Diffuse Vs. Localized Instability in Compacting Geomaterials Under Undrained Conditions

Abstract

The coupling between the pore fluid diffusion and deformation of geomaterials can alter the mechanical response and facilitate or delay material failure. Dilatant or contractive material behavior under conditions of limited drainage and/or of loading rate exceeding the pore fluid diffusion rate causes a reduction or increase in pore pressure, respectively. The latter, via the effective stress principle, results in dilatant strengthening or contractive weakening of frictional materials, namely, an increase or decrease in shear stress that can be sustained by the material from the corresponding value in the underlying drained response. In this work, we use perturbation theory to examine how the contractive weakening affects the stability of undrained deformation and what are the possible instability modes (localized vs. diffuse) on the example of a one-dimensional simple shear of a layer under partially strain-controlled boundary conditions. The effect of material rate-sensitivity on undrained stability is examined. INTRODUCTION Deformation of fluid-infiltrated solids is generally coupled with pore fluid flow. The presence of pore fluids can alter deformation processes and facilitate or delay material failure. Some of geomechanics applications where the coupling of inelastic deformation and pore fluid flow is important include the problems of slope stability and liquefaction in saturated soil deposits (Ishihara 1993), stability of slip in fault gouge zones in the Earth’s crust (Rice 1992), efficient underground storage of natural gas, and terrestrial sequestration of greenhouse gases (carbon dioxide) to mitigate adverse effects on the atmosphere (Rudnicki 1996). It has been recognized for a long time that dilation or contraction of frictional geomaterials in the course of inelastic shear is the key mechanism to cause the coupling. The micro-mechanism of macroscopic inelastic volume changes varies from shear-induced opening of micro-fissures in tight rocks (Brace et al. 1966) to the rearrangement of grains into more loose or dense configuration depending on the initial packing density in sands. 1In Proceedings of the First Japan-U.S. Workshop on Testing, Modeling and Simulation in Geomechanics, Boston, Massachusetts, USA, June 27-29, 2003. 2Department of Civil and Environmental Engineering, Clarkson University, 8 Clarkson Ave., Potsdam NY 13699-5710, garagash@clarkson.edu