基于非侵入式随机有限元法的地下洞室可靠度分析

Reliability analysis of underground rock caverns using non-intrusive stochastic finite element method

提出了地下洞室变形可靠度分析的非侵入式随机有限元法。介绍了随机多项式展开的基本原理,采用GEOSLOPE的SIGMA/W模块进行确定性有限元分析。提出了随机多项式展开与SIGMA/W模块接口方法及其流程图,从而实现了确定性有限元分析和随机分析一体化。最后研究了非侵入式随机有限元法在地下洞室变形可靠度分析中的应用。结果表明:非侵入式随机有限元法使得随机分析与确定性有限元分析互不耦合,其计算效率是传统的蒙特卡罗模拟方法无可比拟的,它是地下洞室变形可靠度问题分析一种有效的方法。采用二次衬砌支护是提高地下洞室可靠度有效的方法。此外,岩体变形模量的变异性对地下洞室变形可靠度有非常明显的影响,而岩体重度的变异性对可靠度基本上没有影响。因此,在地质勘查中要尽可能准确地确定岩体的变形模量,从而有效地提高地下洞室变形可靠度。

A non-intrusive finite element method for the reliability analysis of deformation for underground rock caverns is proposed. First, the polynomial chaos expansion is introduced. The software SIGMA/W is selected to perform the deterministic FEM analysis. Thereafter, a procedure for the interface between stochastic analysis module and software SIGMA/W is presented, and a flowchart is provided as well. The non-intrusive finite element method means there is no need for user-intervention during the calculation of the deterministic finite element code while the normal stochastic finite element methods always do. This is of practical advantage that realistic probabilistic analyses become possible for the practitioners. The computational efficiency of the proposed method is significantly higher than that of the traditional Monte Carlo simulation. It can serve as an alternate method for the reliability analysis of complex geotechnical problems. The liner supporting can improve the reliability of the underground rock caverns effectively. The sensitivity results indicate that the elastic modulus is the most significant random variable, whereas the unit weight almost has no influence on the reliability results. Therefore, to improve the reliability of the underground rock caverns effectively, a detailed geological investigation should be conducted to reduce the uncertainty in the elastic modulus of rock mass.