Probabilistic Slope Stability Analysis Research Articles

Rock mass strength variability for probabilistic open-pit slope stability analysis

ABSTRACT As part of reliability-based design acceptance criteria, probabilistic slope stability analysis is increasingly being used for open-pit slope design. This analysis evaluates the mean factor of safety, probability of failure, and coefficient of variation for the resulting probability density function of factor of safety values. Estimating rock mass strength variability is crucial. Hoek–Brown criteria are commonly used strength parameters, as are equivalent Mohr–Coulomb parameters (calculated from Hoek–Brown), particularly for probabilistic slope stability analysis. This article describes these two strength criteria when considering univariate and bivariate distributions of the unconfined compressive strength and rock material constant. Results demonstrate differences in the variability of the equivalent Mohr–Coulomb parameters under different dependence considerations than the Hoek–Brown parameters, potentially affecting the calculated probability of failure and factor of safety results. Furthermore, they highlight an inherent correlation between Mohr–Coulomb parameters that derives from the algorithm used to calculate them from Hoek–Brown criteria. This inherent correlation is important to obtain mean factors of safety, probabilities of failure, and coefficients of variation that are consistent with the variability in Hoek–Brown parameters estimated by the practitioner and are, therefore, key to informed implementation of reliability-based design acceptance criteria.

Probabilistic slope stability analysis: A novel distribution for soils exhibiting highly variable spatial properties

Slope stability calculation depends on the soil properties (cohesion and the friction angle) of the soil. Heterogeneous terrains are frequently observed in civil and mining projects where the properties are highly spatially variable. Based on a real data from case studies, this paper presents a probabilistic analysis of the slope stability of highly heterogeneous terrains with a very high coefficient of variation (COV) of the cohesion distribution. The existing deterministic and probabilistic approaches for calculating slope stability lack the capability to effectively consider the significant heterogeneity present in the terrain The objective of the paper is to develop a new bounded interval distribution having a COV that is as high (>150%) as the COV of the cohesion distribution The results obtained with this new distribution are compared to 4 other semi-infinite distributions. To consider the correlation between cohesion and the friction angle, a specific formulation was developed to generate friction angles varying between fixed minimum and maximum limits and having the desired correlation coefficient, mean, and standard deviation. The new cohesion and friction angle distributions were incorporated and tested in a probabilistic numerical model. The new distribution can presently be applied to geotechnical studies for terrains and heterogenous materials with properties exhibiting high spatial variability.

A Computationally Efficient Method to Determine the Probability of Rainfall-Triggered Cut Slope Failure Accounting for Upslope Hydrological Conditions

We present a new computationally efficient methodology to estimate the probability of rainfall-induced slope failure based on mechanical probabilistic slope stability analyses coupled with a hydrogeological model of the upslope area. The model accounts for: (1) uncertainty of geotechnical and hydrogeological parameters; (2) rainfall precipitation recorded over a period of time; and (3) the effect of upslope topography. The methodology provides two key outputs: (1) time-varying conditional probability of slope failure; and (2) an estimate of the absolute frequency of slope failure over any time period of interest. The methodology consists of the following steps: first, characterising the uncertainty of the slope geomaterial strength parameters; second, performing limit equilibrium method stability analyses for the realisations of the geomaterial strength parameters required to calculate the slope probability of failure by a Monte Carlo Simulation. The stability analyses are performed for various phreatic surface heights. These phreatic surfaces are then matched to a phreatic surface time series obtained from the 1D Hillslope-Storage Boussinesq model run for the upslope area to generate Factor of Safety (FoS) time series. A time-varying conditional probability of failure and an absolute frequency of slope failure can then be estimated from these FoS time series. We demonstrate this methodology on a road slope cutting in Nepal where geotechnical tests are not readily conducted. We believe this methodology improves the reliability of slope safety estimates where site investigation is not possible. Also, the methodology enables practitioners to avoid making unrealistic assumptions on the hydrological input. Finally, we find that the time-varying failure probability shows marked variations over time as a result of the monsoon wet–dry weather.

Implementing Reliability Analysis of a Soil Slope using First-Order Second Moment Method, Monte-Carlo Simulation Method and Subset Simulation Method in a MS-Excel Spreadsheet

The spatial variation in the soil properties affects the analysis and design of geotechnical structures such as slope stability analysis. This paper presents the reliability analysis of a soil slope using three different methods namely, first-order second moment (FOSM) method, Monte-Carlo simulation (MCS) method and Subset simulation (SS) method. The analysis has been carried out by considering the spatial variation of the soil properties of the slope. The correlation function and the correlation distance (λ) for the uncertain parameters are modelled using random field theory developed by Vanmarcke. The factor of safety (FOS) of the slope is determined using Ordinary method of slices. The reliability based probabilistic slope stability analysis has been carried out in a MS-Excel spreadsheet to determine the probability of failure (P_f ) and reliability index (β) of the slope. The spreadsheet mainly consists of three parts i.e., deterministic analysis, uncertainty analysis and uncertainty propagation. The study shows that the SS method has shown better performance as compared to FOSM method and MCS method especially at low failure probability levels. Also, SS method ensures the generation of samples in the failure region which is not always possible in MCS method.

The impact of assumptions on deterministic and probabilistic analyses of earth fill embankments

This paper considers the impact of assumptions made when formulating analytic approaches to deterministic and probabilistic analyses of slope stability. The assumptions reviewed were presented in a paper, Waddell (2023) that presented semi-quantitative stability assessment using survey data, deterministic and probabilistic slope stability analyses of fill embankments constructed from residual soil and weathered bedrock in Western Sydney. A single variable fill strength was adopted, that was obtained from an Infinite Slope analysis assuming fully saturated fill. Rainfall records were used to predict risk of saturation to calculate annual probability of slope failure. The impacts of assumptions used to calculate the strength parameter, factor of safety and predicted failure probability are addressed in this paper. Saturation assumptions, the choice of limit equilibrium model, shape of the probability distribution functions, and spatial correlation of material properties are considered.

Probabilistic slope stability analysis using subset simulation enhanced by ensemble machine learning techniques

Probabilistic slope stability analysis using subset simulation enhanced by ensemble machine learning techniques

Probabilistic Slope Stability Analysis of Mount St. Helens Using Scoops3D and a Hybrid Intelligence Paradigm

In the past, numerous stratovolcanoes worldwide witnessed catastrophic flank collapses. One of the greatest risks associated with stratovolcanoes is a massive rock failure. On 18 May 1980, we witnessed a rock slope failure due to a volcano eruption, and a 2185.60 m high rock slope of Mount St. Helens was collapsed. Thus, from the serviceability perspective, this work presents an effective computational technique to perform probabilistic analyses of Mount St. Helens situated in Washington, USA. Using the first-order second-moment method, probability theory and statistics were employed to map the uncertainties in rock parameters. Initially, Scoops3D was used to perform slope stability analysis followed by probabilistic evaluation using a hybrid computational model of artificial neural network (ANN) and firefly algorithm (FF), i.e., ANN-FF. The performance of the ANN-FF model was examined and compared with that of conventional ANN and other hybrid ANNs built using seven additional meta-heuristic algorithms. In the validation stage, the proposed ANN-FF model was the best-fitted hybrid model with R2 = 0.9996 and RMSE = 0.0042. Under seismic and non-seismic situations, the reliability index and the probability of failure were estimated. The suggested method allows for an effective assessment of the failure probability of Mount St. Helens under various earthquake circumstances. The developed MATLAB model is also attached as a supplementary material for future studies.

Slope stability analysis using probabilistic approach

Monte Carlo simulation is a method for calculating a deterministic model iteratively using sets of random numbers as inputs, it’s was used widely in probabilistic analysis of slope stability determining  the  minimum safety factor and predicting of slope instability. This paper presents a method of slope stability analysis based on the Hovland method and using the Monte Carlo simulation that defined two parameters as random variable, the cohesion and the friction angle of the soil. In order to evaluate the efficiency and applicability of the proposed method, an example of a slope located in northern Morocco is presented in this study. The results show that the minimum safety factors calculated in this study are very close to those obtained by other researchers, which also revealed that the present method could be applied to predict the stability of homogenous slopes. 

Probabilistic slope stability analysis considering the non-stationary and spatially variable permeability under rainfall infiltration-redistribution

Probabilistic slope stability analysis considering the non-stationary and spatially variable permeability under rainfall infiltration-redistribution

Data augmentation for CNN-based probabilistic slope stability analysis in spatially variable soils

A novel methodology that involves the coupling of Convolutional Neural Networks (CNNs) and a data augmentation technique is proposed for slope reliability calculations. The methodology starts from generating a small set of random field samples, which are then calculated using the shear strength reduction method in the finite-difference scheme to obtain the associated factors of safety. Based on the theoretical relationship between the factor of safety and soil property values derived from the underlying mechanism of the shear strength reduction method, an innovative data augmentation technique is developed to enhance both the quantity and comprehensiveness of the dataset. A CNN model is then trained using the augmented dataset to learn the relationship between the factors of safety and random fields and predict the probability of slope failure. The effectiveness of the methodology is illustrated and validated using a c-φ soil slope and a multi-layered Su slope. The results show that CNNs are effective in interpreting high-dimensional random fields. In addition, through using the data augmentation technique, not only has the predictive capability of the CNN model been effectively boosted, particularly for cases involving low probability levels of failure, but the computational efficiency of the slope reliability analysis has also been improved.

Image based probabilistic slope stability analysis of soil layer interface fluctuations with Brownian bridges

Accurate interpretation of stratigraphic profiles, the phreatic surface and the spatial variability of geomaterials are essential to produce representative behaviour of geomechanical systems through numerical simulations. When considering slope stability, variations in soil layer boundaries and the phreatic surface may result in misleading metrics such as the Factor of Safety (FoS) and the Probability of Failure (PoF). This paper presents an image-based technique for generating continuous stratigraphic profiles, including random fluctuations based on Brownian motion. Brownian bridges are used to produce random walks between known points on both soil layer boundaries and the phreatic level that overlap with the slope profile image. Quadtree decomposition is used to discretise the stratigraphy and the phreatic level through an automatic process using generated digital images for mesh generation while also integrating material properties. The Scaled Boundary Finite Element (SBFEM) is used to analyse the slope stability problem. Images based on random walks along an unknown stratigraphic material boundary and the phreatic surface are randomly generated and have many random possibilities, which are used to undertake probabilistic analysis to obtain PoF. This process is complex when using numerical methods, such as the Finite Element Method, as it requires mesh generation from different slope profiles with alternating material interfaces at each probabilistic instance. When the Scaled Boundary Finite Element Method is applied, probabilistic numerical analyses can be fully automated for randomly generated material interfaces. The feasibility of the proposed method is illustrated through several cases of a slope with multiple material layers, in addition to a slope incorporating a Brownian bridge phreatic surface formulation.

Probabilistic slope stability analysis of Heavy-haul freight corridor using a hybrid machine learning paradigm

With the rising freight demand, specialized heavy-haul railway corridors allow heavier trains to transport heavy freight, improving productivity and lowering unit costs. Generally, a heavy-haul corridor necessitates a significant investment, thus the risk assessment of a rail-track system must be extensively evaluated during the design phase. From the standpoint of serviceability, this study presents a probabilistic slope stability analysis of heavy-haul freight corridor using an efficient hybrid computational technique. The present approach, i.e., ANN-MPA, is an amalgamation of an artificial neural network (ANN) and marine predators algorithm (MPA). The newly constructed ANN-MPA was used to perform probabilistic analysis of a 12.293 m high embankment of heavy-haul freight corridor of Indian Railways with a design axle load of 32.5 MT. The concept of probability theory and statistics were used to map the soil uncertainties through the first-order second-moment method. The results of the proposed ANN-MPA model were evaluated and compared with other hybrid ANNs constructed with seven distinct swarm intelligence algorithms. In the validation phase, the proposed ANN-MPA outperformed (R2 = 0.9931 and RMSE = 0.0233) other hybrid ANNs and was used to perform probabilistic analysis of a 12.293 m high embankment. The reliability index and the probability of failure were computed under seismic and non-seismic conditions, taking into consideration the influence of uncertainties in soil parameters. Using the proposed approach, the failure probability of the 12.293 m high soil slope under different seismic conditions can be evaluated rationally and efficiently.

A short review of probabilistic slope stability analysis considering spatial variability of geomaterial parameters

A short review of probabilistic slope stability analysis considering spatial variability of geomaterial parameters

Dimensional Reduction-Based Moment Model for Probabilistic Slope Stability Analysis

Uncertainty is an inevitable factor that influences the function analysis, design, and safe operation in engineering systems. Due to the complexity property and unclear failure mechanism, uncertainty is an intrinsic property of slope engineering. Hence, stability analysis and design cannot meet the demands of slope engineering based on the traditional deterministic method, which cannot deal with uncertainty. In this study, a practical reliability approach was developed to consider the uncertainty factor in slope stability analysis by combining the multiplicative dimensional reduction method (MDRM) and first-order second moment (FOSM). MDRM was used to approximate the complex, nonlinear, high-dimensional, and implicit limit state function. The statistical moment of safety factor was estimated based on the moment method using MDRM. FOSM is adopted to compute the reliability index based on the statistical moment of the safety factor. The proposed method was illustrated and verified by an infinite slope with an analytical solution. The reliability index and failure probability were compared with Monte Carlo simulations (MCS) in various cases. Then, it was applied to a slope based on numerical solutions. The results show that the proposed method is feasible and effective for probabilistic slope stability analysis. The reliability index obtained from the proposed method shows high consensus with the traditional response surface method (RSM). It shows that the proposed method is effective, efficient, and accurate. MDRM provides a practical, simple, and efficient probabilistic slope stability analysis approach.

Probabilistic slope stability analysis: state-of-the-art review and future prospects

Probabilistic slope stability analysis: state-of-the-art review and future prospects

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.