Probabilistic Slope Stability Analysis Research Articles

Advances in reliability and risk analyses of slopes in spatially variable soils: A state-of-the-art review

Spatial variability of soil properties was rarely taken into account directly in traditional slope stability analyses, rather some “average” or suitably “pessimistic” properties are assumed to act across the whole region of interest. In the last two decades, a large portion of published research papers on slope stability have tried to explicitly model the spatial variability of soil properties. In the first decade, research mainly focused on showing the importance of modeling the spatial variability directly in probabilistic slope stability analysis. In the last decade, a rapid development was observed including quantitative risk assessment of slope failure, improving computational efficiency, and directly using site investigation and field monitoring data. This review tries to summarize these advances in the hope that future research directions can be identified.

The application of failure method probability for analyzing in pit dump stability at West Block ‘X’ pit PT Berau Coal - East Kalimantan

West Block 'X' pit is one of the coal mining locations operated by the Lati Mine Operation – PT Berau Coal. Administratively, the Lati Mine is located as part of Berau Regency – East Kalimantan. The study area is located at the north side of the concession, in a syncline fold structure zone. The disposal design in this area needs to special attention from slope stability aspect due it is located on the wing of a mega syncline with a certain slope and constituent of unconsolidated materials. The pit design needs to be stable. The purpose of this study is to determine the level of stability of the in-pit dump by analyzing the current in-pit dump stability based on the value of the safety factor (FS) and the probability of failure (PoF). The method used in this study is a probabilistic analysis of slope stability based on the Morgenstern-Price method to obtain the value of the safety factor and the probability of failure. The study results show that the slope is in the safe category (stable slope) in the range of PoF values 0 – 1%, marginal slope 1 – 12%, and unstable slope above 12%. Based on such as results, it is necessary to modify the slope geometry categorized as unstable to carry out mine operation safely underneath the toe of slope.

A data driven efficient framework for the probabilistic slope stability analysis of Pakhi landslide, Garhwal Himalaya

A data driven efficient framework for the probabilistic slope stability analysis of Pakhi landslide, Garhwal Himalaya

Probability Methods for Stability Design of Open Pit Rock Slopes: An Overview

The rock slope stability analysis can be performed using deterministic and probabilistic approaches. The deterministic analysis based on the safety concept factor uses fixed representative values for each input parameter involved without considering the variability and uncertainty of the rock mass properties. Probabilistic analysis with the calculation of probability of failure instead of the factor of safety against failure is emerging in practice. Such analyses offer a more rational approach to quantify risk by incorporating uncertainty in the input variables and evaluating the probability of the failure of a system. In rock slope engineering, uncertainty and variability involve a large scatter of geo-structural data and varied geomechanical test results. There has been extensive reliability analysis of rock slope stability in the literature, and different methods of reliability are being employed for assessment of the probability of failure and the reliability of a slope. Probabilistic approaches include Monte Carlo simulation (MCS), the point estimate method (PEM), the response surface method (RSM), first- and second-order reliability methods (FORMs and SORMs), and the first-order second-moment method (FOSM). Although these methods may be complicated, they provide a more complete definition of risk. Probabilistic slope stability analysis is an option in most commercial software; however, the use of this method is not common in practice. This paper provides an overview of the literature on some of the main probabilistic reliability-based methods available for the design of the rock slope in open pit mining. To demonstrate its applicability, the paper investigates the stability of a rock slope in an open pit mine in the Goldfields region, Western Australia. Two different approaches were adopted: deterministic stability analysis using two-dimensional limit equilibrium and finite element shear strength reduction methods using SLIDE and RS2 software, respectively, and probabilistic analysis by applying the MCS and RSM methods in the limit equilibrium method. In this example, the slope stability analysis was performed using the Spencer method with Cuckoo search optimization to locate the critical slip surface. The results obtained were compared and commented on.

Design of borehole deployments for slope stability analysis based on a probabilistic approach

This study proposes a cross-correlation map-based borehole deployment approach for two-dimensional probabilistic slope stability analysis. This approach designs the layout of the proper number of boreholes based on the cross-correlation between the factor of safety and spatially variable soil strength every part of a slope. Numerically synthesized, undrained slopes are investigated as examples to illustrate the effectiveness of the proposed approach. Results demonstrate that the proposed approach is viable, and the cross-correlation maps are the appropriate metric for design slope borehole deployment. Using the cross-correlation maps, a small number of boreholes can sufficiently capture the large-scale heterogeneities that are critical to the slope stability. This information can help to identify the slip surface and improve the slope stability analysis. The small-scale heterogeneity, due to its short correlation structure or the residual covariance of the soil property field after conditioning using the borehole data, leads to a small amount of uncertainty in slope stability analysis. This small uncertainty could be vital to the slope stability analysis when the slope stability is close to the limit equilibrium state.

Reliability of an engineered slope considering the Regression Kriging (RK)-based conditional random field

Many attempts have been made to apply random field theory to the slope reliability analysis in recent decades. However, there are only a few studies that consider real landslide cases by incorporating actual soil data in the probabilistic slope stability analysis with spatially variable soils. In this paper, an engineered slope located in Hong Kong was investigated using the probabilistic approach considering the Regression Kriging (RK)-based conditional random field. The slope had been assessed and considered to be safe by classical deterministic slope stability analyses but failed eventually. In this study, both deterministic slope stability analyses and probabilistic slope stability analyses were conducted, and the comparison was made between the probabilistic approach adopting RK-based conditional random field and that adopting Ordinary Kriging (OK)-based approach. The results show that the deterministic factor of safety (FS) for a slope may not be an adequate indicator of the safety margin. In particular, a slope with a higher deterministic FS may not always represent a lower probability of failure under the framework of probabilistic assessment, where the spatial variability of soil properties is explicitly considered. Besides, the critical portion of the slope could not be found using the OK-based approach that considers a constant trend structure.

Reliability assessment of slopes with three-dimensional rotated transverse anisotropy in soil properties

The influence of soil variability on three-dimensional (3D) probabilistic slope stability analysis has been investigated previously for soils that display isotropic spatial variability features or anisotropic horizontal fabric patterns. However, due to various soil deposition processes, weathering, filling or tectonic movements, the assumptions of isotropy or horizontal layering may not always be realistic. This study presents 3D analyses of slopes with spatially variable soils associated with rotated transverse anisotropy features. The results show that for cross-dip slopes where the strike direction of soil strata is perpendicular to the out-of-plane direction of the slope, the reliability depends on various factors including strata rotation angle and autocorrelation distances, and differs significantly from slopes with horizontally deposited soil fabric. The influence of strata orientation is also pronounced for dip slopes and reverse dip slopes, and these are presented in terms of reliability indices of the slopes and statistics of the length of sliding mass and elaborated by considering the failure mechanism under different scenarios. Through these analyses, this paper discusses the key features of slope reliability considering rotated transverse anisotropy in soil properties, and their major differences from situations involving horizontal soil layers or two-dimensional probabilistic assessments.

Multiseasonal probabilistic slope stability analysis of a large area of unsaturated pyroclastic soils

The analysis of slope stability over large areas is a demanding task for several reasons, such as the need for extensive datasets, the uncertainty of collected data, the difficulty of accounting for site-specific factors, and the considerable computation time required due to the size of investigated areas, which can pose major barriers, particularly in civil protection contexts where rapid analysis and forecasts are essential. However, as the identification of zones of higher failure probability is very useful for stakeholders and decision-makers, the scientific community has attempted to improve capabilities to provide physically based assessments. This study combined a transient seepage analysis of an unsaturated-saturated condition with an infinite slope stability model and probabilistic analysis through the use of a high-computing capacity parallelized platform. Both short- and long-term analyses were performed for a study area, and roles of evapotranspiration, vegetation interception, and the root increment of soil strength were considered. A model was first calibrated based on hourly rainfall data recorded over a 4-day event (December 14–17, 1999) causing destructive landslides to compare the results of model simulations to actual landslide events. Then, the calibrated model was applied for a long-term simulation where daily rainfall data recorded over a 4-year period (January 1, 2005–December 31, 2008) were considered to study the behavior of the area in response to a long period of rainfall. The calibration shows that the model can correctly identify higher failure probability within the time range of the observed landslides as well as the extents and locations of zones computed as the most prone ones. The long-term analysis allowed for the identification of a number of days (9) when the slope factor of safety was lower than 1.2 over a significant number of cells. In all of these cases, zones approaching slope instability were concentrated in specific sectors and catchments of the study area. In addition, some subbasins were found to be the most recurrently prone to possible slope instability. Interestingly, the application of the adopted methodology provided clear indications of both weekly and seasonal fluctuations of overall slope stability conditions. Limitations of the present study and future developments are finally discussed.

Reply to the discussion by Huang on “Probabilistic seismic slope stability analysis and design”

Reply to the discussion by Huang on “Probabilistic seismic slope stability analysis and design”

Finite difference probabilistic slope stability analysis based on collocation-based stochastic response surface method (CSRSM)

Significant damage has been observed due to the landslide along the East–West motorway section, located near Ain Bouzian–El-Harrouch region, Northeast Algeria. In this paper, a probabilistic study was carried out to assess the stability of a slope, with a total height of 60 m and varying inclination angles. Two cases were considered with and without the presence of the groundwater table. To investigate the failure probability of the slope, the collocation-based stochastic response surface method was employed. The input random parameters were the Young modulus E, cohesion C, and friction angle φ, where probabilistic system response is the factor of safety. To identify the effective contribution of each random parameter in the variability of the system response, a global sensitivity analysis based on Sobol indices was conducted. Also, a parametric study was realized to inspect the effect of input geotechnical parameter variations on the reliability of slope stability. The result showed that the slope reliability analysis is strongly influenced by the inherent variability of friction angle and hydrogeological ground conditions.

Probabilistic Seismic-Stability Analysis of Slopes Considering the Coupling Effect of Random Ground Motions and Spatially-Variable Soil Properties

AbstractA probabilistic slope stability analysis framework based on the Newmark permanent displacement method and probability density evolution theory is presented to quantify the coupling impact a...

Evaluation of Probabilistic Slope Stability Due to Updating of Indonesia Seismic Hazard Maps

This paper presents an evaluation of probabilistic slope stability due to updating of Indonesia seismic hazard maps from 2010 to 2017 edition. The evaluation is conducted by presenting case study to compare the probability of failure of slope which subjected to seismic load determined from those seismic hazard maps. At first, simple slope models are built and the horizontal seismic coefficients are selected. Then, the probabilistic slope stability analysis is conducted using Monte Carlo simulation in LEM-based software so called Rocscience Slide 6.0. The simulation results indicate that the revision of Indonesia seismic hazard maps causes increasing of probability of failure of slope in the study area. These results show that the slope models become more prone to failure subjected to seismic load obtained from the seismic hazard maps.

Probabilistic slope stability analysis in Kahrizak landfill: effect of spatial variation of MSW’s geotechnical properties

The geotechnical properties of municipal solid waste (MSW) in landfills vary considerably depending on the composition, time, and the rate of waste density. This variability in geotechnical properties leads to many uncertainties in the analysis of landfill slope stability. This study, using probabilistic methods investigates the slope stability and the probability of failure of a Kahrizak landfill under the conditions of spatial variability of physical and geotechnical properties of MSW. To achieve this goal, the random field theory has been used with a finite difference numerical method in the framework of the Monte Carlo simulation. MSW’s shear strength parameters such as cohesion and friction angle as well as the unit weight of layers are considered as random variables. An extensive literature review was conducted to address the probable variation of above-mentioned parameters in Kahrizak landfill. The results of several different laboratory researches on MSW samples collected from Kahrizak landfill were also employed in the modelings. Output results are presented in the form of probability distributions of the factor of safety as well as the probability of failure corresponding to these distributions. Moreover, the effect of various parameters such as coefficient of variation and correlation distance of input parameters on these output results has been investigated. The results show that considering the spatial variability in probabilistic methods would help to determine the various mechanisms affecting the performance and the probability of failure of the landfill slope. In addition, the output of such probabilistic analyses can be used as guidance for engineers to design safe and reliable landfill.

Comparative Approaches to Probabilistic Finite Element Methods for Slope Stability Analysis

Probabilistic slope stability analyses are often preferable to deterministic methods when soils are inherently heterogeneous, or the reliability of geotechnical parameters is largely unknown. These methods are suitable for evaluating the risk of slope failure by producing a range of potential scenarios for the slope stability factor of safety. Several probabilistic methods including the Point Estimate Method, Monte Carlo Method and Random Finite Element Method, can be combined with the Finite Element technique. In this study, various shear strength distributions are considered for three different probabilistic Finite Element Methods to determine Factor of Safety and Probability of Failure distributions, based on the associated method of slope stability analysis. Results are presented for a case study of an Australian open-cut coal mine, with a range of shear strength parameter distributions for coal and interseam cohesive materials considered. Coal and interseam shear strength parameters are varied independently, to determine the effects of each material on the slope Factor of Safety.

Prediction and classification for finite element slope stability analysis by random field comparison

This paper considers probabilistic slope stability analysis using the Random Finite Element Method (RFEM) combined with processes to determine the level of similarity between random fields. A procedure is introduced to predict the Factor of Safety (FoS) of individual Monte Carlo Method (MCM) random field instances prior to finite element simulation, based on random field similarity measures. Previous studies of probabilistic slope stability analysis have required numerous MCM instances to reach FoS convergence. However, the methods provided in this research drastically reduce computational processing time, allowing simulations previously considered too computationally expensive for MCM analysis to be simulated without obstacle. In addition to computational efficiency, the comparison based procedure is combined with cluster analysis methods to locate random field characteristics contributing to slope failure. Comparison measures are presented for slope geometries of an Australian open pit mine to consider the impacts of associated factors such as groundwater on random field similarity predictors, while highlighting the capacity of the similarity procedure for prediction, classification and computational efficiency.

Risk based decision making in highway slope geometry design

Soil uncertainties should be considered in the safety and economic evaluation of geotechnical structures. The impact of uncertainties in risk assessment help engineer in deciding a safer and economically feasible design of geotechnical structures. This paper studies the effect of red clay soil strength uncertainties on the highway excavated slope geometry designs. Different slope geometries are considered: slope angles of 27, 34, 45 and 63 degrees and slope heights of 5 m, 10 m and 15 m. The probabilistic analysis of slope stability is conducted using SLOPE/W to obtain the probability of failure, as well as the failed soil mass volume. The resulting probabilities are used in the quantitative decision making analysis on slope geometries. The Expected Monetary Value (EMV) derived from the construction costs, the repair costs, as well as the highway closure losses for different Levels of Service, is used in the analysis. The decision-making analysis results provide an overview of how the consequences of slope failures determining the decisions made. The consequences of slope failure indicate the design should lean on the gentle slope.

Worst-case spatial correlation length in probabilistic slope stability analysis

This note investigates the reliability of undrained slopes by the random finite-element method. The focus of this note is on the worst-case spatial correlation length, namely the correlation length at which the probability of slope failure reaches a maximum. It is shown that the worst-case phenomenon is most pronounced when the mean factor of safety is relatively low or the coefficient of variation is relatively high. Knowledge of the worst-case spatial correlation length is valuable, as it can be employed for conservative design in the absence of substantial soil field data.

Probabilistic Slope Stability Analysis: A Case Study

Probabilistic slope stability analyses are becoming more and more popular to evaluate the safety level of slopes and the associated risk and reliability, especially in the recent years. Probabilistic approach can take into account the uncertainties and natural variability in material properties, as well as in environmental factors, by using various statistical distribution fuctions (such as normal, lognormal etc.) for random variables. It is already noted by various researchers that, a slope with a deterministic factor of safety larger than 1.00 using average values of soil parameters may have a significant level of probability of failure, if the material properties are unknown, or contain significant uncertainty/variability. In this study, a well-documented landslide case study is used to demonstrate the importance of probabilistic approach in slope stability; to investigate the effects of considering variabiliy in material properties; and to compare deterministic and probabilistic slope stability analyses results. Deterministic limit eqilibrium, probabilistic limit equilibrium and probabilistic finite element analyses are conducted for Lodalen landslide in Oslo, Norway and the results are compared with each other. The factor of safety, the probability of failure and the most critical failure surface are investigated with and without statistical cross-correlation of soil’s shear strength parameters. The results of this study can provide further insights into the comparison of deterministic and probabilistic approaches in slope safety.

Probability-dependent failure modes of slopes and cuts in heterogeneous cohesive soils

Improbable slope failure is addressed in the framework of reliability analysis of slopes in heterogeneous cohesive soils, as the small subset of realisations that fail without additional measures to trigger failure. The mode of these slope failures, located at the weak tail of the reliability curve, is demonstrated to differ significantly from the deterministic solution as well as the stochastic average solution found when shear strength reduction is applied to trigger slope failure. Subset simulation is applied to compute the probability-dependent difference in failure mode for a range of slopes down to very low levels of probability, which is required to properly account for the actual failure in predominantly safe slopes. The results demonstrate possible differences in the mode of failure when properly accounting for the uncertainty in spatial variability in a full probabilistic slope stability analysis, and highlight that caution may be needed when using the strength reduction method.

Probabilistic Analysis of Weathered Soil Slope in South Korea

Rainfall is a major trigger of shallow slope failures, and it is necessary to consider the spatial correlation of soil properties for probabilistic analysis of slope stability in heterogeneous soil. In this study, a case study of a weathered soil slope in Korea was performed to identify the rainfall-induced landslides considering the spatial variability of the soil properties and the probabilistic rainfall intensity depending on the return period and the rainfall duration. Various laboratory tests were performed to determine the physical properties of the site, and an electrical resistivity survey was carried out to understand the soil strata. Cohesion, friction angle, and permeability were considered as random variables considering the spatial variability, and the probabilistic rainfall intensities for return period of 2, 5, 10, 50, 100, and 200 years were used to consider the effects of rainfall infiltration. The results showed that a probabilistic framework can be used to efficiently consider the spatial variability of soil properties, and various slope failure patterns were identified according to the spatial variability of the soil properties and the probabilistic rainfall intensity.