Interslice Forces Research Articles

A Displacement-Dependent Limit-Equilibrium Slice Method for Slope Stability Analysis

Displacement and factor of safety are two crucial pieces of information about slope stability, but the traditional limit-equilibrium slice method has a significant defect; that is, it cannot reflect slope displacement. In this paper, a displacement-dependent limit-equilibrium slice method is proposed based on the soil shear constitutive model and Morgenstern–Price assumption of interslice forces to establish the relationship between the factor of safety and displacement. In addition to the overall factor of safety, point factors of safety and point displacements can also be obtained using the proposed method to characterize the displacement-dependent slope stability. The point factor of safety and shear displacement of each soil slice calculated using the proposed method are slightly higher and smaller than those calculated by the modified displacement-dependent Janbu method. The iterative process of the proposed method is simpler and more stable than that of the modified displacement-dependent Janbu method. Calculation results of four examples show that the point factors of safety at the upper and lower ends of the slide mass are generally smaller than those at the middle part of the slip body, and the shear displacement of the soil slice near the slope top is generally larger than those at the other positions. The proposed method associates the factors of safety with slope displacements, which allows us to quantitatively assess the slope stability immediately in practice by monitoring the displacements of some key points on it.

A Method for Computing Slip-Line Fields with Stress Discontinuity in Cohesionless Backfills

A method for computing slip-line fields in the case of cohesionless backfills with stress discontinuity was proposed. The potential failure zone is divided into the Rankine zone and the transition zone, and the Rankine zone is rigorously determined using the theory of plastic mechanics. The potential failure zone and the Rankine zone are then further divided into a series of triangular slices. On the basis of the force and moment equilibrium conditions of a typical triangular slice, the recurrence equation of the lateral force is established. Furthermore, the relationship between the failure surface inclination angle and the interslice force inclination angle is established by satisfying the Mohr–Coulomb criterion. An iterative procedure for calculating the lateral force of the triangular slices by changing the failure surface inclination in the transition zone is performed until the interslice force satisfies the stress condition of the transition zone boundary, resulting in a stress discontinuity line if the Rankine zone and the transition zone intersect and the intersection line satisfies the stress characteristics of stress discontinuity. Example studies are performed to verify the present method, which shows that the soil–wall interface friction has the most significant effect on stress discontinuity, and the location of the stress discontinuity line gradually approaches the backfill surface with an increase in retaining wall inclination.

Iterative Horizontal Method of Slices for Global Stability of Slurry Trench in Layered Cohesive-Frictional Soils

This paper presents an iterative horizontal method of slices (iterative HMS) for the global stability analysis of a slurry trench in layered cohesive-frictional soils. The iterative HMS differs from existing HMS models in terms of the assumptions on interslice forces. Preceding HMS techniques postulate that normal interslice forces can be evaluated from overburden pressures, which can lead to the violation of failure criteria along interslice boundaries. The iterative HMS ensures that a limit equilibrium system is established without violating the failure criterion throughout the entire soil mass. This is achieved by iteratively adjusting interslice forces by means of enforcing the failure criterion for the aforementioned problematic slice boundaries violating the failure conditions. The performance of the iterative HMS is evaluated in example problems of a slurry trench in uniform clayey soils and cohesive-frictional strata. The results are compared against solutions obtained using finite-element limit analysis (FELA) and a shear strength reduction FEM (SSRFEM). This comparative analysis shows that the adjustment in interslice forces is important for reasonably assessing trench stability conditions. A parametric analysis is performed by using the iterative HMS to show under what trench construction parameters the adjustment of interslice forces cannot be neglected in the stability analysis of a slurry trench.

Stability Analysis of Composite Soil Nailing Wall Based on Improved Energy Method

Composite soil nailing wall is widely used in slope support because of its low cost and safety, but its global stability still needs more accurate calculation. Based on plastic limit upper limit analysis and vertical strip partition method, the calculation formula of stability coefficient was derived for prestressed anchor composite soil nailing wall. FLAC3D and GeoStudio were used to calculate and analyze an engineering project supported by composite soil nailing wall in Lanzhou City, and the feasibility and correctness of the derived formula were verified. Finally, the grey correlation analysis of the sensitivity of the derived formula was analyzed. The results show that for calculating the stability coefficient, the limit equilibrium method needs to consider the complex force analysis, while the energy method can well avoid the inter-slice force, making the physical meaning of the formula clearer. The formula introduced in this paper is more efficient and feasible. The stability coefficient is most sensitive to the internal friction angle, followed by slope angle, cohesion, and finally unit weight of soil.

A limit equilibrium approach to the use of stability bunds in the design of HDPE-lined tailings storage facilities

In recent years the requirements for a barrier system between the waste body of tailings storage facilities (TSFs) and the natural ground (NG) has necessitated the use of HDPE-lined TSFs in South Africa and other countries. The addition of an HDPE liner creates an interface between, inter alia, the tailings and surrounding soils on the footprint of the TSF. It is known that low-strength materials beneath slopes can cause slope instability. One method which can theoretically mitigate this instability of a lined TSF is the addition of stability bunds along the footprint of the TSF. Altering the profile of the footprint to include slope changes which oppose the direction of the failure creates passive slices in a limit equilibrium analysis. The passive slices actively oppose the movement of active slices, resisting the mobilization of tailings, thus greater active slice forces are required to develop a failure surface running along the liner interface. Two scenarios are presented and compared. The first scenario retains the ground profile unaltered and the second scenario includes stability bunds along the ground profile. An in-depth assessment is made of the interslice forces and the interface shear stresses for each scenario. The theoretical background is discussed in greater detail to determine the mechanisms of reinforcement provided by the bunds.

Stability Analysis Method for a Prestressed Railway Embankment considering the Additional Stresses Propagation Effect

Abstract To evaluate the stability of a prestressed railway embankment (PRE), approximate solutions for the additional normal and shear stresses on an arbitrary potential sliding surface of a PRE are first derived using the elastic theory, by which the propagation effect of additional stresses due to the prestressing loads is appropriately considered. Then, a limit equilibrium slice method incorporating the additional stress effect, equivalent interslice forces, track weight, and train axle load but avoiding repeated iteration calculations is developed to analyze the PRE stability. The additional stress solutions are also introduced to modify three commonly used conventional slope stability analysis methods, and comparative analyses were performed to investigate the applicability of the proposed method. The results showed that the differences between the safety factor (Fs) of a PRE evaluated using the proposed and modified methods were within 2% in this study and the values were less than those yielded by the conventional methods because of the partial negative effect of the additional normal and shear stresses on a few slices around the lateral pressure plate (LPP). Besides, the adaptive genetic algorithm was introduced to search the critical sliding surface of the PRE. Finally, the effect of reinforcement pressure on the stability of a PRE was investigated, where the results indicated that the Fs of the PRE increased from 1.323 to 1.626 with an increase of the reinforcement pressure from 0 to 200 kPa, while the PRE gradually varies from potential integral instability to potential local instability. The accurate and efficient determination of the additional stresses on the sliding surface is important in analyzing the PRE stability, and the developed method can provide an easy-to-use and relatively safer stability analysis method for the design of a PRE.

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.

Comparison of factor of safety using different method of analysis for slope stability

Currently, the construction of slope is increasing, thus, the risk of slope to fail also increase. The series of landslide happen to the man-made slope has been recorded since in the early of 1993 until now. Many efforts such as treating the critical slope, redesigned the failed slope, and analyze the stability of the slope have been done. However, the landslide is still happening in Malaysia. The factor of safety (FOS) from the stability analysis that has been used might not be adequate to determine the safety of the slope in Malaysia. Therefore, in this study, the optimum factor of safety is obtained by using three methods of slice, Bishop’s Simplified method, Spencer method, and Morgenstern-Price method which have been used in many projects. A study place is selected in Ladang Balau, Semenyih, in Selangor and from the CIU test, the important soil parameter for slope is extracted for analysis of slope stability using SLOPE/W and manual calculation. The lambda for Spencer method and Morgenstern-Price method was generated for further discussion on the relationship between lambda and factor of safety. The data generated from both calculation method, from manual and software, were discussed and next the ideal method to achieve the optimum factor of safety determined. The factor of safety for every method basically are influenced by the interslice shear force presence but not Bishop’s Simplified method as moment equilibrium is insensitive towards interslice force function. For lambda, the factor that influenced the value is the function used; constant and half-sine function, however, for Bishop’s Simplified method, the lambda is equal to zero as the method ignored the interslice shear force. The Morgenstern-Price method has been chosen to be the best method to generate a good factor of safety.

Novel Model for Limit-Equilibrium Analysis of Slope Stability with a Nonlinear Strength Criterion

Slope stability has always been a concern of the geotechnical engineering community, and geotechnical scholars have continued to explore the reasonable failure mechanism of slopes and make the theoretical models of slope stability more reliable. This work established a novel model for limit-equilibrium (LE) analysis of slope stability with a nonlinear strength criterion. In this theoretical model, the thrust line of interslice force and corresponding increment are reasonably simplified. Then, the formula of normal stress on slip surface is derived by assuming the increment of normal interslice force. Meanwhile, strength reduction technology is applied to reduce the shear strength of the geotechnical body on the slip surface with slope factor of safety (FOS) to obtain shear stress on the slip surface. Thereafter, mechanical equilibrium conditions satisfied by the whole slope sliding body and newly introduced equation about increments of interslice force are used to solve LE stability of the slope. For stability analysis of a slope with a nonlinear strength criterion via a simple and feasible calculation process, an iterative loop solution strategy is adopted in the analysis. After comparison and analysis of several slope examples, the feasibility and rationality of the present method are verified. Moreover, the present method has high efficiency in terms of calculation speed.

Pseudo-static internal stability analysis of geosynthetic-reinforced earth slopes using horizontal slices method

ABSTRACT In this study, the well-established pseudo-static approach along with the horizontal slices method (HSM) is employed to investigate the seismic internal stability of geosynthetic-reinforced earth slopes. Previous simple HSM analyses were based on a primary assumption stating that the normal inter-slice forces are exerted on the mid-length of horizontal sections. However, this simplifying assumption could give rise to substantial errors in the calculation of design parameters, specifically in the case of high seismic excitations or low soil strength parameters. To address this deficiency, a balancing moment is considered as a new variable to account for the corresponding eccentricity. In the current HSM, two sets of unknown variables, including horizontal inter-slice forces and shear forces along failure surface, are determined using the well-known λ coefficient and the Mohr-Coulomb failure criterion. In this new technique, the traditional ‘5N-1ʹ type of HSM analysis is reduced to a robust and rigorous ‘3N’ one with the same predictive capability. The influence of various parameters, including soil characteristics, slope geometry and different earthquake coefficients are rigorously examined. Moreover, a number of useful graphs is provided to help engineers in the preliminary seismic design of geosynthetic-reinforced earth slopes.

Evaluating the active earth pressure exerted by granular soils with nonlinear strength behaviour using the slice-based limit equilibrium method

ABSTRACT Conventional earth pressure theories are generally applicable to soils with a linear strength envelope. Preferred granular backfill, however, usually exhibits a decreasing peak friction angle with an increasing normal effective stress. In this study, the slice-based limit equilibrium method is used to evaluate the active earth pressure applied by soils that exhibit nonlinear strength behaviour. The force and moment equilibrium equations for a differential soil slice are introduced, and the boundary conditions for the active earth pressure problems are specified. The mathematical nature of the active earth pressure is explored. It is found that the active earth pressure corresponds to a stationary point on a saddle surface. Seeking the active earth pressure is equivalent to identifying the maximum from a series of local minima. By introducing a combination of two functions for the inter-slice force angle distribution, the local minimisation process for each possible failure surface is implemented by varying the combination factor within its valid range. The proposed solution strategy is compared with existing methods and reasonable agreement is obtained. The influences of the inter-slice force angle distribution on the resultant active earth pressure and its position of application are also studied by using three different combination functions.

Active thrust of sand with anisotropic seepage: A generalized limit equilibrium approach

Estimation of the magnitude and location of the lateral earth thrust on a retaining wall considering seepage flow effects within the backfill is necessary to examine the failures of such walls. In this work, the generalised limit equilibrium approach, based on the method of slices, was used to compute the magnitude and location of active earth thrust on the vertical face of a retaining wall taking into account steady seepage flow in the sand backfill. A drainage system along the backfill and wall interface and an anisotropic permeability characteristic of the backfill was considered for describing the pore pressure distribution within the backfill. Using force equilibrium conditions and an assumption regarding the direction of the interslice forces, the total normal stress distribution along the failure surface and the magnitude of total active earth thrust were determined. Subsequently, the location of the active earth thrust was determined to satisfy the moment equilibrium condition. Both planar and curvilinear failures surfaces were analysed to examine the impact on the solutions. It was confirmed that seepage flow within backfill substantially affects both the magnitude and location of active earth thrust, depending upon the degree of anisotropy.

Improved general slice method of limit equilibrium for slope stability analysis

For traditional slice methods of limit equilibrium used to analyze slope stability, some hypothetical conditions on interslice force are generally introduced to solve the problem. In order to reduce the defect theoretically due to the related hypothesis, more rigorous constraints of interslice force are completely considered in light of static equilibrium conditions and energy dissipation principle of the interface between two adjacent slices. Without hypothesis of interslice force, the slope stability analysis is transformed consistently into a non-linear programming problem to be solved. So, a generally improved solution of slice method of limit equilibrium to slope stability is put forward. In particular, influence of the dilation angle of soil on slope stability can be involved in the method. The proposed method can be utilized for any slopes with arbitrary slip surfaces.

Search of Non-circular Slip Surface Based on Improved FOA

The determination of the most critical non-circular slip surface can be attributed to the optimization of complex non-linear multi-peak function due to its numerous control variables and large amount of calculation. It is a trend in recent years to apply intelligent optimization algorithm into slope stability analysis. Considering that the standard Fruit fly Optimization Algorithm (FOA) is prone to fall into local extremum, the improved Fruit fly Optimization Algorithm is obtained by incorporating the standard FOA with the simulated annealing idea. In order to improve the search efficiency, a fixed step size is adjusted to an adaptive step size, and a double tier search strategy is proposed to be applied: the potential non-circular slip surface is obtained from the outer layer, and the factor of safety along the potential slip surface is calculated step by step from the inner layer. The improved FOA is applied to a slope with weak interlayer. The feasibility, superiority and efficiency of the improved algorithm are proved by comparing its answers to the judges'. Different inter-slice force functions, various initial values of Fs and λ are assumed, and the results show that these parameters could hardly affect final solution for safety factor.

Determination of Creep-Induced Displacement of Soil Slopes Based on LEM

The creep of earth slopes is an important challenge of the long-term stability of slopes. This paper develops a limit equilibrium method (LEM)-based analytical approach for calculating the shear displacement of creep-induced failure surface in 2D state for all slices where both force and moment equilibrium equations are simultaneously satisfied as a new research. The relation between shear displacement and creep time is obtained with regard to visco-elastoplastic creep model. The overall safety factor is first calculated for the slip surface using Spencer method. Then, the shear displacements of all slices are obtained based on vertical displacement of crown and using displacement compatibility relation exists between slices. By combining force and moment equilibrium equations and assuming a zero resultant for inter-slice forces, the vertical displacement at crown is determined using visco-elastopastic creep model. A numerical model was developed to calculate slope displacement by the proposed method. Force and moment equilibrium equations are simultaneously satisfied by iteration technique. The proposed method is verified through two numerical examples comparing the new approach and conventional finite element method.

The implementation of the Laplace equation in a slope stability analysis: the streamline method

The Laplace equation satisfies the principle of the minimum potential energy, which means that groundwater flows through soil in an optimized path of minimal energy under a given condition. The essential idea of the proposed method is to convert a pure optimization problem into a boundary value problem by solving an anisotropic Laplace equation. A virtual seepage field is constructed to compute streamlines based on a dedicated permeability tensor. The permeability tensor is deduced according to the slope stress state. The magnitude of the tensor is determined by the stress failure ratio (SFR), and the major principal direction of the tensor is determined by the orientation of the maximum SFR. The boundary conditions can be applied as the entry and exit method used widely in the limit equilibrium method. The most critical slip surface is the streamline with the minimal safety factor. The proposed method is based on an elastic finite element stress and a confined virtual seepage field. Neither iterations nor assumptions about the slip surface shape and the interslice force are required in the proposed method. The major advantage of the proposed method is the optimization dimension reduction. This approach converts a 2D slope stability optimization problem into a 1D problem and greatly increases the efficiency of critical slip surface searching.

Extension of Spencer’s Circular Model to Stability Analysis of Landslides with Multicircular Slip Surfaces

This paper presents a new limit equilibrium method based on analysis of landslides with multicircular slip surfaces in the Three Gorges Reservoir area, China. An important innovation of this method is that the rigid sliding mass is divided into numerous interrelated Spencer’s circles sharing the same factor of stability, so that each of them possesses a real centre of rotation and an independent inclination of interslice forces. The analysis is accomplished by iterations to satisfy both force and moment equilibrium for each circle. Two real cases were then adopted to verify the effectiveness of the method in the analysis of both slope stability and the design forces on piles. Factors influencing the performance of the method were also investigated, which reveal that the concavity of the local slip surface near the slope toe has a major impact. The importance of the proximity between the actual and the fitted sliding surfaces was highlighted for ensuring accuracy of the method when extended to the real cases.

2D slope stability analysis based on Pan’s maximum principle

Traditional slice methods for slope stability analysis must introduce some assumptions regarding the inter-slice forces and hence lack a rigorous theoretical basis. In this study, a new block method for slope stability analysis is proposed based on Pan’s maximum principle. In this method, the slope is cut into a block system, and the search for the maximum factor of safety is accomplished by a nonlinear mathematical programming method. During the searching process, the magnitude, direction and action point of the inter-block forces are taken as a variable system. The static equilibrium and yield criterion that satisfy the requirement of the statically admissible field of Pan’s maximum principle are used as constraints, and the maximum factor of safety is regarded as the optimization objective. Therefore, the problem of slope stability analysis is transformed into an optimization problem. This method does not introduce any other assumptions except for block rigidity. This approach can compensate for not only the lack of theoretical rigour in the traditional limit equilibrium theory but also the low computing efficiency and the optimization difficulty of the limit analysis finite element method. In this new method, a block system is used to simulate the structural characteristics of a toppling slope and the transfer of the toppling load and moment through the balance of the force and moment. The proposed block method is verified by one case with an analytical solution and two ACDAS test questions; additionally, the proposed method offers a satisfactory result for complex engineering slopes. In addition, both slope sliding and toppling failure can be analysed, and the results determined with the proposed method are close to those determined with the Goodman-Bray method. Because the computing precision of this method is comparable with the limit analysis finite element and its computation cost is as low as that of the limit equilibrium method (LEM), this method demonstrates robust slope stability analysis and has great potential in engineering practice.

Study on the limit equilibrium slice method considering characteristics of inter-slice normal forces distribution: the improved Spencer method

The limit equilibrium slice method is a universal method to determine the safety factor of a slope. However, the forms of the inter-slice normal forces distribution are not considered in the traditional limit equilibrium slice method, and the influence of different positions of thrust lines on the safety factor is not considered. Thus, an improved Spencer method is developed here, wherein the characteristics of the inter-slice normal forces distribution are considered. The safety factor of a deep concave sliding surface is calculated, and a difference of approximately 20% is found between the safety factors that are obtained using the improved method and those obtained using the traditional method. The influence rule of different forms of the inter-slice normal forces distribution on the safety factor has been studied, and the influences of various factors on the inter-slice forces contribution, the stress state of the slice and the stress state of the slip surface have been analysed. Finally, two case studies are combined to illustrate the impact of the improved method on engineering safety and economic benefits.

Slope stability analysis using modified Fellenius’s and Bishop’s method

Analysis of slope stability is very important as many structures in hilly areas failed due to instability of slope. The aim of this study is to determine the factor of safety (FOS) of slopes located at Pahang Matriculation College by using limit equilibrium method. Two methods known as modified Fellenius’s method and modified Bishop’s method are used in this study. Laboratory testing involving index and engineering properties are conducted to determine the properties of soil within the study area. The soil at Pahang Matriculation College can be classified as sandy SILT with high plasticity. From the analysis, the FOS values for two slopes in saturated soil conditions (0 kPa suction) are between 1.262-2.885 when using Bishop’s method which are higher compare to 1.199-2.688 when using Fellenius’s method. The percentage differences of FOS between these two methods are between 5.25% to 7.33%. For slopes in unsaturated conditions (20 kPa suctions), the FOS are between 1.550-3.702 when using modified Bishop’s method which always higher compare to 1.492-3.507 when using modified Fellenius’s method. The percentage differences of FOS are between 3.89% to 5.56%. The relative accuracy of Bishop’s method is due to it consider only the vertical equilibrium of each slices and there is no need to consider the horizontal components of the interslice forces without introducing serious error in the FOS value.