Morgenstern-Price Method Research Articles

Research on Reservoir Landslide Thrust Based on Improved Morgenstern-Price Method

Research on Reservoir Landslide Thrust Based on Improved Morgenstern-Price Method

A Generalized Limit Equilibrium-Based Platform Incorporating Simplified Bishop, Janbu and Morgenstern–Price Methods for Soil Slope Stability Problems

Limit equilibrium (LE) method is the most widely used method for slope stability analysis. Different methods based on the LE technique for the analysis of the stability of the slope have been developed. Some are based on satisfying the force equilibrium condition of the failing mass (Janbu’s method), while some focus on satisfying the moment equilibrium condition (Bishop’s method). Among these methods, the most accurate result is provided by the Morgenstern–Price method as it not only satisfies both moments as well as a force equilibrium condition but also considers the interslice shear forces (Vi) and interslice normal forces (Ei), which are neglected by most of the LE methods to avoid the condition of indeterminacy. To accommodate these forces, Morgenstern–Price (MP) gave a relation between the Vi and Ei which depends upon a scaling multiplier (λ). Thus, it becomes necessary to evaluate λ value along with the factor of safety (FS). There is barely any work discussing the detailed methodology of evaluation of λ along with FS. Method for obtaining λ along with FS have been developed and elaborated in details here. While calculating FS (MP method), evaluation of Ei is a must which is dependent upon the values of normal force at the base of each slice (Ni) and FS, which itself is dependent upon the value of Ei, making it a loop of interdependent variables. To avoid this interdependency of above stated variables, a separate formulation of Ei is given which reduces the calculations (run-time) involved. A VBA code-based platform has also been developed incorporating the generalized LE method, including Bishop’s, Janbu’s, and Morgenstern–Price methods which are represented in the form of flowcharts in this work.

A novel stability equation for the estimation of the factor of safety for homogeneous dry finite slopes

AbstractThis 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.

Анализ устойчивости откосов горной дороги месторождения Camarioca Este компании Comandante Ernesto Che Guevara

In the framework of the study, numerical modelling has been conducted to calculate the slope stability of the mining road of the Camarioca Este deposit developed by the Empresa Comandante Ernesto Che Guevara Company. A geotechnical analysis of the deposit area has been carried out, as well as geological surveys to detect the areas prone to stability degradation. A geotechnical model including soil layers, properties of materials, and loading conditions was developed by using software. In order to assess the mining road slope stability, the limit equilibrium methods, in particular, the Morgenstern-Price method have been applied. This method is based on the limit equilibrium principle and the rock shear strength theory. Using the Slide software, the reserve factor has been calculated for different conditions. Modelling and calculation of the reserve factor have been conducted for two conditions: not considering factors reducing stability and considering such factors, namely the seismic level impact and rainfall effects. To determine the parameters of seismic acceleration in the region, the Cuban standard NC 46—2017 of the National Center of Seismological Research of Cuba has been applied. Three sectors with the potential level of stability reduction corresponding to stations with marks 0+250.00 m — 0+306.70 m, 0+380.00 m — 0+420.00 m, and 2+280.00 m — 2+291.68 m have been studied as the fundamental results; the reserve factors have been calculated considering seismic acceleration and intensive precipitation and are equal to 0.80, 1.45, and и 0.91, respectively.

Efficient numerical implementation of limit equilibrium method for stability analysis of unsaturated soil slopes using Gaussian integral

Unsaturated soil is widely distributed around the world but less considered in design due to the absence of a convenient analysis method in practice. The Morgenstern–Price (MP) method incorporating the extended Mohr–Coulomb shear strength equation provides a reliable approach to evaluate slope stability in such conditions. However, this method is time-consuming due to the need for a tedious trial-and-error process in determining the scaling factor, which involves complex iterations during each trial. Furthermore, since the relatively complicated nature of unsaturated soil, a dense slice division is necessary to obtain reliable results, making the analysis even more cumbersome. In this paper, an improved MP method for unsaturated soil slope stability analysis is presented, which eliminates the need for a dense slice mesh by employing only a few strategically placed Gauss points along the slip surface. Moreover, the trial-and-error process for determining the scaling factor with the corresponding complex iterations is replaced by an efficient search algorithm with a more concise iteration process, resulting in a more convenient implementation of the proposed method. Extensive examples are provided to validate the effectiveness of the proposed improved MP method, indicating its potential as an accurate and efficient analysis method for unsaturated soil slopes in practical application and relative study involving repetitive analyses.

Geotechnical and slope stability analysis in the landslide-prone area: A case study in Sawla – Laska road sector, Southern Ethiopia

Examining the factors underlying landslides and assessing the stability of slopes is crucial for reducing the negative impact of landslides on the environment and the lifespan of infrastructure. This study assessed certain slope portions along the Sawla to Laska Road to determine the factors contributing to landslides and identify the mechanisms and conditions that lead to slope failure. Slope stability analysis was conducted using the limit equilibrium method, and a range of laboratory tests were conducted following ASTM standards. The analysis has shown that the three slope portions, specifically sections 1, 2, and 3, had distinct shear strength characteristics, as shown by variations in their cohesion and internal friction angle values. The average values for cohesion were 19.24, 10.41, and 12.9, respectively, while the internal friction angle values ranged from 11.32 to 17.8 for slope section three, 18.96 to 21.12 for slope section two, and 30.08 to 37.26 for slope section one. The limit equilibrium method was utilized to compute the safety factor of slopes. Five methods were employed to evaluate the safety factor: the ordinary method, Bishop method, Janbu method, Spencer method, and Morgenstern-Price method while considering three groundwater conditions (GWT at great depth, GWT at half of the slope, and GWT on the surface). Only slope section one exhibited a slightly stable safety factor that exceeded one under dry conditions. The slope-mass rating analysis showed that rock slopes one and two were deemed stable under class II, rock slopes three and four were partially stable under class III, and rock slope five was unstable under class IV. A slope mass range of 78 to 79 indicates excellent to very good rock mass quality and high stability potential for RSs1. In contrast, RSs5 shows a wide SMR range from 7 to 57, indicating a spectrum of very poor to fair to good quality rock mass and an associated range of stability from extremely low to moderate. RSs2 and RSs3 fall within the SMR range of 71.1–72 and 49.9–55.9, respectively, indicating good to fair rock mass quality with varying degrees of stability potential. Last, RSs4, with an SMR range of 39.6–45.1, shows poor rock mass quality and substantial stability concerns. RSs1 has a UCS of 28.68 MPa, indicating a "Medium strong" classification, and it belongs to the lithology type of "Trachyte." RSs2 showcases a higher UCS value of 32.25 MPa, similarly classified as "Medium strong," and is also identified as "Trachyte." RSs3, with a UCS of 28.83 MPa, falls under the "Medium strong" classification and is categorized as "Basalt." In contrast, RSs4 demonstrates a lower UCS of 18.41 MPa, leading to a "Weak" classification associated with the lithology type "Basalt." Lastly, RSs5 presents a UCS of 25.77 MPa, classified as "Medium strong," and shares the lithology type of "Basalt." The study identified that the landslide types in the study area were rockfall, earth flow, and soil/rock slides. The factors contributing to landslides in the study area were slope steepness, weathering, groundwater, and rainfall.

RELATIONSHIP BETWEEN SOIL PHYSICAL-MECHANICAL PARAMETERS AND EARTH DAM SLOPE STABILITY USING STOCHASTIC AND NUMERICAL MODELING

The main goal of this research is to obtain a mathematical relationship to estimate the initial safety factor in earthen dams, based on a linear regression model. To expand the initial sample that includes the physical-mechanical properties of existing soils in embankments of built earthen dams, it is necessary to apply the Monte Carlo method. Based on numerical modeling, the variation of the safety factor in a 30-meter-high dam is analyzed using the Morgenstern-Price method, considering steady water flow and including unsaturated soil in the analysis. A hybrid numerical model is carried out, which combines the Finite Element Method for the analysis of the filtration and the Limit Equilibrium Method to obtain the safety factor. Among the results of the numerical modeling and the proposed experimental design, it is observed that cohesion is the predominant mechanical variable in the behavior of slope stability of dams with homogeneous embankment. Abacuses are proposed to estimate the initial safety factor in the unsaturated state, fixing the specific weight, for various values ​​of cohesion and angle of internal friction; and a mathematical relationship is established to estimate the safety factor, which presents a coefficient of determination equal to 95%.

Study on the control effect of local basement replacement on the stability of dump.

This study focuses on effectively controlling landslides at the boundary of a soft rock open-pit dump while ensuring safe increases in the dump's capacity and optimal utilization of external dump sites. To achieve this, the adoption of a local filling method for the dump base is proposed. By leveraging the concepts of limit equilibrium theory and equivalent shear strength parameters, the mathematical expression of the slope stability coefficient in the Morgenstern-Price method is derived and improved. This improved method is then applied to a real engineering example to determine the optimal basement replacement rate required to maintain slope stability. The findings reveal that the local filling of the base is well-suited for slopes susceptible to potential landslides associated with cutting layers, bedding layers, and swelling. For practical ease, it is advisable to choose the lowest step in the dump's slope for construction convenience. As the local replacement rate of the base increases, the slope's stability coefficient gradually improves, with the K-Fs ratio showing a prominent role in this process. Additionally, numerical simulation methods are employed to elucidate the mechanism of the dump's landslide following local basement replacement, thereby providing comprehensive evidence of the engineering applicability of this method. The research results demonstrate a promising practical application prospect for effectively controlling the stability of soft base dump slopes.

Comparative study of deterministic and probabilistic critical slip surfaces applied to slope stability using limit equilibrium methods and the First-Order Reliability Method

This work presents the validation of the Morgenstern-Price method implemented in the Risk Assessment applied to Slope Stability (RASS) computational program to carry out deterministic and probabilistic analyses of slope stability. Deterministic analyses, based on the factor of safety approach, are performed using limit equilibrium methods. The probabilistic ones, on the other hand, are carried out through the direct coupling of these methods to the First Order Reliability Method (FORM). Initially, two benchmark cases are presented for validation of the computational routine related to the Morgenstern-Price method. Next, two illustrative examples are presented, with the investigation of the critical surfaces defined by deterministic and probabilistic criteria, which correspond to the minimum factor of safety, the maximum probability of failure, and the maximum quantitative risk. In the set of stability analyses, it was verified that both the numerical responses and the geometry of the critical surfaces can vary depending on the choice of the limit equilibrium method and the criterion for identifying the critical surface. The different possibilities presented by the methodology used in this study define not only a critical surface, but a set of critical surfaces that can help in the engineering decision-making process and slope risk management, complementing the widely used purely deterministic analyses in geotechnics.

Using the Morgenstern–Price Method and Cloud Theory to Invert the Shear Strength Index of Tailings Dams and Reveal the Coupling Deformation and Failure Law under Extreme Rainfall

It is difficult to obtain reliable shear strength parameters for the stability analysis and evaluation of tailings dams in an unstable state. In this study, the sensitivity of the shear strength index to the safety factor of a tailings dam was evaluated. The cohesion C range of a tailings earth rock dam in an unstable state is determined by the safety factor, and the Morgenstern–Price method is used for inversion. During parameter inversion, uncertainty reasoning is established based on cloud theory, which overcomes the problem that the fuzziness and randomness of the quantitative cohesion value are transferred to the qualitative concept of the safety factor. The results show that the change in cohesion C has a greater influence on the safety factor Fs of the tailings dam, and the value of parameter inversion is 8.6901 kPa. The deformation and failure of tailings dams under extreme rainfall conditions are analyzed by using the modified cohesion C value. The dam toe becomes the main response area of plastic deformation and slowly expands to the interior, showing creep deformation. The displacement field gradually transfers from the accumulated tailings to the tailings dam with the flow direction, causing erosion damage. This study provides a new idea and method for parameter inversion of the shear strength index of tailings dams and provides a reference for the disaster prediction and prevention of tailings dams subjected to extreme rainfall.

Optimum Design of Unsaturated Finite Clayey Slopes Using Second-Order Reliability Method

This paper discusses the second-order reliability-based design optimization (SORBDO) of unsaturated finite slopes. An efficient search algorithm is proposed to locate the most probable slip surfaces using the Morgenstern–Price method of slices. The variability of fitting parameters of the soil water characteristic curve (SWCC) and shear strength parameters have been taken into account for evaluating the reliability of unsaturated finite slopes. Six unsaturated shear strength (USS) models are considered for the analysis of unsaturated soils. The most conservative model for the optimum design of finite slopes is recommended. Moreover, the results indicate that the mean and standard deviation of the fitting parameters of SWCC have a significant effect on the critical centers, critical slip surfaces, and reliability index of the unsaturated finite slopes. The results demonstrate a significant change in the critical centers associated with critical slip surfaces due to the change in the mean and coefficient of variation of the fitting parameters of SWCC. Statistical analysis of the experimental data shows that a positive correlation exists between fitting parameters of SWCC related to air entry value (af) and residual water content (mf). Negative correlations are found between the fitting parameters of SWCC related to air entry value (af) and slope (nf). Similarly, the SWCC fitting parameters related to residual water content (mf) and slope (nf) have negative correlations for clayey soils. It is observed that the correlated value of the reliability index is overestimated with reference to the uncorrelated value for clayey soil slopes. The proposed design charts are beneficial for engineers and practitioners for the sustainable design of unsaturated finite slopes. Overall, the developed rigorous SORBDO framework offers a more rational approach for assessing critical failure surfaces and critical centers, considering the interdependency of random variables.

Analisis Kestabilan Lereng Metode Morgenstern-Price Jalan Poros Malino - Sinjai Kabupaten Gowa

Malino-Sinjai Road, Gowa Regency is an area that is prone to landslides in the rainy season, where the geological condition is in the form of Baturape-Cindako Volcano unit, namely volcanic rock of Pliocene. The research location is located on Malino-Sinjai Road Km ± 54 Parangloe District and Km ± 71 Tinggi Moncong District, Gowa Regency, the average slope of the study area is >45 °. The purpose of this research is to conduct geological engineering observations on the slopes in the form of lithological conditions, and discontinuous areas on the slopes. Conduct slope stability analysis using software using the Morgenstern-Price method, and provide technical or design recommendations for the observed slope conditions. The research methodology uses primary data, namely data from observations of engineering geology and geometry of the slopes, as well as secondary data in the form of data from previous studies, books and also the results of laboratory tests of physical and mechanical properties of rocks. The results of the study obtained technical geological observation data that on the slope (A) which is located on Malino-Sinjai Road Km ± 54 Parangloe District in the form of basalt rock has a high level of weathering characterized by an average joint distance of 9 cm and the condition of the top of the slope area has been become residual soil, while on the slope (B) which is located on Malino-Sinjai Road Km ± 71 Kecamatan Tinggi Moncong in the form of tuff rock, the level of weathering is still in the mildly weathered category and the solid condition is not visible. Based on the results of interpretation using the Morgenstern-Price method, the slope safety factor value (A) is FK 1.101 which is considered unstable based on the minimum standard of slope safety factor of the Ministry of Public Works in 2014 which is > 1.25. On the slope (B) the safety factor value is obtained, namely FK 1.371, where the slope is considered stable or safe. As for technical or design recommendations to prevent ground shaking, the slope (A) can use retaining walls or retaining walls and for slopes (B) use wire mesh or wire nets around the observation slope.

Deep neural network and ANN ensemble for slope stability prediction

Application of deep neural networks (DNN) and ensemble of ANN with bagging for estimating of factor of safety (FOS) of soil stability with a comparative performance analysis done for all techniques. 1000 cases with different geotechnical and similar Geometrical properties were collected and analysed using the Limit Equilibrium based Morgenstern-Price Method with input variables as the strength parameters of the soil layers, i.e., Su (Upper Clay), Su (Lower Clay), Su (Peat), angle of internal friction (φ), Su (Embankment) with the factor of safety (FOS) as output. The evaluation and comparison of the performance of predicted models with cross-validation having ten folds were made based on correlation-coefficient (CC), Nash-Sutcliffe-model efficiency-coefficient (NSE), root-mean-square-error (RMSE), mean-absolute-error (MAE) and scattering-index (S.I.). Sensitivity analysis was conducted for the effects of input variables on FOS of soil stability based on their importance. The results showed that these techniques have great capability and reflect that the proposed model by DNN can enhance performance of the model, surpassing ensemble in prediction. The Sensitivity analysis outcome demonstrated that Su (Lower Clay) significantly affected the factor of safety (FOS), trailed by Su (Peat). This paper sets sight on use of deep neural network (DNN) and ensemble of ANN with bagging for estimating of factor of safety (FOS) of soil stability. The current approach helps to understand the tangled relationship of various inputs to estimate the factor of safety of soil stability using DNN and ensemble of ANN with bagging. A dependable prediction tool is provided, which suggests that model can help scientists and engineers optimise FOS of soil stability. Recently, DNN and ensemble of ANN with bagging have been used in various civil engineering problems as reported by several studies and has also been observed to be outperforming the current prevalent modelling techniques. DNN can signify extremely changing and intricate high-dimensional functions in correlation to conventional neural networks. But on a detailed literature review, the application of these techniques to estimate factor of safety of soil stability has not been observed.

An improved morgenstern-price method using gaussian quadrature

The Morgenstern-Price (MP) method is an effective solution to compute the factor of safety (FOS) of a slope against sliding that has been used extensively for decades. In the MP method, the soil mass above the slip surface needs to be tediously divided into vertical slices to compute the force and moment integrals. The proposed research improves the computational efficiency of the MP method by employing the Gaussian quadrature for the integrals, where the soil mass division into a significant number of vertical slices is improved by aligning a few Gauss points along the slip surface. Consequently, the computational efficiency can be dramatically improved, resulting in a reduction in calculation efforts. Moreover, this research further refines the iteration scheme to satisfy the equilibrium conditions for the FOS using a robustly stable numerical algorithm with two initial scaling factors. The critical slip surface was determined by the simulated annealing algorithm. Finally, the proposed method was thoroughly validated via a series of benchmark examples. This research could improve the traditional MP method by enhancing its robustness and efficiency and provide an informative technique for force integrals that may be motivated by other problems in geotechnical engineering.

Determining the Critical Slip Surface of Slope by Vector Sum Method Based on Strength Reduction Definition

Slope-stability assessment involves the location of the critical slip surface and the corresponding factor of safety (FOS). Considering force-vector characteristics, the vector sum method was further studied based on the strength reduction definition of the FOS and stress field of slope, and the FOS can be calculated directly by the force limit equilibrium equation on the global sliding direction of the slope. For the sliding direction, it is rigidly proved to be determined only by the sliding shear stress along the slip surface based on the principle of minimum potential energy. Then, two examples with fixed slip surfaces were analyzed and the results were compared with the rigorous Morgenstern–Price method. Finally, two examples from the literature are investigated for searching the critical slip surface using the proposed method and a real-coded genetic algorithm. The calculated results revealed the rationality of the proposed method for both fixed slip surfaces and critical slip surfaces from the literatures in slope stability assessment. This proposed method provides a new path to assess the slope stability, which is worth to be further studied in practical engineering.

Analytical Reliability Evaluation Framework of Three-Dimensional Engineering Slopes

An analytical three-dimensional slope reliability evaluation framework was developed in this work independent of use of numerical simulations. The slope stability analysis was necessarily carried out by utilizing an extended three-dimensional Morgenstern–Price method, which was characterized by analytical formulations and competitive computational efficiency. Incorporation of the presented stability analysis method into response surface methodology led to an effective slope reliability evaluation framework. The applicability and superiority of this framework was examined and validated using a real complicated landslide case reported in practice, and a hypothetical slope example widely adopted in the literature. The impact of correlation coefficients and probability distribution patterns on the slope reliability assessment results was further addressed to derive additional benefits of this framework.

Seismic Analysis of Earth Slope Using a Novel Sequential Hybrid Optimization Algorithm

One of the most important topics in geotechnical engineering is seismic analysis of the earth slope. In this study, a pseudo-static limit equilibrium approach is applied for the slope stability evaluation under earthquake loading based on the Morgenstern–Price method for the general shape of the slip surface. In this approach, the minimum factor of safety corresponding to the critical failure surface should be investigated and it is a complex optimization problem. This paper proposed an effective sequential hybrid optimization algorithm based on the tunicate swarm algorithm (TSA) and pattern search (PS) for seismic slope stability analysis. The proposed method employs the global search ability of TSA and the local search ability of PS. The performance of the new CTSA-PS algorithm is investigated using a set of benchmark test functions and the results are compared with the standard TSA and some other methods from the literature. In addition, two case studies from the literature are considered to evaluate the efficiency of the proposed CTSA-PS for seismic slope stability analysis. The numerical investigations show that the new approach may provide better optimal solutions and outperform previous methods.

Stability analysis of mine overburden dump and improvement by soil nailing

The conventional method for carrying out stability analysis of dump involving Limit Equilibrium Method (LEM), when compared with the strength reduction method (SRM) using Finite Element Method (FEM) approach, resulted in overprediction of the factor of safety (FoS). In the present study, slope stability analysis of external overburden dump in Sonepur Bazari opencast mine has been carried out. Morgenstern Price method using constant inter-slice force function conducts the analysis of LEM using Geo-studio Slope/w, and the FEM analysis is carried out using the PLAXIS 2D 2016. The study is carried out to assess the effect of the dump’s friction angle, slope angle, height, and bench configuration. Further, the analysis considering the soil nailing is also conducted by optimizing the number of nails, the distance between nails, length of the nails, nail inclination angle. The stability analysis found that the dump is in a critical state (FoS = 0.92) with a circular failure surface. The optimum slope angle is found to be 30˚. It is observed that LEM cannot detect the increased localized stress concentration at the bench edge. Reinforcement of the dump using the soil nailing technique has affected the dump stability substantially, with an increase of 11% in the FoS; however, the effect of nail orientation on dump stability was less pronounced. Further bench provision to the dump slope increases the FoS by 27%, 21% and 19%, considering the total height of 60 m, 80 m and 100 m, respectively.

Optimal design of the high geogrid-reinforced slope at the airfield of an airport

Geogrid reinforced soil slope is a new type of slope supporting structure, which is of great significance for improving the slope stability, saving construction land and preserving the ecological environment. In order to provide the optimal design solution of the reinforced soil slope for high fill slopes, a case study is conducted on the No.6 slope at the northwest corner of the airport runway. Three design schemes with different slope ratios are carried out firstly based on the geological conditions of the slope and the field situation of the high fill slope. Secondly, the simplified Bishop method, Spencer wedge method and Morgenstern price method are used to calculate the stability factors of the reinforced slopes under the natural, rainstorm and earthquake conditions. Finally, the deformation characteristics of the slope and tensile force in reinforcements are investigated based on the finite element method under the natural conditions. The results show that all the proposed design schemes can meet the requirements of slope stability under different working conditions. A zigzag distribution of the tensile force in reinforcements in the multi-stage reinforced soil slope is observed along the slope height, and the maximum axial force of reinforcement increases abruptly at the toe of each slope. Compared with the design scheme of the gentle reinforced soil slope with the slope ratio of 1∶1.5, the reinforced retaining wall with the slope ratio of 1∶0.25 shows obvious advantages in reducing the slope height, consumption of geosynthetics, filling and excavation amount as well as slope protection area. The key issues including the slope stability, construction cost and duration are comprehensively considered, and the design scheme of the reinforced earth wall is reasonable.

Factor of safety of pile-stabilised slopes: an algorithm incorporating soil-arching effect

The current practice of factor of safety computation of pile-stabilised slopes depends substantially on either the extension of methods for normal slopes with the pile-contribution introduced as an additional term or finite-element modelling. Extending conventional methods to analyse pile-stabilised slopes fails to capture the key mechanisms like soil arching, gradual transfer of resistance offered by the pile through the slope, change in slip surface due to introduction of piles and so on. In this paper, a new algorithm is proposed to compute the factor of safety of pile-stabilised slopes, in which the Morgenstern–Price method is modified to incorporate the effect of a pile. The resistance offered by the pile is obtained using a pressure-based method which considers the soil-arching effect in horizontal and vertical directions. The gradual propagation of this resistance offered by the pile is incorporated through an iterative procedure, unlike the conventional methods. The algorithm considers the change in slip surface due to the introduction of the pile. The factor of safety values computed using the proposed algorithm were found to be in close agreement with that obtained from finite-element modelling. Moreover, a simple technique to determine the optimal location of stabilising piles and pile-spacing is also presented.