Modeling fracture and deformation of brittle rock under compressive loading
Axial tensile cracks in a uniaxial or low confining stress, triaxial compression test follow a compression-parallel straight path for long distances, often through the whole length of the test specimen. When no transverse tensile stress is applied, as in the compression test, existing fracture mechanics models do not allow propagation along the compression direction fo a long distance. One way to overcome the problem is to replace the zero-width crack of fracture mechanics with a crack model that has finite width. The approach followed in this work is, however, different. The zero-width crack model is retained, but the fracture mechanics criterion is replaced with a stress-based one that includes the effect of both the maximum and minimum principal stresses. A new fracture model of rock under compressive loading, 'ZUSR ' (Z_ero-width crack with U_nconfined S_trength R_atio fracture criteria), is proposed in this thesis. The proposed model, ' ZUSR', draws on 'LEFM' (L_inear E_lastic F_racture M_echanics) tocompute stresses around the crack tip, non-local elasticity to address the size effect and the 'USR' (U_nconfined S_trength R_atio, safety factor) approach to define conditions of fracture nucleation. An approximate, closed-form solution, relating the far-field compressive stress to crack length, is obtained. When the 'ZUSR' model is applied to simulate the primary fracture propagation from a central cavity in an infinite medium loaded in compression, a closed-form solution is obtained. For the finite medium, both primary crack propagation and remote fracture nucleation is modeled through a finite element, numerical procedure. The 'ZUSR' model is then used to model the wing crack propagation from a sliding crack. The results show that the 'ZUSR' model has all the right properties to capture the experimental evidence on tensile fracture in a dominantly compressive stress field. It allows the propagation of straight, compression-parallel fractures to any length, through a process that includes an initial stage of crack-length hardening and a final stage of crack-length softening that approaches the state of unstable fracture as the far-field compressive stress approaches the compressive strength. When the 'ZUSR' model is built into a constitutive model of the stress-strain diagram, it is shown to be quite successful in describing the essential features of the compressive stress versus axial, lateral and volumetric strain curves of brittle rocks, such as Lac du Bonnet granite.