Evaluating slope stability uncertainty using coupled Markov chain

Geological uncertainty appears in the form of one soil layer embedded in another or the inclusion of pockets of different soil type within a more uniform soil mass. Uncertainty in factor of safety (FS) and probability of failure (Pf) of slope induced by the geological uncertainty is not well studied in the past. This paper presents one approach to evaluate the uncertainty in FS and Pf of slope in the presence of geological uncertainty using borehole data. The geological uncertainty is simulated by an efficient coupled Markov chain (CMC) model. Slope stability analysis is then conducted based on the simulated heterogeneous soils. Effect of borehole layout schemes on uncertainty evaluation of FS and Pf is investigated. The results show that borehole within influence zone of the slope is essential for a precise evaluation of FS statistics and Pf. The mean of FS will converge to the correct answer as the borehole number increases.     

顶点法在边坡稳定性评价中的应用

考虑到边坡稳定性分析中存在的测量数据的不确定性和确定计算参数的复杂性以及描述边坡稳定状态的模糊性, 本文介绍了-种新的适用于边坡稳定性分析的模糊数学方法顶点法, 该法由不确定的土力学参数求得边坡稳定性系数的模糊集合, 然后运用对比法进行分类来确定边坡所处的稳定状态, 文章最后通过-个工程实例阐述了应用过程。     

Efficient Monte Carlo Simulation of parameter sensitivity in probabilistic slope stability analysis

Monte Carlo Simulation (MCS) method has been widely used in probabilistic analysis of slope stability, and it provides a robust and simple way to assess failure probability. However, MCS method does not offer insight into the relative contributions of various uncertainties (e.g., inherent spatial variability of soil properties and subsurface stratigraphy) to the failure probability and suffers from a lack of resolution and efficiency at small probability levels. This paper develop a probabilistic failure analysis approach that makes use of the failure samples generated in the MCS and analyzes these failure samples to assess the effects of various uncertainties on slope failure probability. The approach contains two major components: hypothesis tests for prioritizing effects of various uncertainties and Bayesian analysis for further quantifying their effects. Equations are derived for the hypothesis tests and Bayesian analysis. The probabilistic failure analysis requires a large number of failure samples in MCS, and an advanced Monte Carlo Simulation called Subset Simulation is employed to improve efficiency of generating failure samples in MCS. As an illustration, the proposed probabilistic failure analysis approach is applied to study a design scenario of James Bay Dyke. The hypothesis tests show that the uncertainty of undrained shear strength of lacustrine clay has the most significant effect on the slope failure probability, while the uncertainty of the clay crust thickness contributes the least. The effect of the former is then further quantified by a Bayesian analysis. Both hypothesis test results and Bayesian analysis results are validated against independent sensitivity studies. It is shown that probabilistic failure analysis provides results that are equivalent to those from additional sensitivity studies, but it has the advantage of avoiding additional computational times and efforts for repeated runs of MCS in sensitivity studies.     

Integrated approach of geospatial visualization and modeling for groundwater management in hard rock terrains in Nagpur Urban Area,India

Groundwater management requires complete visualization of aquifer characteristics to understand scientific aspects and hence remains a challenge, especially in hard rock terrains. In the present research paper, a comprehensive approach using 3D stratigraphic model, fence diagrams and numerical modeling has been proposed to understand the groundwater status for effective recharge. The stratigraphy, groundwater flow, and groundwater fluctuations for the period 1999–2010 were analyzed. The total volume of formations, volume of voids, storage capacity, and quantities of recharge of unconfined aquifer system in the Nagpur urban area were estimated. The steady state groundwater flow model of Basalt formation was calibrated to evaluate the subsurface system using Processing Modflow (PMWIN 5.3.2). The calibrated hydraulic head is compared with field observed head. The comparative spatial analysis presents a simple integrated approach in identifying zones with falling groundwater trends suitable for groundwater recharge in hard rock terrain in Nagpur urban area.     

澜沧江某水电站泄洪洞出口边坡稳定性评价

岩土质边坡是一种自然地质体，其稳定性在很大程度上具有不确定性、模糊性。模糊分析是边坡稳定性分析的有效途径之一。文章采用模糊数学分析法，构建了二次模糊综合评判模型，对影响边坡稳定性的诸多因素进行了分类归纳，并根据不同的稳定状态，将边坡划分为5个等级，再结合某水电站右岸泄洪洞出口开挖边坡稳定性的实际问题，利用梯形函数构建了与该边坡稳定性分析相关因素的隶属函数、运用专家评分法确定了各因素的权重，最终对该边坡的稳定性进行了评价。结果表明该评价分析结果与实际相吻合，评价效果较好。     

Probabilistic Methods Applied to Unsaturated Numerical Modeling

The numerical modeling of unsaturated soil processes is becoming more prevalent worldwide. Although numerical modeling is becoming increasingly accepted in geotechnical engineering practice, care must be exercised and improper modeling techniques and procedures must be avoided. Many issues such as nodal resolution and imperfect convergence can result in inaccurate solutions. Unfortunately, analyses of highly nonlinear unsaturated soil flow and slope stability models can significantly increase the modeling time required. As a result, there is a trend to reduce the number of model runs. Results are often presented to client as single model runs or simplistic sensitivity analysis. This paper presents methodologies for applying probabilistic methods to unsaturated soils seepage and slope stability analysis models. The focus is on the application of the alternative point estimate method to practical problems in such a way as to minimize the number of model runs. The demonstration of a successful application to a waste rock pile is presented.     

Probabilistic parameter estimation and predictive uncertainty based on field measurements for unsaturated soil slope

A key issue in assessment of rainfall-induced slope failure is a reliable evaluation of pore water pressure distribution and its variations during rainstorm, which in turn requires accurate estimation of soil hydraulic parameters. In this study, the uncertainties of soil hydraulic parameters and their effects on slope stability prediction are evaluated, within the Bayesian framework, using the field measured temporal pore-water pressure data. The probabilistic back analysis and parameter uncertainty estimation is conducted using the Markov Chain Monte Carlo simulation. A case study of a natural terrain site is presented to illustrate the proposed method. The 95% total uncertainty bounds for the calibration period are relatively narrow, indicating an overall good performance of the infiltration model for the calibration period. The posterior uncertainty bounds of slope safety factors are much narrower than the prior ones, implying that the reduction of uncertainty in soil hydraulic parameters significantly reduces the uncertainty of slope stability.     

基于节理不确定性的可靠度分析

边坡稳定性一直是边坡安全的重点研究对象,针对边坡评价中常见的不确定性因素,可靠度分析是值得利用的方法。为评价某节理发育的岩质岸坡稳定性,通过有限元计算软件,结合现场勘探测绘数据,建立以边坡节理强度参数c、φ为输入变量,安全系数为输出变量的点估计（PEM）计算概率模型,计算结果表明:节理发育对该边坡变形具有明显控制作用;边坡整体可靠性较好,破坏概率极低。最后,通过蒙托卡罗法对可靠度结果进行验证,结果表明两种方法的计算结果不存在显著性差异。研究结果表明节理对岩质边坡稳定具有良好的敏感性,基于节理不确定性的点估计法分析边坡可靠度是一种有效的方法。     

基于强度折减法的顺层路堑边坡土钉墙支护结构稳定性分析

将非线性有限元分析和极限分析相结合形成强度参数折减有限元法,可以灵活地分析强度不均匀顺层路堑边坡支护结构稳定性问题。将岩体力学理论、非线性有限元分析技术和强度折减系数法相结合,对顺层岩体路堑边坡稳定性进行分析。在对密集假设节理有限元模拟中,假设节理在岩体内连续分布,采用连续介质力学方法建立密集分布节理岩体材料模型。采用强度折减系数法计算岩体结构安全系数,建议采用给定的岩体强度参数计算节理岩质边坡开挖、支护完毕后的内力,再逐渐降低岩体强度参数进行岩体边坡非线性有限元分析,直至岩体边坡达到极限状态,从而求出岩质边坡安全系数。采用该方法对渝怀铁路梅江河右岸DK409+989.4～DK410+020段顺层路堑边坡土钉墙支护结构稳定性进行分析,分析结果表明：采用土钉墙支护后的节理边坡塑安全系数为2.3,支护后的岩质边坡处于稳定状态;土钉墙潜在破裂面为岩体弹性区和塑性区的交界面,与测试得到的各排土钉拉力最大值位置一致。     

Development of a probabilistic approach for rock wedge failure

For rock slope engineering, uncertainty and variability are inherent in data collected on orientation and strength of discontinuities, yielding a range of results. Unfortunately, conventional deterministic analysis based on the factor of safety concept, requires a fixed representative value for each parameter without regard to the degree of uncertainty involved. Therefore, the deterministic analysis fails to properly represent uncertainty and variability, so common in engineering geology studies. To overcome this shortcoming, the probabilistic analysis method was proposed and used for more than a decade in rock slope stability analysis. However, most probabilistic analyses included a deterministic model as part of the analysis procedure causing subsequent problems, which went uncorrected. The objectives of this paper are to develop a solution for these difficulties in probabilistic analyses and to propose an appropriate simulation procedure for the probabilistic analysis of rock wedge failures. As part of the solution, probability of kinematic instability and probability of kinetic instability are evaluated separately to provide a proper, combined evaluation for failure probability. To evaluate the feasibility of this new probabilistic approach, the procedure is applied to a practical example, a major, highway rock cut in North Carolina, USA. Results of the probabilistic approach are compared to those of the deterministic analysis; findings are significantly different, indicating that the deterministic analysis does not depict rock slope variations, particularly where significant scatter in parameter data occurs.     

Geologic uncertainty in a regulatory environment: An example from the potential Yucca Mountain nuclear waste repository site

Regulatory geologists are concerned with predicting the performance of sites proposed for waste disposal or for remediation of existing pollution problems. Geologic modeling of these sites requires large-scale expansion of knowledge obtained from very limited sampling. This expansion induces considerable uncertainty into the geologic models of rock properties that are required for modeling the predicted performance of the site.One method for assessing this uncertainty is through nonparametric geostatistical simulation. Simulation can produce a series of equiprobable models of a rock property of interest. Each model honors measured values at sampled locations, and each can be constructed to emulate both the univariate histogram and the spatial covariance structure of the measured data. Computing a performance model for a number of geologic simulations allows evaluation of the effects of geologic uncertainty. A site may be judged acceptable if the number of failures to meet a particular performance criterion produced by these computations is sufficiently low. A site that produces too many failures may be either unacceptable or simply inadequately described.The simulation approach to addressing geologic uncertainty is being applied to the potential high-level nuclear waste repository site at Yucca Mountain, Nevada, U.S.A. Preliminary geologic models of unsaturated permeability have been created that reproduce observed statistical properties reasonably well. A spread of unsaturated groundwater travel times has been computed that reflects the variability of those geologic models. Regions within the simulated models exhibiting the greatest variability among multiple runs are candidates for obtaining the greatest reduction in uncertainty through additional site characterization.     

Locating the Multiple Failure Surfaces for Slope Stability Using Monte Carlo Technique

Owing to the complicated slope stratigraphy (e.g., multiple soil layers and multiple benches or gradients in side slopes), multiple failure surfaces for slope stability have been recognized in geotechnical discipline. This paper aims to develop a systematic and probabilistic approach to locate the multiple failure surfaces combining the traditional limit equilibrium method with Monte Carlo Simulation. Each of the multiple failure surfaces is selected from a large pool of failure surfaces and the correlation coefficient between two failure surfaces in factor of safety (FS) is adopted to characterize the extent to which two failure surfaces are correlated. After eliminating those highly correlated failure surfaces, the multiple failure surfaces can be gradually identified. The number of failure samples and the number of exclusive failure samples corresponding to each of multiple failure surfaces are determined within the proposed methodology. These data are reanalyzed to find the critical failure surface with the maximum failure probability, the critical failure surface with maximum simplified risk, and those failure surfaces dominating the risk of slope failure. The proposed approach is illustrated through two examples excerpted from the literature and validated against the results from the commercial software package and literature. The comparative study manifests that the critical failure surface with the minimum FS does not always coincide with that with the maximum failure probability and with the maximum simplified risk. In addition to FS, the failure surfaces should be received much attention. The proposed methodology provides an effective tool in decision making for slope stabilization and rehabilitation process.     

基于模糊因素的岩质边坡地震稳定性多模型组合评价

岩质边坡地震稳定性评价是岩土边坡地震失稳防治的基础工作,针对评价过程中评价因素的多源模糊性,借鉴工程可变模糊集理论,将模糊可变评价模型应用于岩质边坡地震稳定性评价中。综合考虑岩质边坡内在结构和外部自然条件,选取岩土体特性、新构造运动特征、坡高、坡角、年均降雨量和场地地震烈度6个指标作为评价指标体系并建立等级标准;将改进熵权算法引入该模型中,利用指标实际数据离散性求权重;通过改变模糊可变评价模型参数对岩质边坡地震稳定性进行线性与非线性组合评价,并将均值作为最终评价结果。将该方法应用于天然边坡与路堑边坡实例中,结果表明,模糊可变评价模型评价结果合理、客观,具有更高的可靠性与稳定性,为岩质边坡地震稳定性评价工作提供了一种新的研究方法与思路     

填土边坡稳定性的可靠度分析

为了系统地建立填土边坡稳定性的可靠度分析方法, 首先, 在可靠度分析原理的基础上, 对填土边坡的不确定性进行了讨论; 然后, 建立了多变量影响下填土边坡可靠度分析的基本流程; 最后, 以广西平乐县二塘锰矿区典型填土边坡为例, 基于GeoStudio软件, 应用所提出的分析流程对典型填土边坡的可靠度指标进行了计算, 通过"安全概率"对边坡的安全性进行了评价.研究结果表明: (1)填土边坡的不确定性包括内部结构和环境因素两方面, 前者不确定因素来自于填土土体不确定性和边坡的几何特征不确定性, 后者不确定性因素来自于降雨、地震和人工加载等; (2)可靠度分析的基本流程为填土边坡系统不确定性分析、建立可靠度极限状态方程、求解可靠度指标和边坡安全性评价; (3)广西平乐二塘锰矿填土边坡敏感性因素排序为: 内摩擦角Φ＞黏聚力C＞车辆荷载F; (4)考虑50年一遇极值降雨过程, 稳定性系数在降雨12 h达到最小, 其可靠度指标(β)为8.79, 破坏概率为0.根据《滑坡防治工程设计与施工技术规范》所规定的安全系数, 填土边坡的安全概率为69.84%.      

交通荷载作用下边坡振动响应特性分析

通过对316国道土质边坡及岩质边坡进行振动响应测试,研究交通荷载引起土质及岩质边坡振动加速度大小及其空间变化特征,同时利用FFT方法对振动信号进行频谱分析,得到岩质及土质边坡的振动响应频谱特性。测试及分析结果表明,振动波传播过程中携带了反映介质固有特性的信息,岩质及土质边坡对交通荷载的响应均较为敏感,相同荷载在土质边坡引起的振动加速度及振动幅值大于岩质边坡,其中土质边坡沿坡由下向上振动响应有减弱的趋势,且振动在短距离内衰减较快,而岩质边坡振动响应在短距离内衰减较慢;主频随着振动波的衰减有向低频移动的趋势。测试为分析振动传播途径和研究振动对边坡稳定性的影响提供了宝贵资料,对多因素引起的边坡稳定性评价有重要的实际意义。     

Slope stability analysis in 3D using numerical limit analysis (NLA) and elasto-plastic analysis (EPA)

The present paper addresses the problem of factor of safety (FS) determination in 3D slope stability analysis. For that purpose, use is made of two numerical methods/techniques in three benchmark problems: numerical limit analysis (NLA) and elasto-plastic analysis (EPA). Finite elements are used in both techniques. The primary objective of the study is, by comparing the two techniques, to establish the feasibility of using NLA in the evaluation of 3D slope stability problems and to establish its practical applicability and competitiveness in relation to EPA. Because of their geometry or their boundary conditions, the problems cannot be analysed as plane strain state problems or using the 2D limit equilibrium technique. In both methods, an FS is determined for the slopes by reducing the strength parameters of the geological materials using a scalar factor, known as the strength reduction factor. From the comparison of the FSs and of the computational efforts required for the two numerical techniques, it was possible to establish NLA’s competiveness and viability for the analysis of real 3D slope stability problems when implemented in an efficient manner.     

An extreme learning machine approach for slope stability evaluation and prediction

This paper presents slope stability evaluation and prediction with the approach of a fast robust neural network named the extreme learning machine (ELM). The circular failure mechanism of a slope is formulated based on its material, geometrical and environmental parameters such as the unit weight, the cohesion, the internal friction angle, the slope inclination, slope height and the pore water ratio. The ELM is proposed to evaluate the stability of slopes subjected to potential circular failures by means of prediction of the factor of safety (FS). Substantial slope cases collected worldwide are utilized to illustrate and assess the capability and predictability of the ELM on slope stability analysis. Based on the mean absolute percentage errors and the correlation coefficients between the original and predicted FS values, comparisons are demonstrated between the ELM and the generalized regression neural network (GRNN) as well as the prediction models generated from the genetic algorithms. Moreover, sensitivity analysis of the slope parameters and the ELM model parameters is carried out based on the two utilized evaluation functions. The time expense of the ELM on slope stability analysis is also investigated. The results prove that the ELM is advantageous to the GRNN and the genetic algorithm based models in the analysis of slope stability. Hence, the ELM can be a promising technique for approaching the problems in geotechnical engineering.     

基于蒙特卡罗边坡稳定二元体系的建立与应用

边坡是一个具有明显不确定性、模糊性和时变性的系统,安全系数及可靠度理论在边坡稳定评价上各有优缺点。二元体系是基于确定性指标（安全系数）和不确定指标（可靠度）建立的边坡稳定综合评价指标体系,兼有二者的优点,具有重要的理论意义和实践价值。考虑到边坡材料指标具有区间分布及稳定边坡的安全系数不能小于其临界值的特点,对纯数学理论模型进行修正,提出了一种更加符合工程实际的边坡稳定二元评价体系,同时选取蒙特卡罗模拟法,将该二元评价体系融入GeoStudio软件,借助GeoStudio软件强大的计算能力,形成一套完整而高效的边坡稳定二元指标分析方法。采用该方法进行了降雨条件下花岗岩残坡积土边坡稳定性分析,得出了有益的结论,验证了该方法的可行和高效。     

某电厂工程场址地质灾害防治工程研究

建设工程场址紧邻某露天矿北采坑,最近距离不足10 m,且在场址地基中连续分布厚1.5～3.0m软弱夹层,该软弱夹层南倾并出露于露天采坑边坡,与采坑边坡构成顺向坡.因该场址所处周边环境的特殊性以及特定的地层结构,使得本工程可能遭受场地整体滑移、边坡滑动等地质灾害威胁,且危害后果严重.对场址地基整体稳定性验算与采坑边坡稳定性的计算表明：场址地基整体稳定性可满足规范要求,而采坑高边坡则处于不稳定状态,必须进行工程加固.综合考虑本场区地层结构、周边环境与危害后果等,提出了削坡减载十预应力格构锚固主体加固方案,同时辅以截排水与工程监测措施.依据锚固段岩土体力学特性,确定了各锚杆锚固力,采用Winkler弹性地基梁和连续梁模型计算了格构梁的内力.对削坡、锚固后边坡的稳定性验算表明：其安全稳定性可满足规范要求.     

Risk-based characterisation of an urban building site

The evaluation of the underground soil stratigraphy is a key aspect in geotechnical site characterisation. However, these means of site exploration are only pinholing subsoil conditions and expert knowledge is needed to understand subsoil conditions in order to build a reliable geological-geotechnical model. This contribution employs a geostatistical simulation methodology for the simulation of random fields representing geological uncertainty. This combines borehole data and expert knowledge via a mathematical framework. Moreover a risk-based site characterisation scheme is developed for urban site characterisation. This novel characterisation scheme offers additional insight into the effects of large-scale, geological spatial variability by using fragility curves to quantify these effects.