A new SPH-based continuum framework with an embedded fracture process zone for modelling rock fracture

A new computational approach combining the Smooth Particle Hydrodynamics and a constitutive model that possesses an intrinsic length scale is proposed in this study for modelling rock fracture. In particular, a continuum-based size-dependent constitutive model with an embedded fracture process zone described by a cohesive model is adopted for modelling strain localisation in geomaterials. A length scale is introduced into the constitutive equations to describe the scale effect commonly observed in localised failure of geomaterials. The constitutive model is then employed in a mesh-free Taylor Smooth Particle Hydrodynamics (Taylor-SPH) framework to produce a new computational tool for rock fracture modelling. The key feature of the proposed numerical framework is that it describes the fracture geometry by a set of Lagrangian particles, which carry fracture information such as damage evolution and fracture orientation, thus bypassing the need to represent the fracture's topology and fracture orientation. To test the capability of this computational framework in simulating rock fracture behaviour, three mode-I numerical fracture tests including three-point bending test, Brazilian-disc test and semi-circular bending test are carried out and results validated with experimental data in the literature. The good agreement between numerical and experimental results suggests that the proposed method is a promising numerical approach to modelling rock fracture.