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... Slope stability analyses are conducted using three limit equilibrium methods (LEM), i.e. Bishop [11], Janbu [12,13] and Morgenstern-Price [14]. In the probabilistic analysis, the distribution of the safety factor is determined. ...
... Then, utilizing a search algorithm for the critical slip surface and limit equilibrium method (Morgenstern-Price method), the factor of safety for each Monte Carlo simulation is calculated. The probability of failure using Monte Carlo simulation is possible to calculate using equitation (12): ...
The paper examines a complex methodology for calculating the slope stability of a tailing storage facility based on comparing the results obtained through deterministic and probabilistic approaches. The analysis is performed in GeoStudio software, based on the limit equilibrium method, and with a probabilistic approach that uses a Monte Carlo simulation to compute a probability distribution of the resulting factor of safety. A slope stability assessment of tailing dam was conducted on the example of Ferrexpo Poltava Mining, and a conclusion was reached about their reliability and safety. The results of the deterministic analysis showed that the calculated factor of safety is by those established in Ukrainian regulatory standards. It has been recognized that the factor of safety is not a consistent measure of risk for tailings dam. Considering the variability inherent in the soil materials of tailings dam is a way to achieve more accurate results. The importance of obtaining a failure probability and a reliability index due to tailing dam stability was highlighted by comparing deterministic and probabilistic approaches.
... It is defined as the ratio of the available shear strength of the soil to the shear stress acting on the soil. . available shear strength of the soil shear stress acting on the soil Widely used methods for analyzing the slope stability of embankment ordinary method [16,17], Bishop's simplified method (BSM) [16], Janbu method (JSM) [18][19][20], the Morgenstern-Price method (M-PM) [21], an method (SM) [22]. The analysis has to test the total and effective stress app For criteria in other countries, the FOS for embankments is presented in Tab Table 1. ...
... -Testing for the particle size of materials Widely used methods for analyzing the slope stability of embankments include the ordinary method [16,17], Bishop's simplified method (BSM) [16], Janbu's simplified method (JSM) [18][19][20], the Morgenstern-Price method (M-PM) [21], and Spencer's method (SM) [22]. The analysis has to test the total and effective stress approaches [23]. ...
The development of a country is affected by various multifaceted factors, which are likely to generate the highest benefits. For example, developing water resources by constructing embankments to store water and for transportation must consider high resilience, particularly with the current challenges arising from climate change. Another factor that must be considered is the shortage of essential materials for embankment cores, such as clay, which is the primary material for constructing such cores. This study aims to analyze the stability of soil embankments between the change of materials, namely clay and asphaltic concrete, by varying the water level and increasing the embankment load. The result shows that the asphaltic concrete core exhibits a significantly higher stability than the clay core, such as its reduced water seepage and lower deformation. In the worst-case scenario, the asphalt concrete core has a thickness of 0.3 m and a seepage rate of 15.1 × 10⁻⁴ m³/day. Comparatively, the seepage rate of the clay core is approximately 10-times lower.
... The model must train with known datasets covering a wide range of inputs to predict the intricate relationship between dependent and independent variables. The homogenous slope with the variation of these input parameters was modelled to obtain a FOS for the five different limit equilibrium methods, i.e., Bishop (1955), Fellenius (1936), Janbu (1955), Morgenstern andPrice (1965), andSpencer (1967). ...
... Value of R 2 Training data Testing data Fellenius (1936) 0.96 0.97 Bishop (1955) 0.95 0.96 Janbu (1955) 0.96 0.96 Spencer (1967) 0.97 0.97 Morgenstern and Price (1965) 0.95 0.95 Table 6 Comparison of prediction performance in the ANN model for different stability analysis methods ...
Accurate slope stability prediction is of utmost importance to reduce disastrous effects of slope failures and landslides. However, conventional methods of slope stability analysis are complex and challenging, and more importantly, use of these methods in a wide-area slope stability assessment requires a large number of soil property and field investigation data. These complexities and challenges often demand some simplified statistical slope stability analysis models such as by using machine learning (ML) techniques. So, in this research, we develop slope stability prediction models using multiple linear regression (MLR) and artificial neural network (ANN) and classify the slopes as safe or unsafe using random forest (RF) and support vector machine (SVM) methods. For this purpose, a dataset of 4,208 slope cases was created using limit equilibrium-based Slide software. The effectiveness of each model was then evaluated using statistical metrics and validated through roadside slope cases in Nepal, India, Canada, and the UK. In this study, Spencer’s method-based ANN model was found to have demonstrated the highest reliability. The findings of this work may contribute to simplified and better decision-making process in slope stability assessment, slope safety enhancement, and sustainability improvement in engineering projects involving soil slopes.
... Fellenius proposed the first method of LEM, referred as Ordinary or the Swedish method in 1936. Later, Janbu (1954Janbu ( , 1955Janbu ( , 1973, Bishop (1955) simplified; Bishop (1955) rigorous; Lowe and Karafiath (1960), Morgenstern-Price (1965), Spencer (1967Spencer ( , 1973; Corps of Engineer (1982) were introduced. Chugh (1986) devised a method of general limit equilibrium as an extension of Spencer and Morgenstern-Price method, which considers force and momentum equilibrium simultaneously (Sharma 2002). ...
... Fellenius proposed the first method of LEM, referred as Ordinary or the Swedish method in 1936. Later, Janbu (1954Janbu ( , 1955Janbu ( , 1973, Bishop (1955) simplified; Bishop (1955) rigorous; Lowe and Karafiath (1960), Morgenstern-Price (1965), Spencer (1967Spencer ( , 1973; Corps of Engineer (1982) were introduced. Chugh (1986) devised a method of general limit equilibrium as an extension of Spencer and Morgenstern-Price method, which considers force and momentum equilibrium simultaneously (Sharma 2002). ...
Landslides in the form of circular failures often occur in homogeneous geomaterials like soil, debris and highly weathered or fragile rocks. In slope engineering practices, Factor of Safety (FoS) is commonly determined using Circular Failure Charts (CFCs), Limit Equilibrium Methods (LEM) and Finite Element Methods (FEM). The present study is an attempt to assess the disparities and inter-relationships in FoS using CFCs, LEM and FEM. FoS calculations were performed manually and using an automated Windows-based open-source tool FS Calculator 1.0. Pertinent geomechanical (cohesion, friction, unit weight) and geometrical properties (slope angle and height) of fifty-one slopes from nine case records were considered in the present analysis. A linear correlation occurs in FoS using CFC and LEM i.e., , with the coefficient of determination of 0.99. However, the linear relationship between SRF and FoS (LEM) is having coefficient of determination of 0.63 only. It connotes that FoS using CFCs and LEM is relatively well in comparison to FoS from CFCs and FEM. It is also evident that CFCs provide relatively more conservative FoS than FEM and LEM. Among all three proxies, FEM relies on a wider set of geomechanical parameters and evaluates stability under static and dynamic conditions with capability of applying wider range of remedial measures. Since, most of the FEM tools are commercial, open-source CFCs based FS Calculator may be used and proposed relationships may be utilized as correction factor.
... The analysis involves determining the forces acting on a slice of the slope, and calculating the factor of safety by comparing the resisting forces to the driving forces. Janbu (1954) [5] also proposed a simplified form of limit equilibrium analysis that assumes that the failure surface is polygonal. The analysis involves dividing the slope into a series of polygons, and determining the forces acting on each polygon. ...
... The analysis involves determining the forces acting on a slice of the slope, and calculating the factor of safety by comparing the resisting forces to the driving forces. Janbu (1954) [5] also proposed a simplified form of limit equilibrium analysis that assumes that the failure surface is polygonal. The analysis involves dividing the slope into a series of polygons, and determining the forces acting on each polygon. ...
Slopes along the highway, especially in hilly areas, are highly susceptible to landslides. Several factors such as heavy traffic and abundant rainfall during monsoon can contribute to slope failure. The slope failure can lead to damage to the mankind and the property. To mitigate risk associated with slope failure, different slope stabilization techniques, such as anchors, anti-slide piles, reinforcement, geotextiles, terracing, vegetation, soil nailing, can be adopted. Therefore, it is essential to conduct slope stability analysis for assessing the safety of slopes or embankments and also for the selection of most suitable stabilization technique before commencing any construction activities. In the present study, deterministic 2D slope stability analysis has been performed for a specific slope in Agumbe ghat, Karnataka and another landslide prone region in Dhobighat, Hyderabad. Both slope stability analysis has been performed using limit equilibrium analysis (LEA) and finite element analysis (FEA). Both slopes are found to be unstable according to LEA and FEA. Further, using anchors the slope has been stabilized and the factor of safety (FOS) increases in both FEA and LEA. In addition to that parametric study has been carried out to determine the effect of the design parameters on 2D slope stability analysis using LEA. It has been found that the slope at Dhobighat, where well graded sand is predominant are more affected due to the changes in the design parameters as compared to Agumeb ghat slope, which mainly consisted of stiff clay. The study also concludes that for a specific slope FEA provide more conservative FOS value compare to LEA.
... Since the internal friction angle and cohesion play a fundamental role in determining the depths of the slip surfaces and, consequently, the potential landslide volume and area, to control the material's impact on the simulated landslide, the nondimensional ratio λ is used, which is defined as the ratio between cohesion (c), material unit weight (γ), hillslope height (H), and internal friction angle (φ) (Janbu 1955): ...
Rainfall-induced shallow landslides can rapidly evolve into debris flows, characterized by high velocities and destructive power, posing a significant threat to many communities. These mass movements often occur as clustered events affecting wide areas, making their prediction a challenging task. This study aims to identify a suitable distributed slope stability model to predict such events by assessing the performance of two physically-based distributed models: HIRESSS (HIgh REsolution Slope Stability Simulator) and SCOOPS3D, in predicting shallow landslides in an Alpine region of Italy (Valle d'Aosta). The models simulated two rainfall events in May 2013 and October 2018. The landslides triggered during these events were used to validate and compare the results of slope stability analyses generated by the two models. To perform a significant comparative study, three saturation scenarios (Pre-event, Peak-event, and Post-event conditions), defined by HIRESSS during the modelling process, were provided to SCOOPS3D to carry out the slope stability analyses. HIRESSS incorporates a transient hydrological model to dynamically track soil saturation changes, while SCOOPS3D does not inherently simulate hydrological processes. The results showed that HIRESSS was particularly effective in modelling the primary triggering mechanism for shallow landslides induced by increasing soil saturation in the context of the study area. This can be attributed to the fact that shallow soils and high relief energy, which define the geohydrological and geomorphological context of the area, align better with HIRESSS's infinite slope approach. This alignment enables HIRESSS to more accurately capture rapid hydrological responses and pore pressure dynamics, which are crucial for predicting shallow landslide triggering within this specific geomorphological setting. The findings emphasize the necessity of a comprehensive evaluation of these factors when selecting slope stability models, providing valuable insights for land-use planning, risk assessment, and the development of early warning systems.
... Various methods of slices have different assumptions regarding the interslice force function and static equilibrium equations (Janbu 1954;Bishop 1955;Spencer 1967;Morgenstern-Price 1965;etc.). For the case study analyzed, Spencer's method (Spencer 1967) that satisfies all conditions of static equilibrium, is used to calculate the FS value. ...
The comparative slope stability analysis of the highly fractured rock slope by three different methods is presented. The usually applied slope stability methods of the rock mass obeying the Hoek and Brown failure criterion comprises the limit equilibrium and/or the finite element method, quantifying the slope stability by the factor of safety. The better knowledge of the entire process of rock slope failure, i.e., the initiation, development of micro-cracks and final position of the failure surface, capturing large deformations, damage and breakage through the rock mass material could be achieved by the implementation of discrete element modeling. In this paper, the application of these three methods for the analysis of failed rock slope case study is shown. The analysis showed that all three methods produce similar results regarding the factor of safety value and position of the failure surface, being in line with the position of the failure surface observed in situ. The discrete element method gives the best prediction, providing a more in-depth knowledge of the failure, estimating the factor of safety by a new approach.
... As mentioned before, the line of thrust is assumed. This hypothesis is not new as, for example, Janbu [6] adopted it in his slope stability method. Some researchers argue that by assuming the line of thrust, problems like lack of convergency/solution among many others might arise as the problem is over-constrained. ...
In this paper a general and rigorous slope stability method is described and compared to the General Limit Equilibrium (GLE) and other methods. The new method is unlike most slope stability methods and it presents some interesting qualities like, for example, linear-ity. Most importantly, it is independent of the failure criteria of the material. The results of the comparisons made for several slope cases show that the difference of the safety factor from the new method is, on average, only 4% when compared to other general and rigorous methods.
... This "slicing approach" became widely adopted in the 1950s and 1960s. Since then, various slicing methods within the limit equilibrium framework have been thoroughly examined and compiled (Fellenius, 1936;Bishop, 1955;Janbu, 1954;Price and Morgenstern, 1965;Spencer, 1967;Fredlund et al., 1981;Duncan, 1996). The calculations were performed using the GeoStudio2024 Slope/W software, applying the classical approach, i.e., without considering the partial factors recommended for stability calculations by Eurocode 7. It should be noted that applying partial factors by Eurocode 7 would reduce the final calculation result (or, more precisely, the term Overdesign Factor -ODR should be used in this context). ...
The catastrophic floods in Poland in previous years and the current one in 2024 have highlighted the importance of slope stability in the design, maintenance, and operation of levees, which are crucial for flood protection. While the causes of this year's flood have not been determined yet, as experts are still working on assessing the reasons for the failure of various structures, it is evident that many have failed due to multiple factors, such as overtopping, internal erosion, and slope instability. The article highlights the importance of the observational method, which, during the operation of hydraulic structures often in use for decades, enables data collection on potential seepage through the levee and on adverse filtration phenomena. Such information allows revising previous safety calculations for the structure, adjustments of geotechnical parameters adopted during the design phase, and consideration of factors like the presence of water on the downstream side. Evaluating slope stability under these conditions reflects the actual working environment of the structure and facilitates decision-making regarding potential modernization initiatives. The article analyses the stability of the levee slope before and after its modernization. A transient seepage analysis through the levee was carried out in the selected cross-section for various water levels, and the stability of the embankment in such conditions was also assessed. Next, the modernization of the embankment was briefly described, with particular emphasis on the sealing system. Stability was evaluated under the new filtration conditions through the levee. Based on this, it was concluded that the sealing system plays a crucial role in improving the safety and stability of the slope. The analysis revealed that remedial actions alone—such as soil compaction and raising the levee crest—without the installation of sealing systems would have virtually no significant impact on the structure safety. After implementing the remedial measures, the levee safety factor can be considered safe, and the numerical analysis of water filtration through the levee indicates that future water seepage on the downstream side during river flooding should not occur.
... Notable advancements in LEM include the method developed by Fellenius, which evaluates rotational failures around circular slip surfaces (Fellenius 1936), and Bishop's modification, which improves the model by considering vertical force equilibrium (Bishop 1955). Janbu further expanded LEM's applicability to a wider range of failure mechanisms and slip surfaces (Janbu 1954). ...
Rock slope stability is a pivotal concern in geotechnical engineering, essential for mitigating risks associated with landslides and slope failures. In recent years, there has been a significant shift towards integrating machine learning (ML) techniques alongside traditional methods for enhanced analysis. Traditional Methods such as the limit equilibrium method, finite element method, and finite difference method have long served as the foundation for slope stability analysis. These methods, while well-established, face challenges in addressing the complexity of heterogeneous geological conditions and dynamic environmental factors. Furthermore, empirical systems like rock mass rating and geological strength index are often limited by subjective parameter selection, reducing their predictive reliability. Machine Learning Approaches have shown great promise in overcoming some of these limitations. ML techniques, such as convolutional neural networks, support vector machines, gradient boosting machine, Bayesian networks, random forests, and hybrid models like particle swarm optimization-artificial neural networks, can analyze large, complex datasets more efficiently. These models have been demonstrated to outperform traditional methods by incorporating real-time data, seismic activity, and environmental variability, thus enabling dynamic and real-time assessments. ML models have been shown to improve predictive accuracy for heterogeneous rock masses, facilitating better-informed decision-making in slope stability management and improving safety outcomes. This review presents a comprehensive comparison of various ML techniques, offering guidance on the selection of the most appropriate models based on specific geological conditions while highlighting their advantages. Additionally, the review highlights limitations of current ML models, reviewing real world applications and their results, which may help readers to suggest future research directions, focusing on advanced data processing methods to unlock their full potential in geotechnical engineering. This includes addressing data quality, generalization across diverse geological terrains, and computational complexity.
... Within the slope stability evaluation, two primary methodologies are widely utilized: the limit equilibrium method (LEM) (Janbu 1955;Bishop 1955;Morgenstern and Price 1965;Spencer 1967;Fellenius 1936) and the strength reduction method (SRM) through finite element analysis. The LEM, a traditional approach, utilizes the method of slices to estimate the stability of a slope. ...
This study investigated the performance of machine learning models in predicting the FS and slip surface. The models considered include support vector machine (SVM), random forest (RF), and extreme gradient boosting (XGBoost) algorithms. The slope stability analysis data for training of machine learning algorithms were obtained through the limit equilibrium method. This includes various scenarios of dry and homogeneous slope cases, encompassing a range of slope geometries (height (H), slope ratio (v/h)), and soil shear strength parameters (soil unit weight (γ), cohesion (c), friction angle (ϕ)). According to the evaluation using Taylor's chart metrics, including standard deviation, correlation determination (R 2), and root-mean-square error (RMSE), the XGBoost algorithm demonstrated the best performance. Additionally, employing the SHapley Additive exPlanations (SHAP) methodology revealed the significance order of variables as v/h > H > c > ϕ > γ for the factor of safety (FS) and H > v/h > c > ϕ > γ for the slip surface.
... For rotational slides, the method of slices [15][16][17][18][19][20][21][22][23][24][25] has long been employed to calculate the safety factor 51 of slopes and is implemented in many commercial and non-commercial software (e.g. [26][27][28]). ...
This paper presents an optimised algorithm implementing the method of slices for slope stability analysis. The algorithm features a novel physically based parameterisation of slip surfaces, defined by their geometric characteristics at the endpoints, capturing all and only valid failure mechanisms. The algorithm also employs a hybrid discrete–continuous search strategy to identify the critical slip surface, beginning with a discrete computation of the factor of safety over a coarse grid spanning the entire parameter space, followed by a focused continuous exploration of the most promising region via a simplex optimisation. This methodology reduces computational time up to 92% compared to conventional fully discrete algorithms that compute the factor of safety over a fine grid spanning the entire search domain. The novel physically based parametrisation and the hybridisation of the search algorithm allow consideration of slip geometries that are necessarily neglected by conventional fully discrete approaches, leading to an accuracy gain of about 5%. Furthermore, compared to recent fully continuous algorithms, which perform an unbroken exploration of the entire search domain, the computational effort is reduced by up to 33 times while preserving accuracy. These efficiency gains are particularly advantageous for numerically demanding applications like the statistical assessment of slopes with uncertain hydro-mechanical and geometrical properties.
... To assess the slope stability under static conditions, different methods have been proposed, for instance, limit equilibrium method (LEM) [5,28,58,79], limit analysis (LA) [11,56], strength reduction finite element analysis (SRFEA) [9,20,52,55,84], finite element limit analysis (FELA) [10,36,52,78] or stress-based approaches [18,21,40,90]. As these studies primarily focused on stability analyses applying simple elastoplastic models, further research has been conducted combining strength reduction schemes with barodesy [74,85] and clay hypoplasticity [30] as well as using a stress-based approach [61] which allows using any constitutive model for the stability analysis. ...
The determination of the factor of safety (FoS) of slopes during seismic excitation can be complex if the relevant effects of pore water pressure accumulation, nonlinear material response and variable shear strength are duly accounted for. A rational two-step approach to tackle this task based on a hydro-mechanically coupled dynamic simulation and finite element limit analyses is henceforth introduced. To ensure accurate transfer of the hydro-mechanical soil state, a mapping concept is presented, accounting for spatial distributions of stresses, excess pore water pressures, inertial forces and shear strength. The proposed approach is compared to limit equilibrium method (LEM) for the case of a large-scale water-saturated open cast mine slope subjected to seismic loading. In comparison with LEM, the new approach to assess seismic slope stability proves to be simpler in its implementation and straightforward, which could be an important asset for practitioners.
... In this research, integrated limit equilibrium methods are utilized (Janbu, 1954;Morgenstern and Price, 1965;Spencer, 1967) . These methods satisfy both moment and force equilibriums. ...
Dam failure can occur due to foundation instability, downstream and upstream slopes instabilities. This study assesses the stability of upstream and downstream slope cuts at Khalid-Dijo irrigation dam project, which is located in Southern Ethiopia, 3 km south of Werabe town. Limit equilibrium and finite element shear strength reduction methods are adopted. Validation of results and comparisons between those methods are carried out. The analysis considers anticipated site conditions, including static dry, static saturated, dynamic dry and dynamic saturated conditions. Slope material properties are measured from insitu, laboratory tests and used as input parameters for the analysis to obtain factor of safety and critical strength reduction factors. The properties considered in the analysis include unit weight, cohesion, angle of internal friction, poison's ratio, dilation angle and Young's modulus. The analysis indicates that the factor of safety values for limit equilibrium methods and the critical strength reduction factor for finite element method are very similar across the three slope cuts under all anticipated conditions. The lowest factor of safety and critical strength reduction factor is 1.56 and 2.07 respectively. Generally, the proposed dam project is safe against upstream and downstream slope failures. These studies suggest that maintained the average safety factor values of both methods during the design stage are crucial to avoid unnecessary risk.
... The programme is widely used by geotechnical engineers and researchers for analysing the stability of soil and rock slopes, designing safe slopes, and evaluating the risk of slope failures at a low computational cost [48][49][50]. The analysis incorporates different LE solutions, such as the simplified Bishop method [26] and simplified Janbu method [51], as well as the Spencer method [27], to compute the FS of critical slip surfaces. ...
Legacy colliery spoil tip failures pose a significant hazard that can result in harm to persons or damage to property and infrastructure. In this research, the 2020 Wattstown tip landslide caused by heavy rainfall was examined to investigate the likely mechanisms and developmental factors contributing to colliery spoil tip failures in Welsh coalfields. To achieve this, an integrated method was proposed through the combination of remote sensing mapping, stability chart analysis, 2D limit equilibrium (LE) modelling, and 3D finite difference method (FDM) analysis. Various water table geometries were incorporated into these models to ascertain the specific groundwater condition that triggered the occurrence of the 2020 landslide. In addition, sensitivity analyses were carried out to assess the influence of the colliery spoil properties (i.e., cohesion, friction angle, and porosity) on the slope stability analysis. The results indicate that the landslide was characterised by a shallow rotational failure mode and spatially constrained by the critical water table and an underlying geological interface. In addition, the results also imply that the landslide was triggered by the rise of water table associated with heavy rainfall. Through sensitivity analysis, it was found that the properties of the colliery spoil played an important role in confining the extent of the landslide and controlling the process of its development. The findings underscore the detrimental effects of increased pore pressures, induced by heavy rainfall, on the stability of colliery tips, highlighting the urgent needs for local government to enhance water management strategies for this region.
... ( (Bishop, 1955;Spencer, 1967;Janbu, 1955Janbu, , 1973dan Morgenstern & Price, 1967, 1965. Metode irisan mengasumsikan bahwa tanah di atas permukaan bidang gelincir dibagi menjadi beberapa baji atau blok, dengan bidang pemisah antar blok selalu vertikal. ...
A landfill is an example of essential geotechnical constructions that support human life in controlling waste processing. The height of landfill in Indonesia has reached tens of meters, as reviewed in this article, which is 60 m. The stability of the slopes of the landfill is a critical matter that needs to be studied to ensure that the landfill remains standing firmly and that landslides do not occur, which can cause huge losses both financially and even to the point of loss of life. One of the slope analysis methods is the Limit Equilibrium Method (LEM) with a two-dimensional (2D) model using a computer program. Stratigraphy and origin soil parameters were obtained from the results of field and laboratory test interpretations and parameter correlations. The landfill parameters will be varied into three types, lower bound with values c'=3 kPa and ϕ' = 210, medium bound with values c'=4 kPa and ϕ' = 250, and upper bound with values c'=6 kPa and ϕ ' = 300. The landfill slope is varied into five models with a ratio of vertical dimensions as 1 and horizontal dimensions as 1, 1.5, 2, 2.5, and 3. The analysis will be carried out in two conditions: static and dynamic. With several limitations and simplifications of the model, such as uniform landfill parameters for a total height of 60 m, this parameter study can still provide insight into the pattern of the slope of the landfill slope that meets the minimum stability criteria both in static and dynamic conditions. The analysis results show that the landfill's safe slope is 1:3.0 (V:H) with a few notes for the type of lower bound landfill parameter.
... The stability of slopes is often evaluated by the factor of safety. Limit equilibrium methods (LEM) like method of slices [1], Bishop's method [2], Janbu's method [3], Morgenstern and Prince's method [4], Spencer's method [5] use different methodologies to arrive at the factor of safety of a slope. However, all of them have the same basic definition of factor of safety as the ratio of shear strength to the shear stress. ...
... In numerical analysis, the foremost method to analyze overburden is based on limit equilibrium approach which consists of Fellenius [83], Janbu [84], Bishop [85], Morgenstern and Price [86], Spencer [87], and Generalized Limit Equilibrium [88] for its slope stability. Additionally, the dumping method and shape of the floor, rainfall, and spontaneous combustion due to minimal amount of coal or minerals when dumped without treatment can be responsible for or accelerate the instability of the slope [89][90][91][92]. ...
The paper reviews the different strengthening techniques to control the displacement of piles of coal overburden wastes. In the present era, the urge for power and minerals is increasing due to rapid growth in industrialization. Thus, extracting minerals buried in the earth require the removal of topsoil or cover if the method involves open-cast mining. This method is only being applicable to minerals that are at shallow depths. Therefore, this method has been active in the industry for the past six decades, which lead to dumping overburden in nearby areas or in-pit. Hence, due to the scarcity of land, the concerned organization is forced to optimize the prior dumping site by increasing height and slope angle. Therefore, strengthening is very important, so it can withstand the additional imposed load generated by coal mine overburden wastes (CMOW). On the other hand, failure of CMOW is a major problem in mining sites, leading to soil erosion, air pollution, and acid mine drainage in those areas. Previously, researchers have proposed various methods of strengthening the CMOW dump using techniques like growing plants on the surface and anchoring the ground due to roots, geosynthetics, lime, cement, and fly ash mixture, etc. Further, the microbial-induced calcite precipitation technique has been established as a natural and beneficial technique in slope stability but has yet to be researched for its applicability in strengthening CMOW dumps in mining areas. Hence, the key motive of this review paper is to bring out various aspects of CMOW, such as status, scenarios, associated challenges, engineering properties, techniques to strengthen, and future action plans to adopt a novel method to overcome issues.
... There are various limiting equilibrium methods for different inter-slice and equilibrium state. In this study, Bishop simplified method [11], that satisfies moment equilibrium and Janbu simplied method [12], that satisfies force equilibrium have been used to calculate FoS. ...
Landslides are one of the major natural hazards occurring in the mountainous areas. Himalayan mountains are tectonically active. Due to presence of highly weathered rock mass, folds and faults, frequent earthquake events, intense seasonal rainfalls, heightened anthropogenic activities such as road widening and construction of infrastructures, the Himalayan region is facing slope instability problems and situations are getting worse. One of the precursors to quantify the risks associated with the existing natural or already cut slopes is to carry out stability assessments prior to the road widening activities. Several methods can be used to assess and analyse the stability of slopes and anticipate probability of any impending landslides. For the present study, two slopes, one rock and the other one debris slope, located in the Garhwal Himalayan region of the Uttarkashi district, have been considered for kinematic analyses, and stability analysis using Limit Equilibrium Method (LEM) and Finite Element Method (FEM) with shear strength reduction (SSR) technique. In kinematic analysis, stereo-net plots of joints data collected for the studied rock slope have been prepared to determine the mode and direction of slope failure. The Mohr-Coulomb (M-C) criterion has been used for stability analysis of debris slope, while the Generalized Hoek-Brown (GHB) criterion has been used for rock slope analysis. The stability assessment has been carried out for dry-static and wet-static conditions. A comparison has been made among the obtained factor of safety values. The stereo-net plot represents formation of a potential wedge failure for the rock slope. The stability analysis revealed that the slope is partially to critically stable when dry, but may become unstable under saturated conditions. Both the slopes are prone to failure during monsoon season. Also, the Factor of Safety (FoS) values obtained from LE analysis are higher than those compared to the values obtained from FE analysis.
... The slope stability is conventionally defined based on the factor of safety using the limit equilibrium method. The limit equilibrium methods were proposed by Janbu (1954), Bishop (1955), and Morgenstern and Price (1965) based on the method of slices. Despite the long-standing experience with limit equilibrium analysis, this method presented several drawbacks, such as the assumption of the shape of the failure plane and the force acting between the slices. ...
... An overall equilibrium condition has been reached in both the examined cases. Such a result has also been confirmed by some 2D limit equilibrium stability analyses, based on the method of slices proposed by Janbu 33 and carried out using the software SLOPE/W of the GeoStudio suite (Bentley Systems, Incorporated), that calculated a resulting safety factor FS ranging from 1.22 to 1.32 (Fig. 11a,b). Assuming nil the vehicle load (q = 0), the previously calculated minimum and maximum values have reached 1.24 and 1.34 respectively: the computed negligible FS increase has consequently highlighted the marginal role of the assigned surcharge. ...
A highway embankment founded on a sloping tectonised marly-sandstone flysch formation located in the Apennines chain (Italy) has been affected for about 30 years by continuous slow movements. Given the strategic importance of the involved infrastructure, different investigation and monitoring campaigns have been carried out to get information about the properties of the involved soils and collect data about the displacements and piezometric regime. Field monitoring, in particular, reveals that the observed displacements result from a failure mechanism involving both the embankment and the foundation soils. However, significant gaps in monitoring jeopardize the possibility to assess the long-term trends in the displacements and piezometric regime and the significance of weather forcing in regulating the phenomena. To address such research questions, a procedure, easily transferable in different contexts, is proposed and applied to the test case: a simple hydrological proxy indeed permits evaluating the rate of movement featured by weatherinduced seasonal variability. Such a mechanical response has been confirmed by the results of a simplified numerical model aimed at finding out the main features of the observed kinematics accounting for a hydrological balance of the involved area.
... The most established models for slope stability evaluation are based on the principle of limit equilibrium (LE) approach and conventional numerical technique based on the theory of elasticity and plasticity (Liao and Liao 2020). The pioneering works on LE methods were done by Fellenius (1936), Bishop (1955), Spencer (1967), Morgenstern and Price (1965), and Janbu (1954). More information on their respective assumed failure mechanism, sliding surface, satisfied equilibrium conditions, and application can be found in Azarafza et al. (2021). ...
Different methods like limit equilibrium and soft computing-based methods are scattered in the literature for the prediction of the factor of safety (FoS) of slopes. However, selecting reliable models among them may be difficult for the users. Therefore in this study, we propose two different hybrid ANN models and perform the reliability analysis of the existing models and the proposed models using the historical datasets. The obtained datasets comprised the geotechnical properties of the soil and the slope geometric parameters. Subsequently, the ANN models were simulated, and the optimum ANN model was selected and then subjected to two stochastic optimization algorithms to improve its performance. Next, the performance of the ordinary and hybrid ANN models was compared using the empirical cumulative frequency distribution (CFD). Thereafter, 19 independent datasets outside those used in developing the models were used to validate the proposed models, the classical slope stability analysis models along with an existing ANN model. The validation was done using both the empirical CFD and mean absolute relative error (MARE). The results in all the validation cases favored hybrid ANNs. Then, the models were further subjected to rigorous statistical analysis by subjecting the models to the normality test, analysis of variance (ANOVA), variance homogeneity test, two-way t test, and nonparametric test. The output of all the tests conducted in this study revealed that the hybrid ANNs are most suitable for the slope stability analysis.
As-compacted soil embankments are partially saturated and, during their lifetime, they experience changes in water content and suction according to interaction with the atmosphere and the groundwater table. However, conventional slope stability assessments often assume either dry or fully saturated conditions, which can lead to inaccurate predictions. This paper presents an analytical framework for the analysis of the stability of unsaturated embankments under different suction profiles. The limit equilibrium analysis is extended to unsaturated slopes by incorporating matric suction, degree of saturation, and rainfall infiltration. A novel design chart is introduced to illustrate the interplay between the hydromechanical parameters of the slope, its geometry, the position of the groundwater table, and the infiltration profile. The outcomes demonstrate the significance of suction and saturation distributions in the sustainable planning and safety evaluation of embankments, offering meaningful perspectives for enhancing design methodologies and prevent failures in unsaturated engineered slopes. A key finding is the identification of the transition infiltration depth, which delineates the shift from deep to shallow slip surfaces. If the wetting front remains above this threshold, the design chart remains applicable. However, if it extends beyond this depth, a more comprehensive stability analysis is required. The method has been successfully used to predict the safety factor of engineered slopes under different suction profiles. Serving also as a benchmark for more advanced stability analyses, the design chart provides engineers with a practical tool for integrating unsaturated soil behaviour into geotechnical design, enhancing risk assessment and failure prevention strategies.
The assessment of slope stability is a complex engineering problem, and the solution requires the selection of a method based on the specific conditions of the studied object. The most common methods have certain shortcomings, therefore the creation of new approaches remains relevant. The stability of buildings and structures in landslide and landslide-prone areas often depends on the stability of the slope itself, therefore, before developing a project for a construction object in such areas, there is a need to determine the slope stability coefficient. The developed and proposed approach based on graph theory can become a convenient tool for solving such problems. In addition, this approach can be easily integrated into computational complexes based on the finite element method, or the assessment can be carried out using a separate software package that uses the results of calculations obtained by the finite element method as input data. The presented work considers the use of such an approach in assessing the stability of a real slope located in the area of Rzhyshchev. The studied site is located on the right bank of the Dnieper River and has long been developed and built up, however, after the completion of three new buildings, landslide processes intensified. On this site, in the period from 2006 to 2014, instrumental studies of the movement of soil masses were carried out using established benchmarks. The study data provide a reliable basis for comparing the calculations of slope stability and predicting its behaviour with the real situation that took place on this slope. The calculation of the stress-strain state of the slope for this problem was carried out using the SATER.SOIL software package, after which the slope stability was assessed using the developed application program using an approach based on graph theory – SATER.LANDSLIDE. Based on the calculations, several potential sliding surfaces were identified, according to which the corresponding stability coefficients were determined. Three different settings were considered, starting from an undeveloped slope and ending with a built-up slope, taking into account technogenic factors of influence. The results obtained are consistent not only with another method for assessing slope stability but also with instrumental studies of this slope over a long period of time.
This report addresses various issues related to slope disaster prevention in Japan in terms of analysis and design techniques. First, mechanical problems in analysis and design technology in practice were explained, and then, as peer－reviewed issues related to analysis and design technology in the field of slope disaster prevention, papers published in academic journals up to around 2000 and recent changes were described. In addition, the author typified and explained the errors in mathematical formulas in academic journals, which have been frequently observed even in recent years. In this connection, the importance of observing the laws of physics in academic fields is described. The applied research on analysis and design techniques is mainly focused on the field of performance－based design. The issues of research on performance－based design in the field of slope disaster prevention are explained in comparison with the field of port and harbor engineering and the field of geotechnical engineering. Next, examples of overseas applied research on slope protection are introduced, and the direction of applied research in the Japan Landslide Society is discussed.
As a primary raw material for rare earth production, monazite is often associated with radioactive isotopes such as lanthanum and cerium. In order to further reduce the possibility of diffusion and enhance the stability of tailings dams, this study attempts to solidify the flowable monazite waste into solid or semisolid states by adding different types and proportions of solidifying materials. The strength characteristics of the modified soil were studied through strength tests, and the results showed that blast furnace slag exhibited the best solidification effect. Discrete element method was employed to conduct numerical calculations on the stability of tailings dams, analyzing the stability of tailings dams under different solidification schemes and slope ratios. It was found that increasing the slope ratio would lead to a decrease in the stability of tailings dams. Macroscopic and microscopic deformation characteristics of the tailings dam were analyzed: the distribution patterns of dam body velocity and displacement were generally consistent, and the simulated principal stresses were slightly larger but distributed similarly to finite element results. Microstructure analysis revealed a significant increase in contact force after solidification compared to before. This study demonstrates that employing solidification measures for monazite waste tailings dams can enhance stability, reduce environmental pollution, save cement consumption and is crucial for establishing a green ecological production system.
This study presents a novel prediction model based on the three-wedge method, utilizing a force-based equilibrium model to evaluate the stability of embankments reinforced by stone columns and geosynthetics. The proposed model utilizes six slip surfaces, enabling it to accommodate diverse geometric configurations, shear strength parameters, reinforcement arrangements (i.e., stone columns and geosynthetic), surcharge, water level, and quasistatic seismic coefficients. A constant factor of safety is initially assumed for each slip surface and reinforcement element, although this assumption can be relaxed by varying the strength parameters. The factor of safety is determined analytically through the solution of a polynomial equation. The proposed analytical solutions, which offer a compact form, provide new insights for the three-wedge method and effectively customize the conditions for geosynthetic-reinforced column-supported embankment applications, characterized by wedge interaction between the embankment, clay, geosynthetics, and columns. Validations of the proposed method are performed using the results obtained from the centrifuge test and numerical modelling, demonstrating the reliability of the analytical solution.
The A2 highway connects the west of the country to its eastern part. The section between Fez and Taza passes through the South Rifain Corridor mainly characterized by marl formations of the Miocene. The mechanical behavior of these marls leads to regular land instability phenomena which represent a high risk for linear features such as roads and the A2 highway. The impact of these land instabilities is more accentuated in the case of embankments such as kilometer point 232.900, which is the subject of this study. This point represents a serious issue despite the different reinforcement measures. In order to better understand the subsoil deformation at this point, a geotechnical campaign concerning the recognition of the subsoil and the installation of inclinometer instruments was carried out. The ground movement monitoring showed some slight movements acting deep downstream of the embankment. The two-dimensional modeling of the stability status of this embankment by GEO-STUDIO geotechnical software allowed us to simulate the events and disorders that could affect the structure. In order to understand the factors causing these ground movements, we evaluated the stability of the embankment in its static and pseudo static state and also during rainy and dry periods of the year. The obtained results show a decrease in the resistance of the soil to sliding during the rainy season, or even a possible triggering in the case of the occurrence of an earthquake, while the adoption of the recommended reinforcement structures has shown a good maintenance of the structure in this kilometer point even in the worse conditions. These structures have been adopted as comfort solutions by the highway manager.
The Ankpa Coal Mine plays a crucial role in meeting the energy demands of Dangote cement plants in Nigeria. However, mining activities at the site pose significant risks to slope stability, potentially impacting the sustainability and safety of mining operations. To ensure responsible and sustainable mining practices, this study conducted a probabilistic slope stability assessment of the mine. Samples of laterite, shale, and coal were collected from three distinct locations (A, B, and C) within the mine, and their physical and strength parameters were determined through laboratory tests. The slope's probabilistic assessment using the factor of safety (FOS) was implemented into numerical modelling utilizing the Point Estimate Method (PEM). The slope random shear strength parameters were used as inputs for the finite-element numerical simulations to determine the corresponding FOS for each location. This study also investigates the influence of slope angle on the probability of slope failure, providing valuable insights into potential instability triggers. The results indicated that location C exhibited higher susceptibility to slope instability compared to the other locations. Consequently, appropriate slope angle recommendations were proposed for each location to mitigate the risk of slope failure effectively.
Rainfall-induced shallow slope instability is a significant global hazard, often triggered by water infiltration that affects soil stability and involves dynamic changes in the hydraulic behavior of unsaturated soils. This study employs a hydro-mechanical coupled analysis model to assess the impact of rainfall on slope stability, focusing on the dynamic hydraulic behavior of unsaturated soils. By simulating the soil water content and slope stability under four different rainfall scenarios based on observational data and historical thresholds, this study reveals that higher rainfall intensity significantly increases the soil water content, leading to reduced slope stability. The results show a strong correlation between the soil water content and slope stability, with a 20 mm/h rainfall intensity threshold emerging as a reliable predictor of potential slope instability. This study contributes to a deeper understanding of slope stability dynamics and emphasizes the importance of proactive risk management in response to changing rainfall patterns while also validating current management practices and providing essential insight for improving early warning systems to effectively mitigate landslide risk.
Stronger soil layer within a layered slope is of no concern as the stronger soil layer provides extra stability. But if the relatively stronger soil layer has less permeability, it will cause hindrance to the natural infiltration processes and makes the slope vulnerable. This paper presents the results of a series of laboratory tests and numerical analyses on 45º inclined homogeneous and non-homogeneous unsaturated sandy slopes subjected to continuous rainfall. The non-homogeneous slopes consist of less permeable but stronger silty-sand (NH) layers located at different locations of an otherwise homogeneous sandy soil slope. It is observed that the inclusions of NH layers within the homogeneous sandy slopes trigger a failure during continuous rainfall. The NH layers prevent the seepage of the infiltrated rainwater through the slope. As a result, the water content increases rapidly just above the NH layers and consequently the suction pressures in the soil and its shear strength just above the NH layers decrease. With the rainfall duration, the positive pore water pressures buildup just above the NH layers. This induces a slope failure with the failure plane passing above the NH layer. A discontinuity of the shear plane is also observed in the case of a multiple NH layered soil slope.
Rainfall-triggered landslides are most deadly in developing countries, and future urban sprawl and climate change could intensify existing risks. In these regions, enhancing efforts in urban landslide risk mitigation and climate change adaptation is crucial. Current landslide probability assessment methodologies struggle to support effective mitigation because they fail to represent local anthropogenic factors (e.g. informal housing) across space and time scales. To meet this challenge, we demonstrated in previous work that hillslope-scale mechanistic models representing such localised changes can be used to create synthetic libraries of urban landslides that account for both data and future scenario uncertainty. Here, we show how these libraries can become an explorative tool for researchers and stakeholders, allowing them to investigate slope stability variations across spatial scales and landscapes. Results highlight, for example, how the main slope instability drivers change according to the location (e.g., upper vs lower catchment), the landcover (e.g. forest vs urban) and the spatial scale analysed (e.g. at hillslope scale slope stability was mostly controlled by water table height, whereas at regional scale by slope geometry). Ultimately, we demonstrate that stochastic analyses can lead to a greater understanding of the system interactions and they can support the identification of mitigation strategies that perform well across spatial scales and uncertain scenarios. These strategies should be prioritised even if future conditions are unknown. This reasoning is shown on a data-scarce region with expanding informal housing. However, the same methodology can be applied to any urban context and with any mechanistic-based model.
This chapter addresses the role of engineering geology in the assessment of slope stability and stabilization. First, phenomena and mechanisms of mass movements are introduced. Specifically, the mechanisms of sliding, toppling, buckling, shearing, falling, flowing and creeping are discussed.
Since matrix energy (ME) implies the expressive merit of collective information, a classification method based on ME has not been investigated in the existing literature, which reflects its research gap in a matrix scenario. Therefore, the purpose of this paper is to propose a slope stability classification model based on the single-valued neutrosophic matrix (SVNM) energy to solve the current research gap in slope stability classification analysis with uncertain and inconsistent information. In this study, we first present SVNM and define the SVNM energy based on true, uncertain, and false MEs. Then, using a neutrosophication technique based on true, false, and uncertain Gaussian membership functions, the multiple sampling data of the stability affecting factors for each slope are transformed into SVNM. Next, a slope stability classification model based on the SVNM energy and score function is developed to solve the slope stability classification analysis under the full SVNM scenario of both the affecting factor weights and the affecting factors of slope stability. Finally, the developed classification model is applied to the classification analysis of 50 slope samples collected from different areas of Zhejiang province in China as a case study to verify its rationality and accuracy under the SVNM scenario. The accuracy of the classification results for the 50 slope samples is 100%.
Despite the widespread application of data-centric techniques in Geotechnical Engineering, there is a rising
need for building trust in the artificial intelligence (AI)-driven safety assessment of road embankments due to its
so-called ‘‘black-box’’ nature. In addition, from the lens of limit equilibrium approaches, e.g., Bishop, Fellenius,
Janbu and Morgenstern–Price, and finite element method, it is essential to carefully examine the interplay of
both topological and physical/mechanical properties during the safety factor (FoS) predictions. First, aside
from having conventional geotechnical inputs for soil in core and foundation and the height of embankments,
this paper codifies geometric features innovatively. The number of slope types with different ratios including
1:1, 1.5:1 and 2:1 as well as the number of berms is introduced. Second, a pool of 19 machine learning (ML)
techniques is effortlessly trained on the dataset using an automated ML (AutoML) pipeline to identify the most
optimized ML algorithm. Finally, to achieve post-hoc interpretability for the internal mechanism of the input–
output relationship unbiasedly, a game-theory-based explainable AI (XAI) method called Shapley additive
explanations (SHAP) values is applied. SHAP-aided importance analysis provides human-interpretable insights
and indicates height, California bearing ratio, slope type 2:1 and cohesion as the most influential parameters.
Exclusively, analyzing hazardous embankments by classifying main and joint contributors exhibits a complex
and highly variable influence on the FoS. This paper harnesses the power of XAI tools to enhance reliability
and transparency for the rapid FoS prediction of slopes. It targets geotechnical researchers, practitioners,
decision-makers, and the general public for the first time.
Knowledge of the critical slip surface is essential for slope stability analysis and design of remedial works. The classical analysis for assessing slope stability uses limit equilibrium methods, which impose the shape of the critical slip surface as a circle. In practice, it can be observed that the shape of the critical slip surface is not circular. In this study, a methodology was proposed and used to determine the position and shape of the critical slip surface using the results of the finite element method. Four types of regression curves were analysed and compared (circle, damped sinusoid, second-degree parabola and logarithmic spiral) via nonlinear optimization using the least-square method. In addition, these results were compared with those obtained using the limit equilibrium methods (Fellenius, Bishop, Janbu, Morgenstern–Price and Spencer).
Failure of slopes, both natural and man-made, include slope instability as well as failures and in the seismic active zones, these slopes can become a real danger to the mankind. The failure consequences can range from the direct cost of failed rock mass to possibly indirect cost which includes the damage to vehicles and livelihood injury on the highways. The slope stability is dependent on various factors such as structural geological characteristics of the region, the local sub-soil conditions of the location, the groundwater conditions, structural loads, surcharge, the discontinuities, active faults in the region and most importantly the seismic zone of the region. These parameters have a critical role in governing the stability of the slope. From the type of soils such as clayey soil to cohesionless soil such as sandy soils to some of the stable rock mass. This paper deals with the parametric study of these cases which involves the assessment of slope stability through Strength Reduction Factor (SRF) analysis for different soil types with different slopes angles and in different seismic zones. The overall stability of the slopes in terms of the Factor of Safety (FoS), displacements as well as shear strain has been discussed and sheds light on the instrumentation of these slopes so that in case of the movements, the corrective measures can be taken at the initial stage so that it doesn’t evolve to become fatal and endanger several lives.
This paper introduces a novel closed‐form equation (surrogate model) for approximating the Morgenstern–Price estimate of the factor of safety of homogeneous dry finite slopes with circular failure surfaces. Unlike typically used methods, the proposed equation does not require the definition of a critical failure surface, splitting the soil mass into slices, or the iterative reduction of soil resistance to the limit state. It can be easily programmed into calculators or computers and accurately determines the minimum factor of safety based on the shear strength parameters and slope geometry—meaning that it is ideally suited for integration into reliability calculations. The equation is determined parametrically for various soil parameters and slope geometry using the Morgenstern–Price method and compares favorably with conventional techniques, such as slope stability charts, limit equilibrium, and strength reduction methods (SRM). From a practical perspective, the proposed equation greatly simplifies the analysis of the slope stability as the creation of a numerical model is not required and is suited to use in the feasibility stage of a project, for example, for large linear infrastructure projects with differing slope geometries or in situations where a quick assessment is desired.
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