Slope reliability analysis using a support vector machine

The first-order second-moment method (FOSM) reliability analysis is commonly used for slope stability analysis. It requires the values and partial derivatives of the performance function with respect to the random variables for the design. Such calculations can be cumbersome when the performance functions are implicit. Implicit performance functions are normally encountered when the slope is geologically complicated and the limit equilibrium method (LEM) is used for the stability analysis.

To address this issue, this paper presents a support vector machine (SVM)-based reliability analysis method which combines the SVM with the FOSM. This method employs the SVM method to approximate the implicit performance functions, thus arriving at SVM-based explicit performance functions. The SVM method uses a small set of the actual values of the performance functions obtained via the LEM for complicated slope engineering. Using the SVM model, a large number of values and partial derivatives of the performance functions can be obtained for conventional reliability analysis using the FOSM. Examples are given to illustrate the proposed SVM-based slope reliability analysis. The results show that the proposed approach is applicable to slope reliability analysis which involves implicit performance functions.     

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.     

A comparative review of commercially-available software for soil slope stability analysis

Summary The main purpose of this paper is to carry out a comparative review of four commercial computer programs for the stability analysis of soil slopes. The review is carried out in two parts and should prove useful for potential users of the software. Part I reviews the facilities offered in terms of the range of limit equilibrium methods, the geotechnical modelling abilities, the operational features and the supporting documentation, and includes a general impression of friendliness. Part II assesses the use, accuracy and validity of each program by presenting and discussing the results of a number of model tests. Also included is a brief discussion of slope stability analysis, in particular the limit equilibrium method. The requirements of a practical computer program for soil slope stability analysis are defined and then used as a means of assessing the effectiveness of each program.     

Probabilistic and fuzzy reliability analysis of a sample slope near Aliano

Slope stability assessment is a geotechnical problem characterized by many sources of uncertainty. Some of them, e.g., are connected to the variability of soil parameters involved in the analysis. Beginning from a correct geotechnical characterization of the examined site, only a complete approach to uncertainty matter can lead to a significant result. The purpose of this paper is to demonstrate how to model data uncertainty in order to perform slope stability analysis with a good degree of significance.

Once the input data have been determined, a probabilistic stability assessment (first-order second moment and Monte Carlo analysis) is performed to obtain the variation of failure probability vs. correlation coefficient between soil parameters. A first result is the demonstration of the stability of first-order second moment (FOSM) (both with normal and lognormal distribution assumption) and Monte Carlo (MC) solutions, coming from a correct uncertainty modelling. The paper presents a simple algorithm (Fuzzy First Order Second Moment, FFOSM), which uses a fuzzy-based analysis applied to data processing.     

Effect of spatial variability of shear strength on reliability of infinite slopes using analytical approach

This paper develops an analytical approach for reliability analysis of infinite slope stability in presence of spatially variable shear strength parameters. The analytical approach considers spatial autocorrelation of each parameter and cross-correlations between different parameters. It is robust, computational efficient and provides insight to the importance of spatial correlation scale on slope reliability analysis. This paper also explores the difference in continuous and discrete random fields and emphasizes the importance of fine discretization in relation to correlation scale. Finally, it shows that conditioning the stability analysis with information about trends and spatial data leads to reliability assessments with less uncertainty.     

Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables

This paper proposes a stochastic response surface method for reliability analysis involving correlated non-normal random variables, in which the Nataf transformation is adopted to effectively transform the correlated non-normal variables into independent standard normal variables. Transformations of random variables that are often used in reliability analyses in terms of standard normal variables are summarized. The closed-form expressions for fourth to sixth order Hermite polynomial chaos expansions involving any number of random variables are formulated. The proposed method will substantially extend the application of stochastic response surface method for reliability problems. An example of reliability analysis of rock slope stability with plane failure is presented to demonstrate the validity and capability of the proposed stochastic response surface method. The results indicate that the proposed stochastic response surface method can evaluate the reliability of rock slope stability involving correlated non-normal variables accurately and efficiently. Its accuracy is shown to be higher than that for the first-order reliability method, and it is much more efficient than direct Monte-Carlo simulation. The results also show that the number of collocation points selected should ensure that the Hermite polynomial matrix has a full rank so that different order SRSMs can produce a robust estimation of probability of failure for a specified performance function. Generally, the accuracy of SRSM increases as the order of SRSM increases.     

边坡三维极限平衡法的通用形式

基于以下假定条件:(1) 稳定系数定义为材料的强度折减系数;(2) 土体为刚体,底滑面服从Mohr-Columb强度破坏准则;(3) 微条柱底部法向力dNz的作用点处于条柱底部中点;(4)滑面剪力与底滑面和xoz平面交线的夹角为。本文建立了边坡三维极限平衡法的通用形式,通过给定不同的限制条件,可分别得到三维普通条分法 、三维简化毕肖普法 、三维简化简布法 、三维Spencer法 等三维极限平衡的具体算法。     

北京某建筑边坡场地工程地质条件与坡体稳定性评价

边坡的稳定性对工程建设有重要影响, 为了保障建筑场地的安全, 本文对北京某建筑边坡场地工程地质条件进行了详细调查和论述, 并针对场地内的6个典型坡体, 分别采用赤平投影法和极限平衡法对边坡的稳定性进行了综合评价, 其中极限平衡法采用了复杂平面滑动和三维楔形体分析模型。分析结果表明, 该工程场区工程地质条件较为简单, 岩体结构主要为层状结构, 工程场区内所涉及的6个边坡稳定性均较好, 但由于区内有一条断裂穿过, 对边坡2的稳定性有一定的影响。针对边坡的稳定性和建筑场地的高效可用性, 建议采用放坡护面+坡脚挡墙支护等方式进行防护。     

Slope inclinometers for landslides

Slope inclinometers/indicators are used to determine the magnitude, rate, direction, depth, and type of landslide movement. This information is usually vitally important for understanding the cause, behavior, and remediation of a landslide. However, many inclinometer measurements fail to achieve these intended aims because of lack of appreciation of the many factors that need to be correctly implemented during installation, monitoring, and data reduction to yield useful data. This paper presents some guidelines for understanding, installing, and interpreting slope inclinometers and presents three case histories that illustrate some of the pitfalls that can develop if these guidelines are not followed.     

边坡稳定性极限平衡条分法的探讨

系统分析了常用的边坡稳定性极限平衡条分法，在任意滑而条件下，推导了瑞典条分法；讨论了它们的适用性与极限平衡条分法的发展方向，具有一定的理论和实践意义。     

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.     

A reliability based approach for evaluating the slope stability of embankment dams

Embankment dams are important and costly civil engineering structures that provide an essential infrastructure for the management of water. One of the critical aspects of dam design is the analysis of stability and safety of the earth structure under various operating and environmental conditions. Traditionally, a deterministic approach is used for such analysis. However, the determination of variables such as soil strength parameters, pore pressure and other pertinent properties involves uncertainties, which cannot be handled in the traditional deterministic methods. It is, therefore, highly desirable to develop a reliability based analytical/numerical methodology for stability analysis of dams taking into account these uncertainties. Reliability and probability theories are developed in this paper for assessing the reliability index and the corresponding probability of failure of multi-layered embankment dams and slopes. Two definitions were used to calculate the reliability index (i.e. the normal distribution and the log–normal distribution). The computer program was developed and validated by the Congress Street open cut failure case. The developed approach was used to study the stability of the King Talal embankment dam. The results are discussed and conclusions drawn.     

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.     

Slope stability analysis: a support vector machine approach

Artificial Neural Network (ANN) such as backpropagation learning algorithm has been successfully used in slope stability problem. However, generalization ability of conventional ANN has some limitations. For this reason, Support Vector Machine (SVM) which is firmly based on the theory of statistical learning has been used in slope stability problem. An interesting property of this approach is that it is an approximate implementation of a structural risk minimization (SRM) induction principle that aims at minimizing a bound on the generalization error of a model, rather than minimizing only the mean square error over the data set. In this study, SVM predicts the factor of safety that has been modeled as a regression problem and stability status that has been modeled as a classification problem. For factor of safety prediction, SVM model gives better result than previously published result of ANN model. In case of stability status, SVM gives an accuracy of 85.71%.     

A comparative study of various commercially available programs in slope stability analysis

The objective of this paper is to study the effect of different slip surface search techniques on the factors of safety obtained using the limit equilibrium (LE) slope stability methods. This objective is accomplished by comparing results from the finite element method, the linear grid method, the rectangular grid method, and the Monte-Carlo searching techniques using different commercially available programs. The results showed that the LE methods are very efficient methods when coupled with a robust searching technique namely the Monte-Carlo method. In addition, the selected slip surface search technique highly influenced the location of the critical slip surfaces as well as the value of the calculated factors of safety.     

粘质海底稳定性实例分析

本文对南海珠江口盆地大陆架区和东海浙江沿岸象山港的粘质海底进行了稳定性分析。通过实例分析判定了该地区不稳定性的原因, 并给出了稳定性估计的直观图。文中还指出了今后研究的方向。     

船台滑道下含软弱层岸坡的空间稳定分析

芜湖江东船厂新建船台滑道位于有较厚软弱土层的岸坡上。本文采用三维有限元和刚体极限平衡理论结合的方法分析岸坡稳定, 对不同潜在滑动面进行探索, 求解最小安全系数及相应滑动面位置。分析结果已在施工实践中得到证实。     

Upper bound finite element analysis of slope stability using a nonlinear failure criterion

In this study, upper bound finite element (FE) limit analysis is applied to stability problems of slopes using a nonlinear criterion. After formulating the upper bound analysis as the dual form of a second-order cone programming (SOCP) problem, the stress field and corresponding shear strength parameters can be determined iteratively. Thus, the nonlinear failure criterion is represented by the shear strength parameters associated with stress so that the analysis of slope stability using a nonlinear failure criterion can be transformed into the traditional upper bound method with a linear Mohr–Coulomb failure criterion. Comparison with published solutions illustrates the accuracy and feasibility of the proposed method for a simple homogeneous slope stability problem. The proposed approach is also applied to a seismic stability problem for a rockfill dam to study the influence of different failure criterions on the upper bound solutions. The results show that the seismic stability coefficients obtained using two different nonlinear failure criteria are similar but that the convergence differs significantly.     

Slope stability analysis by SRM-based rock failure process analysis (RFPA)

The fundamental principles of the strength reduction method (SRM) are incorporated into the rock failure process analysis (RFPA) code to produce an RFPA–SRM method for analysing the failure process and stability of rock and soil slopes. The RFPA–SRM method not only satisfies the global equilibrium, strain-consistent, and non-linear constitutive relationship of rock and soil materials but also takes into account the heterogeneous characteristics of materials on the micro- and macro-scales. When the proposed method is used for slope stability analysis, both the critical failure surface and the safety factor can be obtained directly without any assumptions regarding the shape and location of the failure surface. The numerical results agree well with those obtained using conventional limit equilibrium and other FEM strength reduction methods. The proposed technique is applied to a number of more complex cases, including slopes in mixed rock–soil formations, rock layer formations, and highly jointed rock masses. It is shown that the RFPA–SRM method can describe the mechanism of failure of slopes and has potential applications in a large range of geoengineering problems.     

极限平衡理论下边坡强度参数反演及加固稳定性分析

参数反演是获得较为可靠的边坡强度参数的一种有效手段。本文在对边坡临界滑动面进行判别的情况下,以瑞典法为基础,通过建立强度参数之间及其与临界滑动面一一对应的关系推导得边坡强度参数反演的显式计算公式。然后,将反演结果用于锚索加固条件下的边坡稳定性研究。经工程算例分析验证了本文方法的可行性和实用性,并得到如下结论:(1)预应力锚索能对边坡形成有效的加固作用,且锚索在坡面上的位置越靠近滑动面的滑出点时其对边坡的稳定性越有利; (2)锚索的预应力越大则计算得到的安全系数越大,而锚索水平倾角的增大对计算得到的安全系数影响微小。