Analysis of discontinuous bifurcations for elasto-plastic geomaterials with effect of damage

The failure process of geomaterials can be regarded as the one in which the undamaged part of the material is transformed into the damaged part gradually. Thus by considering geomaterials as the mixture of the undamaged and damaged parts. a formulation of discontinuous bifurcation including the damage effect is presented. and the hardening modulus corresponding to the onset of discontinuous bifurcation is given in an explicit form. The damaged part is assumed not being able to support shear loading but having certain capacity to bear hydrostatic pressure as the hydrostatic pressure can make the micro-cracks closed to some extent, As a result. the properties of discontinuous bifurcation are much dependent on damage and the capacity of bearing hydrostatic pressure of the damaged part. Generally, damage may induce an earlier onset of discontinuous bifurcation and lead to instability of geomaterials.