A general multi-plane model for post-liquefaction of sand

A multi-plane model for the post-liquefaction of the undrained behaviour of sand is presented. The model incorporates the critical/steady state concept that postulates the existence of a state where sand continuously deforms at a certain constant effective stress depending two main parameters of both initial bulk parameters (i.e. void ratio or relative density) and stress level (i.e. mean stress). The local instability of saturated sand within post-liquefaction is highly dependent on the residual inherent/induced anisotropy, bedding plane effects, and stress/strain path. Most of the models developed using stress/strain invariants are not capable of identifying the parameters depending on orientation such as fabric. This is mainly because stress/strain invariants are quantities similar to scalar quantities and not capable of carrying directional information with themselves. The constitutive equations of the model are derived within the context of the non-linear elastic behaviour of the whole medium and the plastic sliding of interfaces of predefined multi-planes. The proposed multi-plane based model is capable of predicting the behaviour of soils on the basis of plastic sliding mechanisms, elastic behaviour of particles and possibilities to see the micro-fabric effects as natural anisotropy as well as induced anisotropy in plasticity. The model is capable of predicting the behaviour of soil under different orientations of the bedding plane, and the history of strain progression during the application of any stress/strain paths. The influences of the rotation of the direction of principal stress and strain axes and induced anisotropy are included in a rational way without any additional hypotheses. The spatial strength distribution at a location as an approximation of the probable mobilized sliding mechanism is presented by an ellipsoid function built up on the bedding plane.