Discrete and continuum methods for numerical simulations of non-linear wave propagation in discontinuous media

The main objective of this paper is to develop a methodology to model dynamic loading of various discontinuous media. Two methods for modeling non-linear waves in a media with multiple discontinuities are considered. The first one, a discrete method, is based on the Simple Common Plane contact algorithm. This method can be applied both to compliant contacts characterized by finite thickness and elastic moduli (such as joints in geomechanics) as well as to non-compliant frictional contacts traditionally described by the slide lines in finite element/finite difference codes. The second one, a continuum method, assumes that the contacts are not compliant and can be modeled as one or several weakness planes cutting through the elements of the computational mesh. Both discrete and continuum methods described in the paper can be applied to derive equivalent continuum properties for media with multiple discontinuities. An example of such application for a randomly jointed media is given in the paper. Copyright (C) 2010 John Wiley & Sons, Ltd.