Abstract
We study the stability of the solutions of the governing equations for soil liquefaction, assuming perturbations in the form of plane wave and of spherical wave. We model the dilatancy effect of soil for stability analysis by setting relevant components of constitutive tensors. Theoretical analysis shows that perturbations in the form of plane wave are always stable without dilatancy and can be unstable when dilatancy ratios exceed a certain critical value. We derive the critical dilatancy ratio explicitly for the plane wave case. For perturbations in the form of spherical wave, numerical simulations reveal similar dependency of stability on dilatancy ratios. As the existence of unstable solution is confirmed, our analysis provides a new perspective on possible initiation of liquefaction: a transition from stable to unstable solutions of the governing equations.
