基于随机响应面法的边坡系统可靠度分析

System reliability analysis of slope with stochastic response surface method

提出了一套基于随机响应面法的边坡系统可靠度分析方法。该方法首先从大量潜在滑动面中筛选出代表性滑动面。针对每条代表性滑动面,采用Hermite多项式展开建立其安全系数与土体参数间的非线性显式函数关系(即随机响应面)。然后,采用直接蒙特卡洛模拟计算边坡系统失效概率。在蒙特卡罗模拟中,采用所有代表性滑动面的随机响应面计算每一组样本所对应的边坡最小安全系数。最后,以两个典型多层边坡系统可靠度问题为例验证了该方法的有效性。结果表明:文中提出的边坡系统可靠度分析方法能够有效地识别边坡代表性滑动面,具有较高的计算精度和效率,并且确定代表性滑动面时无需计算滑动面间的相关系数。同时该方法可以有效地计算低失效概率水平的边坡系统可靠度,为含相关非正态参数的边坡系统可靠度问题提供了一条有效的分析途径。此外,多层边坡可能同时存在多条潜在滑动面,基于单一滑动面(如临界确定性滑动面)或者部分代表性滑动面进行边坡系统可靠度分析均会低估边坡失效概率。

This paper develops an effective approach to evaluate the system reliability of slope with stochastic response surface method. Firstly, the proposed approach selects the representative slip surfaces from a large number of potential slip surfaces. For each representative slip surface, a stochastic response surface（SRS） is constructed to estimate its factor of safety with the Hermite polynomial chaos expansion. Then, the direct Monte Carlo simulation（MCS） is employed to calculate the system probability of slope failure. The minimum factor of safety for each random sample during the MCS is calculated with SRSs of representative slip surfaces. For illustration, the proposed approach is applied to estimate the system reliability of two slopes with multiple soil layers. The results show that the proposed approach can effectively identify the representative slip surfaces of the slope and yield the system probability of slope failure with reasonable accuracy. It can also evaluate the system reliability of slope at small probability levels, and provide an effective tool for system reliability analysis of slope considering correlated nonnormal soil parameters. In addition, the tedious procedure of calculating correlation coefficients between potential slip surfaces to determine the representative slip surfaces is avoided in the proposed approach. There may be multiple failure modes for a slope with multiple soil layers. If only one critical slip surface（e.g. critical deterministic slip surface） or insufficient representative slip surfaces are considered in system reliability analysis, the probability of slope failure would be underestimated.