基于响应面与重要性抽样的岩土工程可靠度分析方法研究

 由于功能函数非线性强且难以显式表达，岩土工程可靠度分析以往多采用响应面方法解决，但其求解的可靠度指标为几何可靠度。阐明几何可靠度与一般可靠度的实质和两者之间的差异，指出对于功能函数非线性较强的岩土工程问题，采用几何可靠度指标存在较大误差，需进行改进。然后引入V空间重要抽样方法将基本变量随机空间通过Rosenblatt变换和线性正交变换转换至V空间，在响应面方法得到岩土工程的设计验算点及其附近的响应面的基础上，采用重要性抽样方法求解岩土工程可靠度。几个数值算例和工程实例的对比分析表明该方法可行、有效、精度较高，适用于非线性强的岩土工程可靠度求解。

GEOTECHNICAL ENGINEERING RELIABILITY ANALYSIS METHOD BASED ON RESPONSE SURFACE APPROACH AND IMPORTANCE SAMPLING

The geotechnical engineering reliability is often analyzed by the response surface approach as its performance function of strong nonlinearity and it is difficult to explicitly express. But the result obtained by this approach is geometric reliability value. The substance and difference between geometric reliability value and ecumenical reliability value are clarified. It is pointed out that there is exiting error to substitute geometric reliability value for ecumenical reliability value to the strong nonlinear performance function problems in geotechnical engineering and it needs to be improved. Based on the checking points and its region response surface which worked out by response surface approach and importance sampling in V-space，the geotechnical engineering reliability value is worked out by counterchanging the original random variable space to independent random variable in V-space using Rosenblatt transformation and linear orthogonal transformation. The comparative analysis of several numerical examples and practical engineering shows that the approach proposed is feasible，effective with high precision and suitable for complex geotechnical engineering reliability analysis of strong nonlinear performance function.