Modeling of crack initiation, propagation and coalescence in rocks

Abstract

Natural or artificial fracturing of rock plays a very important role in geologic processes and for engineered structures in and on rock. Fracturing is associated with crack initiation, propagation and coalescence, which have been studied experimentally and analytically by many researchers. The analytical models developed to describe the initiation and propagation of cracks in brittle materials can be incorporated in Finite Element (FE) and Displacement Discontinuity (DD) codes. Corresponding research has been going on at MIT and has led to the development of a DDM code - FROCK - which currently uses a stress-based criterion proposed by Bobet (1997) to model crack initiation and propagation. Even though the predictions obtained with this criterion generally correspond to the experimental results, there are cases, in which the results obtained with FROCK are not satisfactory. This thesis proposes and implements new crack initiation and propagation criteria in the DDM code FROCK, namely a strain-based criterion and two stress-dependent criteria. It also studies the crack initiation and propagation processes numerically, using the FEM code ABAQUS. Existing crack initiation and propagation criteria (stress, strain and energy based) are also investigated with ABAQUS. The crack development processes are studied by modeling pairs of pre-existing flaws (double-flaw geometries) embedded in specimens subjected to vertical compressive loads in both ABAQUS and FROCK. For the different flaw arrangements studied, the difference between the stress and strain fields around the flaw tip gradually increases as the horizontal distance between the inner flaw tips increases. In terms of crack initiation, the results obtained with the stress and strain-based criteria studied were more consistent with the experimental observations than the results obtained with the energy-based criterion. The proposed strain-based criterion implemented in FROCK yielded better results than Bobet's stress-based criterion currently used in FROCK, for the five flaw arrangements studied. The results obtained with the two proposed stress-dependent criteria indicate that the critical shear stress at which a crack propagates in rock does not depend upon the normal stress applied, since the best crack propagation results were obtained for very low or zero friction angles.