This paper presents a new numerical approach to modelling rock fracture and fragmentation by combining the advantages of the mesh-free smoothed particle hydrodynamic (SPH) method with a new continuum constitutive model with embedded cohesive cracks. The new constitutive model is capable of providing the links of the continuum mechanics and the non-linear (decohesive) fracture mechanics. It will also possess an intrinsic length scale and hence can automatically capture size effects to produce mesh independent numerical solutions. The proposed numerical approach is illustrated at particle level to show essential features and advantages compared to traditional continuum based constitutive models in the context of SPH simulations.
It has been clear that particle based methods have several advantages over traditional mesh based methods (like the Finite Element Method) for the simulation of fracture, fragmentation and flow of fragmented materials. This is especially true for mining problems such as block caving that usually involves the transition from solid to granular trigged by detonation, which leads to fracture and fragmentation of rock mass, followed by flow of granulated materials under large deformation/displacement conditions. In this study, we propose a new approach to modelling rock fracture, fragmentation and material flow by combining the advantages of a particle method, the Smooth Particle Hydrodynamics (SPH), with a new constitutive modelling approach with embedded cohesive cracks. The key points of the approach are the separation of SPH governing equations and cohesive cracks, together with the development of a new constitutive modelling structure with embedded cohesive zone. In particular, our new constitutive models associated with SPH particles possess enhanced kinematical fields to correctly characterise bulk elastic and cohesive zone phases during fracturing process. This enhanced kinematics is only activated at the initiation of fracture, and once activated, it will help decompose the macro strain associated with an SPH particle into an elastic strain for the bulk and a displacement jump vector across the cohesive surface. This facilitates the implementation in SPH, as the new constitutive structure with embedded cohesive cracks can be treated like any standard constitutive model that takes strain increments as inputs, and returns corresponding stress increments governed by both bulk elastic and cohesive behaviour. This new constitutive modelling approach also possesses an intrinsic length scale and hence can automatically capture size effects, and result in discretisation dependent numerical solutions. Beyond the fracture process, once cohesion is completely lost, SPH algorithms for the approximation of field functions will take place to capture the traction free surface and material separation. In this paper, the theoretical developments together with implementation algorithms for both SPH and constitutive models are described and numerical examples at particle levels are used to demonstrate the potentials of the new approach.
