Probabilistic Slope Stability Analysis Research Articles

Stochastic Rock Slope Stability Analysis: Open Pit Case Study with Adjacent Block Caving

AbstractIn last decades, numerical modelling become a useful tool for solving complex geoengineering problems such as slope stability. On the other hand, probabilistic slope stability analyses are able to consider the variability of the rock mass properties in the decision making process. However, the application of probabilistic slope stability analysis with large three-dimensional numerical models is still limited due to the computational expenses of evaluating a substantial number of considered models. It is well-known that response surface methodology (RSM) couples the mathematical and statistical techniques to relate input variables to the response, allowing a reliable outcome and reasonable time of the analysis. Taking these advantages, this article presents an application of RSM in probabilistic slope stability analysis using three dimensional distinct element modelling. For this purpose, the most influencing factors including: uniaxial compressive strength, geological strength index (GSI), and shear strength of discontinuities, were taken into consideration to determine the probability of failure of an open pit slope located in vicinity of a block caving-induced subsidence crater. Numerical analysis of slope stability was conducted for an open pit slope using the Distinct Element Method code-3DEC. Probability distribution of the factor of safety (FS) was determined and possible slope failure mechanism was observed. In addition, the block caving-induced subsidence was investigated. The final outcomes indicate that Response Surface Methodology is applicable when couples with numerical modelling of complex issues, GSI is considered the most influential variable. The studied slope is considered stable due to the low value of the FS probability distribution (2.2%). This research is expected to provide a reference for slope stability analysis in case of transition from Open Pit to Underground Mining.

Non-parametric fragility curves for probabilistic risk assessment of rainfall-triggered landslides

Fragility analysis of slopes under rainfall condition express the conditional probabilities of exceeding prescribed slope limit states under a range of rainfall intensities, which is the basic and pivotal procedure in rainfall-triggered landslide risk assessment. Classical fragility analysis methods of slopes always develop fragility curves with the assumption of lognormal distribution. The validation of assuming the shape of fragility curves as lognormal distribution remains a open question in practice. In addition, the existing fragility analysis of slopes under rainfall condition have not dealt with the effect of spatially-variable geo-material parameters. In the present study, a novel fragility analysis methodology is proposed for the construction of non-parametric fragility curves of slopes under rainfall condition, in which the spatially-variable soil properties are taken into account. The non-parametric fragility curves are developed by the calculated slope failure probabilities under various rainfall intensities on the basis of probability density evolution theory, without restricting fragility functions to some assumed distribution models. With the proposed method and a set of probabilistic slope rainfall seepage and stability analyses, non-parametric fragility curves, fragility surface using two rainfall intensity measures and time-dependent fragility curves of a slope subjected to various rainfall scenarios are obtained for rainfall-triggered landslides risk assessment.

Stability Analysis of Jointed Rock Slopes Based on the Universal Elliptical Disc Model

A discrete fracture network (DFN) represents the random distribution of fractures within rock masses in three dimensions and has been widely used in the stability analysis of jointed rock slopes. This study introduces a novel method for constructing three-dimensional DFN models to address the limitations of traditional circular or polygon-based models. This method employs the universal elliptical disc (UED) model, combined with the discrete element method (DEM) in 3DEC, for the probabilistic analysis of jointed rock slope stability. The paper begins with an explanation of the fundamental principles of the UED model, and continues to detail the procedures for creating a three-dimensional DFN using the UED model and for analyzing slope stability using the DEM. An open-pit mine rock slope in the USA serves as a case study to illustrate the application of the proposed method. This approach facilitates the integration of the UED model into 3DEC and offers a more realistic depiction of the three-dimensional DFN, which enhances both the accuracy and efficiency of stability analysis in jointed rock slopes.

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.