节理泊松圆盘模型直径分布推断的解析方法

›› 2011, Vol. 32 ›› Issue (4): 1149-1156.

节理泊松圆盘模型直径分布推断的解析方法

张国强^{1, 2}，费文平^{1, 2}，张茹^{1, 2}，邓建辉^{1, 2}

1. 四川大学水力学与山区河流开发保护国家重点实验室，成都 610065；2. 四川大学水利水电学院，成都 610065

收稿日期:2010-09-20 出版日期:2011-04-10 发布日期:2011-04-29
作者简介:张国强，男，1981年生，在读博士研究生，主要从事岩体数值计算方面的研究工作
基金资助:
国家重点基础研究发展规划(973)项目(No. 2010CB226802，No. 2010CB732005)；国家自然科学基金项目(No. 50639100，No. 509794091)

Analytical method for estimating diameter distribution of Poisson disc joint model

ZHANG Guo-qiang^{1, 2}，FEI Wen-ping^{1, 2}，ZHANG Ru^{1, 2}，DENG Jian-hui^{1, 2}

1. State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China; 2. School of Water Resources and Hydropower, Sichuan University, Chengdu 610065, China

Received:2010-09-20 Online:2011-04-10 Published:2011-04-29

摘要/Abstract

摘要：

节理圆盘直径分布是节理网络模拟中的重要参数之一。在节理为Poisson圆盘的假设下，根据三维齐次Poisson点过程的数学特征，给出迹长分布概率密度函数的多项式形式和相应的约束条件；对Warburton提出的迹长分布概率密度函数和节理直径分布概率密度函数关系公式进行Santalo变换，推导了多项式形式的迹长分布所对应的直径分布概率密度函数的解析解，并采用Priest给出的解析解验证其正确性；根据概率密度函数的性质，给出了直径分布概率密度函数定义域的推断方法。编制节理网络模拟程序，采用Monte Carlo方法验证节理Poisson圆盘直径分布概率密度函数解析解的正确性和直径分布概率密度函数定义域推断方法的适用性。

关键词: 节理网络, 节理Poisson圆盘模型, 节理直径分布, 解析方法

Abstract:

One of the key procedures in statistical joint modeling is the determination of the joint size distribution. The mathematical features of the Poisson point process was considered. When the joint diameter distribution is continuous, the trace length lower bound must be zero; and the upper bound must be equal to the joint diameter upper bound. Since any continuous function could be fitted by a polynomial with high accuracy, a polynomial trace length distribution and constraints were proposed in the infinite sampling window for the Poisson disc joint model. Santalo closed-form integral solution was used to derive a closed-form expression for the equation, which determined the trace length distribution from the joint diameter distribution proposed by Warburton. Based on the polynomial trace length distribution, an analytical equation was derived to estimate the joint diameter distribution, and the complex numerical methods were avoided. The analytical equation was verified by the formula proposed by Priest. Based on the characteristic of the probability density function, a method for estimation of diameter distribution range was proposed, and the joint diameter lower bound was inferred by small step search algorithm. The inference method was checked for validity through Monte Carlo simulation.

Key words: joint network, Poisson disc joint model, joint diameter distribution, analytical method

中图分类号:

TU 45

张国强，费文平，张茹，邓建辉. 节理泊松圆盘模型直径分布推断的解析方法[J]. , 2011, 32(4): 1149-1156.

ZHANG Guo-qiang，FEI Wen-ping，ZHANG Ru，DENG Jian-hui. Analytical method for estimating diameter distribution of Poisson disc joint model[J]. , 2011, 32(4): 1149-1156.

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