基于Kriging的边坡稳定可靠度主动搜索法

边坡等岩土工程的复杂性不仅体现在各类岩土参数的变异性,同时还在于其功能函数模式的隐含性、非解析性甚至未确知性,针对这一特性,以边坡极限平衡模式为范例研究出一种易于执行的边坡工程稳定可靠度直接求解算法。首先,调用边坡极限平衡模式获得岩土基本参数及其对应的边坡稳定系数的适量样本；然后,采用地质统计学中的Kriging各向异性关联映射方法,将边坡功能函数值表达为随机过程并通过样本确定该过程的控制变量,再结合蒙特卡洛模拟与主动学习方法,基于搜索规则调整训练样本,通过迭代循环确定随机过程表示的边坡功能函数所在的最可能失效区域；最后,调用随机过程函数在该区域通过简易的直接计算获得边坡失效概率。工程实例分析与计算结果表明该方法精度与蒙特卡洛海量模拟方法相当,但计算过程直接简易,计算代价低,具有较好的实用性。

Active searching algorithm for slope stability reliability based on Kriging model

The complexity of slope engineering is not only reflected in the variability of geotechnical parameters, but also in the implictic, nonanalytic and unascertain properties of the performance function. In response to these characteristics, based on the limit balance model, a direct solution algorithm for slope stability reliability is introduced. First, the limit balance model for slopes is called to obtain the geotechnical parameters and the samples corresponding to the slope stability factors. Secondly, the Kriging anisotropic dependence mapping method is used to change the performance function into a random process and to determine the control variables of the process. Then combined with the Monte Carlo simulation and active learning method, and based on the searching rules to adjust the training samples, the probable failure zone of the random process is found by iterative loop. Finally, the random process function of the failure zone is called to work out the failure probability of slopes. The case studies and calculated results show that the accuracy of the proposed method is quite similar to that of the Monte Carlo simulation, and it is simpler and more practical.