Extensive second-order method for reliability analysis of complicated geotechnical structures

Abstract

In stability reliability analysis of complicated geotechnical structure, the analytical expression of limit state function (LSF) is often highly non-linear, implicit or indefinable. This results in the classical second-order reliability method (SORM) not to be applied directly. The present study is devoted to eliminating this dilemma. Firstly, universal solving methods of partial derivatives of LSF to its basic random variables are derived using finite difference principle. Secondly, the universal methods supplement SORM to substitute for Newton–Leibniz derivation method; then, an improved algorithm of SORM is developed in conjunction with Breitung’s notion. Thirdly, reliability evaluation of three examples with explicit/implicit LSF are carried out, an available constant quantity of step length coefficient is sought out in the independent standard normal space (u-space) through theoretical inference and trial. Fourthly, an extensive SORM (ESORM) that does not resort to any abstruse mathematic theories is further formulated. Fifthly, combined with numerical simulation, stability reliability degree of one excavation, of which LSF is indefinable, is analysed immediately. Therefore, a practical alternative approach of SORM for complicated geotechnical structure is constructed in the present study.

Keywords:

• Geotechnical structure
• limit state function
• second-order reliability method
• partial derivative
• step length coefficient

Acknowledgements

The authors would like to thank the reviews for their critical comments and valuable feedback which are very useful in improving the work presented in this paper. The authors also cordially thank Dr Hong Yun-peng (an English native person) for his help in correcting the English.