Numerical algorithm based on implicit finite-difference schemes for analysis of dynamic processes in blocky media

Abstract

Abstract Dynamic processes in block-structured media are described within the framework of a mathematical model where elastic blocks interact with each other through pliable interlayers possessing complex mechanical properties. The case of elastic interaction is considered, the effects of plasticity and viscoelastic shear in block interlayers are taken into account. We use the model of porous fluid-saturated material in interlayers in which pores collapse during sudden or prolonged application of compressive stresses. An implicit difference scheme is constructed for numerical implementation of the model based on principles for construction of Ivanov’s schemes with controlled energy dissipation. Using MPI (Message Passing Interface), we developed parallel software for modelling wave motion in a two-dimensional formulation. The results of numerical analysis are presented for the waves initiated by rotation of blocks, which indicates a strong anisotropy of the blocky medium.