| 岩石分形断裂的统计理论 |
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| 引用本文： | 牛志仁,施行觉.岩石分形断裂的统计理论[J].地球物理学报,1992,35(5):594-603. |
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| 作者姓名： | 牛志仁 施行觉 |
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| 作者单位： | 1. 陕西省地震局 西安 710068;
2. 中国科学技术大学 合肥 230026 |
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| 摘 要： | 本文研究了岩石分形断裂的统计理论.认为岩石断裂是岩石内部微裂缝成核、形成和传播的非平衡过程,导出了描述这个过程的微分方程.运用位错塞积成核机理,得到了岩石发生分形断裂的微裂缝大小的统计分布函数和平均长大速率.从理论上得出了岩石非弹性体积应变与微裂缝数目成正比,从而解释了实验室研究的结果.另外发现岩石的分维是决定岩石脆性的一个重要因素,分维值愈小,岩石愈脆.但岩石的分维值与岩石强度无明显关系.最后,从微裂缝大小的统计分布函数出发,导出了b值与岩石分维值的关系.
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| 关 键 词： | 岩石断裂 分形 分维 统计理论 |
| 收稿时间： | 1990-09-29 |
STATISTICAL THEORY OF ROCK FRACTAL FRACTURE |
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| NIU ZHI-REN.STATISTICAL THEORY OF ROCK FRACTAL FRACTURE[J].Chinese Journal of Geophysics,1992,35(5):594-603. |
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| Authors: | NIU ZHI-REN |
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| Institution: | 1. Seismological Bureau of Shaanxi Province, Xian 710068;
2. University of Science and Technology of China, Hefei 230026 |
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| Abstract: | 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. |
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| Keywords: | Rock fracture Fractal D mension Statistical theory |
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