基于多重响应面法的空间变异土坡系统可靠度分析

System reliability analysis of spatially variable soil slopes using the multiple response surfaces method

空间变异土坡可靠度问题应该视为系统可靠度问题,多重响应面法为高效、准确地对其进行求解提供了一条有效途径。针对单一滑面确定了合理的空间变异土坡安全系数的响应面形式,并探讨了可靠度分析精度和随机场离散精度间的近似线性关系。建立基于大量潜在滑面的多重响应面,计算系统失效概率,并识别其中的代表性滑面。通过两个土坡算例验证所提方法的有效性。结果表明:随着空间变异性的增强,土坡可靠度的系统性增强,单一滑面的失效概率将显著低估土坡整体失效概率;通过控制随机场离散精度,可以事先保证一定的可靠度分析精度,从而有效地避免离散出过多并不重要的随机变量;合理地选择多重响应面形式有利于进一步提高计算效率和计算精度;多重响应面法可以同时分析所有潜在滑面的失效概率以及系统失效概率,并识别出代表性滑面,为边坡防治提供参考。

The reliability analysis of a spatially variable soil slope should be considered as a system reliability problem. The multiple response surfaces method（MRSM） provides a rational vehicle to evaluate it efficiently and accurately. This study firstly determines the reasonable response surface function for safety factor with considering spatial variability based on single slip surface. Then the approximate linear relationship between the accuracy of reliability analysis and that of random field discretization is explored. Using the MRSM on a large amount of potential slip surfaces, several representative slip surfaces（RSSs） are identified with the assessment of slope system reliability. The proposed method is illustrated and verified using two spatially variable soil slopes. The results indicate that as the spatial variability becomes stronger, the slope reliability becomes more systematic, and the failure probability obtained using single slip surface significantly underestimates the system failure probability. It is possible to ensure the accuracy of reliability analysis by predefining a proper value of the accuracy of random field discretization, aiming at reducing the number of unimportant random variables. In addition, choosing a proper response surface function helps improve both efficiency and accuracy of the proposed method. In addition, MRSM can simultaneously calculate the failure probability of all potential slip surfaces and the system failure probability, and identify RSSs, providing a guidance to make slope remedy measure.