基于产状Fisher分布的岩石节理最小样本容量确定方法

A Method for Determining the Minimum Sample Size of Joints Based on Fisher Distribution of Orientation

节理产状是影响岩体结构及其工程性质的关键参数之一,因此准确计算节理的平均产状是岩体工程性质研究的基础。由于节理产状的离散性,合理确定节理的最小样本容量对于计算节理组的平均产状具有重要意义。基于Fisher分布,阐释了节理产状随机数的生成方法,提出一种考虑“超越上半球投影产状”(OEBEUHP)的平均产状计算方法。随机生成不同数量、不同κ值的Fisher分布产状来研究节理样本容量对平均产状准确性的影响,在保证准确率不低于0.95的情况下,建立了最小样本容量与Fisher分布常数κ值的经验关系。研究结果表明:节理样本容量对平均产状的统计准确性影响显著,样本容量越大,平均产状的统计准确率越高;最小样本容量与κ值呈明显的反比例关系,反比例系数为1 007.23。通过对三峡地下厂房上游边墙和乌东德水电站平洞PD5-2节理的统计分析,验证了该经验关系的适用性,能够有效指导节理产状的采样工作。

The orientation of joints is one of the key parameters affecting the structure of rock mass and its engineering properties.Therefore,accurate calculation of the mean orientation of joints is the basis for the study of engineering properties of rock mass.Due to the dispersion of the joint orientation,it is of great significance to reasonably determine the minimum sample size of the joint for calculating the mean orientation of the joint group.Based on the Fisher distribution,this paper explains the generation method of random numbers for joint orientation,and proposes a calculation method for the mean orientation that considers the orientations extending beyond the edge of an upper hemisphere projection(OEBEUHP).To investigate the effect of joint sample size on the mean orientation accuracy,the empirical relationship between the minimum sample size and theκvalue was established under the condition that the accuracy rate was not less than 0.95.The results show that the joint sample size has a significant impact on the statistical accuracy of the mean orientation.The larger the sample size,the higher the statistical accuracy of the mean occurrence.The minimum sample size has an obvious inverse proportional relationship with theκvalue,and the inverse proportionality coefficient is 1007.23.The applicability of this empirical relationship is verified through statistical research on the upstream side wall joints of the Three Gorges underground powerhouse and joints in the adit PD5-2 of the Wudongde hydropower station,which can provide effective guidance on the sampling of joint orientations.