| 岩石介质的分形空隙模型及其维数解析 |
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| 引用本文： | 王鲜霞,王彩贤,隋丽丽.岩石介质的分形空隙模型及其维数解析[J].中北大学学报,2012(1):79-82. |
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| 作者姓名： | 王鲜霞 王彩贤 隋丽丽 |
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| 作者单位： | 太原理工大学数学学院;华北科技学院基础部 |
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| 基金项目： | 国家自然科学基金资助项目(51174142);国家科技支撑计划资助项目子课题(2009BAB48B02);山西省科技攻关项目(20110321015-03);山西省高等学校优秀青年学术带头人支持计划 |
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| 摘 要： | 为了探讨岩石介质的空隙结构及分布机理,从分形几何学的角度建立了一种更接近实际情况的岩石介质空隙结构的统计自相似分形模型,并通过随机破碎个数与自相似比的数学期望,给出了岩石介质中空隙分布的分形自相似维数的计算公式.讨论了岩石初始结构的分布维数与破碎后块度的分布维数之间的关系及其意义,为岩石初始结构的探讨和破碎机理的研究奠定了理论基础.
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| 关 键 词： | 分形几何学 统计自相似维数 空隙分布 岩体结构 |
Fractal Model of Gap Distribution in Rock and Its Dimension Analysis |
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| WANG Xian-xia,WANG Cai-xian,SUI Li-li.Fractal Model of Gap Distribution in Rock and Its Dimension Analysis[J].Journal of North University of China,2012(1):79-82. |
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| Authors: | WANG Xian-xia WANG Cai-xian SUI Li-li |
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| Affiliation: | 1.College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China;2.Dept.of Basic Course,North China Institude of Science and Technology,Beijing 101601,China) |
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| Abstract: | To study the gap structure and its distribution in the rock,a statistical self-similarity based fractal model describing gap structure was established.The calculate formula of the dimension of self-similarity about gap distribution was obtained through mathematical expectation of random fragmentation number and selfsimilar ratio.The relationship between the fractal dimension of initial structure and fractal dimension of crushed structural was discussed.The above work laid theoretical foundation for further study of the gap structure of rock and its cracking mechanism. |
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| Keywords: | fractal geometry statistical self-similarity dimension gap distribution rock structure |
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