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

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. © 2018, Editorial Department of Journal of Hunan University. All right reserved.