基于勒让德多项式逼近法的M-C强度参数概率分布推断

 在岩土工程可靠度分析中, M-C 强度参数概率分布类型研究是一项基础性工作, 为此提出了岩土抗剪强度参数概率分布函数的勒让德多项式推断法。以岩石常规三轴试验数据为原始信息, 根据组合理论和线性回归分析方法, 构建了内摩擦角φ、摩擦系数f 和黏聚力c 的小样本信息库, 对样本数据的概率分布类型进行假设检验, 通过有限比较法得到M-C 强度参数的最优经典概率分布类型为正态分布。基于勒让德正交多项式逼近法得到了φ、f 和c 的概率分布函数, 并利用K-S 检验法与正态分布进行计算精度比较。结果表明, 勒让德多项式推断得到的概率分布函数的K-S 检验值比正态分布的小, 更符合样本实际观测数据的分布规律。

Deduction of probability distribution of M-C strength parameters by Legendre polynomial

It is a fundamental and important topic to study the probability distribution of M-C strength parameters in reliability analysis of geotechnical engineering. The Legendre polynomial is introduced to infer the probability distribution functions of geotechnical shear strength parameters. With the conventional triaxial test data as the original information, an information basis of internal friction angle, friction coefficient f and cohesion c is constructed based on combination theory and linear regression analysis method. Subsequently, hypothesis testing of the probability distribution functions of sample data is conducted. The optional classical probability distribution types of M-C strength parameters are normal distribution, as verified by limited comparison method. The probability distribution functions of internal friction angle, friction coefficient and cohesion are deduced by Legendre orthogonal polynomial numerical approximation method. The K-S test method is used to compare the results of the presented method and normal distribution. It is shown that the K-S test results of probability distribution functions of M-C shear strength parameters deduced by Legendre polynomial are smaller than those of the normal distribution and can be more close to the actual probability distribution.