工程科学与技术2026，Vol.58Issue(1)：80-89,10.DOI:10.12454/j.jsuese.202500145
考虑土体参数空间变异性的3维土质边坡可靠度分析
Reliability Analysis of Three-dimensional Soil Slopes Considering Spatial Variability of Soil Parameters
摘要
Abstract
Objective Three-dimensional(3D)slope reliability analysis encounters two primary challenges:1)the stochastic modeling of soil properties in-volves complex spatial variability,requiring extensive data processing and imposing substantial computational demands;and 2)brute-force trial-and-error methods for locating critical failure surfaces are computationally inefficient,hindering real-world implementation despite the need for precise stability evaluations in civil infrastructure.Therefore,this study employs the covariance matrix decomposition method to generate 3D log-normal random fields for soil parameters,enabling efficient modeling of spatial variability.The particle swarm optimization(PSO)algorithm is refined with enhanced termination criteria and integrated with the 3D Bishop method to search for the minimum factor of safety(F).This ap-proach significantly improves the accuracy and computational efficiency of slope reliability analysis. Methods The core of this framework lies in employing a stepwise covariance matrix decomposition method to generate 3D lognormal random fields for slope soil parameters.The stepwise covariance matrix decomposition efficiently partitions the problem into tractable components,drasti-cally reducing computational demands while enabling high-resolution random field generation with limited resources by systematically decom-posing the covariance matrix.This decomposition facilitated rapid simulation of spatially variable soil parameters without excessive overhead.An enhanced PSO algorithm was proposed for 3D slope stability analysis to complement the random field modeling.The algorithm integrated the 3D Bishop method,a well-established limit equilibrium technique,into PSO's global search mechanism,combining PSO's exploratory capacity with the Bishop method's precise stability calculations.This interaction enhanced the identification of critical slip surfaces.Refined iteration termina-tion criteria were incorporated to expedite convergence toward the minimum factor of safety(F)and the corresponding critical surface,improving computational efficiency for reliability analysis.The failure probability of 3D slopes was assessed through Monte Carlo simulation,which ac-counted for inherent soil property uncertainties.The method's accuracy and effectiveness were validated through numerical examples that system-atically analyzed diverse slip surface geometries(for example,cylindrical and cylindrical-ellipsoidal combinations). Results and Discussions The proposed method was applied to analyze Example 1.Excluding spatial variability of soil parameters and assuming a cylindrical sliding surface,a deterministic analysis yielded an F of 1.352 4,which closely matched previous result of 1.352 5.For a sliding sur-face combining cylindrical and ellipsoidal shapes,F decreased as the failure surface width(B)increased,gradually approaching the two-dimensional analysis outcome.When spatial variability of soil parameters was incorporated,the calculated failure probability(Pf)range of 0.090 5-0.091 6(average 9.11%)for Example 1 closely aligned with previous finding of 9.25%,with a relative error of approximately 1.5%.The com-parative analysis of safety factors and failure probabilities confirmed the accuracy of the proposed method and the computational procedure.Sys-tematic studies were conducted for various slip surface forms that encompassed combinations of cylindrical and cylindrical+ellipsoidal shapes,as well as different correlation lengths and coefficients of variation.When the sliding surface was cylindrical,and the characteristic length scale in the out-of-plane direction(ly)was set to 20 m,Pf gradually decreased as B increased.This observation indicated that the spatial variability of soil parameters was one of the pivotal factors contributing to the enhanced stability assessment accuracy of 3D slope analysis compared to its two-dimensional counterparts.When ly approaches infinity(ly→+∞),as B increases,Pf gradually rises while the average safety factor(Fav)decreases.These findings indicated that B significantly influences the stability of 3D slopes.When the coefficient of variation for cohesion(Vc)increased from 0.1 to 0.6,Pf rose from 0.0 to 0.25,reflecting an approximate increment of 0.25.When the coefficient of variation for the internal friction angle(Vφ)increased from 0.1 to 0.4,Pf increased from 0.04 to 0.14,corresponding to an approximate increment of 0.10.When the correlation co-efficient between cohesion and the internal friction angle(ρc,φ)increased from-0.5 to 0.5,Pf rose from 0.055 to 0.070,indicating an approximate increment of 0.015.These findings demonstrated that Vc,Vφ,and ρc,φ all exert significant influences on the failure probability.When the character-istic length scale in the x-direction(lx)increased from 10 m to 40 m,Pf increased by approximately 0.03.In contrast,when ly increased from 10 to 40 m,Pf increased by approximately 0.075.This result indicated that ly had a more pronounced impact on slope failure probability compared to lx.In addition,when the characteristic length scale in the z-direction(lz)increased from 1 to 4 m,Pf increased by approximately 0.05,indicating an influence on failure probability. Conclusions The results demonstrate that the enhanced PSO algorithm,when integrated with the 3D Bishop method,markedly improves the com-putational efficiency of 3D slope reliability analysis without compromising accuracy.When only spatial variability is considered,the failure prob-ability decreases as the width of the failure surface increases.In contrast,when only the 3D effect is considered,the failure probability increases with the width of the failure surface.When both factors are considered simultaneously,their effects on the failure probability tend to offset each other,resulting in a significantly lower failure probability for 3D slopes compared to 2D slopes.When accounting for the variability of soil param-eters and 3D effects,the failure probability of slopes initially increases and then decreases with the widening of the failure surface.This pattern in-dicates that 3D effects dominate when the failure surface is narrow,because geometric constraints and stress redistribution play a critical role.In contrast,spatial variability of soil properties becomes the primary factor when the failure surface exceeds a critical width,because material hetero-geneity governs the failure process.The analysis reveals a critical failure surface width that marks the transition from geometry-controlled to material-controlled failure mechanisms in slope stability assessment.关键词
边坡/失效概率/协方差矩阵分解方法/3维效应/空间变异性Key words
soil slope/failure probability/CMD/three-dimensional effect/spatial variability分类
建筑与水利引用本文复制引用
万愉快,周玉麒,邵琳岚,王钰轲,张飞..考虑土体参数空间变异性的3维土质边坡可靠度分析[J].工程科学与技术,2026,58(1):80-89,10.基金项目
国家自然科学基金项目(52408373) （52408373）
宁夏自然科学基金优秀青年项目(2024AAC05036) （2024AAC05036）
宁夏高等学校一流学科建设(水利工程)项目(NXYLXK2021A03) （水利工程）
