Brittle and ductile failure of rocks: Embedded discontinuity approach for representing mode I and mode II failure mechanisms

In this work, we present a discrete beam lattice model with embedded discontinuities capable of simulating rock failure as a result of propagating cracks through rock mass. The developed model is a two-dimensional (plane strain) microscale representation of rocks as a two-phase heterogeneous material. Phase I is chosen for intact rock part, while phase II stands for pre-existing microcracks and other defects. The proposed model relies on Timoshenko beam elements enhanced with additional kinematics to describe localized failure mechanisms. The model can properly take into account the fracture process zone with pre-existing microcracks coalescence, along with localized failure modes, mode I of tensile opening and mode II of shear sliding. Furthermore, we give the very detailed presentation for two different approaches to capturing the evolution of modes I and II, and their interaction and combination. The first approach is to deal with modes I and II separately, where mode II can be activated but compression force may still be transferred through rock mass which is not yet completely damaged. The second approach is to represent both modes I and II being activated simultaneously at a point where complete failure is reached. A novel numerical procedure for dealing with two modes failure within framework of method of incompatible modes is presented in detail and validated by a set of numerical examples. Copyright (c) 2015 John Wiley & Sons, Ltd.