基于正态信息扩散原理的Mohr-Coulomb强度准则参数概率模型推断方法

PROBABILITY MODEL DEDUCTION METHOD OF MOHR-COULOMB CRITERIA PARAMETERS BASED ON NORMAL INFORMATION DIFFUSION PRINCIPLE

为构建Mohr-Coulomb强度准则可靠度判别表达式,需要研究岩石抗剪强度参数的概率分布规律,为此提出小样本容量下基于正态信息扩散原理的抗剪强度参数概率模型推断方法。考虑到一般情况下岩石抗剪强度参数样本量较小,以岩石单轴和三轴压缩试验数据为基本信息,根据排列组合理论构建小样本容量下的抗剪强度参数信息库,并利用稳健回归估计方法得到黏聚力c,内摩擦角和摩擦因数f的样本数据。最后,基于正态信息扩散原理,推断获得3个强度参数的概率分布函数。为和传统拟合检验法所得到的结果进行比较,采用精度较高的K-S检验法进行检验。研究结果表明,基于正态信息扩散原理得到的抗剪强度参数的概率分布更加接近参数的实际分布规律,不论是在检验值还是累积概率值方面,所得结果都优于传统拟合检验法。

In order to construct the reliability discriminant of Mohr-Coulomb strength criterion, it is essential to study the probability distribution of shear strength parameters. Based on normal information diffusion principle, a probability model deduction method of shear strength parameters with small sample size is presented. Considering that the sample size of rock shear strength parameters is small in general, the testing data of rock uniaxial and triaxial compression were regarded as basic information, and information base of shear strength parameters with small size was constructed according to the permutation and combination theory. And the sample data of cohesion c, internal friction angle ψ and friction coefficientfwere also obtained using robust regression estimation method. Finally, based on the normal information diffusion theory, the probability distribution functions of c, ψ andfwere deduced. K-S test method was used to compare the results of traditional fitting-test method and presented method. The results show that the probability distribution of shear strength parameters based on normal information diffusion principle is more close to the actual probability distribution. Whether in terms of test value and the cumulative probability, the results of presented method are better than those of the traditional fitting-test method.