Second-order Second-moment Evaluation Method for Failure Probability of Rock-soil Structures

DOI：

 作者 单位 苏永华1，2?覮，李帅1，苏雅1 （1.湖南大学 土木工程学院，湖南 长沙 410082；2.湖南大学 建筑安全与节能教育部重点实验室，湖南 长沙 410082）

常规二次二阶矩可靠性方法只适用于功能函数偏导数（一阶和二阶）能够简便地由解析法求解的工程，使得其难以解决复杂岩土体结构的稳定可靠度问题.针对这一局限，基于数值差分原理，导出功能函数在验算点处各阶导数近似表达式，结合随机变量在X空间和Y空间的变换，构建了基于差分方法的梯度矢量数值求解工具；以该工具置换Breitung二次二阶矩方法中的梯度计算准则，形成一种适用于任意形式功能函数的二次二阶矩可靠度算法，消除了经典方法的局限；利用所提方法解决了功能函数为隐式和未知形式的边坡可靠度问题，展示了该方法解决复杂岩土体结构概率稳定性问题的能力，并同时在基准Y空间内建议了具有普遍意义的合适步长系数值0.01.

Conventional second-order second-moment reliability method (SORM) is only applicable to the engineering where the first and second order partial derivative of performance functions can be easily calculated by analytic method，which results in the difficulty in solving reliability problems of complex geotechnical engineering structures.Aiming at above limitation， firstly，approximate calculation expressions for partial derivatives on the checking point are deduced based on finite difference principle. Combine with conversion method of random variables between X space and Y space， solving method for gradient vectors is formed. Secondly， calculation criterion of gradient in Breitung′s SORM is substituted by the above solving method， and then，an improved SORM which is suitable for arbitrary form of performance function is proposed. The limitation of the conventional SORM is eliminated. Finally，reliability problem of two slopes which performance functions are implicit and indefinable are solved by using the proposed method， and it shows the accuracy and availability of the proposed method to deal with complex structures reliability problem. Meanwhile，the value of step length coefficient c = 0.01 in the benchmark space（Y-space) which possess the universal meaning is also achieved.