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基于国内103个水利水电工程1 174组岩基抗剪强度试验数据,采用Copula函数研究岩基抗剪强度参数联合分布模型,探讨水利水电工程中岩基抗剪强度参数联合分布模型构建方法。利用最小二乘法求出岩基抗剪强度参数试验数据的相关统计参数,基于AIC准则识别出岩基抗剪强度参数边缘分布。选择4种Copula函数构造岩基抗剪强度参数二维分布模型,探讨了基于Copula函数的岩基抗剪强度参数二维分布模型的优越性。结果表明:水利水电工程岩基抗剪强度参数存在明显的统计负相关性。Copula方法能够构造具有任意边缘分布和任意相关结构的岩基抗剪强度参数联合分布模型,它为构造抗剪强度参数联合分布模型提供了一种简便的工具。已知岩基抗剪强度参数的边缘分布函数和相关系数不能唯一确定岩基抗剪强度参数的联合概率分布模型,在抗剪强度参数边缘分布函数和相关系数完全相同的前提下,不同Copula函数建立的抗剪强度参数联合概率分布模型差异显著。与常用的抗剪强度参数二维正态分布模型相比,基于Copula函数的抗剪强度参数二维分布模型具有较强的灵活性,它能更好地拟合原始观测数据。水利水电工程中惯用小值平均法确定标准值,当摩擦系数取较小值时,不同Copula函数构造的黏聚力的条件累积分布函数差异显著,这将对抗剪强度参数标准值的选取以及相应的设计方案具有明显的影响。
Based on the test data of 1 174 groups of rock mass in 103 domestic hydraulic and hydropower projects, the Copula function is used to study the joint distribution model of the shear strength parameters of the rock foundation and to discuss the construction method of the joint distribution model of shear strength parameters of the rock foundation in water conservancy and hydropower projects. Based on the AIC criterion, the edge distribution of the shear strength parameters of the rock foundation was identified by using the least square method to obtain the relevant statistical parameters of the test data of the rock-based shear strength parameters. Four Copula functions were chosen to construct the two-dimensional model of the shear strength parameters of the rock foundation. The superiority of the two-dimensional model of the shear strength parameters of the rock foundation based on the Copula function was discussed. The results show that there is a significant statistical negative correlation between the shear strength parameters of rockfill and water conservancy projects. Copula method can be used to construct a joint distribution model of rock-based shear strength parameters with arbitrary edge distribution and any related structure, which provides a convenient tool for constructing a joint distribution model of shear strength parameters. It is known that the edge distribution function and the correlation coefficient of the shear strength parameters of the rock foundation can not uniquely determine the joint probability distribution model of the rock foundation shear strength parameters. Under the condition that the edge distribution function and the correlation coefficient of the shear strength parameters are exactly the same, different Copula functions The shear strength parameters established by joint probability distribution model have significant differences. Compared with the commonly used two-dimensional normal distribution model of shear strength parameters, the two-dimensional distribution model of shear strength parameters based on Copula function is more flexible and can better fit the original observation data. The usual small average method in water conservancy and hydropower project determines the standard value. When the friction coefficient takes a small value, the conditional cumulative distribution function of the cohesion of different Copula functions has significant difference, which will select the standard value of the shear strength parameter and The corresponding design has a significant impact.