Effect of pore fluid compressibility on localization in elastic-plastic porous solids under undrained conditions

Conditions are derived for band-shaped localization, i.e. for the existence of discontinuous bifurcations of the incremental strain field, in elastic-plastic porous materials, under undrained conditions. It is assumed that the pores are filled with nearly incompressible liquid/gas mixture, and the significant parameter is the bulk modulus of the pore fluid. The extreme situation is complete incompressibility, which would correspond to full saturation of a liquid with an infinite bulk modulus. In this case the surprising result is obtained that, for plane strain and cylindrical stress states, the critical bifurcation direction is always 45 degrees to a principal stress axis regardless of the adopted yield criterion. It is also shown in the paper that incompressibility usually (although not generally) has a stabilizing effect. For example, when the how rule is associated, the critical hardening modulus is always non-positive. A discontinuity in strain rate is always accompanied by discontinuous pore pressure rate across the characteristic surface, and the magnitude of this jump is related to the strength of the displacement jump. One restrictive assumption used in the analysis is that the gradient of the yield criterion and the flow direction are coaxial. A numerical evaluation of the critical bifurcation direction and the corresponding hardening modulus is given for the Mohr-Coulomb criterion, which is representative for the behavior of cohesionless granular materials such as soil.