基于拟牛顿近似二阶法的岩土工程系统可靠性分析

System reliability of geotechnical problems using quasi-Newton approximation-based sorm

岩土工程问题往往存在多种失效模式,需要进行系统性的分析与评价,而目前的系统可靠性方法尚不能在精度与计算量之间达到很好的平衡,据此提出一种更加高效的系统可靠度计算方法。此方法基于2种拟牛顿近似算法的耦合,首先利用HLRF-BFGS算法确定各极限状态方程的验算点以及单位方向矢量,然后采用SR1算法逼近海森矩阵从而得到精度优良的二阶可靠度指标。在此基础上,通过改进线性化法进一步使用每个极限状态方程的二阶可靠度指标及单位方向矢量计算系统失稳概率。以半重力式挡土墙和多层土坡为算例,通过与经典系统可靠性方法计算结果的对比分析,表明所采用的拟牛顿近似二阶法能够凭借少于经典一阶法(FORM)的计算量得到与经典二阶法(SORM)相当的系统失稳概率计算精度,证明此算法的高效性与准确性,在岩土工程系统可靠性问题中具有较好的应用前景。

Multi-failure modes inherently exist in geotechnical engineering practices,which are typically considered as series system problems in literature. However,the existing system reliability methods can hardly achieve a good balance between the computational cost and accuracy. Given this limitation,a novel method integrates a highly efficient second order reliability method（SORM） and a practical system reliability approach was proposed in this paper. Specifically,the quasi-Newton approximation-based SORM was used to approximate the second order reliability index for each limit state function（LSF）,providing a basis for the further linearization transformation,so as to ultimately implement the improved linearization approach to obtain the system reliability results. In addition,two examples of common geotechnical problems featuring series system reliability analyses-a semi-gravity retaining wall and a soil slope with multiple layers were reviewed for illustration. The computed results with the proposed method show good computational efficiency and accuracy.