Development of a local degradation approach to the modelling of brittle fracture in heterogeneous rocks

At the microscopic scale (say, of the order of grain size), rock is a heterogeneous material whose brittle fracture is a complicated progressive process caused by isolated microstructural changes, known also as dissipative processes, These processes are particularly difficult to predict and model in the compressive field. This paper develops a novel numerical methodology for the simulation of these isolated processes, particularly in compressive fields, such that the resulting non-linear macroscopic behaviour can be predicted. The core of the model is elemental degradation. As suggested by laboratory investigations, the microscopic processes involved in rock fracture can be classified into a combination of brittle and ductile processes. The former cause degradation in both local material elasticity and strength, with the extent of degradation being determined by the degree of bond break-age in forming crack surfaces or the like. The latter, however, lead only to plastic deformation. Thus, when brittle processes dominate the deformation of a material, more degradation occurs than if ductile processes dominate. Elemental degradation is represented by a new parameter termed the degradation index, which is introduced in this research and defined as the ratio of the degradation occurring at a certain confining stress level to the corresponding degradation occurring under uniaxial conditions. In combination with an clasto-plastic constitutive relation, the degradation model yields an elastic-brittle-plastic elemental constitutive behaviour. In the model, failure of an element causes disturbance of the local stress field, which may lead to progressive failure of surrounding elements. An explicit finite difference scheme is used to implement the degradation model. An engineering application of the degradation model to the plane strain analysis of mine pillar behaviour is presented. In terms of isolated fracture processes and the corresponding macroscopic mechanical behaviour, the degradation model produces simulation results that are similar to field observations. That is, the fracture process of a squat pillar begins with the initiation of local failure at random sites, and progresses through extension of these failed sites, coalescence of the extended sites, and slabbing or spalling of the ribsides, until development of large shear fractures ultimately occurs. The results suggest that the degradation model is a powerful approach to the study of macroscopic brittle behaviour encountered in rock mechanics and rock engineering. The application of the degradation model to the simulation of brittle fracture of rock specimens in laboratory compression tests is the subject of a companion paper. (C) 2002 Elsevier Science Ltd. All rights reserved.