岩石抗剪强度参数的加权线性回归估计与验证

本文研究了岩石抗剪强度参数的优化估计方法，针对岩石抗剪强度数据中存在的异方差问题，引入了加权线性回归方法。在岩石抗剪强度的线性回归分析中，一般假定因变量观测值的观测误差都服从同一正态分布，但忽略了三轴强度数据中所存在的异方差问题。本文利用以位于四川省西南地区的露天砂岩为研究对象，获取砂岩在不同围压下的三轴强度数据并应用加权线性回归方法进行分析并解决了数据的异方差问题。本文首先介绍了岩石抗剪强度的理论基础和相关的统计方法，然后详细阐述了加权线性回归的概念及应用范围。提出了加权线性回归的理论公式和检验方法，并解释了加权回归中的权重定义和计算方法。最后通过位于四川省西南地区的露天砂岩的试验数据进行验证，研究结果证明了加权最小二乘法在岩石抗剪强度参数的估计中的有效性，研究成果可为抗剪强度参数的选取提供相关的理论依据。

Weighted linear regression estimation and verification of rock shear strength parameters

In this paper, the optimal estimation method of rock shear strength parameters is studied. Aiming at the heteroscedasticity problem in rock shear strength data, a weighted linear regression method is introduced. In the linear regression analysis of rock shear strength, it is generally assumed that the observation errors of dependent variables obey the same normal distribution, but the heteroscedasticity problem in triaxial strength data is ignored. In this paper, the open-pit sandstone in the southwest of Sichuan Province is used as the research object, and the triaxial strength data of sandstone under different confining pressures are obtained. The weighted linear regression method is used to analyze and solve the problem of heteroscedasticity of the data. This paper first introduces the theoretical basis and related statistical methods of rock shear strength, and then elaborates the concept and application scope of weighted linear regression. The theoretical formula and test method of weighted linear regression are proposed, and the definition and calculation method of weight in weighted regression are explained. Finally, the experimental data of open-pit sandstone in the southwest of Sichuan Province are verified. The research results prove the effectiveness of the weighted least squares method in the estimation of rock shear strength parameters. The research results can provide relevant theoretical basis for the selection of shear strength parameters.