基于面样本的完整迹长分布推断方法初探

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摘要假设节理为Poisson圆盘，利用与测窗相交迹线的全迹长推导矩形和圆形测窗下的迹长原点矩估计公式，推导矩形测窗在涵盖无限测窗下的最大迹长时相关迹线个数的估计公式，并提出同心测窗法来估计测窗的合适尺寸。基于三维齐次Poisson点过程的数学特征，给出无限测窗下迹长分布的多项式近似形式和约束条件，并提出完整迹长分布推断方法。编制节理网络模拟程序，采用Monte Carlo方法与理论公式验证迹长原点矩估计公式的正确性及同心测窗法和完整迹长分布推断方法的适用性。

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关键词 ：岩石力学, 节理网络, 迹长原点矩估计, 测窗尺寸, 同心测窗法, 完整迹长分布, Monte Carlo方法

Abstract：A sampling window method is adopted to estimate the origin moments of trace length for the Poisson disc joint model，and the origin moment equations of trace length are deduced from the complete trace intersected with the circular and rectangular sampling windows. When the rectangular sampling window covers the maximum trace length of the infinite sampling window，the three trace number equations are proposed to estimate the number of the traces. On this basis，the concentric sampling window method is proposed to estimate the appropriate sampling window size which not only covers the maximum trace length of the infinite sampling window，but also contains the appropriate number of complete trace length samples. Based on the mathematical characteristics of the Poisson point process，when the joint diameter distribution is continuous，the approximate form and constraints of polynomial of the trace length distribution are proposed in the infinite sampling window. If the appropriate rectangular sampling window size was verified by concentric sampling window method，an estimation method is proposed to estimate the complete trace length distribution. The maximum trace length of the infinite sampling window is inferred by using the small step searching algorithm. The origin moment equations of trace length are tested for accuracy by theoretical solutions of two cases. To check the validity of concentric sampling window method and complete trace length distribution inference method，an case is simulated by Monte Carlo method，and their results are compared with theoretical solutions.

Key words： rock mechanics joint network origin moment of joint trace length sampling window size concentric sampling window method complete trace length distribution Monte Carlo method

收稿日期: 2010-04-30

引用本文:

张国强1，2，邓建辉1，2，费文平1，2，张茹1，2. 基于面样本的完整迹长分布推断方法初探[J]. 岩石力学与工程学报, 2011, 30(S1): 2720-2729.
ZHANG Guoqiang1，2，DENG Jianhui1，2，FEI Wenping1，2，ZHANG Ru1，2. PRELIMINARY RESEARCH ON COMPLETE TRACE LENGTH DISTRIBUTION BASED ON AREAL SAMPLES. , 2011, 30(S1): 2720-2729.

链接本文:

http://www.rockmech.org/CN/Y2011/V30/IS1/2720

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