Multi—Scale Model of Damage Evolution in Stochastic Rocks: Fractal Approach

The spatiotemporal evolution of damage in stochastic rocks is studied in terms of the multi—scale approach with the fractal tree used as an analogue of a discretization scheme for the region under study. Such an approach, based on the fractal theory, allows quantitative information on spatial (morphology of fracture surface) and temporal scaling of the failure process to be obtained. The numerical simulation for different types of stochasticity has shown that the fractal dimension of the fractured zone is the invariant characteristic of the failure process and depends totally on the stochastic properties of material. The analysis of the load vs time—to—fracture relation for a vast interval of loads proved the scale—invariance of the fracture process. The multifractal properties of the load distribution near fractures are studied.