Interslice Forces Research Articles

LEM-DEM coupling for slope stability analysis

Slope stability analysis is a keen area of interest to researchers of geotechnical engineering and geological hazards. To date, the most popular approach applied in slope engineering design is the limit equilibrium method (LEM). However, for this method, some assumptions are required when obtaining the sliding force and the resistance force on the slide face. The discrete element method (DEM) presents an advantage in the calculation of the interaction forces between adjacent blocks without assumptions. This paper introduces a new slope stability analysis based on coupling of both approaches, herein referred to as LEM-DEM. The main LEM-DEM procedure is to transform the slice model of a slope in LEM into the DEM model and obtain the sliding force and the resistance force to calculate the factor of stability (Fos). The sensitivity analysis of the parameters in DEM, such as normal and shear stiffness, was conducted to illustrate that LEM-DEM suggests higher contact stiffness. A comparison between the Fos values in DEM and LEM-DEM was also conducted to indicate the rationality and advantages of LEM-DEM, especially for a gentle slope with a changing shear force direction in the slice model where the interslice forces in LEM are unreasonable. Furthermore, this study carried out a 3D landslide stability analysis extension, along with the results, for the proposed method.

Limit Equilibrium Stability Analysis of Layered Slopes: a Generalized Approach

Traditionally, application of the conventional logarithmic spiral in limit equilibrium (LE) analyses has been limited to homogenous materials. Herein, a modification of the conventional logarithmic spiral LE approach is proposed to account for transitions in soil conditions and provide insight into the internal statics associated with this approach, termed the compound log-spiral (CLS). Comparing both factor of safety (FS) and failure surfaces for a range of frictional strength combinations, the CLS approach demonstrates good agreement with results derived from both generalized, commercially available rigorous LE analyses and finite element analyses. The utility of the CLS method is further demonstrated through an example where the stability of a heavily stratified seacliff is considered. The proposed method satisfies equilibrium at a limit state without resorting to internal statistical assumptions associated with traditional LE approaches. Furthermore, it enables the explicit determination of internal statics, such as inter-slice shear forces, inter-slice normal forces, inter-slice angle, line of thrust, and normal stress distributions, which is a less-than-trivial task for the complex slip surface geometry realized in heterogeneous slope failures. Subsequently, the reasonableness of results could be assessed.

The inclination of the interslice resultant force in the limit equilibrium slope stability analysis

Currently, all of the semi-precise slice methods are developed based on the assumed relationships between interslice shear and normal forces (or interslice force directions). These assumed relationships lack theoretical basis, and reduce the accuracy of determination of the thrust force of sliding mass in the reinforced structure design. Therefore, a precise relationship of interslice forces is required. A functional relationship between the interslice force direction and influencing factors including the gradient of the sliding surface, the gradient of the slope surface and the shear strength of the sliding surface is deduced based on the Mohr-Coulomb failure criterion. Then, the deduced equation is employed to determine the interslice force directions and assess the stability of the Houzishi landslide, which is a case in the Three Gorges Reservoir area in China. The comparison among the inclinations of the interslice resultant force obtained by the numerical simulation, our derived equation and assumed values of other slice methods shows that our derived equation provides the best match with the simulation results. In addition, the safety factor of our method that incorporates the newly derived equation, is consistent with the precise slice method, further demonstrating the effectiveness of the equation. Therefore, the semi-precise slice method that incorporates the derived relationships of interslice forces provides a more reliable approach for estimating the thrust force in the design of reinforced constructions.

Analytical Calculation for slope stability based on the Combination of Horizontal Slice Method and Oblique Slice Method

An analytical method for analyzing the stability of the homogeneous slope based on horizontal slice method is presented. A combination model of horizontal slice and oblique slice are used for analysis the inter-slice forces. The analytical expression of factor of safety is obtained with the assumption that the shear strength of soil meets the Mhor-Coublum strength criterion. The position of critical slip surface and its corresponding factor of safety computed by the development of the optimization technique are in good agreement with Bishop’s method. The advantages of presented method are straightforward in analyzing the stability of slope.

Limit equilibrium analysis for rock slope stability using basic Hoek–Brown strength criterion

Hoek–Brown (HB) strength criterion can reflect rock’s inherent failure nature, so it is more suitable for analyzing the stability of rock slopes. However, the traditional limit equilibrium methods are at present only suitable for analyzing the rock slope stability using the linear equivalent Mohr–Coulomb (EMC) strength parameters instead of the nonlinear HB strength criterion. Therefore, a new method derived to analyze directly the rock slope stability using the nonlinear HB strength criterion for arbitrary curve slip surface was described in the limit equilibrium framework. The current method was established based on certain assumptions concerning the stresses on the slip surface through amending the initial normal stress σ 0 obtained without considering the effect of inter-slice forces, and it can satisfy all static equilibrium conditions of the sliding body, so the current method can obtain the reasonable and strict factor of safety (FOS) solutions. Compared with the results of other methods in some examples, the feasibility of the current method was verified. Meanwhile, the parametric analysis shows that the slope angle β has an important influence on the difference of the results obtained using the nonlinear HB strength criterion and its linear EMC strength parameters. For β≤45°, both of the results are similar, showing the traditional limit equilibrium methods using the linear EMC strength parameters and the current method are all suitable to analyze rock slope stability, but for β>60°, the differences of both the results are obvious, showing the actual slope stability state can not be reflected in the traditional limit equilibrium methods, and then the current method should be used.

Limit equilibrium method for slope stability based on assumed stress on slip surface

In the limit equilibrium framework, two- and three-dimensional slope stabilities can be solved according to the overall force and moment equilibrium conditions of a sliding body. In this work, based on Mohr-Coulomb (M-C) strength criterion and the initial normal stress without considering the inter-slice (or inter-column) forces, the normal and shear stresses on the slip surface are assumed using some dimensionless variables, and these variables have the same numbers with the force and moment equilibrium equations of a sliding body to establish easily the linear equation groups for solving them. After these variables are determined, the normal stresses, shear stresses, and slope safety factor are also obtained using the stresses assumptions and M-C strength criterion. In the case of a three-dimensional slope stability analysis, three calculation methods, namely, a non-strict method, quasi-strict method, and strict method, can be obtained by satisfying different force and moment equilibrium conditions. Results of the comparison in the classic two- and three-dimensional slope examples show that the slope safety factors calculated using the current method and the other limit equilibrium methods are approximately equal to each other, indicating the feasibility of the current method; further, the following conclusions are obtained: 1) The current method better amends the initial normal and shear stresses acting on the slip surface, and has the identical results with using simplified Bishop method, Spencer method, and Morgenstern-Price (M-P) method; however, the stress curve of the current method is smoother than that obtained using the three abovementioned methods. 2) The current method is suitable for analyzing the two- and three-dimensional slope stability. 3) In the three-dimensional asymmetric sliding body, the non-strict method yields safer solutions, and the results of the quasi-strict method are relatively reasonable and close to those of the strict method, indicating that the quasi-strict method can be used to obtain a reliable slope safety factor.

Optimization Model for Determining Safety Factor and Thrust Line in Landslide Assessments

AbstractWhen the limit-equilibrium method is employed in the stability assessment of complicated landslides, some eccentric results are often encountered with the use of rigorous methods. These eccentric results may be attributable to irrationally assumed interslice forces. Furthermore, engineers should verify the rationality of the thrust-line position in a landslide after the safety factor of the landslide is solved with the use of such rigorous methods. In this paper, a new global analysis method is proposed based on the Morgenstern–Price assumption for interslice forces. The global equilibrium equations, normal stresses on the sliding surface, and position of the thrust line were employed as constraint conditions to construct an optimization model. The relationships between the constraint conditions and the safety factors and thrust line were investigated through the analysis of some typical landslides with some interesting results.

A global procedure for stability analysis of slopes based on the Morgenstern-Price assumption and its applications

By combining the numerical stability of the global analysis method and the flexibility of the Morgenstern-Price method, a global procedure for the stability analysis of slopes is developed. Firstly, based on the Morgenstern-Price assumption of inter-slice forces, an expression for the distribution of normal stress on the sliding surface is derived. Then, the equilibrium equations of the sliding body are built. Finally, three different expressions for the distribution of normal stress on the sliding surface are proposed, followed by the comparison of their effects and the stability analysis of a large-scale landslide exposed during the construction of a hydropower project.

Slope Stability Analysis Using Radial Slices: A Mathematical Model

In this paper, a mathematical model has been formulated for calculating the factor of safety of a slope. Corresponding computer code has also been developed. Limit equilibrium method (moment equilibrium) has been adopted for calculating the net resulting driving and resisting forces. The probable slip circle region has been divided into radial slices for the simulation process. In this approach, the inter-slice shear forces are zero. Thus, the calculation process becomes simpler as compared to that with vertical slices. The slope stability analyses were done. Validation of the present program was done with existing limit equilibrium based methods. Various models were prepared and analysed with varying geometry and soil strength parameters. These models were also analysed with other limit equilibrium methods like Bishop, Janbu and Spencer method. The results were found to be in agreement with the results of other limit equilibrium methods for the same dump soil properties and slope parameters.

Practical slip circle method of slices for calculation of bearing capacity factors

The slip circle method of slices is commonly used in the analyses of slope stability and bearing capacity for multi-layered ground. However, in the case of ground consisting of horizontal sandy layer, it is known that modified Fellenius׳ method tends to underestimate the factor of safety, while simplified Bishop׳s method tends to overestimate the factor of safety. In this study, a new slip circle method was proposed for the purpose of improving the accuracy of the analysis for a ground consisting of sand and clay layers. In the proposed method, β of the ratio of inter-slice shear force to inter-slice normal force i.e tan(βαi) is assumed constant as 0.25 for all slices. This is named as circle bearing capacity factor (CBCF) method. It was found that the bearing capacity factors, Nc, Nq, and Nγ calculated for shallow foundation on horizontal ground from CBCF method agreed well with that obtained from the plastic solution. The back-analyses carried out for a few case studies on the stability of slopes on earth structures found in sand and clay layers showed that the factor of safety calculated from CBCF method explains the actual performance of earth structures well. The proposed CBCF method proves it reliability in calculating bearing capacity for shallow foundations. This was achieved from the results obtained from centrifugal model test, which were carried out for dense sand layer overlying soft clay with various conditions by Okamura et al. (1998). It was examined that the factor of safety calculated for the stability of slopes from CBCF method can explain the actual performance of geotechnical structures constructed on ground consisting of sand and clay layers.

Finite element model with imposed slip surfaces for earth mass safety evaluation

The study of earth masses requires numerical methods that provide the quantification of the safety factor without requiring detrimental assumptions. For that, equilibrium analysis can perform fast computations but require assumptions that limit its potentiality. Limit analysis does not require detrimental assumptions but are numerically demanding. This work provides a new approach that combines the advantage of both the equilibrium method and the limit analysis. The defined hybrid model allows probabilistic analysis and optimization approaches without the assumption of interslice forces. It is compared with a published case and used to perform probabilistic studies in both a homogeneous and a layered foundation. Analyses show that the shape of the density probability functions is highly relevant when computing the probability of failure, and soil elasticity hardly affects the safety of factor of the earth mass.

Slope Stability Analysis Using Slice-Wise Factor of Safety

The concept of slice-wise factor of safety is introduced to investigate the state of both the whole slope and each slice. The assumption that the interslice force ratio is the same between any two slices is made and the eccentric moment of slice weight is also taken into account. Then four variables equations are formulated based on the equilibrium of forces and moment and the assumption of interslice forces, and then the slice-wise factor of safety along the slip surface can be obtained. The active and passive sections of the slope can be determined based on the distribution of factor of safety. The factor of safety of the whole slope is also defined as the ratio of the sum of antisliding force to the sum of sliding force on the slip surface. Two examples with different slip surface shapes are analysed to demonstrate the usage of the proposed method. The slice-wise factor of safety enables us to determine the sliding mechanism and pattern of a slope. The reliability is verified by comparing the overall factor of safety with that calculated by conventional methods.

Determining the Factors of Safety of Spatially Variable Slopes Modeled by Random Fields

AbstractThe merits of incorporating the spatial variability of soil properties into slope reliability analyses have been demonstrated by many researchers. However, the suitability of the use of limit equilibrium methods (LEMs) for calculating the minimum factor of safety (FS) of a spatially variable slope modeled by a random field is not well understood. The present paper investigates this topic by performing a series of analyses using circular and noncircular LEMs and a strength reduction method based on finite-element analysis (FE SRM). The LEMs are found to encounter three possible issues in random fields, including (1) noncircular slip surfaces, (2) a significant increase in the complexity of an optimization problem, and (3) failure to converge. The LEM analysis results in random fields can only be reliable when these three issues are adequately addressed. It is found that a noncircular rigorous LEM with a carefully selected interslice force function may work adequately in random fields. Moreover, the...

New Analysis Method for Slope Stability Considering Force-Vector Characteristics

AbstractA new definition of the factor of safety—the vector-sum factor of safety (VFOS) considering force-vector characteristics—is introduced and is defined as the ratio of projection of the resistance force to that of shear force in the potential sliding direction of the slope. This study develops a new analysis method for solving the VFOS of slope with a noncircular slip surface considering interslice forces based on slice method. The analysis method developed for slope stability is implemented in the spreadsheet software Microsoft Excel for efficient calculation. The proposed method is verified through comparison with the VFOS by the FEM and the rigorous limit-equilibrium method, and the significance of the proposed method is highlighted.

Use of internal and external variables and extremum principle in limit equilibrium formulations with application to bearing capacity and slope stability problems

Limit equilibrium methods, satisfying both force and moment equilibrium can be formulated using assumptions on the internal variables or the external variables. Even though most stability methods are based on force and moment equilibrium, as well as the Mohr–Coulomb yield criterion, there are great differences between the results of the different formulations due to variations in the assumptions. The authors believe that the use of the interslice force function f(x), the thrust line or the base normal forces should provide an equivalent concept at the ultimate/failure state. In the present study, the authors have used the well-known bearing capacity solutions to determine f(x), the thrust line and the base normal forces for a “horizontal slope”. The equivalence between the different formulations under the ultimate condition is demonstrated. It is shown that it is not important which forces are used in the stability formulation, external boundary forces or internal forces, if only that the ultimate state is considered. It is also demonstrated in the present paper that the maximum extremum from the limit equilibrium analysis is equivalent to the slip line solution using a classical bearing capacity problem.

Extremum solutions to the limit equilibrium method subjected to physical admissibility

In the slope stability analysis, the interslice force calculated by the method of slices is the internal force of the slope in the limit equilibrium state, which is vital to the design of reinforcement. However, none of the existing methods can guarantee a priori the interslice force is reasonable. Starting from the global analysis procedure, an optimization problem for maximizing the factor of safety is posed under the constraints that the system of forces in the sliding body is physically admissible. In the problem, both the factor of safety and the normal stress along the slip surface are taken as the independent variables. With weak nonlinearity and no numerical problems inherent in the methods of slices, the optimization problem can be solved by those conventional optimization techniques. No assumption is made regarding the interslice forces, but the system of forces from the optimization problem is physically admissible. To bracket the factor of safety, meanwhile, the minimum of the factor of safety is calculated through a minimization process under the same constraints as the maximization process. It is illustrated that for smooth slip surfaces, the solutions to the maximum and the minimum almost coincide, and for non-smooth slip surfaces, the interval of the solution is very narrow.

Closure to “Evaluation of Interslice Force Function and Discussion on Convergence in Slope Stability Analysis by the Lower Bound Method” by Y. M. Cheng, Z. H. Zhao, and Y. J. Sun

Closure to “Evaluation of Interslice Force Function and Discussion on Convergence in Slope Stability Analysis by the Lower Bound Method” by Y. M. Cheng, Z. H. Zhao, and Y. J. Sun

Discussion of “Evaluation of Interslice Force Function and Discussion on Convergence in Slope Stability Analysis by the Lower Bound Method” by Y. M. Cheng, Z. H. Zhao, and Y. J. Sun

Fauziah Ahmad; Mohammad Tabarroki; and Roodabeh Banaki Professor, School of Civil Engineering, Univ. Sains Malaysia, 14300 Nibong Tebal, Penang, Malaysia. E-mail: cefahmad@eng.usm.my Graduate Research Student, School of Civil Engineering, Univ. Sains Malaysia, 14300 Nibong Tebal, Penang, Malaysia (corresponding author). E-mail: mohammad@tabarroki.com Graduate Research Student, School of Civil Engineering, Univ. Sains Malaysia, 14300 Nibong Tebal, Penang, Malaysia. E-mail: banaki .r@gmail.com

Stability Analysis of Reinforced Slopes Using Upper Bound Limit Analysis Method

The kinematic method of limit analysis approach is applied to study stability of reinforced slopes. The amount and length of reinforcement required to prevent the slope to collapse are determined based on different mechanisms. A new method consisting of horizontal blocks is used in translational mechanism. The failure wedge is divided into a number of horizontal slices involving reinforcements. The reinforcements do not intersect the slices. Thus, they have no direct influence on the inter-slice forces. The presented method can reduce difficulties of stability analysis for reinforced slopes. In this paper, the seismic stability of slopes reinforced with geosynthetics is investigated. The seismic analysis procedure is substituted with pseudo-static horizontal forces. While such an approach ignores the acceleration history of a structure, it is routinely used in practice. It has been assumed that the geosynthetics are uniformly distributed in the height of slope. Based on these assumptions, different possible failure mechanisms are considered and necessary analytical expressions for determining the design parameters are derived for each mechanism. The results of these analyses are presented to illustrate the influence of different parameters such as geometrical parameters of slopes, soil characteristics, and seismic forces on the stability of reinforced earth structures.

General Slice Method Based on Rigorous Equilibrium to Solve the Factor of Safety

For a general slice, force and moment equilibrium equations are developed, the recurrence equations of inter-slice force and inter-slice moment are derived, the general formulation based on rigorous equilibrium to solve the factor of safety is studied, hence, the theoretical framework of rigorous method of general slice is developed, rigorous method of vertical slice is a special case of it. Analyzing the applicability of Sarma’s method, two new inter-slice shear force equations are presented based on the compatible relationship among slice’s displacements by leading in the scaling parameter λ and inter-slice force function f(x),hey make the relationship between the inter-slice shear forces and slip surface geometry clear, and indicate that the reduction factor for shear strength along inter-slice boundaries varies from one boundary to the next depending on the geometry of the slices and the slip surface. The rigorous methods of general slice can be developed based on the modified inter-slice shear force equations, they think that the reduction factor for shear strength along inter-slice boundary is different from that for shear strength along slip surface. The example analysis indicates that the proposed new methods work better than Sarma’s method, the reasonable value of safety factor can be obtained by using them. Even if the shape of slice is varied, the proposed new methods can also give consistent values of safety factor and ensure that the iteration is stably convergent.