中文摘要：

响应面方法是地下复杂结构稳定可靠性分析的有效方法之一。目前常用的响应面函数不能模拟复杂结构极限状态方程曲面的多峰性。采用包含随机变量交叉项的二次函数从曲面状态上可克服这一缺陷。因此，提出采用1带交叉项函数的响应面函数代替不带交叉项的响应面函数，同时对相应的试验设计程序进行改进以确定包含交叉项函数的具体解析表达式。由于该解析式的空间超曲面具有多峰性质，在试验程序中，引入遗传算法以搜索到全局的最优解，确定结构的可靠度指标和验算点。实例计算证明：该方法比采用不舍交叉项函数的响应面方法精度要高。

英文摘要：

Response surface method（RSM）is an efficient method to analyze the stability reliability degree for complicated structure, such as underground structure. However, general response surface function can not simulate a character of curve surface of limit state equation for a complicated structure, for the curve surface has more than one peak-value on its parameter space. Quadratic equation that contains mixed terms of random variables can overcome the above-mentioned defect. Therefore, it is presented that function with mixed terms of random variables is adopted to replace function without mixed terms of random variables in response surface method and test procedure, which are used to decide coefficients of function without mixed terms of random variables and calculate reliability index. It is improved to make it suitable to response surface function with mixed terms of random variables. The analytical expression that contains mixed terms of random variables can be decided by the improved general test procedure. Due to more than one peak value on curve surface of the analytical expression containing mixed terms of random variables, genetic algorithm is adopted to search a globe optimal solution, reliability index, and checking point in the improved test procedure. The improved test procedure and response surface method, considering quadratic equation that contains mixed terms of random variables as response surface function, is to used to research stability reliability degree for a large-scale underground rock mass structure. Other method, to take quadratic equation without mixed terms of random variables as response surface function, is adopted to analyze the reliability degree of the same structure too. Calculated results of Monte Carlo method are regarded as criterion, and it shows that the calculated result of the former method is more accurate than the later.