基于响应面法的边坡稳定逆可靠度设计分析方法

Inverse reliability design analysis of slope stability by response surface method

岩土工程稳定性潜在失效风险问题日益引起人们的重视。分析了岩土边坡极限平衡理论特征,针对其滑动模式的稳定性系数计算公式为隐式表达,逆可靠度极限状态方程偏导数不易求解等问题,以极限理论中的Bishop模式为例,结合响应面途径,导出了将边坡稳定性系数隐式表达函数近似为显式二次多项式的简化方法。然后将其与基于一次二阶矩的结构逆可靠度算法融合,构建出基于风险控制的边坡稳定逆可靠度分析设计方法。基于该设计方法得出的方案具有可靠度与稳定性系数的双重控制指标。通过对示例边坡的拓展分析,阐述了该方法的实施过程,展示了边坡稳定失效风险与稳定系数的关系及相关因素对风险影响程度的分析方法。本文为边坡工程的风险设计提供了有效的可选途径。

The potential failure risk problem of stability in geotechnics is increasingly drawing the attention of researchers. By analyzing the theoretical characteristics of slope limit equilibrium method and taking the Bishop＇s mode as an example, we find that the formula for the slope stability factor has implicit character istics and thus it is not easy to obtain the corresponding partial derivatives. Then the response surface meth od （RSM） is introduced, and the implicit expression equation can be simplified in a way that uses an ex plicit quadratic polynomial. Additionally, the quadratic polynomial is combined with the inverse reliability analysis based on the first order second moment in order to propose a new design method for slope stabili ty based on the risk control hierarchy, which enables it to possess the dualindicators involving both reli ability index and stability factors. By analyzing the illustrative examples of slopes, this paper elaborates the implementation process of such a method and shows the relationship between the failure risk and stability factor, and it also displays analysis methods of some influencing factors on the risk level. Therefore, the ,roDosed method is effective for the risk desizn of slope en~,ineerinz as an alternative means.