Meta-Analysis of 301 Slope Failure Calculations. II: Database Analysis

In response to the growing need for statistical information regarding slope stability risk analysis, this work applies inferential analysis to a compiled database of 157 failed slopes and corresponding 301 safety factor (SF) calculations. As presented in the companion paper, this database also includes a number of slope stability factors, including analytical method used, stress approach (effective versus total), assumed slip surface geometry, slope type, applied correction factors, and soil Atterburg limits. Although the SF data were found to be fairly well fit by a lognormal distribution, pronounced curvature of the residuals was observed, likely related to various unaccounted slope factors. In response, inferential statistics are used in this paper to analyze the effects of analytical method, slope type, soil plasticity, and effective versus total stress analysis. ANOVA hypothesis testing indicated significant differences between analytical methods and significant interactions between slope types and pore-water stress approaches. Direct SF calculation methods, such as infinite slope, wedge, and the ordinary method of slices were found to produce SF near 1 as expected, but higher order methods in general, and force methods in particular, predicted safety factors significantly greater than 1. Clay content alone was not a discernible influence on SF calculations. A reduced factor ANOVA model was developed to predict SF, given analytical method (a main effect) and the interactions between analytical method with both slope type and pore-water pressure approach.     

Stability Analysis of Strain-Softening Slope Reinforced with Stabilizing Piles

Stabilizing piles have been used extensively over the past few decades to support unstable slopes. A new simplified method is described to analyze the stability level of a strain-softening slope reinforced with stabilizing piles. An equivalent principle is proposed to account for the three-dimensional effect of the piles on the stability level of slopes. The formulation is derived on the basis of the displacement distribution assumptions of the slope by extending the simplified Bishop slice method. The parameters can be easily determined by element tests. This method is used on a real-world slope to discuss the influential factors. The results show that the slope geometry and pile layout, which includes pile spacing, pile location, and pile depth, have a significant effect on the safety factor and critical slip surface of the reinforced slope. The stability level of a strain-softening slope is dependent not only on the strength parameters but also on the stress-strain relationship of soil.     

基于PEM-JFEM方法的节理岩质边坡稳定性评价

以赞比亚一露天铜矿南帮边坡(矿体下盘)为研究对象,将Rosenbluth点估计方法与节理有限元方法相结合应用于该节理发育的岩质边坡稳定性评价中.建立以边坡岩体材料强度参数(内摩擦角和黏聚力)为输入变量,安全系数为输出变量的概率模型,点估计状态函数的求解过程引入节理有限元方法.通过现场节理及结构面调查,建立边坡节理有限元模型求解边坡安全系数,得到基于安全系数的边坡变形破坏概率统计指标,对边坡稳定性进行了概率分析,分析结果与现场失稳情况一致.该方法既考虑了岩体材料参数在赋值过程中实际存在的不确定性,同时也考虑了节理岩质边坡的节理属性,充分体现了岩层接触作用的非线性关系,使得对节理岩质边坡的稳定性评价更加合理.      

基于极限平衡法和强度折减法的边坡稳定性分析

考虑传统的极限平衡法和FLAC二维非线性数值分析方法的优缺点,将边坡稳定性分析的Slide极限平衡法和FLAC2D强度折减法相结合,以某排土场为工程实际,进行了边坡在天然、天然地震、降雨和降雨地震四种不同工况下的稳定性验算比较;鉴于影响边坡稳定因素的不确定性,采用基于Spencer法的Mont-Carlo法进行了边坡可靠度指标的计算,并对强度参数C、（φ）和容重γ对边坡稳定的影响进行了分析,得出边坡稳定对内摩擦角（φ）的敏感性高于内聚力C的敏感性,而容重γ的影响较C、（φ）可忽略不计.该方法通过两者的相互校核,不仅给出边坡非线性应力-应变关系和安全系数来共同评价边坡的稳定性,而且结合排土场边坡安全系数的概率分析提供边坡潜在的失效概率使边坡稳定性评价更加科学、精确.     

Unsaturated Infinite Slope Stability Considering Surface Flux Conditions

A slope stability model is derived for an infinite slope subjected to unsaturated infiltration flow above a phreatic surface. Closed form steady state solutions are derived for the matric suction and degree of saturation profiles. Soil unit weight, consistent with the degree of saturation profile, is also directly calculated and introduced into the analyzes, resulting in closed-form solutions for typical soil parameters and an infinite series solution for arbitrary soil parameters. The solutions are coupled with the infinite slope stability equations to establish a fully realized safety factor function. In general, consideration of soil suction results in higher factor of safety. The increase in shear strength due to the inclusion of soil suction is analogous to making an addition to the cohesion, which, of course, increases the factor of safety against sliding. However, for cohesive soils, the results show lower safety factors for slip surfaces approaching the phreatic surface compared to those produced by common safety factor calculations. The lower factor of safety is due to the increased soil unit weight considered in the matric suction model but not usually accounted for in practice wherein the soil is treated as dry above the phreatic surface. The developed model is verified with a published case study, correctly predicting stability under dry conditions and correctly predicting failure for a particular storm.     

Coke Collapse Model and Collapse Profile Variation Law for Bell-Less Top BF

 The mathematical model of minimum safety factor that investigated the collapse trends of coke layer under different charging parameters was established firstly on the basis of the slope stabilization theory in soil mechanics, and then the model of burden profile after coke collapse was improved by adopting the predetermination of quadratic curve and energy correction methods. The research will provide theoretical evidences for describing the coke profile more accurately and technical direction for choosing suitable charging parameters of blast furnace. The results show that: it is helpful to improve the stability of coke layer with increasing chute inclining angle and length of the coke flat; when the main falling point of ore moves toward furnace wall or the coke flat is wider, the curve radian of burden profile after coke collapse becomes smaller; the ore to coke ratio distribution agrees with the gas top temperature measurement well under considering coke collapse comparing with the result of ignoring coke collapse.     

Stability Analyses of Rainfall Induced Landslides

The slope stability issues concerning rainfall induced slope failures are investigated and presented. Specifically, the effect of both negative and positive pore water pressures on the stability of initially unsaturated slopes are carefully explained and coupled with infinite slope analysis methods in order to present a predictive formulation of slope failures that occur as a result of rainfall events. The formulation serves as a baseline analysis method for evaluating potentially unstable soil slopes that are subject to surface infiltration and explains the various triggering mechanisms that may occur based on individual combinations of the slope geometry, soil strength, and infiltration parameters. A procedural method is outlined for utilizing the analytical formulation to predict the change in the factor of safety for a slope subject to infiltration and a detailed analysis of a case study is presented to verify the method. Quantitative statements are made concerning the time and depth of failure in relationship to the soil, slope, and rainfall parameters.     

Effect of Antecedent Rainfall Patterns on Rainfall-Induced Slope Failure

Rainfall-induced slope failure occurs in many parts of the world, especially in the tropics. Many rainfall-induced slope failures have been attributed to antecedent rainfalls. Although it has been identified as a cause of rainfall-induced slope failure, the pattern or distribution of the antecedent rainfall has not received adequate attention. In this study, parametric studies were performed by using three typical rainfall patterns, identified by analysis of available rainfall data for Singapore and two different soil types to represent high- and low-conductivity residual soils of Singapore. Antecedent rainfall patterns were applied on soil slopes and a transient seepage analysis was conducted. The computed pore-water pressures were used in stability analyses to calculate the safety factor of the slope. Results indicated that antecedent rainfall affected the stability of both high-conductivity (HC) and low-conductivity (LC) soil slopes. However, the stability of the LC soil slope was more significantly affected than the HC soil slope. Patterns of antecedent rainfall controlled the rate of decrease in factor of safety, the time corresponding to Fs(min) and the value of Fs(min). Delayed rainfall pattern resulted in the lowest minimum factor of safety, Fs(min), for the HC soil slope, and advanced rainfall pattern resulted in the lowest Fs(min) for the LC soil slope.     

Limit Analysis and Stability Charts for 3D Slope Failures

The kinematic approach of limit analysis is explored in three-dimensional (3D) stability analysis of slopes. A formal derivation is first shown indicating that, in a general case, the approach yields an upper bound to the critical height of the slope or an upper bound on the safety factor. A 3D failure mechanism is used to produce stability charts for slopes. The slope safety factor can be read from the charts without the need for iterations. While two-dimensional (2D) analyses of uniform slopes lead to lower safety factors than 3D analyses do, a 3D calculation is justified in cases where the width of the collapse mechanism has physical limitations, for instance, in the case of excavation slopes, or when the analysis is carried out to back-calculate the properties of the soil from 3D failure case histories. Also, a 3D failure can be triggered by a load on a portion of the surface area of the slope. Calculations indicate that for the 3D safety factor of the loaded slope to become lower than the 2D factor for the same slope (but with a load-free surface), the load has to be very significant and equal to the weight of a soil column of the order 10?1 of the slope height.     

Factors Controlling Instability of Homogeneous Soil Slopes under Rainfall

Rainfall-induced slope failure is a common geotechnical problem in the tropics where residual soils are abundant. Although the significance of rainwater infiltration in causing landslides is widely recognized, there have been different conclusions as to the relative roles of antecedent rainfall to landslides. The relative importance of soil properties, rainfall intensity, initial water table location and slope geometry in inducing instability of a homogenous soil slope under different rainfall was investigated through a series of parametric studies. Soil properties and rainfall intensity were found to be the primary factors controlling the instability of slopes due to rainfall, while the initial water table location and slope geometry only played a secondary role. The results from the parametric studies also indicated that for a given rainfall duration, there was a threshold rainfall intensity which would produce the global minimum factor of safety. Attempts have also been made to relate the findings from this study to those observed in the field by other researchers. Results of this parametric study clearly indicated that the significance of antecedent rainfall depends on soil permeability.     

Effects of Groundwater Table Position and Soil Properties on Stability of Slope during Rainfall

Rainfall, hydrological condition, and geological formation of slope are important contributing factors to slope failures. Parametric studies were carried out to study the effect of groundwater table position, rainfall intensities, and soil properties in affecting slope stability. Three different groundwater table positions corresponding to the wettest, typical, and driest periods in Singapore and four different rainfall intensities (9, 22, 36, and 80 mm/h) were used in the numerical analyses. Typical soil properties of two main residual soils from the Bukit Timah Granite and the sedimentary Jurong Formation in Singapore were incorporated into the numerical analyses. The changes in factor of safety during rainfall were not affected significantly by the groundwater table near the ground surface due to the relatively small changes in matric suction during rainfall. A delay in response of the minimum factor of safety due to rainfall and a slower recovery rate after rainfall were observed in slopes from the sedimentary Jurong Formation as compared to those slopes from the Bukit Timah Granite. Numerical analyses of an actual residual soil slope from the Bukit Timah Granite at Marsiling Road and a residual soil slope from the sedimentary Jurong Formation at Jalan Kukoh show good agreement with the trends observed in the parametric studies.     

降雨和蒸发对粉质黏土边坡稳定性影响分析

以山西某露天矿粉质黏土边坡为工程背景,基于饱和-非饱和渗流理论及流固耦合原理,采用有限单元法研究了降雨和蒸发作用下边坡孔隙水压力、体积含水量、位移及应变变化特点,并对不同降雨强度和蒸发强度下的边坡孔隙水压力和安全系数进行了对比分析。研究结果表明:降雨入渗导致浅层土体含水量增大,基质吸力降低,降低边坡稳定性,降雨强度越大,边坡稳定性下降越快;蒸发会降低浅层土体的含水量,增加吸力,提高边坡稳定性,且蒸发强度越大,安全系数提高越快;边坡孔隙水压力和安全系数与天气条件之间存在滞后关系,滞后时间随土体深度增加而增加。     

Efficient Probabilistic Back-Analysis of Slope Stability Model Parameters

Back-analysis of slope failure is often performed to improve one’s knowledge on parameters of a slope stability analysis model. In a failed slope, the slip surface may pass through several layers of soil. Therefore, several sets of model parameters need to be back-analyzed. To back-analyze multiple sets of slope stability parameters simultaneously under uncertainty, the back-analysis can be implemented in a probabilistic way, in which uncertain parameters are modeled as random variables, and their distributions are improved based on the observed slope failure information. In this paper, two methods are presented for probabilistic back-analysis of slope failure. For a general slope stability model, its uncertain parameters can be back-analyzed with an optimization procedure that can be implemented in a spreadsheet. When the slope stability model is approximately linear, its parameters can be back-analyzed with sensitivity analysis instead. A feature of these two methods is that they are easy to apply. Two case studies are used to illustrate the proposed methods. The case studies show that the degrees of improvement achieved by the back-analysis are different for different parameters, and that the parameter contributing most to the uncertainty in factor of safety is updated most.     

Optimal Design of a Stable Trapezoidal Channel Section Using Hybrid Optimization Techniques

A cost effective channel section for a specified flow rate, roughness coefficients, longitudinal slope, and various cost parameters can be determined using an optimization technique. However, the derived optimal channel section may not be feasible for construction because of in situ conditions. The local soil conditions may not support the optimal side slope of the channel and if constructed, the slope may fail. It is therefore necessary to also incorporate the criteria for side slope stability in designing an optimal open channel section. In this paper, a new methodology has been developed to design a stable and optimal channel section using hybrid optimization techniques. A genetic algorithm based optimization model is developed initially to determine the factor of safety of a channel slope for given soil parameters. This optimization model is then externally linked with a separate sequential quadratic programming based optimization model to evaluate the parameters of the stable and optimal channel section. Solution for various example problems incorporating different soil parameters are illustrated to demonstrate the applicability of the developed methodology.     

基于机器学习的边坡安全稳定性评价及防护措施

为了更加快捷、高效地判定边坡稳定与否,基于机器学习,融合主成分分析法（PCA）、参数调整、影响因素权重分析等,建立了一种边坡安全稳定性评价体系。研究发现,运用PCA可以在保留80%数据原信息的前提下将输入变量维度从六维降至三维,但此时模型效果有所下降;随机森林及梯度提升(XGBoost) 两种学习算法均可搭建有效的边坡安全稳定性评估模型,通过对其预测效果的对比分析,确定XGBoost为最佳评价模型。与此同时,采取卡方检验、F检验以及互信息法3种相关性检验手段,并通过计算评价因子的重要程度且加以可视化展示,明确了容重、坡高、内摩擦角以及内聚力4个内在因素的重要性,最终将评估结果与实际结合提出了边坡安全防护措施。      

Slope Stability Analysis with Nonlinear Failure Criterion

A linear failure criterion is widely used in slope stability analyses. However, the strength envelope of almost all geomaterials has the nature of nonlinearity. This paper computes rigorous upper bounds on slope stability factors under the condition of plane strain with a nonlinear yield criterion by employing the upper bound theorem of plasticity. A stability factor (or a limit load) computed using a linear Mohr-Coulomb (MC) failure criterion which circumscribes the actual nonlinear failure criterion is an upper bound value of the actual stability factor (or limit load). In this paper, an improved method using a “generalized tangential” technique to approximate a nonlinear failure criterion is proposed to estimate the stability factor of a slope on the basis of the upper bound theorem of plasticity. Using the “generalized tangential” technique, the curve of the nonlinear failure criterion is simplified as a set of straight lines according to the linear MC failure criterion. The straight line is tangential to the curve of the nonlinear failure criterion. The set of straight lines of the linear MC failure criterion is employed to formulate the slope stability problem as a classical optimization problem. The objective function formulated in this way is minimized with respect to the location of sliding body center and the location of tangency point. Two typical slope stability problems (a homogeneous soil slope with two slope angles and a vertical cut slope with a tension crack) are analyzed using the proposed method. For the soil slope with two slope angles, the computed results are compared with published solutions by others. The comparison shows that the proposed method gives reasonable and consistent values of the stability factor of the slope. For the vertical cut slope with a tension crack, a statically admissible stress field is constructed for the slope. The stress field does not violate the nonlinear failure criterion. Lower bound solutions are obtained by satisfying stress equilibrium conditions. The upper bound solutions obtained from the proposed method are equal to the lower bound solutions for the vertical cut slope. The agreement further supports the validation of the proposed approach. The influences of the strength parameters in the nonlinear criterion on the stability of slopes are also studied and discussed in this paper.     

Probabilistic Assessment of Slope Stability That Considers the Spatial Variability of Soil Properties

In this paper, a numerical procedure for probabilistic slope stability analysis is presented. This procedure extends the traditional limit equilibrium method of slices to a probabilistic approach that accounts for the uncertainties and spatial variation of the soil strength parameters. In this study, two-dimensional random fields were generated based on a Karhunen-Loève expansion in a fashion consistent with a specified marginal distribution function and an autocorrelation function. A Monte Carlo simulation was then used to determine the statistical response based on the generated random fields. This approach makes no assumption about the critical failure surface. Rather, the critical failure surface corresponding to the input random fields of soil properties is searched during the process of analysis. A series of analyses was performed to verify the application potential of the proposed method and to study the effects of uncertainty due to the spatial heterogeneity on the stability of slope. The results show that the proposed method can efficiently consider the various failure mechanisms caused by the spatial variability of soil property in the probabilistic slope stability assessment.     

Impacts of Unsaturated Zone Soil Moisture and Groundwater Table on Slope Instability

The combined effect of soil moisture in unsaturated soil layers and pore-water pressure in saturated soil layers is critical to predict landslides. An improved infinite slope stability model, that directly includes unsaturated zone soil moisture and groundwater, is derived and used to analyze the factor of safety’s sensitivity to unsaturated zone soil moisture. This sensitivity, the change in the factor of safety with respect to variable unsaturated zone soil moisture, was studied at local and regional scales using an active landslide region as a case study. Factors of safety have the greatest sensitivity to unsaturated zone soil moisture dynamics for shallow soil layers (<2?m) and comparatively deep groundwater tables (1 m). For an identical groundwater table, the factor of safety for a 1 m thick soil mantle was four times more sensitive to soil moisture changes than a 3-m thick soil. At a regional scale, the number of unstable areas increases nonlinearly with increasing unsaturated zone soil moisture and with moderately wet slopes exhibiting the greatest sensitivity.     

顺层岩质边坡变形破坏特征及稳定性数值模拟

针对顺层岩质边坡岩层结构面倾角θ和边坡角α两个参数,采用离散单元法研究了不同工况下总计270个边坡模型的变形破坏特征,统计得到不同变形破坏模式对应的岩层结构面倾角θ与边坡角α的范围,并基于强度折减法研究了两个参数与边坡稳定性的关系,揭示了顺层岩质边坡变形破坏机制及稳定性特征.研究结果表明:依据边坡变形破坏特征,提出了四种顺层岩质边坡变形破坏模式,即坡脚沿岩层结构面的滑移-剪切破坏,坡顶沿岩层结构面的滑动-剪切破坏,岩层下缘弯曲-剪切破坏,以及岩层上缘翻折-拉裂破坏.在此基础上,分析并归纳了这四种模式的产状、变形特征以及可能的破坏模式等一般规律.边坡安全系数f_s随结构面倾角θ的增大先减小后增大,在减小过程中达到最小值后迅速上升,然后变缓回落.边坡安全系数f_s随结构面倾角θ变化过程中,当θ约等于α-7.3°时,f_s取得最小值,此时对应的边坡稳定性最差.      

Spatial Distribution of Safety Factors

Classical limiting equilibrium analysis seeks the minimum factor of safety and its associated critical slip surface. This objective is mathematically convenient; however, it limits the analysis' practical usefulness. Introduced is a general framework for safety maps that allow for a physically meaningful extension of classical slope stability analysis. Safety maps are represented by a series of contour lines along which minimal safety factors are constant. Each contour line is determined using limit equilibrium analysis and thus represents a value of global safety factor. Since most problems of slope stability possess a flat minimum involving a large zone within which safety factors are practically the same, representation of the results as a safety map provides an instant diagnostic tool about the state of the stability of the slope. Such maps provide at a glance the spatial scope of remedial measures if such measures are required. That is, unlike the classical slope stability approach that identifies a single surface having the lowest factor of safety, the safety map displays zones within which safety factors may be smaller than an acceptable design value. The approach introduced results in a more meaningful application of limiting equilibrium concepts while preserving the simplicity and tangibility of limit equilibrium analysis. Culmann's method is used to demonstrate the principles and usefulness of the proposed approach because of its simplicity and ease of application. To further illustrate the practical implications of safety maps, a rather complex stability problem of a dam structure is analyzed. Spencer's method using generalized slip surfaces and an efficient search routine are used to yield the regions within the scope where the safety factors are below a certain value.