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改进了相关非正态变量变换到相关标准正态空间时相关系数计算的Hermite多项式方法.介绍了Hermite多项式方法计算等效相关系数的基本原理.系统地比较了Hermite多项式方法与Nataf变换方法的计算精度、计算效率及适用范围.最后研究了变量变换时相关系数的变化对边坡可靠度的影响.结果表明:Hermite多项式方法具有与Nataf变换方法相同的精度,不受变量分布类型的影响,适用范围广,避免了无穷积分问题及非线性积分方程的求解问题,计算效率高,建议优先采用;忽略黏聚力和内摩擦角变换到相关标准正态空间时相关系数的变化将会严重高估边坡失效概率,使得边坡设计偏于保守.
The Hermite polynomial method for calculating the correlation coefficient when the related non-normal variables are transformed into the related standard normal space is improved. The basic principle of Hermite polynomial method for calculating the equivalent correlation coefficient is introduced. The computations of Hermite polynomial method and Nataf transform method are systematically compared Accuracy, calculation efficiency and application range.Finally, the influence of the change of correlation coefficient on slope reliability is studied.The results show that the Hermite polynomial method has the same precision as Nataf transform method, and is not affected by the type of variable distribution. A wide range, to avoid the problem of infinite integral and nonlinear integral equation solving, computational efficiency is high, it is recommended to give priority to; ignoring cohesion and internal friction angle transformed into the relevant standard normal space when the correlation coefficient changes will be seriously over-estimated The failure probability of the slope makes the slope design conservative.