformation in the rock (corresponding to a frictionless sample-platen interface); the second is for a perfectly bonded interface between the marble and the platen (i.e. no slip between marble and metal). The third configuration models a frictional interface he-tween the platen and marble, with several different coefficients of friction. Whole-sample nominal stress and strain curves are nearly unaffected by friction at the sample-platen interface, differing by less than one percent relative to the case of homogeneous deformation for all strains that are reached in the non-homogenous cases. We do, however, find a surprising variety of mechanical responses within the samples for all non-homogeneous cases. These appear to be due primarily to variations in mean stress. For example, non-zero friction at the interface results in hardening at the center of the sample and near the upper outside edge. Al the center, the hardening occurs at a negative plastic hardening modulus and is due entirely to increasing mean stress white the other location shows hardening at a positive hardening modulus. Also, near the outside edge along the middle of the sample and near the top centerline we find that the mean stress increases and then decreases as loading progresses. The decrease at the former location results from deformation into the softening regime; the mean stress decrease near the top center is from elastic unloading from a previously plastic state. We compare the finite element analyses of deformation in axisymmetric test pieces with those of plane strain samples. The plane strain samples do not show the variety of mechanical responses that are discussed above for the axisymmetric test pieces, but show strain hardening and not softening or elastic unloading.