SPH procedures for modeling multiple intersecting discontinuities in geomaterial

Abstract

A methodology is developed in SPH framework to analyze the behavior of preexisting multiple intersecting discontinuities or joints in rock material. The procedure does not require any additional unknowns to represent discontinuities and to capture velocity jump across them. Instead, a discontinuity is represented by a set of joint particles placed along the discontinuity plane, in which relative velocity and traction vector is evaluated, obeying the Mohr-Coulomb friction law with zero tension constrain. For failure of continuous rock material, the Drucker-Prager yield criterion with tensile cracking is employed in the elastic-plastic constitutive model. Free-sip, no-slip, and symmetric boundary conditions are also implemented in SPH framework for proper representation of physical system.The paper analyzes behavior of a rock sample having a discontinuity plane under uniaxial loading and compares velocity and stress with a theoretical solution derived considering effective vertical stiffness of the joint planes. The efficacy of the proposed method is successfully demonstrated by solving another two problems of jointed rock mass under uniaxial and gravitational loading conditions.