Reliability Analysis Of Non-stationary Random Field Slope Based On Active Learning Kriging Method

In recent years,the surrogate model method has become a research hotspot in the field of reliability analysis.Using the surrogate model to replace the original performance function can greatly improve the efficiency of reliability analysis.Because the Kriging method is more efficient and accurate than the surrogate model method with a fixed form(such as Response Surface Method,Polynomial Chaos Expansion Method,etc.),this paper is based on the Kriging model.In addition to the reliability analysis method,the simulation of the spatial variability of the slope soil property parameters also has a great influence on the slope reliability.Nonstationary random field method is used to effectively characterize the spatial variability of soil parameters,and on this basis,the reliability analysis of slope is carried out.The main content of this paper can be briefly summarized as follows:1.Basic theories of reliability and random field are introduced,including limit state,probability of failure,random field,K-L expansion method and its implementation.Compared with other discretization methods of random field(such as the Cholesky),the K-L method only generates a small number of random variables,which is beneficial to improve the efficiency of slope reliability analysis.2.The Kriging method can provide the information of the predicted mean value and standard deviation of the unknown point.,The smaller the absolute value of the predicted mean value is,the closer the unknown point is to the limit state surface.And the standard deviation quantifies the uncertainty degree of the predicted result at the unknown point.So the Kriging method is very suitable to construct an adaptive modeling process of "modeling ? error analysis ? supplementing samples by learning function ? modeling".The AK-MCS method(Active learning reliability method combining Kriging and MCS)is such a method.But it ignores the influence of the random variable probability density function(PDF)in the process of selecting sample point.Actually PDF determines the influence degree of candidate points on the calculation of probability of failure.Therefore,this paper proposes a new active learning Kriging method(Active learning reliability method combining Kriging,PDF and MCS,AKPMCS),which introduces a learning function that simultaneously considers the effects of predicted mean value,standard deviation,and PDF when selecting the best sample.Meanwhile,new iteration termination conditions are set accordingly to avoid excessive learning.Multiple examples show that the improved method can improve the calculation efficiency while ensuring the calculation accuracy.3.In the reliability analysis of slope stability,random variable model is often used to simulate soil property parameters.This model assumes that the soil parameters are homogeneously distributed within the slope.But the environment in which the soil is formed is complex,which makes the soil parameters have spatial variability.Therefore,the stationary random field model is proposed accordingly.In the stationary random field model,the mean and standard deviation of the soil parameters are regarded as constants.However,a large number of in-situ exploration data shows that the soil parameters often have non-stationary distribution characteristics along the depth,i.e.,the mean value or standard deviation or both vary with the buried depth.So scholars started to study the non-stationary random field model.Since the existing non-stationary random field model only focuses on the spatial variability of trend components or only the random fluctuation components,this paper proposes a new nonstationary random field model of undrained shear strength parameters,which considers the variability of both the trend component and the random fluctuation component of soil parameters.Based on the proposed random field model and AKP-MCS method,this paper conducted reliability analysis of non-stationary random field slope.The examples show that the proposed non-stationary random field model has small variability in the shallow layer of the slope,and the variability increases with the increase of the buried depth,which well simulates the non-stationary characteristics of the soil parameters.4.At present,the reliability analysis of slope stability is usually based on the two-dimensional model.Two-dimensional model assumes the slope is under plane strain and when a landslide occurs,the landslide body is infinitely wide or has the same length as that of the threedimensional long slope.In other words,the influence of the "end effects" of the landslide body on the slope stability is ignored.Actually,when the slope is damaged,there are often multiple landslide segments,and each landslide segment will form a landslide body with a certain width.If only the failure probability of the "most dangerous landslide segment" is calculated,other landslide segments are ignored,which would lead to underestimation of the probability of failure of the long slopes.Therefore,this paper regards three-dimensional long slope as a "series system" composed of landslide segments,which considers not only the " end effects " of the landslide body but also the effect of the "sub-dangerous landslide segment" on the probability of failure.In reliability analysis,the AKP-MCS method is used to calculate the probability of failure of each landslide segment,and then the "system reliability" of the long slope is calculated.