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The Use of the Slip Circle in the Stability Analysis of Slopes
Geotechnique
... Numerical modeling and field assessments provide a complementary, processbased understanding of riverbank instability. Hydrodynamic models, combined with bank erosion algorithms, simulate flow events and resultant bank retreat [10,11]. Field investigations-including erosion pin studies, bank profiling, and geotechnical testingfurther validate these numerical models [12,13]. ...
... The riverbank safety coefficient (Kat) was calculated using the following formula [10]: ...
... Determination of riverbank safety coefficient (K at ). The riverbank safety coefficient (K at ) was calculated using the following formula [10]: ...
This study assessed riverbank erosion and stability along the Mekong and Bassac Rivers to propose safe river corridors and mitigate erosion risks in the Mekong Delta. Using Landsat imagery (2000–2023), field surveys, and numerical simulations, we identified severe erosion hotspots, where erosion rates reach up to 40 m annually, in the meandering sections of the Mekong River,. In contrast, the Bassac River exhibited significant sedimentation, though this trend was diminishing due to upstream sediment deficits caused by hydropower dams. Stability assessments revealed optimal safety corridor distances ranging from 20 to 38 m, influenced by local geotechnical conditions and structural loads. A significant proportion of riverbanks in Dong Thap (88%) and An Giang (48%) do not comply with conservation standards, exacerbating erosion risks and threatening infrastructure. The results of this study highlight the urgent need for enforcing conservation regulations, implementing nature-based solutions like riparian buffers, and adopting sustainable land-use planning. By addressing the interplay between natural processes and anthropogenic pressures, these findings offer actionable insights to enhance riverbank stability, protect ecosystems, and sustain livelihoods in the Mekong Delta amidst growing environmental challenges.
... Slope stability is a classical problem in geotechnical engineering design. In addition to the conventional analytical methods to assess its stability with relatively uniform soils, such as slip circle, the methods of slices, and FEM methods [1][2][3][4][5], model tests have been used broadly to explore the slope stability with relatively complex soils (i.e., layered soils) [6][7][8][9]. Due to the large geometrical dimensions of slopes in the prototype, reduced-scale model tests, such as centrifuge tests and small-scale model (i.e., 1 g) tests, are commonly used to explore the failure mechanisms of slopes and evaluate slope stability in the laboratory by researchers [10][11][12][13][14][15][16]. ...
... Here, F SSR represents the strength reduction factor associated with the shear strength parameters. In prior research on slope stability [2,36], the factor of safety F s is traditionally defined as the ratio of the actual shear strength of the soil (i.e., c and φ) to the minimum shear strength needed to prevent failure (i.e., c f SSR and φ f SSR ). This is, ...
... Among the various methods used for slope stability analysis, the sliding arc approach by Bishop (1955) [2] is chosen for its simplicity and effectiveness. Figure 12a illustrates the sliding arc, with its center denoted by O s and its radius represented by R s , within a local coordinate system that is defined with the slope toe as the origin. ...
Small-scale model tests have been used widely to examine the behavior of slopes. When all similarity principles are conformed, the test results can be translated to the behaviors of slopes in the prototype. However, when the similarity principles cannot be fully conformed, the model test results need to be interpreted. The interpretation of the slopes stability behaviors from the small-scale model test under non-conformity conditions to that of the prototype is investigated, considering various slope scales and soil properties, undertaken through the finite element (FE) method conducted by the ABAQUS package. Prior to conducting the finite element (FE) parametric study, the numerical results were verified by comparing them with data from previous studies, with good agreement obtained. According to the findings from the parametric study, a framework was developed to allow the 1 g model-scale test results to be translated to the parameters used for the prototype slope design. The study examined both the sliding surfaces and the safety factors of slopes to establish a connection between model tests and their full-scale counterparts. This framework provides a means to effectively utilize 1 g of small-scale test data for designing and analyzing prototype slopes.
... This method generally involves two main tasks: calculating the safety factor and identifying the critical slip surface. For simple slope structures, the slip surface is often assumed to be circular, with calculations performed using the Fellenius method 19 or the simplified Bishop method 20 . The LEM is frequently combined with global optimization algorithms to identify the critical slip surface 21 . ...
... Equations (17) to (20) incorporate the anisotropic strength characteristics into the limit equilibrium analysis through the introduction of the AIF χ. Consequently, we obtain the simplified form of Eq. (18) as: ...
In slope stability analysis, identifying the critical slip surface has always been a complex challenge. This study proposes a method to determine the critical slip surface of heterogeneous slopes while accounting for anisotropy. This method is grounded in a generalized soil anisotropic constitutive model and establishes a global equilibrium framework. It integrates global optimization techniques and employs the well-established Morgenstern-Price method to formulate the optimization objective function. The reliability, applicability, and stability of the method are demonstrated through comparative analysis with the results of two classical slope cases and the improved log-spiral limit equilibrium method. Additionally, the study investigates the impact of anisotropy-related parameters on the stability of heterogeneous slopes, providing new insights into how anisotropy influences slope stability and failure mechanisms.
... To protect people and property, it is necessary to analyze the stability of excavation slopes, embankments, dams, and road embankments. Slope stability is largely evaluated in light of the limit equilibrium method (LEM) (Bishop, 1955;Janbu, 1973;Morgenstern & Price, 1965). In reality, during the construction of structures, more complex stress histories occur than during laboratory tests determining material strength, for example, loading at a constant strain rate followed by stress relaxation or creep, and then subsequent loading at a constant strain rate. ...
... where: W -weight of the specimen (kN); b -width of the specimen (m); a -angle of inclination of the base of the specimen; u -water pressure in the pores (kN/m 2 ); and φ' c' -effective strength parameters of the soil (specifically, internal friction angle and cohesion) (Bishop, 1955). ...
Due to their effectiveness, environmental friendliness, and economic benefits, geosynthetics are increasingly utilized in civil engineering, especially woven geotextiles for soil stabilization reinforcement. Standard strength testing assumes a constant rate of elongation for samples, but in practice, the loading rate of geosynthetics in the field is much lower. Selecting appropriate materials is crucial for the effectiveness and durability of structures. For polymeric materials like woven geotextiles, the strain rate affects their properties. Understanding these properties is essential for safe design and construction. This article explores the potential application of polypropylene geotextiles for soil reinforcement in embankments. The polymer properties are discussed, along with the methodology for strength testing of geosynthetics and the results of the research. The findings allowed for the calculation of the long-term strength of samples at different elongation rates, which was used to verify changes in the factor of safety for a slope model. The highest tensile strength was 33.44 kN/m at a stretching speed of 20 mm/min. At 2 mm/min, it was 30.35 kN/m, and at 0.2 mm/min, it was 28.70 kN/m. These results determined the factor of safety: F = 2.08 for the fastest stretched sample and F = 1.97 for the slowest. Theoretical approaches to understanding changes in strength parameters due to variations in strain rate have been presented, as well as computational approaches using the Bishop method in GEO5 software, based on the results from tensile strength tests.
... For nearly a century, several methods have been developed for analyzing slope stability. Among the oldest, those of the limit equilibrium methods Bishop [1]; Lowe and Karafiath [2]; Morgenstern and Price [3]; Spencer [4]; Janbu [5]; Sarma [6]. It is important to note that these methods are based on simplifying assumptions and should be used with caution. ...
... The results of the variation in the safety factor as a function of the slope inclination obtained with SDIM were compared with those from the simplified Bishop method [1] and the Spencer method [4] included in SLIDE 6.0 and are presented in the Table 1. ...
Given the well-known shortcomings of the traditional limit equilibrium methods (LEMs) in addressing slope stability issues, there has been a growing interest towards employing finite element analysis as a viable alternative in recent years. However, due to the inherent limitations in the conventional finite element analysis, the application of finite element method (FEM) as a strength reduction method (SRM) or as finite element limit analysis (FELA) does not consistently yield successful results. To improve the efficiency of finite element analysis for addressing slope stability problems, a new methodology called 'Stress Deviator Increasing Method' (SDIM) has been recently proposed. It involves gradual expansion of the mobilized stress Mohr's circles until the soil failure takes place according to a predefined non-convergence criterion. In this paper an attempt is made to analyze the effects of surcharge loading on both factor of safety (FOS) value and location of the slip line using the finite element by SDIM by carrying out a restricted parametric study. Specifically, the effects of surcharge loading magnitude, the proximity of the surcharge with respect to the slope edge and the load distribution span were thoroughly analyzed and documented in the light of FOS values and plastic strain regions. The paper ends by proposing design stability charts in which, for a given surcharge magnitude and a geometric configuration, the user is able to determine the FOS for a combination of soil strength parameters.
... El método de Bishop Simplificado (1955) asume una superficie de falla circular y considera las fuerzas normales y de corte en cada rebanada (Bishop, 1955). Expresando el FS como: ...
... Estos hallazgos concuerdan con estudios previos que destacan que factores como cohesión, peso específico y ángulo de fricción interna son determinantes para la estabilidad estructural (Budhu, 2011). La relación identificada resalta la importancia de monitorear continuamente los parámetros geotécnicos del depósito, tal como lo señalan Fellenius (1936) y Bishop (1955), quienes enfatizan que la identificación temprana de puntos críticos permite tomar medidas correctivas antes de que se presenten fallos estructurales. ...
La investigación; tuvo como objetivo analizar los diversos escenarios que afectan la estabilidad física del depósito de relave de la planta de Huari y su influencia en la seguridad a largo plazo; empleando una investigación, de tipo aplicada y nivel explicativo, y el método científico con enfoque deductivo y diseño correlacional. La muestra fue censal, abarcando 240 reportes generados entre marzo y junio de la operación del depósito. Como instrumento se empleó el análisis de documentos, cuya confiabilidad fue evaluada mediante el Alfa de Cronbach, garantizando precisión en la correlación entre los escenarios del depósito y los factores de seguridad. Los resultados demostraron que, bajo condiciones estáticas, los factores de seguridad calculados mediante los métodos de Bishop Simplified (FS = 1.730260), Janbu Simplified (FS = 1.607460) y Spencer (FS = 1.722750) superan el estándar normativo peruano de FS ≥ 1.5, lo que evidencia un comportamiento estable. Sin embargo, en escenarios pseudo-estáticos con una carga sísmica de 0.25 gal, los factores de seguridad obtenidos (Bishop Simplified = 1.036950, Janbu Simplified = 0.951900, Spencer = 1.035210) no alcanzan el mínimo normativo de FS ≥ 1.2, indicando vulnerabilidad frente a condiciones dinámicas. El coeficiente de correlación (ρ=0.95\rho = 0.95ρ=0.95) entre los escenarios y los factores de seguridad resalta la relación directa entre los parámetros geotécnicos (peso específico, cohesión, ángulo de fricción) y la estabilidad estructural del depósito, subrayando la necesidad de monitoreo continuo y medidas de refuerzo para garantizar la seguridad a largo plazo. Palabras clave Estabilidad física; Parámetros Geotécnicos; Depósito de relave; Coeficiente sísmico; Factor de seguridad estático (Fse); Factor de seguridad pseudo-estático (Fsp).
... Also indicated was the force related to partial submergence of the slope. Bishop [3] derived three main equations; namely, i.) a moment equilibrium equation for the overall mass with respect to the center of rotation, ii.) a force equilibrium equation for the overall mass in the horizontal direction, and iii.) a vertical force equilibrium equation for each slice comprising the sliding mass. While the equations associated with complete equilibrium of the sliding mass were derived, it was not possible to simultaneously satisfy both the horizontal equilibrium and moment equilibrium equations using longhand calculations. ...
... Bishop's Simplified method of slices[3]. ...
... LEM is widely used to evaluate the Factor of Safety (FOS) by analyzing force and moment equilibrium along potential slip surfaces. It is particularly effective for simple slope configurations and has been foundational in slope stability analysis (Fellenius 1936), (Bishop 1955), (Kar et al. 2025). 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). ...
... It is particularly effective for simple slope configurations and has been foundational in slope stability analysis (Fellenius 1936), (Bishop 1955), (Kar et al. 2025). 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.
... The limit equilibrium method (LEM) has been proposed in various studies in the literature for slope stability analysis (Hovland 1977;Ugai 1985;Hungr et al. 1989). Two-dimensional Bishop's method presents a formulation for evaluating the 3D factor of safety (FOS) (Bishop 1955;Hungr 1987). Hungr (1987) proposed a 3D method derived from Fredlund and Krahn (1977) general limit equilibrium methodology. ...
... The simplest possible threedimensional geometry is that of a spherical potential failure mass, which is not limited by any internal structures or discontinuities, so a spherical failure surface is considered in this analysis. The method employs a 3D extension of the 2D simplified limit-equilibrium analysis proposed by Bishop for rotational failure (Bishop 1955). This analysis is executed via the Scoops3D computer code (Reid et al. 2015). ...
This study investigates the stability of three-dimensional (3D) earth slopes with complex topographies via machine learning models, specifically deep neural networks (DNNs), convolutional neural networks (CNNs), and recurrent neural networks (RNNs). A dataset comprising 500 samples was generated using the Scoops3D computer program, incorporating cohesion (c), internal angle of friction (ϕ), unit weight of soil (), and pseudostatic horizontal loading () as input parameters and the factor of safety (FOS) as the output parameter. The analysis is based on the case history of the 1980 Mount St. Helens slope failure in Washington, USA. The critical surface failure is determined using the box search method, and the limit equilibrium method (Bishop's simplified method) is used to determine the factor of safety. The results of the sensitivity analysis performed on the dataset for the performing model indicate that the parameters c, ϕ, and have similar significances and that the effect has a relatively less significant parameter in estimating the FOS for the particular dataset. The novelty of this study lies in developing and applying advanced neural network models (DNNs, RNNs, CNNs) trained on 3D slope stability assessments for the first time at Mount St. Helens, which consider both seismic and nonseismic conditions. The predictive performance of the proposed models was analyzed via various performance indices, rank analysis, and an error matrix. An analysis of the obtained results reveals that the DNN model (R2 = 0.999 in training and R2 = 0.997 in testing) yields more accurate results than the CNN and RNN models do in predicting the safety factor of the 3D earth slope.
... The software analyses the stability of numerous potential landslide surfaces by using a three-dimensional (x, y, z) approach within a predetermined range of areas or volumes. The program assesses the stability of each potential sliding area by analysing spherical rotational sliding surfaces involving numerous DEM cells using two possible methods: the simplified Bishop method (Bishop 1955) and the ordinary Fellenius method (Fellenius 1936). Thus, each DEM cell is involved in numerous analyses that define multiple failure surfaces. ...
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.
... The stability of artificial slopes under unsaturated soil conditions was analysed using the method of the slices, following Bishop's approach [38] and assuming a circular slip surface. Over the years, the Bishop method has gained popularity due to its simplicity, the clear physical meaning of the parameters, and the good agreement with the experimental data [39]. ...
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.
... 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.
... The results of the back analysis have been controlled with the help of experimental methods, which are largely consistent with each other. In this research, the cross-section of the landslide using the Fellenius (Fellenius, 1936), simplified Bishop (Bishop, 1955), simplified-modified Janbu (Janbu, 1968), Morgenstern-Price (1965) and Spencer (Spencer, 1967) methods was stability analyzed and the results were analyzed. In the analysis, in addition to static analysis, a series of pseudo-static analyses have also been performed in different groundwater conditions and internal friction angle changes. ...
In this study, the stability of the Gougerd landslide of Khoy was investigated
with respect to changes in the soil internal friction angle. Statistical analysis of
the results of changes in the FS of different methods in analyzing the stability of
the Gougerd landslide in 282 analyses showed that: 1) In static conditions,
under the influence of groundwater conditions, the results of the stability
analysis of various methods showed up to 35.2% changes in the FS, and the
largest differences in the FS values were obtained in the conventional Fellenius,
Spencer, and Morgenstern-Price methods. 2) In static conditions, the FS of
various methods showed changes of up to 35% with respect to the effect of the
internal friction angle, and the largest difference in the FS values compared to
other methods was obtained in the conventional Fellenius method and the
Spencer method. 3) In pseudo-static conditions and in the dry state, up to 5%
changes in the FS were obtained in different analysis methods, and under the
influence of groundwater conditions, the changes in the FS were up to 39.9%.
The largest changes in the FS of the dry state were obtained in the simplified
Janbu method, Spencer and Morgenstern-Price methods, and under the
influence of groundwater, the largest changes in the FS were obtained in the
conventional Fellenius method and Spencer method. In examining the results of
this research, the effect of different conditions of groundwater level, soil
internal friction angle, and earthquake force on the analytical mechanism of the
relationships existing in various methods is recognized as the main cause of the
difference in the results of different stability analysis methods
... A análise de estabilidade foi realizada utilizando o método de Bishop (1955), que considera uma superfície de ruptura circular e divide a massa deslizante em fatias para calcular o fator de segurança (F.S). Este método é amplamente reconhecido na engenharia geotécnica pela sua precisão. ...
Os escorregamentos de taludes em rodovias geram problemas de paralização do fluxo de veículos e riscos de desastres. Para que um empreendimento rodoviário funcione com a devida segurança é necessário um mapeamento geotécnico como princípio para estabelecimento de medidas preventivas. Este estudo tem como objetivo analisar a estabilidade do talude no km 06 da rodovia SC-446. Utilizou-se o software GEO5 2020® para realizar a modelagem matemática e análise de estabilidade do talude. Os cálculos foram baseados na teoria de Mohr-Coulomb, que permite determinar os parâmetros de resistência ao cisalhamento dos solos. A análise de estabilidade foi realizada utilizando o método de Bishop (1955). A análise de estabilidade do talude rodoviário no km 06 da SC-446 revelou que o talude apresenta uma situação de instabilidade tanto em condições secas quanto em condições parcialmente saturadas. Os fatores de segurança calculados, 1,06 para o estado seco e 1,02 para o estado parcialmente saturado, estão significativamente abaixo do valor mínimo recomendado pela norma NBR 11.682:2009, que é de 1,5. Esta situação indica a necessidade de intervenções urgentes para garantir a segurança dos usuários da rodovia. A técnica de solo grampeado com paramento em concreto projetado mostrou-se uma solução viável para aumentar o fator de segurança do talude, sendo recomendada a implementação desta técnica com uma malha regular de grampos com espaçamento de 1,45 metros, comprimento variando de 7 a 11 metros e diâmetro de 32 m.
... technicality. So, to get rid of the technical jargon, the deterministic slope stability analysis, based on the limit equilibrium methods (Bishop 1955;Fellenius 1936;Janbu 1955;Morgenstern and Price 1965;Spencer 1967) or Finite element analysis (Hammah et al. 2009;Luo et al. 2016;Dyson and Griffiths 2024) is generally used in practice because of its simplicity. Among all the limit equilibrium methods, the Morgenstern-Price (M&P) method is the most advanced one, considering both force and moment equilibrium (Duncan and Wright 1980). ...
Probabilistic slope stability analysis has proven effective in assessing the impact of uncertainty and variability in soil properties. In this paper, the probability density functions (PDFs) of the factor of safety (FOS) were determined for five limit equilibrium methods (namely Fellenius, Janbu simplified, Bishop simplified, Spencer and Morgenstern-Price), and the finite element method (FEM) using Monte Carlo simulation for single random variable conditions of the embankment. The random variables used for the limit equilibrium analysis are cohesion (c), friction angle (φ), and unit weight (γ). In contrast, Young’s modulus (E) is used instead of unit weight in finite element analysis (FEA). All the random variable parameters have been modelled as normal distributions except unit weight. Unit weight has been modelled as log-normal distribution. Further probabilistic analysis of embankment for the spatially varied condition has been performed under different pseudo-static loading using the random limit equilibrium method (RLEM) with the M&P approach, and the random field having the least factor of safety for each pseudo-static loading has been validated using the random finite element method (RFEM). A further effect of cross-correlation between c and φ and correlation length (θh and θv) has also been studied using the Morgenstern-Price approach. A series of seismic time-history analyses have been performed on an embankment containing single random variable and spatially variable soil properties. Results are compared in terms of the mean value of PGA (m/s²) and standard deviation at different locations. The results revealed that stability analysis assuming single random variable conditions always has a high level of uncertainty in terms of FOS and critical seismic coefficient (Ky) as compared to spatially variable conditions. The deviation in PGA values with the change in random field sample is higher under spatially variable conditions as compared to single random variable soil conditions.
... It was initially used in the assessment of the equilibrium between the forces and moments around potential failure surfaces, thus providing slope stability analysis through its simple frameworks. Forerunners, including Terzaghi's theory of effective stress, and Bishop's method of circular failure surface were among the earliest developments that marked greater use of LEM in geotechnical engineering (Terzaghi 1943), (Bishop 1955). Janbu later extended these methods to noncircular failure surfaces, broadening the concept of noncircular surfaces and expanding the influence of LEM to more complex forms (Janbu 1973). ...
Slope stability analysis is a critical aspect of geotechnical engineering with significant implications for infrastructure safety and disaster mitigation. This study presents a framework that integrates the limit equilibrium method (LEM) with machine learning (ML) techniques to enhance the accuracy, computational efficiency, and adaptability of slope stability assessments. The methodology begins with a comprehensive dataset of geotechnical and geometrical parameters that undergo rigorous pre-processing to ensure robustness and reliability. Sensitivity analysis was performed to quantify the influence of the key parameters on the safety factor (FSlope). This study evaluates various ML models, including bagging methods such as Random Forest (RF) and Extra Trees (XT), and boosting algorithms such as Adaptive Boosting (AdaBoost), Gradient Boosting (GBoost), CatBoost (Categorical Boosting), and XGBoost (eXtreme Gradient Boosting). GBoost emerged as the top-performing model, achieving an exceptional R² of 0.998, weighted mean absolute percentage error of 0.011, and root mean square error of 0.018. Surrogate modeling is employed to further enhance the computational efficiency while maintaining the predictive accuracy. The developed framework was validated through real-world case studies, thereby demonstrating its practical applicability across diverse geotechnical scenarios. By combining the theoretical rigor of LEM with the adaptability of ML and surrogate models, this study provides a transformative approach for slope stability analysis, offering a balance between computational efficiency and predictive reliability. The results highlight the potential of this hybrid framework to revolutionize geotechnical engineering practices, enabling safer and more efficient slope stability assessments in critical infrastructure projects and landslide-prone areas.
... 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.
... The relationship between slope and landslide occurrence is consistent with previous studies that indicate steeper areas are more prone to landslides due to gravitational forces, reduced vegetation cover, and erosion susceptibility s. This is because steeper slopes have a greater component of downward force that can overcome the resisting forces, such as friction and cohesion, thus triggering landslide events (Bishop, 1955). Landslides tend to occur more frequently on slopes that exceed a certain angle, which varies depending on soil composition, vegetation cover, and other factors (Kohno and Higuchi, 2023). ...
Introduction
Landslides are a major geohazard in the northern Ethiopian highlands, causing significant damage to farmland, infrastructure, and settlements, with profound socio-economic consequences. This study aims to address the pressing need for enhanced natural hazard management by investigating landslide susceptibility in the Debek region of South Wollo, Ethiopia.
Methods
The study employs advanced geospatial modeling techniques to assess landslide susceptibility. Key causative factors—slope gradient, aspect, elevation, proximity to streams and springs, slope material, distance to lineaments, and land use/land cover (LULC)—were identified and analyzed through field surveys and satellite imagery. A total of 328 landslide events were documented, with data divided into training (75%) and validation (25%) sets. Landslide susceptibility maps were generated using the Frequency Ratio (FR) and Analytical Hierarchy Process (AHP) models. Validation of the models was conducted through landslide density indices (R-index) and receiver operating characteristic (ROC) curves.
Results
The analysis revealed that slope material and proximity to springs were the most influential factors contributing to landslide susceptibility. The FR model demonstrated a slightly better performance than the AHP model, with an ROC success rate of 0.828 and a prediction rate of 0.835, compared to 0.826 and 0.832, respectively, for the AHP model. The models were validated through the R-index and ROC curves, which showed a high degree of concordance between the predicted and observed landslide events.
Discussion
This study highlights the effectiveness of GIS-based geomatics approaches in landslide susceptibility mapping in a data-scarce region. The comparative analysis of the FR and AHP models demonstrates the strengths and limitations of each, offering valuable insights for landslide risk mitigation. The findings underscore the importance of integrating geospatial modeling in natural hazard management, supporting more informed land-use planning, targeted mitigation strategies, and comprehensive disaster prevention initiatives.
Conclusion
This research contributes to advancing the understanding of landslide dynamics in the Ethiopian highlands and provides critical resources for policymakers and stakeholders involved in disaster risk management. The study's findings enhance the capacity for effective landslide-prone area identification and susceptibility reduction, reinforcing the importance of geospatial modeling in improving natural hazard management frameworks.
... The limit equilibrium method considers the slope behavior as a rigid-plastic model that reaches its strength at imminent failure and at the same time throughout the failure, it does not analyze the stress-strain relationship or the corresponding deformation within the soil body (Fredlund 1984). Based on the above conditions, the factor of safety (FoS) is defined as a numerical ratio that compares the shear strength of the soil with the shear stress at the failure surface (Bishop 1955). The LEM used is the Spencer method, which satisfies all the static stability equations and assumes that the interslice forces are parallel (Spencer, 1967). ...
Generally, stability analysis in heap leach pad determines that the most critical failure surface develops along the liner system. However, specific conditions in the foundation, such as the presence of clayey soils, justify an analysis aimed at evaluating potential failure surfaces through it. This paper presents a slope stability analysis on foundation failure applied to both two-and three-dimensional models of a heap leach pad located in Peru; just under its toe, the local presence of clayey soils-resulting from the weathering of andesitic tuffs-was identified, and combined with saturation, these would cause regions of weakness. These conditions motivate a comparison between two-and three-dimensional stability analysis, the latter considers geometry of the stacked mineral, spatial distribution of the foundation materials and relief of the foundation. The analyses employed the limit equilibrium method, using the Mohr-Coulomb and generalized Hoek-Brown failure criteria. The results and paid special attention to the concave and convex zones of the pad and were compared in terms of safety factors and extent of the failure surface in these areas, these results show that the FoS in a 3D analysis are higher than in a 2D analysis and show the ratio between these two FoS varies between 2% and 46%.
... This discrepancy arises because the YS-Slope model assumes a planar failure surface, which is suitable for analysing shallow landslides but does not sufficiently capture the ellipsoidal or hemispherical failure surface geometry that is characteristic of deep-seated landslides. To evaluate the stability conditions of deep-seated landslides, more advanced limit equilibrium techniques should be used that are capable of accounting for the hemispherical or ellipsoidal geometry of deep-seated failures (Bishop 1955;Mergili et al. 2014;Miller 1995;Reid et al. 2015;Van den Bout et al. 2021). Typically, the deep-seated landslides have been studied on an individual slope by using the limit equilibrium method and the finite element method to analyse the rotational slope stability (Arai and Chigira 2018;Nguyen, Tien, and Do 2020;Van Tien et al. 2018). ...
In mountainous areas, understanding the sizes and types of rainfall-induced landslides, and identifying areas at high risk, are critical challenges for disaster management. Shallow and deep-seated landslides are the two major types in mountainous regions, distinguished by their failure mechanisms, geomaterials, depths and sizes. Shallow landslides typically involve planar failures at depths less than 3 m. In contrast, deep-seated landslides exhibit ellipsoidal or hemispherical geometries, with rotational failure planes exceeding 3 m in depth. The infinite slope stability model is commonly used to analyse shallow landslides, but it tends to overestimate the occurrence of deep-seated landslides due to its unsuitability for ellipsoidal or hemispherical failure surface geometries. To address this issue, this study proposes modifying the slope stability model by incorporating a hemispherical shape aligned with the failure characteristics of deep-seated landslides as hemispherical slope stability. This is coupled with infiltration and groundwater recharge analysis, and is used to simulate rainfall-induced deep-seated landslides induced within GIS environment. Model validation was conducted by comparing the predictions of the hemispherical slope stability model with historical landslide data and the traditional Scoops3D model, using ROC-AUC values. The hemispherical slope stability model demonstrated good agreement with historical data, achieving AUC values of 81.08% to 83.85%, and showed consistent results with the Scoops3D model in predicting stable and unstable zone. Therefore, these advancements are particularly valuable for real-time application as they enable the precise delineation of landslide susceptibility area.
... O método de (Hovland, 1977) juntamente com o método de (Ugai, 1988) e (Zheng, 2009) foram desenvolvidos como extensões do método comum de fatias. O método simplificado de (Bishop, 1955) serviu de base para os métodos 3D de (Hungr, 1987), (Ugai, 1988), (Hungr et al. 1989) e (Cheng e yip, 2007). Ugai, (1988), (Hungr et al., 1989), (Yamagami e Jiang, 1997), (Cheng e Yip, 2007) propuseram diferentes métodos 3D, desenvolvendo o método de (Junbu, 1973). ...
As análises de estabilidade de talude mais comumente utilizadas na prática da engenharia geotécnica são em duas dimensões. Porém, a avaliação em três dimensões tende a ser mais rigorosa, e mais justificável para representar a condição real de geometria da massa do terreno instável. Assim os avanços na teoria da análise de estabilidade tridimensional, o aumento do poder de processamento dos computadores pessoais e o desenvolvimento de pacotes de software mais robustos, tem permitido que os engenheiros, projetistas e pesquisadores apresentassem estas análises de maneira mais assertiva e pragmática. Desta forma, o artigo desenvolve a análise de estabilidade de talude bidimensional e tridimensional de uma cava de uma mina a céu aberto situada dentro do Complexo Mineral de Patrocínio-MG, com altura na ordem de 375m, com bancos de 10m, avaliando a consistência da base de dados disponível e, na sequência, os resultados obtidos. A geologia da região é caracterizada por depósito econômico alcalino de fosfato que ocorre na área central localizada integralmente dentro do domo Salitre I. Para setorização do trecho crítico do talude da cava desta pesquisa, utilizou-se a ferramenta de busca automática do Software Slide3 da empresa Rocscience®. O método de estabilidade adotado para a presente pesquisa foi o Método do Equilíbrio Limite Geral (GLE) proposto por Morgenstern-Price (1965) para problemas bidimensionais com lamelas (fatias) de 1 (um) metro de espessura, posteriormente adaptado para problemas tridimensionais, onde as lamelas 2D foram substituídas por colunas 3D, generalizando, assim, sua utilização. Obteve-se então um fator de segurança com os parâmetros de resistência médios dos materiais de 1,22 2D e (FS) médio 1,32 3D, próximo do (FS) mínimo = 1,30 recomendado por vários autores para taludes de cava, os suficientes para definir uma condição instável do talude. Considerando o modelo analítico 2D como referência, em termos absolutos, a diferença entre as análises está na ordem de 8,2%, mostrando-se, assim, convergência entre as análises. Palavras-chave: análises de estabilidade 2D e 3D, equilíbrio-limite, busca automática, trecho crítico, mina a céu aberto.
... Substituting l by b∕cos( ) , it is possible to solve for the undrained shear strength required to achieve a state of limit equilibrium, as S u = sub H sin cos + k sat sub cos 2 (Haneberg 2012). Hence, the fac-tor of safety ( FS ) is defined as the ratio between the resisting and the loading forces using Eq. 1 (Bishop 1955). ...
Current practice to model the occurrence of submarine landslides is based on methods that assess the potential of site-specific failures, all with the objective of providing elements to identify and quantify regional features associated to geohazards, before a project development takes place. Also, survey data to estimate parameters required to model submarine landslides show typically limited availability, mainly because of the cost associated to offshore surveying campaigns. In this paper, a probabilistic calibration approach is introduced using Bayesian statistical inference to maximize the use of available site investigation data, and to best estimate the occurrence of a marine landslide. For this purpose, a landslide model thought for its simplicity is used to illustrate the applicability and potential of the calibration methodology. The aim is to introduce a systematic approach to produce prior probability distributions of the model parameters, based on an actual integrated marine site investigation including geological, geophysical, and geomatics data, to then compare it with a posterior probability distribution of the same model parameters, but estimated after collecting in situ soil samples and testing them in the laboratory to produce the corresponding soil strength properties. This comparison allows to explore (a) the influence of the number of in situ samples, (b) the influence of a landslide factor of safety, and (c) the influence of the soil heterogeneity, into the likelihood of the occurrence of a marine landslide. The model parameters that are considered for calibration include the initial state of the submerged and saturated soil unit weight, the thickness of the soils’ unit layers, the pseudo-static seismic coefficient, and the slope angle, while the soil undrained shear strength is considered as the reference parameter to conduct the calibration (i.e., to compare model predictions vs. actual observations). Results show the potential of the proposed methodology to produce landslide geohazard maps, which are needed for the planning and design of marine infrastructure.
... To assess the rainfall-induced slope stability both the LEM and FEM are adopted to have a comparative assessment for the study slope. A variety of methods are utilized in LEM slope stability analysis to determine the critical slip surface of the slope, among which is Bishop's Simplified method (Bishop, 1955) and GLE/Morgenstern Price Method (Morgenstern and Price 1965). In FEM Shear Strength Reduction (SSR) technique and plane-strain method have been operated in the FEM slope stability analysis to get the FoS and the critical slip surface. ...
Rainfall is a key factor triggering slope failures, leading to geohazards and affecting civil infrastructure. Traditional slope stability assessments use dry-state analysis and groundwater table models, which may be insufficient for predicting the Factor of Safety (FoS) under rainfall conditions. This study investigated the governing factors that can induce slope failure due to rainfall infiltration in non-tropical areas, focusing on a previously failed slope in Northern New Jersey. A two-dimensional Limit Equilibrium Method (LEM) and Finite Element Method (FEM) were employed. Initial dry-state and subsequent post-rainfall slope stability analyses were conducted. The results indicated a reduction in FoS due to rainfall (LEM: 1.59 to 1.46, FEM: 1.49 to 1.11), attributed to reduced matric suction and increased soil saturation. Further analysis revealed a 6%−25.5% FoS decrease, with shear strain (+139%) and displacement (+95%) increasing. The findings suggest that rising rainfall events may destabilize slopes, necessitating slope protection work for long-term stability.
... GIS-based slope stability models assume an infinite slope with a planar, slope-parallel failure plane (Van Westen et al., 2006), and are best suited for analysing shallow slope instability. More complex models consider the threedimensional geometry of possible slope failures, and are suitable for the analysis of deep-seated slope stability (e.g., Bishop, 1954;Janbu et al., 1956). The latter models rely on complex neighbourhood relationships, and their implementation in GIS environments is not trivial (attempts were made, e.g., by Xie et al., 2003Xie et al., , 2004aXie et al., , b, 2006Marchesini et al., 2009;and Jia et al., 2012). ...
The GIS-based open source software r.slope.stability computes broad-scale spatial overviews of shallow and deep-seated slope stability through physically-based modelling. We focus on the landslide-prone 90 km2Collazzone area, central Italy, exploiting a comprehensive set of lithological, geotechnical and landslide inventory data available for that area. Inevitably, the geotechnical and geometric parameters are uncertain, particularly for their three-dimensional variability. Considering the most unfavourable set of geotechnical parameters (worst case scenario, appropriate for engineering purposes) is less useful to obtain an overview of the spatial probability (susceptibility) of landslides over tens of square kilometres. Back-calculation of the parameters based on topographic and geotechnical considerations would be experimental. Instead, we estimate the slope failure probability by testing multiple combinations of the model parameters sampled deterministically. Our tests indicate that (i) the geotechnical parameterization used allows to reproduce the observed landslide distribution partly (a challenge consists in the appropriate treatment of the variation of the geotechnical parameters with depth); (ii) the evaluation outcome depends strongly on the level of geographical aggregation; and (iii) when applied to large study areas, the approach is computing-intensive, and requires specific strategies of multi-core computing to keep the computational time at an acceptable level.
... Stability analysis of rock slopes is performed based on various approaches such as empirical, theoretical, numerical, artificial intelligence and probabilistic methods [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Among these approaches, the limit equilibrium method (LEM) has been frequently used for stability analysis of rock slopes due to its accuracy and easy utilization [29][30][31][32][33][34]. In this technique, SF is defined as the ratio of resistance loads to driving forces on a possible sliding face. ...
... LEM calculates the factor of safety over a trial slip surface of the given slope, primarily using methods of slices. Originally based on engineering intuition, slice techniques gained widespread acceptance in the 1950s and 1960s as rigorous mechanical principles were developed, leading to the analysis and summarization of different limit equilibrium slice methods (Bishop, 1955;Fellenius, 1936;Janbu, 1954;Morgenstern and Price, 1965;Spencer, 1967). The second approach, the Strength Reduction Method (SRM), was developed in the 1990s (Swan et al., 1999;Zou et al., 1995) that reduces strength parameters in elastic-plastic finite element analysis until slope failure occurs, and its main advantage is the absence of a need for a predefined slip surface. ...
Landslides in the Nepal Himalayas are a common phenomenon because of the coupling effect of seismo-tectonic activities and the Asian Monsoon. Understanding landslides in this complex environment, particularly the behavior of active large landslides, is vital for sustainable infrastructure development. This study conducted comprehensive slope investigations, including geological, geophysical, and geotechnical investigation, along with instrumentation using inclinometers and a raingauge station, to identify the causes and mechanisms of failure at the active landslide slope at Guthitar on the Dharan-Dhankuta road. This landslide is active since 1987 but the movement has intensified from 2020 onwards. The detailed investigation reveals that the landslide exhibits multiple shallow-seated and deep-seated failure surfaces, some of which extend to the ground. Slope stability was modeled and analyzed using the Limit Equilibrium and Strength Reduction Methods. The results indicate multiple slip surfaces, with some discrepancies compared to field investigations, underscoring the limitations of numerical methods and the critical role of field monitoring systems. Furthermore, a comparison of rainfall data with deformation patterns from slope monitoring clearly demonstrates that prolonged rainfall increases the rate of movement by threefold. Thus, continuous landslide monitoring is essential to understand the mechanisms and triggers, enabling the implementation of effective landslide management strategies in the Himalayas.
This paper focuses on the stability issues of geological and engineering structures and conducts research from two perspectives: the mechanism of slope landslides under micro-seismic action and the cyclic failure behavior of concrete materials. In terms of slope stability, through the combination of model tests and theories, the cumulative effect of circulating micro-seismic waves on the internal damage of slopes was revealed. This research finds that the coupling of micro-vibration stress and static stress significantly intensifies the stress concentration on the slope, promotes the development of potential sliding surfaces and the extension of joints, and provides a scientific basis for the prediction of landslide disasters. This helps protect mountain ecosystems and reduce soil erosion and vegetation destruction. The number of cyclic loads has a power function attenuation relationship with the compressive strength of concrete. After 1200 cycles, the strength drops to 20.5 MPa (loss rate 48.8%), and the number of cracks increases from 2.7 per mm3 to 34.7 per mm3 (an increase of 11.8 times). Damage evolution is divided into three stages: linear growth, accelerated expansion, and critical failure. The influence of load amplitude on the number of cracks shows a threshold effect. A high amplitude (>0.5 g) significantly stimulates the propagation of intergranular cracks in the mortar matrix, and the proportion of intergranular cracks increases from 12% to 65%. Grey correlation analysis shows that the number of cycles dominates the strength attenuation (correlation degree 0.87), and the load amplitude regulates the crack initiation efficiency more significantly (correlation degree 0.91). These research results can optimize the design of concrete structures, enhance the durability of the project, and indirectly reduce the resource consumption and environmental burden caused by structural damage. Both studies are supported by numerical simulation and experimental verification, providing theoretical support for disaster prevention and control and sustainable engineering practices and contributing to ecological environment risk management and the development of green building materials.
Understanding slope stability is crucial for effective risk management and prevention of slides. Some deterministic approaches based on limit-equilibrium and numerical methods have been proposed for the assessment of the safety factor (SF) for a given soil slope. However, for risk analyses of slides of earth dams, a range of SFs is required due to uncertainties associated with soil strength properties as well as slope geometry. Recently, several studies have demonstrated the efficiency of artificial neural network (ANN) models in predicting the SF of natural and artificial slopes. Nevertheless, such techniques operate as black-box models, prioritizing predictive accuracy without suitable interpretability. Alternatively, multivariate polynomial regression (MVR) models offer a pragmatic interpretability strategy by combining the analysis of variance with a response surface methodology. This approach overcomes the difficulties associated with the interpretability of the black-box models, but results in limited accuracy when the relationship between independent and dependent variables is highly nonlinear. In this study, two models for a quick assessment of slope SF in earth dams are proposed considering the MVR and the ANN models. Initially, a synthetic dataset was generated considering different soil properties and slope geometries. Then, both models were evaluated and compared using unseen data. The results are also discussed from a geotechnical point of view, showing the impact of each input parameter on the assessment of the SF. Finally, the accuracy of both models was measured and compared using a real-case database. The obtained accuracy was 78% for the ANN model and 72% for the MVR one, demonstrating a great performance for both proposed models. The efficacy of the ANN model was also observed through its capacity to reduce false negatives (a stable prediction when it is not), resulting in a model more favorable to safety assessment.
Adanya kelongsoran yang terjadi pada lereng highwall pit FSP F34 Timur PT Fajar Sakti Prima, menyebabkan akses jalan menjadi terganggu. Keadaan ini mengharuskan Perusahaan untuk melakukan kajian analisis balik terhadap longsor, sehingga lereng kembali stabil. Tujuan penelitian yaitu melakukan analisis balik lereng untuk mendapatkan nilai parameter batuan pada saat longsor dan mendapatkan rekomendasi lereng yang aman sesuai dengan parameter hasil analisis balik. Dalam penelitian ini dilakukan analisis balik dengan cara mengurangi nilai parameter batuan seperti kohesi (c) dan sudut geser dalam (Φ) hingga kondisi lereng labil (FK ≤ 1). Nilai c dan Φ yang dihasilkan diasumsikan sebagai kondisi lereng saat longsor, kemudian hasil dilakukan analisis kestabilan lereng untuk rekomendasi geometri lereng yang aman. Analisis kestabilan lereng menggunakan metode kesetimbangan batas. Hasil rekomendasi geometri lereng, yaitu: tinggi single slope 10 m, sudut single slope 58º, tinggi overall slope 50 m, sudut overall slope 37º serta lebar bench 5 m. Dengan nilai FK dinamis sebesar 1,16; PF 0,00%. Sedangkan nilai FK statis sebesar 1,42; PF 0,00%, dengan geometri tinggi single slope 10 m, sudut single slope 50º, tinggi overall slope 50 m, sudut overall slope 33º serta lebar bench 5 m. Keduanya dikategorikan sebagai nilai yang stabil menurut Kepmen 1827 tahun 2018.
Landslides are mass movements of rock, soil, or debris under the influence of gravity. These phenomena occur due to the loss of slope stability or imbalance of external loads. The intensity and consequences of landslides depend on various factors such as topography, geological structure, and precipitation regime. This study investigates the characteristics of rainfall-induced landslides in red basaltic soils on the basis of field investigations, geotechnical surveys, and slope stability modeling under anthropogenic triggers. The results indicate a close relationship between soil moisture and shear strength parameters, which significantly influence slope stability. A real-time observation system recorded groundwater level fluctuation in relation to surface runoff and precipitation rates. It is revealed that intense rainfall and low temperatures regulate soil moisture, resulting in a reduction of cohesion and shear strength parameters. These findings enhance the understanding of landslide mechanism in basaltic soil regions, which are highly sensitive to precipitation. The results also highlight that human activities play a significant role in triggering landslides. Therefore, a real-time monitoring system for rainfall, soil moisture, and groundwater is essential for early warning and supports the integration of smart technologies and Internet of Things (IoT) solutions in natural disaster management.
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.
Responding to the upsurge in demand for freight transportation, exclusively heavy-haul rail embankments (HHRE) were constructed to carry trains with high gross weights, huge axle loads, or unusually high traffic volumes. However, to facilitate these demands smoothly, the embankment needs a proper investigation. This study reports the slope stability assessment of the 12.293 m high HHRE using AI-based three distinctive ML models, viz., recurrent neural network (RNN), long short-term memory (LSTM), and bi-directional LSTM (Bi-LSTM). For this purpose, the SLOPE/W module was used as a deterministic analysis, and the FOS was calculated using Bishop’s simplified method; furthermore, three distinct ML models were used for the prediction of the FOS for the proposed embankment. Following the construction of the model, multiple key performance indicators were used to map the model. The results show that the Bi-LSTM outperformed the other developed model in terms of TIC = 0.0016 and R2 = 0.9995 during the development stage, while TIC = 0.0016 and R2 = 0.9996 during the validation stage. Additionally, the AIC value has also been calculated to find the relative superiority of all the developed models. This result suggests that Bi-LSTM achieves the lowest AIC value (i.e., –14657.78 in training and –9818.31 for testing) compared to other models, which indicates an outstanding fit and is universal. Furthermore, sensitivity analysis was investigated using the cosine amplitude method for the embankment fill input parameters to the output. The results indicate that unit weight has the highest influence on the FOS of the proposed embankment.
This study evaluates the static and seismic stability of the Narasimharaya Sagar (Gorukallu Balancing Reservoir) earthen dam, located in India’s seismically active Zone II. Using GeoStudio software, seepage, slope stability, and liquefaction analyses were conducted to assess the dam’s performance under static and dynamic conditions. Static analysis revealed factors of safety above permissible limits, ensuring stability under normal conditions. Seismic analysis, incorporating ground shaking with a peak acceleration of 0.1 g, highlighted significant displacements (0.984 m) and a reduced factor of safety (FOS) (1.279), approaching the allowable threshold. Liquefaction zones were identified, particularly in the back shell, indicating a high vulnerability to seismic‐induced shear strength loss. To address these risks, geosynthetic reinforcements were applied, with optimized configurations (horizontal layers, 4 m vertical spacing, 20 m length) improving the FOS to 1.503. These findings demonstrate the effectiveness of geosynthetics in mitigating soil liquefaction and enhancing seismic resilience, providing a robust framework for improving the safety of earthen dams in earthquake‐prone regions.
Despite extensive research on landslides globally, there is a notable knowledge gap on mechanisms influenced by combined rainfall and earthquake events to induce landslides in non-tropical coastal areas, and how to mitigate such failures. This study assessed the factors governing landslide susceptibility in the non-tropical coastal regions under the combined influence of rainfall and earthquake, and further proposes a novel slope protection work that can potentially mitigate such hazard. Adopting datasets from two distinct coastal regions in the United States, this study employed both the Limit Equilibrium Method (LEM) and the Finite Element Method (FEM). Hazard analysis was conducted using Factor of Safety (FoS) from LEM and Strength Reduction Factor (SRF) from FEM on the identified slopes to gain insights into combined rainfall- and earthquake-induced landslides. The results indicate that LEM exhibits limitations in reliability of slope stability analysis with complex failure mechanisms, and is primarily suitable for simple slopes without the influence of non-anthropogenic activities. Contrarily, FEM demonstrated relatively superior applicability for stability analysis of the slopes with complex failure mechanisms and under the influence of environmental stressors in coastal regions. FEM-based assessment of slopes under the dry state and the combined state (earthquake and rainfall) conditions revealed high susceptibility to failure in non-tropical coastal areas under the combined state conditions. Coupled earthquake and rainfall influence on soil mass slopes in non-tropical coastal areas induced shear strain propagation and matric suction reduction along shallower depths, leading to decreased slope stability. Further, we proposed a novel slope protection work that demonstrated higher efficiency in reducing shear strain and increasing SRF (+ 16%), presenting a potentially viable slope protection strategy for non-tropical coastal areas.
Rainfall-induced debris slides are a major geological hazard in the Himalayan region, where slopes often comprise heterogeneous debris—a complex mixture of rock and soil. The complex nature makes traditional soil or rock testing methods inadequate for assessing such debris's engineering behaviour and failure mechanisms. Alternatively, reduced-scale flume experiments may aid in understanding the failure process of debris slopes. Here, we present findings from reduced-scale laboratory flume experiments performed under varying slope angles (ranging from shallow to steep), initial volumetric water contents (ranging from dry to wet), and rainfall intensities (ranging from light to heavy) using debris materials with a median grain size (D50) 20.7 mm sampled from a rainfall-induced debris slide site in the Himalayas. Hydrological variables, including volumetric water content and matric suction, were monitored using sensors, while slope displacement was tracked indirectly, and rainfall was monitored using rain gauges. The entire failure process was captured via video recording, and index and shear strength tests were performed to characterize the debris material. Our results reveal that the failure of debris slopes is not driven by sudden increases in pore water pressure but by the loss of unsaturated shear strength due to reduced matric suction and a decreased frictional strength from reduced particle contact between grains during rainfall. We also find that the saturation of debris slope by rainfall was quick irrespective of the slope angles and initial moisture contents, revealing the proneness of debris slopes to rainfall-induced failures. These findings provide critical insights into the stability of debris materials and have important implications for improving risk assessment and mitigation strategies for rainfall-induced debris slides in the Himalayas and similar regions worldwide.
Large or deep-seated progressive landslides pose significant challenges due to the complex failure mechanism and the potential for recurring failures. Progressive landslides are characterized by a gradual and continuous downslope movement of soil and rock material over an extended period. Analysing the evolution of deformation within a large landslide can provide valuable insights about the location and direction of progressive sliding events which may lead to severe instability. Identification of the progressive failure in large and deep-seated landslides is essential for risk assessment, timely adopting mitigation strategies, and ensuring public safety. The August 2017 Kotropi landslide in the Mandi district of Himachal Pradesh is an example of a deep-seated progressive landslide. The landslide has experienced continuous sliding events since its initiation and become a threat to local community. This research aimed to analyse the evolution of progressive deformation in Kotropi Landslides (Himachal Pradesh) using the 3D limit equilibrium method. This study uses field data of different time intervals, back analysis, and 3-Dimensional numerical modeling to estimate the stability of the Kotropi landslide. Two 3D models were constructed using the field data conducted in two phases: Phase 1 (year 2017–20) and Phase 2 (year 2021–23) to determine the probability of failure in different time period. The stability analysis examines the evaluation of instabilities in the Kotropi landslide for a period of year 2017–20 and year 2021–23, taking into account factors like changes in surface geometry, pore water pressure, ground deformation, and so on. The results obtained were combined with satellite imagery to check the location and direction of progressive failure with in Kotropi landslide. The results indicate that the progressive failures are concentrated in right flank near to the crown area. Contrary to initial failure which occurred in NE-SW direction, the progressive failures are taking place in N-NW direction.
Many engineering fields involve the analysis of slope stability, such as building foundation pits, open-pit mines, embankments in road engineering and embankments dams in hydraulic engineering. The stability of slopes directly affects the economic benefits and safety of these engineering projects.
Slope failures and landslides often result in enormous economic losses, including considerable loss of life and injuries to human beings. To improve the stability of both natural and manmade slopes in geotechnical engineering, researchers require an extensive knowledge of different methods to evaluate slope stability and their limitations. Various methods have been employed to stabilize slopes, with each one finding appropriate under specific conditions. Over the past few decades, applying conventional piles as a means to mitigate active landslides or protect instability in currently stable slopes became a prominent technique for slope reinforcement. In recent decades, stabilizing the slopes using micropiles has become an alternative to conventional piles for reinforcing a diverse range of slopes/landslides due to their successful performance and faster construction. This review paper primarily discusses slope/landslide protection using micropiles based on simplified analytical methods, numerical modeling, and experimental investigations through a review of relevant recent literature.
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