Traditional Limit Equilibrium Method Research Articles

Stability Grade Evaluation of Slope with Soft Rock Formation in Open-Pit Mine Based on Modified Cloud Model

In recent years, the frequent occurrence of slope failures has brought the issue of slope problems to the forefront of widespread public concern, which significantly impedes progress toward the secure and sustainable development of open-pit mines. And, high and steep slopes of weak rock strata, being a more complex type of slope, pose a greater potential for danger. In order to ensure the reliability of the safety evaluation results of the high and steep open-pit slope containing soft rocks, an evaluation index system with quantized grade intervals was created based on the thought of an analytic hierarchy process, and the MATLAB R2021a was used to calculate the numerical characteristic values of the cloud model. Then, a standard stability cloud model based on cloud theory was established. With the opening pit mine as an example, its slope stability practice cloud image was generated and the similarity between this image and the grades of the cloud model was calculated through the ECM algorithm to effectively identify the stability and verify the scientificity and validity of the model. The results show that the similarity between the practice cloud image and the standard stability cloud image for the total evaluation of the stability of an open-pit mine is 0.021, 0.279, 0.594, and 0.106, respectively. The slope stability is at grade C, which is basically consistent with the numerical simulation and the analysis results of the traditional limit equilibrium method, verifying that the model is scientific and effective to a certain extent. The method provides substantial guidance to ensure production safety in this specific open-pit mine. It provides ideas and means for other similar complex slope stability analysis and prevention. Meanwhile, it promotes the safe and sustainable development of open-pit mines.

Force distribution on polymeric geostrip reinforcements in MSE walls under seismic excitation

In this experimental study, the values and distributions of dynamic tensile force along the polymeric geostrip reinforcements were investigated under stepped increasing sinusoidal excitations with a series of shaking table tests on 1500 mm high or 1/3 scale physical mechanically stabilized earth wall (MSE) model. The effects of the peak ground acceleration ([Formula: see text]), slope angle of the cohesionless backfill material ([Formula: see text]), and stiffness of the polymeric geostrip reinforcement were assessed on both the potential failure surface geometry in the backfill soil and dynamic tensile forces along the lengths of polymeric geostrips. Three potential failure surfaces from the results of shaking table tests in the backfill cohesionless soil were detected as for states of quasi-elastic, plastic, and failure. However, neither the current design codes for MSE walls nor the theoretical recommendations truly reflect potential failure surface geometry in the backfill soil. Additionally, the values and distribution geometry of maximum incremental dynamic tensile forces ([Formula: see text]) on the reinforcements along the height of MSE wall recommended by design codes are not compatible with test results; however, the normalized location of total maximum incremental dynamic tensile force ([Formula: see text]) acclaimed by design codes is consistent with the test results. The traditional pseudo-static limit equilibrium methods result in over conservative horizontal dynamic earth pressure coefficient ([Formula: see text]) values generally as compared with the test results. The slope angle of the backfill material and stiffness of reinforcement have a negligible effect on the potential failure surface geometry; however, incremental dynamic tensile forces, total maximum incremental tensile forces, and horizontal dynamic earth pressure coefficient values increase with an increase in the stiffness of reinforcement and inclination angle of the backfill and peak ground acceleration value.

Probability analysis of rock slope using FORM based on a nonlinear strength criterion

Various uncertainties are frequently encountered in the assessment of landslide stability. However, the uncertainty of parameters in the Mohr–Coulomb strength criterion is a major concern in the studies, neglecting the uncertainty related to the strength criterion itself that is used to describe the strength of geotechnical materials. To assess the reliability of landslides, a new probabilistic analysis method is proposed in this study. According to the traditional limit equilibrium framework, an improved method based on a nonlinear strength criterion is deduced to determine the safety factor of landslides. The local mean value of the random variables on the failure surface is estimated by the analytical method, avoiding random field simulation. The first-order reliability method (FORM) is applied to estimate the failure probability of landslides. An example is analyzed using the proposed probability analysis method, and its effectiveness is primarily verified. The results show that the traditional limit equilibrium method based on the linear Mohr–Coulomb strength criterion estimates the stability and failure probability of landslides inaccurately.

The relict landslide in bimsoils in downtown Genova, Italy: a new modeling approach

Stability problems occurring in geological units with a block-in-matrix fabric are often analyzed with deterministic approaches and/or assuming block-in-matrix rocks/soils (bimrocks or bimsoils) to be homogeneous equivalent geomaterials. However, recent studies have demonstrated that since these formations are characterized by a great (dimensional, spatial and lithological) variability, reliable results can only be obtained if a stochastic approach accounting for different block arrangements and dimensions is used.This paper extends and improves a previous study from Minuto and Morandi (2015) to evaluate the stability of a relict landslide in bimsoil located in downtown Genova (Italy), where a deterministic approach and the traditional limit equilibrium method were used. In this work, different slope models with elliptical blocks of variable eccentricity, size and positions are generated by means of a stochastic approach and are analyzed with the FEM code RS2. Moreover, since the slope can be considered to be a bimsoil, interfaces between the blocks and matrix are introduced in order to better simulate the lower strength at the block/matrix contacts. The numerical analyses of the slope reveal that shallow failure surfaces have a higher probability of occurrence as compared to the deep failure surfaces considered by Minuto and Morandi (2015). Furthermore, lower safety factors are obtained when a block-matrix interface strength smaller than that of the matrix (i.e., a bimsoil) is simulated.

Evaluation of rock slope using q-slope, limit equilibrium and failure probability at andesite mine of Sidomulyo Village

For an open pit mine, the rock slope stability is one of the major significant challenges at every stage in the operation. It became a concern from the planning until the mining closure. Mining activities in the research location have entered the mining closure phase and produced the final slope that consists of 4 single slopes with an overall slope height of 65m and an angle of 62° that its stability is not yet known. The actual overall slope has discontinuities which affect the potential for failure. Most of the methods used in geotechnical practice for estimating slope stability are based on the traditional limit equilibrium methods. On the other side, very few empirical techniques exist to assess the slope stability. The empirical method of the Q-Slope is a relatively new methodology for assessing the slope stability in terrains built from rock masses. This method was developed over the last decade by Barton and Bar (2015), with modifications to the original Q-System for application in rock slope stability through the parameter of RQD, Jn, Jr, Ja, O-Factor, Jwice, SRFa, SRFb and SRFc. The stability analysis by Q-Slope method has resulted the slope in stable condition because the value of βQ-Slope > βSlope. The factor of safety limit equilibrium method and probability of failure used the actual geometry and Q-Slope geometry is known in stable condition because it fulfils acceptance criteria with FoS ≥ 1.1 and PoF ≤ 37,5% according to the regulation Ministry of Energy and Mineral Resources Decree 1827/K/30/MEM/2018.

Theoretical and numerical analysis of flexural toppling failure in soft-hard interbedded anti-dip rock slopes

Soft-hard interbedded structures are commonly found in anti-dip rock slopes and endow the slopes with special properties. In this work, a simple two-beam model was first used to discuss the possible failure modes of rock layers with different lithology. The exact failure sequence of rock layers depends on their tensile strengths, elastic moduli, and thicknesses. Then, based on the deformation compatibility of rock layers, a novel theoretical method called the DCM for assessing the stability of soft-hard interbedded anti-dip rock slopes was proposed. A centrifuge test and a numerical model were used to verify the feasibility of the DCM. The calculated critical g-level of 47 g for the centrifuge model and a safety factor of 0.96 for the numerical model agree well with the results of the centrifuge test (45 g) and numerical simulation (0.98). Moreover, the traditional limit equilibrium method (LEM) was also adopted to explore these two models. The calculated results of 68 g and 1.79 using the traditional LEM were found to be much larger than the validated values, with deviations of more than 50%. This finding implies that the traditional LEM is not suitable for assessing the stability of soft-hard interbedded anti-dip rock slopes. In addition, the failure evolution of toppling failure in soft-hard interbedded anti-dip rock slopes was investigated using numerical modelling. The results show that the soft and hard rock layers do not fail at the same time; the rock layers of one type of lithology are destabilized first, then the other rock layers begin to fail until the entire slope undergoes flexural toppling.

Finite element analysis of slope stability by expanding the mobilized principal stress Mohr's circles – Development, encoding and validation

In recent years, finite element analysis is increasingly being proposed in slope stability problems as a competitive method to traditional limit equilibrium methods (LEMs) which are known for their inherent deficiencies. However, the application of finite element method (FEM) to slope stability as a strength reduction method (SRM) or as finite element limit analysis (FELA) is not always a success for the drawbacks that characterize both methods. To increase the performance of finite element analysis in this problem, a new approach is proposed in this paper. It consists in gradually expanding the mobilized stress Mohr's circles until the soil failure occurs according to a prescribed non-convergence criterion. The present approach called stress deviator increasing method (SDIM) is considered rigorous for three main reasons. Firstly, it preserves the definition of the factor of safety (FOS) as the ratio of soil shear strength to the mobilized shear stress. Secondly, it maintains the progressive development of shear stress resulting from the increase in the principal stress deviator on the same plane, on which the shear strength takes place. Thirdly, by introducing the concept of equivalent stress loading, the resulting trial stresses are checked against the violation of the actual yield criterion formed with the real strength parameters rather than those reduced by a trial factor. The new numerical procedure was encoded in a Fortran computer code called S 4 DINA and verified by several examples. Comparisons with other numerical methods such as the SRM, gravity increasing method (GIM) or even FELA by assessing both the FOS and contours of equivalent plastic strains showed promising results.

Comprehensive Analysis of the Stability and Design of a High Cutting Rock Slope

To realize the harmonious unification of safety and economy when designing slopes, we used geological analysis and performed a qualitative evaluation to investigate the controlling factors affecting slope stability. The finite element strength reduction method (SRM) and traditional limit equilibrium method were used to investigate the stability safety factor of a high and steep rock cutting slope in Northern Guangdong. The results showed that the influence of the structure surface on slope stability is determined by the combination of the structure surface, shape of the structure surface, filling between structure surfaces, penetration of the structure surface, and water content and sensitivity of the structure surface, the influence of only one factor on slope stability is limited. We analyzed the slope and design it optimally, the results showed after reinforcement of the second-level slope, the slope revealed an incompletely penetrated shallow slip zone and an evident deep potential slip zone. Compared to the reinforcement that was without an anchor cable, the safety factor increased when the potential slip zone moved down. Based on the SRM and traditional limit equilibrium method, the design scheme of this slope meets the safety requirements of permanent slopes, and the excavated stone can be used for roadbed filling. Thus, the optimized design scheme can coordinate safety and economic indicators. Moreover, the application of strong engineering measures to the joint development of slope in engineering practice is conservative and unreasonable. The design of these slopes can provide a reference for slope design and construction.

Upper Bound Analysis of Non-Persistent Jointed Rock Slope Using Rigid Block Element Method

The upper bound method analyzing the stability of the non-persistent jointed rock slopes is proposed by considering rock bridge mechanical effects, which combines the upper bound theorem, the discretization technique of rigid block element and the nonlinear mathematical programming. The kinematically admissible velocity fields of non-persistent jointed rock are constructed. The non-linear mathematical programming models are established for solving the rigorous upper bound solution of ultimate load or safety coefficient by using successive linear programming algorithm. two numerical examples are performed and analyzed. The proposed method is successfully validated by comparing the simulation with those produced by other classical methods. The method has the following advantages: (1) it can simultaneously simulate the discontinuous mechanism properties of the rigid rock blocks and the continuous medium mechanism properties of the rock bridge failures. Both the tensile and shear mechanism effects of the rock bridges can be considered simultaneously; (2) comparing with the exiting numerical methods such as finite element method or discrete element method, this method can not only consider the tensile and shear effects of the rock bridges simultaneously, but also avoid the complex constitutive relationship between the rock masses and the joints. The safety factor and its corresponding failure mechanism can be obtained simultaneously; (3) comparing with the traditional rigid limit equilibrium method, this method does not need to make any assumption of the failure surfaces. The final critical failure mechanism can be directly obtained through mathematically programming method; (4) this method has the characteristics of clear concept, simple in the program composition and high computational efficiency.

Comparative assessment of slope stability in weathered schists using Q-slope and LEM

The slope stability in weathered schists formations has always been of great importance for studies in rock mechanics. The majority of the methods used in the geotechnical practise for estimating the slope stability are based on the traditional limit equilibrium methods, analysing the possibilities of circular and non-circular failures. On the other side, very few empirical methods exist for assessment of the slope stability. Q-slope is a relatively new methodology for the assessment of slope stability in terrains built from rock masses. This method was developed over the last decade by Barton and Bar (2015, 2017), with modification of the original Q-system and it is based on the results of more than 500 case studies all over the world in reinforcement-free slopes. This paper presents results of the slope stability assessment with the limit equilibrium and Q-slope method at four characteristic cut sections with unusual general heights (ranging from 30 m to 92 m), along the route of the A2 motorway, section Kicevo-Ohrid in the Republic of N. Macedonia, which is under construction. The subject cuts presented in this paper were excavated in the period 2014 – 2018 without the application of special measures for protection. The research area is built mainly from phyllite, sericite schists, quartz-sericite schists and graphitic schists, which are folded, tectonically disturbed and affected by the process of degradation. According to the results of the analyses, it can be emphasised that both limit equilibrium method and Q-slope are applicable at terrains built from weathered and tectonically disturbed schists because the stability conditions on site were confirmed with these two methodologically different approaches. As a general conclusion, we can summarize that the best way to assess the slope stability condition is when we combine different tools and methodologies, especially when we face highly variable rock mass conditions.

Stability evaluation of cut slopes in highly weathered schists using limit equilibrium, kinematical and empirical methods

1. Extended abstractThe traditional limit equilibrium method and the kinematic analyses are the first choices in the geotechnical practice for the assessment of the slope stability of a particular rock slope. The reason is that very few empirical methods exist for this purpose.This paper presents results of the slope stability assessment with limit equilibrium, kinematical and empirical methods for over 50 deep cut slopes in highly weathered schists along the A2 motorway section Kicevo-Ohrid in RN Macedonia. The research area is mainly composed of phyllite, sericite schists, quartz-sericite schists and graphitic schists. These rocks are highly weathered, tectonically disturbed and often folded, which means they are prone to local deformations, especially in aspects of the long-term impact of atmospheric influences and the existence of unfavourable joint sets. Although most of the failures that occurred had local character, on several cut slopes global failure occurred. The slope stability assessment of the subject rock formations is a difficult challenge because the highly weathered phyllite and schists are difficult to be characterised, considering the uncertainties associated with the material anisotropy and the network of discontinuities.This study employs different failure mechanisms of cut slope stability in complex geological media. The rock masses were modelled according to the generalized Hoek-Brown criterion while the joints behaviour was modelled using the Barton-Bandis shear strength criterion. Rocscience software package was used for executing the limit equilibrium analyses and the stability analyses along discontinuities. The relatively new and intuitive empirical method Q-slope was applied for the stability assessment of the excavated rock slopes.According to the results and the findings, it can be emphasized that although the limit equilibrium analyses showed relatively stable slopes, significant failures on several cut slopes occurred on site. The stability conditions on site were confirmed with the kinematical analyses and the Q-slope method.The final decision of the slope geometry should be made after the inspection of the excavated surfaces because it is very difficult to register the discontinuity conditions before the construction phase starts. The best way to assess the stability condition is with a combination of different tools and methodologies, especially when we face highly weathered rock formations.The next step of this research will be to propose a methodology, where the long-term rock slope stability and the associated level of risk will be evaluated using graphical diagrams.

Influence of Basalt Fiber-Reinforced Cement-Based Composite on Slope Stability

Slope instability may be caused by the action of external load or the lack of internal shear strength. The traditional limit equilibrium method cannot accurately calculate the safety coefficient of slopes enhanced by fiber-reinforced cement piles. Few scholars have discussed the anti-slip property, structural form, and design calculation of fiber-reinforced composite cement piles. Therefore, this paper chooses to analyze the influence of basalt fiber-reinforced cement-based composite (BFRCBC) on slope stability. On the one hand, the authors analyzed the anti-crack mechanism of BFRCBC: the strength analysis was carried out by the rule of mixtures, the anti-crack analysis was implemented by the fiber spacing theory, and the entire anti-crack process was discussed in details. On the other hand, the authors constructed a slope model, and performed the relevant stability analysis. Experimental results show that the BFRCBC cement piles can effectively enhance the stability of the slope.

Analysis of the failure modes and development of landslides using the material point method

Abstract Mass movements are frequent natural phenomena and especially dangerous due to increased population and irregular settlements in mountainous areas. Carrying out studies using methods that allow the numerical evaluation of their behavior is essential to mitigate and prevent these events' possible impacts. The traditional Limit Equilibrium and Finite Element methods fail to reproduce the problem from the beginning of the movement until the end of its development, so it is necessary to use new formulations. In this work the Material Point Method was selected to evaluate these movements in the stages of failure mode formation and development of landslide through an analysis of the soil shear strength and deformability parameters of a slope using the elastoplastic model with Mohr-Coulomb failure criterion. Maintaining a geometry and assuming soil mass behaves like a fluid, a single strength parameter and a single deformability parameter are analyzed to understand their influence before and after the failure.

Analyses of the Impacts of Climate Change and Forest Fire on Cold Region Slopes Stability by Random Finite Element Method

Increasing number of landslides occurred in the cold regions over the past decades due to rising temperature or forest fires associated with climate change. The instability of thawing slopes caused serious damages to transportation infrastructure, residential properties, and losses of human lives. These types of landslides, however, are difficult to analyze by the traditional limit equilibrium methods due to the coupled thermos-hydro-mechanical multiphysics processes involved. This paper describes a novel microstructure-based random finite element model (RFEM) to simulate the stability of permafrost slope subjected to climate change, including the increasing extent of thawing by warm atmosphere and thermal load due to forest fire. The properties of frozen soil are captured with random finite element model incorporating soil-phase coding. The thermomechanical responses of a permafrost slope are simulated to obtain the temperature, displacement, and stress fields. From these, the local factors of safety are obtained, which predict failure slumps along the slope that are consistent with the field-observed failure behaviors in permafrost slopes. The effects of climate change on the permafrost slope stability are analyzed for the years of 1956, 2017, and 2045. The results demonstrated appreciable amount of effects of climate change on the extent of slope failure zones. Forest fire led to melting of frozen soil and also affects the slope stability primarily in the shallow depth.

Probabilistic evaluation of the seismic stability of infinite submarine slopes integrating the enhanced Newmark method and random field

For evaluation of the seismic stability of submarine slopes, traditional deterministic methods may not reflect the actual situation due to the uncertainties in input values such as seismic acceleration, soil properties, and hydraulic conditions. In this study, probabilistic analyses were conducted based on the use of an enhanced Newmark method to evaluate the seismic stability of submarine slopes. In the probabilistic workflow, the infinite slope model was used, whereby the spatially varied strengths of marine sediments were simulated by non-stationary random fields discretized by the Karhunen-Loeve expansion. The positions of the potential slip surfaces were searched automatically, rather than being predefined as in the traditional limit equilibrium method. Artificial earthquake accelerations, exhibiting the same spectral characteristics, were simulated as the input ground motions in the probabilistic analysis. The pore water pressure generation and dissipation models were incorporated into the enhanced Newmark method when calculating the permanent displacements of the submarine slopes. Monte Carlo simulations were conducted for statistical characterization of the slope displacements and their failure probabilities. The results of the analysis indicate the superiority of the probabilistic framework and demonstrate the significant effects of pore water pressure and the spatial variability of the soil strength on the displacements and failure probabilities of submarine slopes.

Limit equilibrium solution for the rock slope stability under the coupling effect of the shear dilatancy and strain softening

In addition to obeying the generalized Hoek-Brown (GHB) strength criterion, the shear behavior of the rock mass sometimes has the effect of the shear dilatancy and characteristics of the strain softening. However, the traditional limit equilibrium (LE) methods can only solve the slope factor of safety (FOS), and it is difficult to calculate the displacement of sliding body (DOSB) of slope. Therefore, it is rarely reported that the LE analysis on rock slope stability under the coupling effect of the shear dilatancy and strain softening. Here, referred to the effect of the shear dilatancy and characteristic of the strain softening for rock mass, the calculation model for slope DOSB is constructed. Then, based on the assumptions of the stresses on the slip surface, the LE solution for rock slope stability is established according to the mechanical equilibrium conditions satisfied by the sliding body. Meanwhile, the calculation formula of slope DOSB is derived by introducing the energy balance equation of sliding body for the slope with the small sliding displacement. Further, the iterative loop calculation strategy is given to solve the slope FOS and slope DOSB for achieving the purpose of quickly obtaining the implicit solution. By comparison and analysis on some slope examples, the feasibility of the present method is verified. Compared to the traditional LE methods, the present method can not only analyze the stability of rock slope under the nonlinear strength criterion, but also study the influence of the shear dilatancy and strain softening of rock mass on the rock slope stability.

Searching for critical slip surfaces of slopes using stress fields by numerical manifold method

This study first reviews the numerical manifold method (NMM) which possesses some advantages over the traditional limit equilibrium methods (LEMs) in calculating the factors of safety (Fs) of the slopes. Then, with regard to a trial slip surface (TSS), associated stress fields reproduced by NMM as well as the enhanced limit equilibrium method are combined to compute Fs. In order to search for the potential critical slip surface (CSS), the MAX-MIN ant colony optimization algorithm (MMACOA), one of the best performing algorithms for some optimization problems, is adopted. Procedures to obtain Fs in conjunction with the potential CSS are described. Finally, the proposed numerical model and traditional methods are compared with stability analysis of three typical slopes. The numerical results show that Fs and CSSs of the slopes can be accurately calculated with the proposed model.

Variational calculus method for passive earth pressure on rigid retaining walls with strip surcharge on backfills

In light of the limit equilibrium conditions of soil mass retained by rigid retaining walls with distanced strip surcharge on its top surface, a variational calculus method is provided to calculate the passive earth pressure on the wall. By establishing the functional relationship between the earth pressure and potential slip surface as well as normal stress on it under a specified action point of the resultant force of the earth pressure, a unified closed-form solution to the passive earth pressure is derived and preformed easily by an implicit solution tactic via Matlab. It can quantitatively exhibit the influences of fundamental parameters on the force and corresponding critical slip surface including the soil properties, soil-wall interface friction angle, dip angle of the wall back, dip angle of the top surface of the retained soil, strip surcharge, net distance from the wall back to the surcharge, distribution width of the surcharge, and so on. These parameters except for unit weight, cohesion of soil and strip surcharge have nonlinear influence on the value of the passive earth pressure. Analysis results of some examples indicate the passive earth pressure by the proposed method is usually less than that by traditional limit equilibrium methods, and equal to the Coulomb's solution under certain conditions.

Three-Part Wedge Method for the Stability Calculation of Embankment Supported on Rigid Pile Foundation

Rigid piles have been widely used to reinforce soft subgrade. However, some studies do not consider the bending failure of piles and wedge sliding surfaces, which may lead to an overestimation of stability. In this study, a stability calculation method for a multi-section linear sliding surface is first derived and then simplified to three-part wedge method based on the numerical modeling of the failure evolution process. The real safety factor is replaced by the average value of the upper and lower bound solutions of the embankment stability safety factor. Through calculations, then the average value or the approximate solution of the real value, of both the upper and lower bound solutions can be obtained. The accuracy of the approximate solution can be verified through an analysis of the relative error of the average and true values. Finally, the proposed method was verified by a three-dimensional numerical simulation method and compared with the traditional limit equilibrium method and the equivalent shear strength parameter method. The results indicate that the support contribution of rigid piles to the embankment can be effectively reflected by considering wedge sliding surfaces, and a more reasonable stability safety factor can be obtained through the proposed method.

Implementation of a large deformation finite element modelling technique for seismic slope stability analyses

Post-slide investigations show large displacement of failed soil mass in many earthquake-triggered landslides. An Eulerian-based finite-element modelling (FEM) of large deformation of soil, for pseudostatic and dynamic loadings, is presented in this study. The Eulerian FEM is compared with Lagrangian-based explicit and implicit finite-element (FE) modelling approaches. The dynamic FE modelling of two hypothetical slopes for eight earthquake acceleration–time histories show that the failure surfaces develop progressively, which cannot be modelled using the traditional limit equilibrium method (LEM). A large plastic shear strain concentration (i.e. shear band formation) occurs when the strain-softening behaviour of soil is considered. The similarities and differences between the results of dynamic and pseudostatic FE analyses based on estimated pseudostatic coefficient from acceleration–time records are presented. The duration of an earthquake influences the failure process and displacement of the failed soil mass. The displacement of the toe obtained from FEM is compared with Newmark's simplified approach. The developed Eulerian-based FE modelling technique has been used to simulate large-scale landslides in sensitive clays due to earthquake loading [1].