岩石抗剪强度参数的理论概率分布形态研究

岩石抗剪强度参数的概率分布形态是岩石工程可靠度分析和设计的基础。在考虑完整岩石压缩强度为服从正态分布随机变量的条件下,针对Mohr-Coulomb和Drucker-Prager屈服准则的线性系数形式,基于随机变量函数分布理论推导出岩石抗剪强度参数内摩擦角φ和黏聚力c的概率密度函数。φ和c概率密度函数显示:不仅岩石压缩强度和抗剪强度参数概率分布具有非一致性,而且根据不同屈服准则计算得出的岩石抗剪强度参数概率分布也具有非一致性。在进一步分析屈服准则系数具有不同变异系数和相关系数时的抗剪强度参数概率密度函数特征的基础上,提出根据概率分布的偏度和峰度确定一般情况下抗剪强度参数概率分布形态的方法,从理论上解决岩石压缩强度与抗剪强度参数分布的协调性问题。最后,对大理岩常规三轴压缩试验得出的抗剪强度参数进行大样本统计分析,验证了其概率密度函数理论推导的正确性以及概率分布形态确定方法的合理性。该研究为实际岩石强度概率分析时选择抗剪强度参数合理概率分布形式提供了理论指导。

Theoretical probability distribution of shear strength parameters for rock

Probability distribution of rock strength parameters is the foundation of reliability analysis and design in rock engineering. Based on the linear yielding criterion (Mohr-Coulomb and Drucker-Prager), the probability density functions (PDF) of friction angle and cohesion are obtained through the theory of distribution for function of the random variable, on the condition that intact rock compression strength follows normal distribution. The PDFs of and show: the probability distributions of rock compression strength and , are not consistent, as do the probability distribution of and calculated under different yield criteria. Then, based on the characters of and ’s PDFs under different variation coefficients and correlation coefficients of yield criteria’s coefficients, the general forms of and ’s probability distributions are analyzed according to the skewness and kurtosis. The coordination problem between the distribution of rock compression strength and shear strength parameters is solved in theory. Finally, the correctness of PDF’s theoretical deduction and the analytical rationality of the method to determine probability distribution form for and are verified by large sample statistics and analysis for and which are obtained from the lots of marble conventional triaxial compression tests. It is believed that the research can provide a theoretical guidance to choose reasonable probability distributions of rock shear strength parameters in probability analysis of rock strength.