A Numerical Model for Fracture Propagation Leading to Primary Fragmentation in Block Caving Mines

A numerical method is proposed to propagate multiple discrete fractures leading to primary fragmentation in a mine that is being worked using block caving. Deformation is computed using the finite element method, fractures are represented explicitly, and the mine domain is discretized by an unstructured mesh. Bedding planes are represented by systematically varying the elastic modulus of the rock and by defining horizontal weakness planes. Fractures and matrix are represented using parametric surfaces, and tips are defined by their boundary curves. Tip advance is controlled by a failure criterion, and a criterion for propagation direction and magnitude, based on the evaluation of the modal stress intensity factors. A novel domain integral approach is applied to accurately compute stress intensity factors (K) ahead of fracture tips in three dimensions. The method does not require a structured volumetric mesh structure around the crack tip, as integration is performed over a series of virtual surface domains along the crack front. The method is efficient, as it makes direct use of automatically generated, arbitrary tetrahedral meshes, and approximates stress intensity factors (KI, KII, KIII) along each crack front using Interaction-integrals. As opposed to the JIntegral, the method does not decompose K a-posteriori, but instead uses an auxiliary field to directly compute modal K. When using this method, numerical approximations of K do not exhibit dependence on the mesh layout, and require meshes that can generally be ten times coarser than are required by displacement- and stress-based methods. Volumetric meshing requires only, on average, 17% of each computation step. Thus, cracks do not follow any pre-existing mesh structure, and the method is well suited for high-density fracture datasets. The method is demonstrated for primary fragmentation of a mine area covering 110 initial draw points, immediately beneath a 2m high undercut. Displacement is constrained at all boundaries except the surface of the undercut. The growth of the fractures is investigated at the onset of the undercut. Ninety initial disc-shaped fractures are taken into account, each having an initial radius of 10 m. Fractures grow around the undercut, intersect the bedding plane boundaries, and the domain is fragmented as a result.