求解岩体裂隙产状三维概率分布的数值方法  

A Numerical Method for Solving Three-Dimensional Probability Distribution of Rockmass Fracture Orientations

作　　者：赵萌[1] 唐辉明[1,2] 詹红兵 张俊荣[1] Zhao Meng;Tang Huiming;Zhan Hongbing;Zhang Junrong(Faculty of Engineering,China University of Geosciences,Wuhan 430074,China;Three Gorges Research Center for Geo-Hazard,Ministry of Education,China University of Geosciences,Wuhan 430074,China;Department of Geology&Geophysics,Texas A&M University,Texas 77843-3115,USA)

机构地区：[1]中国地质大学工程学院,湖北武汉430074 [2]中国地质大学教育部长江三峡库区地质灾害研究中心,湖北武汉430074 [3]美国德州农工大学地质与地球物理系,美国德州77843-3115

出　　处：《地球科学》2022年第4期1470-1482,共13页Earth Science

基　　金：国家重点研发计划项目(No.2017YFC1501305);国家重大科研仪器研制项目(No.41827808);中国地质大学(武汉)中央高校基本科研业务费专项资金资助项目(No.1810491T13)。

摘　　要：测线法是一种广泛使用的裂隙几何特征野外观测技术,但它获得的一维产状观测数据不能代表三维空间内的概率分布.在实测裂隙倾向和倾角之间相互独立的假设基础上,借用概率论和微积分建立了一维数据和三维分布的数值解关系式,进而提出一种由一维观测数据求解三维概率分布的方法.该方法的实现步骤是:(1)通过关系式数值求解产状的三维累积概率;(2)使用如Kolmogorov-Smirnov逼近法对累积概率进行分布形式和分布参数的估计.结合两类裂隙(层理面和节理面)的观测数据,比较了本文方法与Fouché方法的求解误差,并调查了样本容量对本文方法求解误差的影响.结果表明,本文方法求解误差更低.样本容量接近150时,可实现最低求解误差;当超过150时,求解误差不会随样本容量的增加而显著降低.同时,应用于互不平行的裂隙个体如节理面时,本文方法效果明显.而应用于近似平行的裂隙个体如层理面时,效果不明显.The scanline mapping is a widely-used 1D field technique for fracture geometry observation. However, the 1D orientation observations from this technique poorly represent the 3D probability distribution. In this work, a numerical method for solving the 3D probability distribution of orientations is presented. It makes the assumption of observed dip direction-angle independence and adopts a mathematical relationship between the 1D observations and the 3D distribution. This method follows a two-step procedure that first using the relationship to solve the 3D cumulative, and then estimating the distribution type and parameters over the probabilities by employing the Kolmogorov-Smirnov approximation. Two cases of fractures(bedding planes and joints) illustrate that the presented method provides a smaller-error solution in comparison with the Fouché method. The minimum solution error of the presented method can be attained when the sample size is closely 150;if the sample size exceeds this value, the solution error will not decrease significantly as sample size increases. Moreover, the effectiveness of the presented method is investigated. The results show that the presented method performs effectively when applied to non-parallel fracture individuals, e.g. joints, whereas with low effectiveness when applied to sub-parallel fracture individuals, e.g. bedding planes.

关 键 词：产状三维概率分布 Fouché方法 样本容量 裂隙几何特征 测线法 工程地质 

分 类 号：P64[天文地球—地质矿产勘探]