A zeroth-order statistical model for fracture in rock in compression

Abstract

Rocks are known to fracture in compression via the formation, extension and coalescence of extensile cracks. These cracks are generally oriented in the direction of the maximum principal stress and as more cracks are formed or existing cracks grow, crack interaction becomes very important. The formation and extension of these cracks under conditions of compression is attributed to local tensions at the microscale that may be caused by heterogeneity in the shape, orientation and strength of grains and other factors [1]. Moreover, fracture mechanics analysis shows that the stress intensity factor for cracks under tensile stress is proportional to the stress difference ([sigma][sub 1]-[sigma][sub 2]) at the site [2]. In addition, it is known that the local stress and strain fields in a rock are dependent on the loading path for the rock. That is, when a crack forms and opens, strain energy is stored in the rock that is not recovered upon unloading [3]. We have developed a model for fracture of rock in compression that incorporates these and other aspects of rock behavior. Our model utilizes afield theory approach to the analysis of microcracking at the grain scale. This approach incorporates the concept of superposition and the techniquesmore » of boundary element analysis [4] and percolation theory [5] to form a simple yet powerful method for the study of progressive fracture of rock and other disordered materials. We have simulated triaxial laboratory compression tests using the model and produced strain hardening behavior and patterns of cracking similar to that observed in rocks tested in compression. This technical note describes the detail of the model formulation and presents results for a simulated triaxial test.« less