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《Chinese Journal of Geophysics》 1992-05
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NIU ZHI-REN(Seismological Bureau of Shaanxi Province, Xian 710068)SHI XING-JUE (University of Science and Technology of China, Hefei 230026)  
The statistical theory of rock fractal fracture is studied in this paper. Describing rock fracture as a non-equilibrium process in which micro-cracks nucleate, grow and propagate, a set of differential equation describing this evolution process is derived. By means of dislocation pile-up mechanism, the statistical distribution function of micro-cracks, the rate of micro-crack growth and the criteria of brittle fracture are obtained in the condition of fractal fracture of rock. We show that unelastic volumetric strain is directly prepositional to the number of micro-cracks, which is observed in laboratory experiments. In addition, we find that the fractal di-mention is an impotant factor for determining the property of brittle rock. The smaller the fractal dimension is, the brittle the rock will be. Rock strength is not relative to its fractal dimension. Finally, the relation between the b value and the fractal dimension is given from the statistical distribution function of micro-cracks.
【Fund】: 地震科学联合基金
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