ABSTRACT:

We have developed a numerical simulation methodology where different materials can be analyzed in the same framework. At the interface between different phases, the necessary velocity and stress continuity conditions are maintained, allowing interaction between particles from different materials when solving the momentum equation. The SPH approximation to the continuity equation is corrected in order to handle the density discontinuity at the interface between different materials. For the different types of layered rock, each rock type is presently assumed to be homogeneous and isotropic, with perfect bonding at the interface. Failure of the rock or de-bonding of the layers occurs due to elasto-plastic damage model which includes the Drucker-Prager plasticity model and the Grady-Kipp damage model. We begin with a description of the theory governing this SPH framework. Following this, validation results are presented for the simulation of layered materials. Results using this SPH framework are compared to an analytical solution for geostatic stress, where good agreement is observed. Following this, the three point bending of a layered material as reported by Lee et al. (2015) is simulated. Simulation of the three-point bending experiment shows that inclined layers in the path of a propagating tensile fracture may have a significant influence in the ultimate fracture propagation direction.

1. INTRODUCTION
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