Identification of representative slip surfaces for reliability analysis of soil slopes based on shear strength reduction

Although a slope may have numerous potential slip surfaces, its failure probability is often governed by several representative slip surfaces (RSSs). Previous efforts mainly focus on the identification of circular RSSs based on limit equilibrium methods. In this paper, a method is suggested to identify RSSs of arbitrary shape based on the shear strength reduction method. Monte Carlo simulation is used to generate a large number potential slip surfaces. The RSSs are identified through analyzing the failure domains represented by these samples. A kriging-based response surface model is employed to enhance the computational efficiency. These examples shows that the RSSs may not always be circular, and that the suggested method can effectively locate the RSSs without making prior assumptions about the shape of the slip surfaces. For the examples investigated, the system failure probabilities computed based on the shear strength reduction method are comparable to, but not the same as those computed based on the limit equilibrium methods. The suggested method significantly extends our capability for identifying non-circular RSSs and hence probabilistic slope stability analysis involving non-circular slip surfaces.     

Uncertainty of rainfall-induced landslides considering spatial variability of parameters

A cross-correlation analysis is conducted to determine the impacts of the heterogeneity of hydraulic conductivity K_s, soil cohesion c′ and soil friction angle (tan φ′) on the uncertainty of slope stability in time and space during rainfall. We find the relative importance of tan φ′ and c′ depends on the effective stress. While the sensitivity of the stability to the variability of K_s is small, the large coefficient of variation of K_s may exacerbate the variability of pore-water pressure. Therefore, characterizing the heterogeneity of hydraulic properties and pore-water distribution in the field is critical to the stability analysis.     

Effect of 2D spatial variability on slope reliability: A simplified FORM analysis

To meet the high demand for reliability based design of slopes, we present in this paper a simplified HLRF(Hasofere Linde Rackwitze Fiessler) iterative algorithm for first-order reliability method(FORM). It is simply formulated in x-space and requires neither transformation of correlated random variables nor optimization tools. The solution can be easily improved by iteratively adjusting the step length. The algorithm is particularly useful to practicing engineers for geotechnical reliability analysis where standalone(deterministic) numerical packages are used. Based on the proposed algorithm and through direct perturbation analysis of random variables, we conducted a case study of earth slope reliability with complete consideration of soil uncertainty and spatial variability.     

Numerical and analytical observations on long and infinite slopes

Interest in the mechanics of landslides has led to renewed evaluation of the infinite slope equations, and the need for a more general framework for estimating the factor of safety of long and infinite slopes involving non‐homogeneous soil profiles. The paper describes finite element methods that demonstrate the potential for predicting failure in long slope profiles where the critical mechanism is not necessarily at the base of the soil layer. The influence of slope angle is also examined in long slopes, leading to some counter‐intuitive conclusions about the impact of slope steepness on the factor of safety. Copyright © 2010 John Wiley & Sons, Ltd.     

Reliability bearing capacity analysis of footings on cohesive soil slopes using RFEM

Reliability analysis of bearing capacity of a strip footing at the crest of a simple slope with cohesive soil was carried out using the random finite element method (RFEM). Analyses showed that the coefficient of variation and the spatial correlation length of soil cohesion can have a large influence on footing bearing capacity, particularly for slopes with large height to footing width ratios. The paper demonstrates cases where a footing satisfies a deterministic design factor of safety of 3 but the probability of design failure is unacceptably high. Isotropic and anisotropic spatial variability of the soil strength was also considered.     

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.     

Three-dimensional slope reliability and risk assessment using auxiliary random finite element method

This paper aims to propose an auxiliary random finite element method (ARFEM) for efficient three-dimensional (3-D) slope reliability analysis and risk assessment considering spatial variability of soil properties. The ARFEM mainly consists of two steps: (1) preliminary analysis using a relatively coarse finite-element model and Subset Simulation, and (2) target analysis using a detailed finite-element model and response conditioning method. The 3-D spatial variability of soil properties is explicitly modeled using the expansion optimal linear estimation approach. A 3-D soil slope example is presented to demonstrate the validity of ARFEM. Finally, a sensitivity study is carried out to explore the effect of horizontal spatial variability. The results indicate that the proposed ARFEM not only provides reasonably accurate estimates of slope failure probability and risk, but also significantly reduces the computational effort at small probability levels. 3-D slope probabilistic analysis (including both 3-D slope stability analysis and 3-D spatial variability modeling) can reflect slope failure mechanism more realistically in terms of the shape, location and length of slip surface. Horizontal spatial variability can significantly influence the failure mode, reliability and risk of 3-D slopes, especially for long slopes with relatively strong horizontal spatial variability. These effects can be properly incorporated into 3-D slope reliability analysis and risk assessment using ARFEM.     

Probabilistic analysis of reinforced slopes using RFEM and considering spatial variability of frictional soil properties due to compaction

Probabilistic stability analyses of constructed wrapped-face reinforced slopes (or embankments) using frictional soils were carried out using the random finite element method (RFEM). Soil properties reported in the literature for unsaturated frictional fills compacted to different densities were used in the simulations. Bar elements were added to the RFEM code to simulate extensible geosynthetic reinforcement layers and the Davis approach was used to improve numerical stability for purely frictional soil slopes at collapse. The influence of isotropic and anisotropic spatially variable soil strength was investigated and shown to have a large influence on the variation of maximum mobilised tensile forces in reinforcement layers for the steep 5 m-high slopes in the study. The influence of fill placed at different layer thickness and compacted to different levels was simulated by adjusting the soil strength and unit weight, and the vertical strength correlation length in the anisotropic spatially variable strength field used in each slope realisation. Numerical results showed that vertical strength correlation lengths approaching the magnitude of fill lift heights can control the probability of failure for reinforced slopes constructed with weak fills placed in lift heights close to but less than the wrapped reinforcement spacing used in the study.     

不排水抗剪强度非平稳随机场模拟及边坡可靠度分析

边坡可靠度分析中通常假定采用平稳或准平稳随机场表征土体参数的空间变异性,然而大量现场试验数据表明,土体参数如不排水抗剪强度沿土体埋深常呈现明显的非平稳分布特征,即其均值和标准差均随埋深发生变化,因此亟需发展土体参数非平稳随机场模型及其模拟方法。针对目前不能有效单独模拟土体参数趋势分量和随机波动分量的不确定性,提出了一种有效的不排水抗剪强度参数非平稳随机场模型,并给出了土体参数二维非平稳随机场模拟方法计算流程,同时将新提出的模型与现有非平稳随机场模型及平稳随机场模型进行了系统比较。最后通过不排水饱和黏土边坡算例验证了提出模型的有效性,并揭示了不排水抗剪强度非平稳分布特征对边坡可靠度的影响规律。结果表明：提出模型能够有效地单独模拟土体参数趋势分量和随机波动分量的不确定性,考虑土体参数均值和标准差随埋深增加而增大的特性,可为表征土体参数非平稳分布特征提供了一条有效的途径。此外,与采用非平稳随机场模拟土体参数空间变异性相比,采用常用的平稳随机场模型会低估边坡失效概率,从而造成偏危险的边坡工程设计方案。     

考虑砂土抗剪强度空间变异性的盾构开挖面稳定性分析

采用传统研究方法对盾构开挖面稳定性的分析多基于土体是均质、各向同性材料的假设,显然与其本身的非均质性相违背。为此,开展了考虑土体抗剪强度参数的空间变异性对盾构开挖面稳定性的影响研究。在随机场理论的基础上,采用协方差矩阵分解法建立了描述砂土内摩擦角空间变异性的三维随机场模型,借助于数值分析软件平台研究了内摩擦角的变异系数、自相关距离对开挖面失稳模式、极限支护应力的影响规律,并采用概率分析法探讨了极限支护应力特征值的选取。结果表明：砂土内摩擦角的空间变异性对开挖面稳定性有重要的影响;随内摩擦角的变异系数的增大,极限支护应力的概率分布离散性越大;开挖面失稳模式与自相关距离的大小密切相关,当自相关距离与隧道直径比较接近时,开挖面可能出现局部失稳;提出了开挖面极限支护应力特征值的概念,并结合失稳概率给出了其初步确定方法。     

Shear strength of municipal solid waste for stability analyses

This paper investigates the shear strength of municipal solid waste (MSW) using the back analysis of failed waste slopes as well as field and laboratory test results. Shear strength of MSW is a function of many factors such as waste type, composition, compaction, daily cover, moisture conditions, age, decomposition, overburden pressure, etc. These factors together with non-standardized sampling methods, insufficient sample size to be representative of in situ conditions, and limited shear displacement or axial strain imposed during the laboratory shear testing have created considerable scatter in reported results. Based on the data presented herein, large shear displacements are required to mobilize the peak shear strength of MSW which can lead to displacement incompatibility between MSW and the underlying material(s) such as geosynthetic interfaces and foundation soils. The data presented herein are used to develop displacement compatible shear strength parameters for MSW. Recommendations are presented for modeling the displacement and stress dependent strength envelope in stability analyses.     

抗剪强度参数概率分布的最大熵估计及边坡可靠度分析

提出了基于最大熵原理的抗剪强度参数概率分布估计方法。首先简要介绍了最大熵原理估计抗剪强度参数概率分布的基本步骤。其次,基于模拟数据分别验证了最大熵原理估计抗剪强度参数概率分布和边坡失效概率的有效性,并比较了最大熵原理、选优识别和核密度估计方法的不确定性建模精度和稳健性。最后,以一组残积土抗剪强度参数试验数据并结合无限边坡稳定分析为例研究了最大熵原理在抗剪强度参数概率分布和边坡失效概率估计中的应用。结果表明：最大熵原理能够有效地估计抗剪强度参数的概率分布和边坡失效概率。与传统的选优识别和核密度估计相比,最大熵原理估计抗剪强度参数概率分布和边坡失效概率的精度和稳健性都更高。最大熵原理避免了核密度估计过分依赖有限样本数据的缺点,又克服了选优识别可能未将真实分布包括在备选概率分布集合中的缺陷。此外,基于有限数据估计的抗剪强度参数概率分布和边坡失效概率具有较大的离散性。     

Full probabilistic design of slopes in spatially variable soils using simplified reliability analysis method

ABSTRACT

A simplified reliability analysis method is proposed for efficient full probabilistic design of soil slopes in spatially variable soils. The soil slope is viewed as a series system comprised of numerous potential slip surfaces and the spatial variability of soil properties is modelled by the spatial averaging technique along potential slip surfaces. The proposed approach not only provides sufficiently accurate reliability estimates of slope stability, but also significantly improves the computational efficiency of soil slope design in comparison with simulation-based full probabilistic design. It is found that the spatial variability has considerable effects on the optimal slope design.     

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。     

边坡岩体抗剪强度参数的非线性确定方法

影响工程岩体抗剪强度参数的因素很复杂,建立定量与定性相结合的多指标综合模型可有效地确定岩体抗剪强度。将多元非线性统计方法引入到岩体抗剪强度指标的研究中,选取了12个影响岩体抗剪强度的定性、定量指标,通过收集到的大量工程数据,分别建立凝聚力和内摩擦角非线性显式方程,决定系数分别为0.992 729,0.999 998。该方法可考虑定量、定性因素的影响,经现场实测数据验证,该模型具有较高的计算精度。运算过程简单,可方便工程现场使用,具有较高的工程实用价值。     

基于一种新强度理论的非饱和土边坡稳定性分析

非饱和土强度及其边坡稳定性一直是工程界和理论界的一个重要课题。Bishop和Fredlund提出的抗剪强度公式虽被广泛接受,但应用工程仍存诸多不便。针对于此,作者提出了一种有效应力与土水特征曲线发展成的一种新的非饱和土强度公式。该公式不需多组的非饱和土剪切试验,便于工程应用。基于此强度公式,采用VB语言,结合Bishop法,编写了非饱和土边坡稳定性的计算程序,讨论了强度分层的影响,还分析了裂隙对非饱和土边坡稳定性的影响。研究结果表明,对于膨胀土边坡,强度的分层是合理的,也是必要的。     

基于强度折减的土质边坡破坏及稳定分析

边坡的破坏过程是由土体局部破坏向整体失稳发展的过程,其塑性区的开展及其水平位移增量的变化较完美地展现了这个过程。根据边坡的实际破坏和有限元数值模拟情况,提出了以特征点位移增量的突变及塑性区贯通作为边坡的失稳判断准则;并以此为判据,采用基于强度折减的大变形有限元方法分析了土质边坡的破坏及稳定性。研究表明,采用强度折减有限元法可有效分析边坡的破坏及其稳定性;此外还分析了带有软弱夹层黏土边坡的破坏性状及其稳定性,并比较了大、小变形有限元的计算结果,结果表明,带有软弱夹层黏土边坡的破坏性状随软弱夹层土体性质的变化而变化,由大小变形有限元分析得到的边坡稳定安全系数较为一致,但边坡的破坏机制随软弱夹层土体性质变化的转变点不同。     

Shear strength of soils containing amorphous clay-size materials in a slow-moving landslide

The shear behavior of soils rich in amorphous clay-size materials was not well reported in the literature. This study analyzed the direct shear and ring shear test data of soil samples containing 55–74% amorphous materials in the clay fraction from a slow-moving landslide in eastern Honolulu, HI. The direct shear test results showed that the undisturbed soil samples when not sheared internally had peak cohesion (c) of about 50 kPa and internal friction angle (Ø) of about 10°. This implies that the amorphous clay-size materials provided strong interparticle bonds for the soils. Breaking of the bonds during the softening process and redistribution of the amorphous clay-size materials were primarily responsible for the drop from the peak strength to the residual strength (c=0, Ø=10° from back calculation with SLOPE/W and c=0, Ø=5–7° from the ring shear test). The drained residual failure envelope is stress dependent due to the interaction of the gel-like amorphous clay-size materials with crystalline silt- and sand-sized particles. The amorphous clay-size materials act as the contact between crystalline particles. The contact increases with increasing consolidation stress, resulting in a decrease in the shear strength and the residual friction angle.     

A simplified approach for studying the influence of vertical accelerations on seismic response of slopes

ABSTRACT

A simplified approach is presented for estimating permanent displacements in slopes as a result of both vertical and horizontal seismic accelerations. A study of 52 earthquake records showed that the time difference between maximum horizontal and vertical accelerations varied between 0 and 10.3 s. The approach is illustrated for an earth dam embankment by analysing the effects of five of the above earthquake records. The approach combines a pseudo-static slope stability analysis for estimation of the critical (or yield) horizontal-vertical acceleration combinations, and a Newmark type displacement analysis. Guidelines are presented for conservative choice of soil strength parameters of saturated clays for use in the stability analysis. While permanent displacements of up to 40 cm were predicted without considering the vertical acceleration component, no additional displacement above 3.5 cm resulted when this component was included. The predicted additional displacement was consistently less than 10%, and in 50% of the analyses, vertical acceleration led to smaller predicted displacements. The simple approach may be applied in analysis for any slope using real earthquake records. Using existing, empirical expressions for permanent displacement, based only on horizontal accelerations, the effect of the vertical accelerations may be conservatively estimated by increasing the displacement by 10%.