基于表征分形维数的结构面产状分组效果评价方法及应用  

An evaluation method of clustering results of discontinuity orientation based on the representative fractal dimension and its application

作　　者：李立辰 吴文兵[1,2,3,4] 杨松 姚赵田 LI Lichen;WU Wenbing;YANG Song;YAO Zhaotian(Faculty of Engineering,China University of Geosciences,Wuhan,Hubei 430074,China;Engineering Research Center of Rock-Soil Drilling and Excavation and Protection,Ministry of Education,China University of Geoscienees,Wuhan,Hubei 430074,China;College of Civil Engineering and Architecture,Guangxi University,Nanning,Guangxi 530004,China;Guangxi Key Laboratory of Disaster Prevention and Structural Safety,Guangxi University,Nanning,Guangxi 530004,China)

机构地区：[1]中国地质大学工程学院,湖北武汉430074 [2]中国地质大学岩士钻掘与防护教育部工程研究中心,湖北武汉430074 [3]广西大学土木建筑工程学院,广西南宁530004 [4]广西大学广西防灾减灾与工程安全重点实验室,广西南宁530004

出　　处：《岩石力学与工程学报》2018年第7期1641-1648,共8页Chinese Journal of Rock Mechanics and Engineering

基　　金：国家自然科学基金资助项目(51309207,51678547); 中国地质大学岩土钻掘与防护教育部工程研究中心开放基金项目(201402)

摘　　要：进行结构面产状分布特征的分形描述时,传统分形维数同时受到产状样本数和样本自身分布特征的影响,考虑到传统方法的不足,提出表征分形维数的概念。引入蒙特卡洛法生成服从Fisher分布的不同离散程度的样本,对结构面产状分形维数随样本数的变化趋势进行分析得出,分布曲线总体呈"三段式"分布,即分形维数曲线增长先较快,后变慢,最终趋于平稳;取分形维数增长速率第一次出现减小对应的样本数为最优样本数,并以最优样本数对应分形维数作为表征分形维数对样本产状分布特征进行描述。结合一实际矿山边坡工程,引入聚类算法对结构面产状进行分组,将表征分形维数与传统有效性指标的分组效果进行比较,结果表明,表征分形维数不用预先假设产状样本的分布形式,能很好地反映结构面实际的分布特征。The traditional fractal dimension describing the characteristics of discontinuity orientation is influenced by both the joint number and the characteristics of discontinuity orientations. The definition of representative fractal dimension is proposed to overcome the limitations of traditional methods. Monte Carlo method is introduced to generate the discontinuity samples that conform to the Fisher distribution and to represent different dispersion levels. The analysis of the fractal dimension with changing sample size reveals that there is a＂three-level＂trend generally,i.e.,the fractal dimension increasing fast at first,then slowly and finally reaching almost stable. The joint number at the increasing rate of fractal dimension slowing down for the first time is defined as the optimal joint number,and the corresponding fractal dimension is defined as the representative fractal dimension. The clustering method is introduced to group the joint data in a mining slope project. Comparison between the clustering results of representative fractal method and traditional validity index indicates that the fractal dimension does not require a pre-defined distribution form for joint sample and can describe the characteristics of discontinuity orientation better.

关 键 词：岩石力学 结构面产状 蒙特卡洛法 表征分形维数 Fisher分布 聚类算法 

分 类 号：TU45[建筑科学—岩土工程]