Probabilistic calibration of a coupled hydro-mechanical slope stability model with integration of multiple observations

Multiple types of responses, such as displacements, ground water level, pore water pressures, water contents, etc., are usually measured in comprehensive monitoring programmes for rainfall-induced landslide prevention. In this study, a probabilistic calibration method for coupled hydro-mechanical modelling of slope stability is presented with integration of multiple types of measurements. A numerical example of a soil slope under rainfall infiltration is illustrated to compare the effects of single and multiple types of responses on parameter estimation and model calibration. The results show that the soil parameters can be estimated with less uncertainty and total uncertainty bounds are narrower with multiple types of responses than with a single type of response. Model calibration based on multiple types of responses can compromise different responses and hence the means and standard deviations of model error are the smallest. A feasible correlation coefficient between soil modulus and permeability can be obtained from model calibration with multiple types of responses and single type of response as long as the responses include displacement data.     

基于MCMC法的非饱和土渗流参数随机反分析

基于贝叶斯理论,以马尔可夫链蒙特卡罗方法（Markov chain Monte Carlo Simulation, MCMC法）的自适应差分演化Metropolis算法为参数后验分布抽样计算方法,建立利用时变测试数据的参数随机反分析及模型预测方法。以香港东涌某天然坡地降雨入渗测试为算例,采用自适应差分演化Metropolis算法对时变降雨条件下非饱和土一维渗流模型参数进行随机反分析,研究参数后验分布的统计特性,并分别对校准期和验证期内模型预测孔压和实测值进行比较。研究结果表明,DREAM算法得到的各随机变量后验分布标准差较先验分布均显著减小;经过实测孔压数据的校准,模型计算精度很高,校准期内95%总置信区间的覆盖率达到0.964;验证期第2～4个阶段95%总置信区间的覆盖率分别为0.52、0.79和0.79,模型预测结果与实测值吻合程度较高。     

Reduction of slope stability uncertainty based on hydraulic measurement via inverse analysis

The determination of slope stability for existing slopes is challenging, partly due to the spatial variability of soils. Reliability-based design can incorporate uncertainties and yield probabilities of slope failure. Field measurements can be utilised to constrain probabilistic analyses, thereby reducing uncertainties and generally reducing the calculated probabilities of failure. A method to utilise pore pressure measurements, to first reduce the spatial uncertainty of hydraulic conductivity, by using inverse analysis linked to the Ensemble Kalman Filter, is presented. Subsequently, the hydraulic conductivity has been utilised to constrain uncertainty in strength parameters, usually leading to an increase in the calculated slope reliability.     

The role of uncertainty in bedrock depth and hydraulic properties on the stability of a variably-saturated slope

We investigate the uncertainty in bedrock depth and soil hydraulic parameters on the stability of a variably-saturated slope in Rio de Janeiro, Brazil. We couple Monte Carlo simulation of a three-dimensional flow model with numerical limit analysis to calculate confidence intervals of the safety factor using a 22-day rainfall record. We evaluate the marginal and joint impact of bedrock depth and soil hydraulic uncertainty. The mean safety factor and its 95% confidence interval evolve rapidly in response to the storm events. Explicit recognition of uncertainty in the hydraulic properties and depth to bedrock increases significantly the probability of failure.     

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。     

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.     

含弱透水层岸坡地下水渗流特征的数值分析

库岸滑坡同坡体内地下水渗流场的动态变化具有密切的关系。传统的饱和土渗流分析方法无法正确描述水位升降过程中岸坡内孔压场的动态变化规律。从饱和-非饱和非稳定渗流理论出发,选取典型的岩土体的渗流参数,对含有弱透水夹层的理想层状岸坡进行有限元数值分析,得到水位升降过程中岸坡内孔隙水的渗流规律。同时,也得到了坡体内基质吸力和体积含水率随库水位升降变化的历时曲线。分析表明,岩土体的饱和渗透系数、土水特征曲线以及坡体的结构特征等共同决定了水位升降过程中岸坡内孔隙水压力和浸润线的分布。模拟结果可为库岸尤其是含弱透水层边坡的稳定性评价及岸坡的排水加固提供参考依据。     

一种基于贝叶斯理论的区域斜坡稳定性评价模型

本文结合滑坡物理模型和统计模型的优点,针对小流域滑坡稳定性分析,建立了一种基于贝叶斯理论的区域斜坡稳定性评价模型。该模型主要采用灾害自身信息来修正原始模型中的参数,解决了区域稳定性评价中参数难以确定的问题。该方法首先设定模型的初始参数分布,然后利用采样点雨前和雨后稳定性不同的信息建立验证方程,再根据马尔科夫链蒙特卡罗模拟和贝叶斯方法确定最终的参数分布,进而得出区域稳定性分布。应用该模型对福建省蔡源小流域的6 13滑坡群发性事件进行分析。结果显示,蔡源小流域地区的无量纲黏聚系数C为0.028,有效摩擦角为16.7,土壤的导水系数T和降雨量q的比值为529.026m,可能不稳定地区和不稳定地区达到76.0%。该模型利用历史灾害数据自动模拟出合适的参数,对区域滑坡稳定性评价具有重要意义。     

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.     

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。     

Comparison of single- and dual-permeability models in simulating the unsaturated hydro-mechanical behavior in a rainfall-triggered landslide

Landslide-prone slopes in earthquake-affected areas commonly feature heterogeneity and high permeability due to the presence of cracks and fissures that were caused by ground shaking. Landslide reactivation in heterogeneous slope may be affected by preferential flow that was commonly occurred under heavy rainfall. Current hydro-mechanical models that are based on a single-permeability model consider soil as a homogeneous continuum, which, however, cannot explicitly represent the hydraulic properties of heterogeneous soil. The present study adopted a dual-permeability model, using two Darcy-Richards equations to simulate the infiltration processes in both matrix and preferential flow domains. The hydrological results were integrated with an infinite slope stability approach, attempting to investigate the hydro-mechanical behavior. A coarse-textured unstable slope in an earthquake-affected area was chosen for conducting artificial rainfall experiment, and in the experiment slope, failure was triggered several times under heavy rainfall. The simulated hydro-mechanical results of both single- and dual-permeability model were compared with the measurements, including soil moisture content, pore water pressure, and slope stability conditions. Under high-intensity rainfall, the measured soil moisture and pore water pressure at 1-m depth showed faster hydrological response than its simulations, which can be regarded as a typical evidence of preferential flow. We found the dual-permeability model substantially improved the quantification of hydro-mechanical processes. Such improvement could assist in obtaining more reliable landslide-triggering predication. In the light of the implementation of a dual-permeability model for slope stability analysis, a more flexible and robust early warning system for shallow landslides hazard in coarse-textured slopes could be provided.     

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.     

Regional-scale back-analysis using TRIGRS: an approach to advance landslide hazard modeling and prediction in sparse data regions

Landslides in Kerala, India, have been shown to be preceded not only by critical rainfall over a short period but also a much longer period of elevated pore pressure. Such rainfall-triggered landslides are difficult to monitor due to a lack of adequate data on the locations of failures and precipitation. Here, a method is presented using Transient Rainfall Infiltration and Grid-based Regional Slope stability (TRIGRS) as a tool to model the relationship between critical rainfall and antecedent pore pressure as they relate to slope stability, which can be useful for hazard assessment in sparse data regions. This is demonstrated by parameterizing the model with a combination of regional data sources, remote sensing, and temporal back-analysis based on two known failure events (June 2004 and July 2007). Ranges of possible geotechnical and hydraulic parameters were obtained from various local and regional sources, and soil thickness was modeled as a function of slope angle. Rainfall was estimated using satellite microwave radiometry data. For back-analysis, combinations of cohesion, friction angle, and water table depth were then tested in TRIGRS using trial and error until the predicted and observed failure times coincided for the two failure events. While the spatial prediction accuracy of the model is low and multiple solution sets are expected to exist, the results confirm that information regarding the critical pre-failure conditions and stability changes over time can be derived despite data-poor circumstances. Future studies can be undertaken extending this method to characterize many parameter combinations and incorporate more failure cases to develop probabilistic early-warning thresholds.     

Hierarchical approach to hydrological model calibration

Hydrological models have been widely used for water resources management. Successful application of hydrological models depends on careful calibration and uncertainty analysis. Spatial unit of water balance calculations may differ widely in different models from grids to hydrological response units (HRU). The Soil and Water Assessment Tool (SWAT) software uses HRU as the spatial unit. SWAT simulates hydrological processes at sub-basin level by deriving HRUs by thresholding areas of soil type, land use, and slope combinations. This may ignore some important areas, which may have great impact on hydrological processes in the watershed. In this study, a hierarchical HRU approach was developed in order to increase model performance and reduce computational complexity simultaneously. For hierarchical optimization, HRUs are first divided into two-HRU types and are optimized with respect to some relevant influence parameters. Then, each HRU is further divided into two. Each child HRU inherits the optimum parameter values of the parent HRU as its initial value. This approach decreases the total calibration time while obtaining a better result. The performance of the hierarchical methodology is demonstrated on two basins, namely Sarisu-Eylikler and Namazgah Dam Lake Basins in Turkey. In Sarisu-Eylikler, we obtained good results by a combination of curve number (CN2), soil hydraulic conductivity, and slope for generating HRUs, while in Namazgah use of only CN2 gave better results.     

Stability of earth dam contaminated by chemical transport

When chemicals are introduced into the oil, they affect soil properties such as hydraulic conductivity and stress–strain behavior. In this study, several chloride concentrations are varied from 0 to 20 per cent to analyse the effect of chemicals on soil properties. A series of laboratory triaxial tests are performed on the cylindrical specimens of sand–bentonite mixture with different sodium chloride contents (5, 10, 15 per cent) by Nannapaneni. Deformation (elastic modulus, E) and strength (cohesion, c′, and angle of friction, ϕ′) parameters are obtained from the triaxial tests as functions of confining pressure and sodium chloride concentrations, and variations of parameters are incorporated into stability analysis. The stress–strain–strength behaviour based on the above strength parameters is introduced in a finite element procedure with a modified residual flow procedure (RFP). By integrating a slope stability procedure in the finite element method, the stability with time of earth dam contaminated by sodium chloride is examined. It is found that increasing sodium chloride concentration for the soil considered increases stability. However, the procedure is general and can allow stability analysis under the influence of other chemical which may lead to decrease in stability. Copyright © 1999 John Wiley & Sons, Ltd.     

The effect of pressure-grouted soil nails on the stability of weathered soil slopes

Pressure-grouted soil nails have been increasingly used for stabilizing slopes. The pullout resistance of a soil nail is the main factor for reinforcing the slope stability. In this study, a two-dimensional axisymmetric finite element model is developed to simulate the pullout behavior of a pressure-grouted soil nail. This model is verified with field pullout tests result of a pressure-grouted soil nails by comparing with gravity-grouted soil nails. Based on the analysis, a three-dimensional finite element model is proposed for stability analysis of a slope reinforced with pressure-grouted soil nails using the shear strength reduction method. A series of numerical slope stability analyses for a slope composed of weathered soil are performed to investigate the effects of grouting pressure on the slope stability and the behavior of the soil nails. Special attention is given to the installation effect of a pressure-grouted soil nails. It is found from the result of this study that the pressure-grouted soil nails increase the safety factor by fifty percent in a slope by increasing the stiffness of the nailed slope system. Numerical analysis results confirm the fact that the pullout resistance of a soil nail is the main factor for stabilizing slopes rather than the shear resistance of the soil nail.     

水库蓄水过程中堆积体边坡瞬态稳定性分析

由现场试验结合Fredlund和Xing方法确定了堆积体的非饱和渗透性函数分布曲线。根据概化的地质模型,建立了非饱和渗流分析的有限元模型,模拟得到蓄水过程中不同时刻坡体中孔隙水压力的分布。把暂态孔隙水压力的分布和非饱和土强度理论应用到普遍极限平衡法（GLE）中,进行了库水上升过程中边坡瞬态稳定性分析。结果表明,库水上升过程中,坡体整体稳定性是下降的,而在受库水变动影响的局部区域,其稳定性系数随着库水位的上升表现出先减小后增大的趋势,即存在一个危险水位,在一定条件下,可能会诱发坡体下部局部区域失稳。     

Simulation of a slope failure induced by rainfall infiltration

On 1 November 2000, Typhoon Xangsane brought heavy rainfall that caused serious disasters in many areas of northern Taiwan. A slope located at the upstream of the Shanher Stream in Taipei County failed and induced a debris flow. To investigate the environmental influencing factors that caused the slope failure and the debris flow disaster, laboratory tests and slope stability analysis were performed. A series of tests were conducted to obtain the mechanical and hydraulic properties of the soil under unsaturated and saturated conditions. Then, limit equilibrium method and numerical analysis simulating the process of infiltration were utilized to explore the slope stability, the stress variation, and the pore-water pressure in the soil during rainwater infiltration. The results of the stability analysis show that the rainfall intensity–time history is the most significant influence factor, and the analyzed failure zone and the predicted time when the slope failed are comparable to the field observation.     

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 soil hydraulic properties model on slope stability analysis based on strength reduction method

Soil hydraulic properties models which have been proposed were derived based on the empirical fitting curve such as Brooks-Corey model (BC) and Van Genuchten model (VG), or based on soil pore radius distribution such as Lognormal model (LN). Each model has different accuracy for predicting soil moisture distribution. In the analysis of rainfall-induced slope failure, the soil hydraulic properties model was needed to describe the physical phenomena of behavior characteristic of water in unsaturated soil. As moisture content has an effect on soil strength, it is vital to select the suitable soil hydraulic properties model for predicting Factor of Safety (FOS) especially in forecasting landslide hazard. In this study, a numerical model of seepage finite element analysis using BC, VG, and LN model were used and compared in order to analyze the soil moisture distribution, water movement phenomenon, and slope stability characteristic in unsaturated soil slope based on the strength reduction method (SRM). The results showed that the variations of the parameters predicting the moisture content of soil leads to differences of FOS in some cases. The parametric study showed that for the unsaturated soil condition, BC model has the greatest FOS value than the other model, while VG model has the lowest. On the other hand, the FOS of all models have the same result for the saturated condition. Other than that, it was found that the increasing of ESP value in the surface layer has significant effect in the sub-surface layer.