基于高效随机有限元法的边坡风险评估

提出了基于子集模拟的边坡风险评估的高效随机有限元法（RFEM）,推导了基于子集模拟的边坡失效概率和失效风险的计算公式,并给出了基于高效RFEM的边坡可靠度分析和风险评估流程图。采用一个边坡算例验证了所提方法的有效性。结果表明,基于子集模拟的高效RFEM可以视为是对基于蒙特卡洛模拟的传统RFEM的改进,显著地提高了失效概率和失效风险的计算效率以及失效样本的产生能力,非常适用于分析小失效概率的可靠度问题,极大地增强了RFEM在边坡可靠度分析和风险评估中的实用性。高效RFEM将边坡的整体失效风险分解为对应不同概率水平的边坡失效风险,并量化了它们对整体风险的相对贡献度。在该方法中,边坡可靠度分析和风险评估与确定性边坡有限元分析互不耦合,极大地简化了它们的计算过程。此外,土体不排水抗剪强度的竖向空间变异性对边坡失效风险具有显著的影响。     

Advanced reliability analysis of slopes in spatially variable soils using multivariate adaptive regression splines

This study aims to extend the multivariate adaptive regression splines(MARS)-Monte Carlo simulation(MCS) method for reliability analysis of slopes in spatially variable soils. This approach is used to explore the influences of the multiscale spatial variability of soil properties on the probability of failure(P_f) of the slopes. In the proposed approach, the relationship between the factor of safety and the soil strength parameters characterized with spatial variability is approximated by the MARS, with the aid of Karhunen-Loeve expansion. MCS is subsequently performed on the established MARS model to evaluate Pf.Finally, a nominally homogeneous cohesive-frictional slope and a heterogeneous cohesive slope, which are both characterized with different spatial variabilities, are utilized to illustrate the proposed approach.Results showed that the proposed approach can estimate the P_f of the slopes efficiently in spatially variable soils with sufficient accuracy. Moreover, the approach is relatively robust to the influence of different statistics of soil properties, thereby making it an effective and practical tool for addressing slope reliability problems concerning time-consuming deterministic stability models with low levels of P_f.Furthermore, disregarding the multiscale spatial variability of soil properties can overestimate or underestimate the P_f. Although the difference is small in general, the multiscale spatial variability of the soil properties must still be considered in the reliability analysis of heterogeneous slopes, especially for those highly related to cost effective and accurate designs.     

Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using Subset Simulation

Random finite element method (RFEM) provides a rigorous tool to incorporate spatial variability of soil properties into reliability analysis and risk assessment of slope stability. However, it suffers from a common criticism of requiring extensive computational efforts and a lack of efficiency, particularly at small probability levels (e.g., slope failure probability P _f ?<?0.001). To address this problem, this study integrates RFEM with an advanced Monte Carlo Simulation (MCS) method called “Subset Simulation (SS)” to develop an efficient RFEM (i.e., SS-based RFEM) for reliability analysis and risk assessment of soil slopes. The proposed SS-based RFEM expresses the overall risk of slope failure as a weighed aggregation of slope failure risk at different probability levels and quantifies the relative contributions of slope failure risk at different probability levels to the overall risk of slope failure. Equations are derived for integrating SS with RFEM to evaluate the probability (P _f ) and risk (R) of slope failure. These equations are illustrated using a soil slope example. It is shown that the P _f and R are evaluated properly using the proposed approach. Compared with the original RFEM with direct MCS, the SS-based RFEM improves, significantly, the computational efficiency of evaluating P _f and R. This enhances the applications of RFEM in the reliability analysis and risk assessment of slope stability. With the aid of improved computational efficiency, a sensitivity study is also performed to explore effects of vertical spatial variability of soil properties on R. It is found that the vertical spatial variability affects the slope failure risk significantly.     

约束随机场下的边坡可靠度随机有限元分析方法

目前边坡可靠度中常用的简化分析方法,不考虑边坡土体的空间变异性,每次计算整个边坡都取用相同的强度参数,由离散点试样试验得到的土体参数统计特性只能反映点特性,而边坡的稳定性受滑面上平均抗剪强度特性控制,因此,需要考虑空间范围内的平均特性。描述空间变异性的随机场理论对变异性较高的土体,实际上高估了其空间变异性。把随机场理论和地质统计中的区域化变量理论结合起来,建立约束随机场,并在此基础上进行Monte-Carlo随机有限元分析。计算实例表明,在高变异性条件下约束随机场能有效降低完全随机场的模拟方差,得到更低的破坏概率。对比了随机有限元和简化法的计算结果表明,简化法在土体强度变异性很高时其结果并非偏于保守。另外也指出了可靠度分析中存在的边坡尺度效应和简化法的适用条件。     

考虑参数空间变异性多层土坡系统可靠度分析

多层土坡在岩土工程实际中十分常见,不仅土体参数存在一定的空间变异性,而且土体框架呈现明显的层状分布特征,然而目前对考虑土体参数空间变异性的多层土坡稳定可靠度研究的远远不够。提出了基于多重响应面边坡系统可靠度分析的蒙特卡洛模拟（MCS）方法,给出了计算流程图,系统地研究了考虑土体参数空间变异性的多层土坡系统可靠度问题。结果表明,提出方法能够有效地分析考虑参数空间变异性低失效概率水平的多层土坡系统可靠度问题,并且具有较高的参数敏感性分析计算效率。     

Influence of length effect on embankment slope reliability in 3D

Embankment slopes composed of spatially variable soils have a variety of different failure modes that are affected by the correlation distances of the material properties and the geometry and total length of the slope. This paper examines the reliability of soil slopes for embankments of different length and uses parallel computing to analyse very long embankments (up to 100 times the embankment height) for a clay soil characterised by a spatially varying undrained shear strength. Based on a series of analyses using the 3D random finite element method (RFEM), it is first shown that the reliability of slopes of various length can be efficiently computed by combining simple probability theory with a detailed 3D RFEM analysis of a representative shorter slope of length 10 times the slope height. RFEM predictions of reliability indices for longer slopes are then compared with results obtained using Vanmarcke's (1977a) simplified 3D method and Calle's (1985) extended 2D approach. It is shown that these methods can give significantly different results, depending on the horizontal scale of fluctuation relative to the slope length, with RFEM predicting a lower slope reliability than the Vanmarcke and Calle solutions in all cases. The differences in the solutions are evaluated and attributed to differences in the assumed and computed failure surface geometries.     

Design Charts for the Stability Analysis of Unsaturated Soil Slopes

Simple limit equilibrium analyses can be performed to determine the Factor of Safety (FOS) against slope failure of unsaturated soil slopes. However, many of the input parameters needed for these analyses are highly variable, and the FOS value obtained is critically dependent on assumptions made by the designer. This paper describes a suite of reliability analyses on unsaturated soil slopes performed using an invariant reliability model. The results are presented in design charts from which a designer can choose the FOS value required to ensure a given target reliability index for a slope. The approach ensures that despite the variability of input parameters the slope will have a probability of failure of 2.23% or less.     

Efficient system reliability analysis of soil slopes using multivariate adaptive regression splines-based Monte Carlo simulation

System effects should be considered in the probabilistic analysis of a layered soil slope due to the potential existence of multiple failure modes. This paper presents a system reliability analysis approach for layered soil slopes based on multivariate adaptive regression splines (MARS) and Monte Carlo simulation (MCS). The proposed approach is achieved in a two-phase process. First, MARS is constructed based on a group of training samples that are generated by Latin hypercube sampling (LHS). MARS is validated by a specific number of testing samples which are randomly generated per the underlying distributions. Second, the established MARS is integrated with MCS to estimate the system failure probability of slopes. Two types of multi-layered soil slopes (cohesive slope and c–φ slope) are examined to assess the capability and validity of the proposed approach. Each type of slope includes two examples with different statistics and system failure probability levels. The proposed approach can provide an accurate estimation of the system failure probability of a soil slope. In addition, the proposed approach is more accurate than the quadratic response surface method (QRSM) and the second-order stochastic response surface method (SRSM) for slopes with highly nonlinear limit state functions (LSFs). The results show that the proposed MARS-based MCS is a favorable and useful tool for the system reliability analysis of soil slopes.     

Slope vulnerability to earthquakes at subregional scale, using probabilistic techniques and geographic information systems

The susceptibility of slopes to failure during earthquakes is calculated, in terms of critical horizontal acceleration, on a subregional scale for the upper part of the Serchio River basin (Tuscany, Italy). According to the working scale (1:10 000) and to the availability and accuracy of the input data, the infinite slope analysis was judged to be the most appropriate method, but particular attention was devoted to the error evaluation due to spatial variability of the geotechnic, geometric, and hydrologic parameters. A geologic, geomorphologic and hydrologic survey of the area was therefore performed, and the geotechnic parameters were collected at local administrations. All the data were stored in a GIS, used as a tool to build the spatial and attribute data base and to prepare the input data layers for the stability analysis. In order to assess the variability of geotechnic parameters, a statistical analysis was performed to assign the best-fitting probability distribution to cohesion, angle of internal friction and unit weight of the soil. As hydrogeologic data were not available for the area, only surface hydrology information could be used; a map of probability of spring occurrences was derived by a bayesian method, the Weight of Evidence Modelling, and was used as groundwater indicator. A Monte Carlo procedure and a first-order second-moment method were applied and compared as error estimators in assessing the slope susceptibility to failure. The differences between the two methods are discussed, and two maps showing, respectively, the critical horizontal acceleration and the probability of failure associated with each slope are presented, together with the curve plotting the reliability index against the probability of failure.     

Influence of the spatial variability of shear strength parameters on rainfall induced landslides: a case study of sandstone slope in Japan

Rainfall-induced landslides frequently occur in humid temperate regions worldwide. Research activity in understanding the mechanism of rainfall-induced landslides has recently focused on the probability of slope failure involving non-homogeneous soil profiles. This paper presents probabilistic analyses to assess the stability of unsaturated soil slope under rainfall. The influence of the spatial variability of shear strength parameters on the probability of rainfall-induced slope failure is conducted by means of a series of seepage and stability analyses of an infinite slope based on random fields. A case study of shallow failure located on sandstone slopes in Japan is used to verify the analysis framework. The results confirm that a probabilistic analysis can be efficiently used to qualify various locations of failure surface caused by spatial variability of soil shear strength for a shallow infinite slope failure due to rainfall.     

Risk analysis of landslides – A case study

The effects of uncertainty due to the variability of soil parameters on the risk of landsliding in the Himalayan region are investigated using a random field model combined with slope stability analyses. Effects of spatial variability both in horizontal and vertical directions, number of test samples, variations in piezometric level and the influence of earthquake on the reliability of a typical slope in a slide area are investigated. The results show that the reliability of slopes in the slide area is significantly affected by the coefficients of variation of soil parameters, spatial variations of soil parameters, number of test samples and piezometric variations. The results also show that the assumption of isotropic variations to assess slope reliability isconservative. The results of the study are useful in providing guidelines and pointing to remedial measures in the form of sub-surface drainage to improve slope reliability in the area.     

Modeling uncertainty in stability analysis for design of embankment dams on difficult foundations

A probabilistic 3-D slope stability analysis model (PTDSSAM) is developed to evaluate the stability of embankment dams and their foundations under conditions of staged construction taking into consideration uncertainty, spatial variabilities and correlations of shear strength parameters, as well as the uncertainties in pore water pressure. The model has the following capabilities: (1) conducting undrained shear strength analysis (USA) and effective stress analysis (ESA) slope stability analysis of staged construction, (2) incorporation of field monitored data of pore water pressure, and (3) incorporation of increase of undrained shear strength with depth, effective stress, and pore water pressure dissipation. The PTDSSAM model is incorporated in a computer program that can analyze slopes located in multilayered deposits, considering the total slope width.

The main outputs of the program are the geometric parameters of the most critical sliding surface (i.e., center of rotation/radius of rotation and critical width of failure), mean 2-D safety factor, mean 3-D safety factor, squared coefficient of variation of resisting moment, and the probability of slope failure. The program is applied to a case study, Karameh dam in Jordan. Monitored data of induced pore water pressure in the dam embankment and soft foundation were gathered during dam construction.

The stability of Karameh dam embankment and foundation was evaluated during staged construction using deterministic and probabilistic analysis. Foundation stability was evaluated based on the monitored data of pore water pressure.

The study showed that the mean values of the corrective factors which account for the discrepancies between the in situ and laboratory-measured values of soil properties and for the modeling errors have significant influence on the 2-D safety factor, 3-D safety factor, slope probability of failure, and on the expected failure width.

The degree of spatial correlation associated with shear strength parameters within a soil deposit also influences the probability of slope failure and the expected failure width. This correlation is quantified by scale of fluctuation. It is found that a larger scale of fluctuation gives an increase in the probability of slope failure and a reduction in the critical failure width.     

考虑参数空间变异性的非饱和土坡可靠度分析

在考虑多个土体参数空间变异性的基础上,提出了基于拉丁超立方抽样的非饱和土坡稳定可靠度分析的非侵入式随机有限元法。利用Hermite随机多项式展开拟合边坡安全系数与输入参数间的隐式函数关系,采用拉丁超立方抽样技术产生输入参数样本点,通过Karhunen-Loève展开方法离散土体渗透系数、有效黏聚力和内摩擦角随机场,并编写了计算程序NISFEM-KL-LHS。研究了该方法在稳定渗流条件下非饱和土坡可靠度分析中的应用。结果表明：非侵入式随机有限元法为考虑多个土体参数空间变异性的非饱和土坡可靠度问题提供了一种有效的分析工具。土体渗透系数空间变异性和坡面降雨强度对边坡地下水位和最危险滑动面位置均有明显的影响。当降雨强度与饱和渗透系数的比值大于0.01时,边坡失效概率急剧增加。当土体参数变异性或者参数间负相关性较大时,忽略土体参数空间变异性会明显高估边坡失效概率。     

Probabilistic infinite slope analysis

Research activity in the mechanics of landslides has led to renewed interest in the infinite slope equations, and the need for a more general framework for giving insight into the probability of failure of long slopes involving non-homogeneous vertical soil profiles and variable groundwater conditions. This paper describes a methodology in which parameters such as the soil strength, slope geometry and pore pressures, are generated using random field theory. Within the limitations of the infinite slope assumptions, the paper clearly demonstrates the important “seeking out” effect of failure mechanisms in spatially random materials, and how “first order” methods that may not properly account for spatial variability can lead to unconservative estimates of the probability of slope failure.     

考虑时间效应的滑坡风险评估和管理

提出了考虑时间效应的滑坡风险评估和管理方法。以香港地区近20年的16 000个切破的观测资料为基础,从统计学的角度提出了边坡的时变可靠性分析方法。推导了新建边坡在未来服役时间内的年失效概率的计算公式,并对现役边坡在未来服役时间内的年失效概率进行了预测。确定了基于年死亡人数的滑坡风险接受准则,并分析了基于滑坡时变风险的边坡加固时间。结果表明,考虑时间效应的滑坡风险评估和管理方法能够更加真实地反映滑坡随时间变化的特性。新建边坡的年失效概率随边坡服役时间逐渐增大,尤其是当边坡服役超过10年时,每年发生滑坡的概率急剧增大。现役边坡的年失效概率基本与继续服役时间呈线形关系。此外,香港斜坡维修指南规定的边坡加固时间能够有效地将滑坡风险降低到ALARP区或可接受的风险区。     

路堤边坡稳定可靠度计算中的模型不确定性分析

基于均质路堤边坡Monte Carlo法的稳定可靠度计算,分析了临界滑面搜索策略和稳定分析方法两类模型不确定性对边坡可靠度的影响特性,讨论了边坡失效概率随土工参数变异性的变化规律。研究表明,选用不同的临界滑面搜索策略所得可靠度结果差异不大,参数滑面法（overall slope）的失效概率略大于均值滑面法（global minimum）,但差别对边坡稳定性分析没有实质性影响;土性参数变异水平是影响边坡可靠度的最重要因素,边坡在相同设计参数安全系数下的可靠度指标随参数变异性增大而急剧降低;不同稳定性分析方法对应的安全系数概率密度函数曲线形态基本一致,但失效概率差异明显,因此目标可靠度指标取值应与稳定性分析方法相适应。提出的考虑土工参数变异水平的安全系数取值修正原则,对改进确定性设计的边坡稳定分析技术有积极意义。     

Modeling 2-D spatial variation in slope reliability analysis using interpolated autocorrelations

This paper deals with slope reliability analysis incorporating two-dimensional spatial variation. Two methods, namely the method of autocorrelated slices and the method of interpolated autocorrelations, are proposed for this purpose. Investigations are carried out based on the limit equilibrium method of slices. First-order-reliability-method (FORM) is coupled with deterministic slope stability analysis using the constrained optimization approach. Systematic search for the probabilistic critical slip surface has been carried out in this study. It is shown that both methods work well in modeling 2-D spatial variation. The results of slope reliability analysis are validated by Monte Carlo simulations. Failure probabilities obtained by FORM agree well with simulation results. It is found that 2-D spatial variation significantly influences the reliability analysis, and that the reliability index is more sensitive to vertical autocorrelation distance than to horizontal autocorrelation distance. Based on this study, failure probability is found significantly overestimated when spatial variation is ignored. Finally, the possible use of the method of interpolated autocorrelations in a probabilistic finite element analysis is suggested.     

Three-dimensional reliability analysis of earth slopes

Reliability of cohesive soil slopes is assessed using a three-dimensional (3D) probabilistic stability analysis algorithm. Spatial variability of soil properties is represented by an anisotropic random field. Parametric studies are performed for a typical earth structure. The influence of the model parameters, including expected value, variance and correlation distance of soil shear strength, on the reliability associated to particular failure mechanisms is evaluated. The effect on reliability of the dimensions and shape of potential slip surfaces for a given random field is also assessed. It is shown that the mechanisms that contribute most significantly to global probability of failure of the slope may be quite different from those identified as critical by standard deterministic evaluations assuming soil homogeneity. Some practical implications of this fact are discussed.     

考虑空间变异性条件下的边坡稳定可靠度高效敏感性分析

在有限数据条件下,可靠度敏感性分析是研究各种不确定性因素对边坡失稳概率影响规律的重要途径。基于直接蒙特卡洛模拟和概率密度加权分析方法提出了一种高效边坡稳定可靠度敏感性分析方法。所提出的方法通过随机场表征岩土体参数的空间变异性,并采用局部平均理论建立岩土体参数的缩维概率密度函数,用于概率密度加权分析中高效、准确地计算不同敏感性分析方案对应的边坡失稳概率。最后,通过一个工程案例--詹姆斯湾堤坝说明了所提出方法的有效性和准确性。结果表明：在敏感性分析过程中,所提出的方法只需要执行一次直接蒙特卡洛模拟,避免了针对不同敏感性分析方案重新产生随机样本和执行边坡稳定分析,节约了大量的计算时间和计算资源,显著提高了基于蒙特卡洛模拟的敏感性分析计算效率;在概率密度加权分析中采用岩土体参数的缩维概率密度函数能够准确地计算边坡失稳概率,避免了有偏估计,使概率密度加权分析方法适用于考虑空间变异性条件下的边坡稳定可靠度敏感性分析问题。     

Probabilistic failure analysis of infinite slopes under random rainfall processes and spatially variable soil

Rainfall-induced landslides occur during or immediately after rainfall events in which the pore water pressure builds up, leading to shallow slope failure. Thereby, low permeability layers result in high gradients in pore water pressure. The spatial variability of the soil permeability influences the probability such low permeability layers, and hence the probability of slope failure. In this paper, we investigate the influence of the vertical variability of soil permeability on the slope reliability, accounting for the randomness of rainfall processes. We model the saturated hydraulic conductivity of the soil with a one-dimensional random field. The random rainfall events are characterised by their duration and intensity and are modelled through self-similar random processes. The transient infiltration process is represented by Richards equation, which is evaluated numerically. The reliability analysis of the infinite slope is based on the factor of safety concept for evaluating slope stability. To cope with the large number of random variables arising from the discretization of the random field and the rainfall process, we evaluate the slope reliability through Subset Simulation, which is an adaptive Monte Carlo method known to be especially efficient for reliability analysis of such high-dimensional problems. Numerical investigations show higher probability of slope failure with increased spatial variability of the saturated hydraulic conductivity and with more uniform rainfall patterns.