Rigorous Limit Equilibrium Method Research Articles

Stability analysis of unsaturated–saturated soil slopes under rainfall infiltration using the rigorous limit equilibrium method

Stability analysis of unsaturated–saturated soil slopes under rainfall infiltration using the rigorous limit equilibrium method

An efficient method for computing slope reliability calculation based on rigorous limit equilibrium

Abstract Traditional rigorous limit equilibrium methods satisfy all equilibrium conditions and usually have high accuracy, however, which are less efficient for slope reliability analysis. The main reason is that the limit state functions are highly nonlinear implicit functions of safety factor. Complex numerical iterations are required, which may sometimes lead to computational convergence problems. A new method for computing slope reliability calculation with high efficiency and accuracy was proposed. This method was based on the rigorous limit equilibrium method by modifying normal stresses over the slip surface. The critical horizontal acceleration factor K c {K}_{c} , which can be expressed explicitly, was used to replace the implicit safety factor as a representation of slope stability. The difference between K c {K}_{c} and the known value K c 0 {K}_{c0} was used as the limit state function. Two slope examples were analyzed. The results showed that the calculation results of this method were in good agreement with those of the traditional Morgenstern–Price limit equilibrium method, but the computational efficiency was significantly improved. When this method was combined with the subset simulation method, the calculation time was only a few seconds. Therefore, this method can be used for rapid calculation of slope reliability.

A methodology for road cutting design guidelines based on field observations

Road networks in low and lower-middle income countries (LIC/LMICs) are rapidly expanding to enhance social and economic growth. The construction of a new road often requires cuttings to be made, especially in hilly topography. In LIC/LMICs, many practitioners rely on guidelines to design roadside cuttings, however, some of these guidelines lack accuracy as they are not developed using rigorous stability analysis methods. Stability charts offer a more reliable alternative to some guidelines; however, these are difficult to use in the field. To overcome this gap, we present a new methodology to develop rigorous and user-friendly guidelines for the preliminary design of roadside cuttings. The guidelines are developed using failure criteria commonly employed by practitioners (i.e. Generalised-Hoek-Brown for rock and Mohr-Coulomb for soil) and a rigorous Limit Equilibrium Method, Morgenstern-Price, for stability analyses. In addition, we consider upslope geometric boundary conditions and slope seepage. The guidelines are designed to be user-friendly by including categories with accessible descriptions to characterise the slope material and geometry that can be selected by a practitioner in the field. Then the methodology is showcased by producing new guidelines for the design of road cuttings in Nepal and Ethiopia. We believe the systematic use of guidelines developed following the novel methodology here illustrated will reduce design error, and thus lead to road cuttings of increased life span.

New Green-Ampt model based on fractional derivative and its application in 3D slope stability analysis

The infiltration process in slopes is an essential issue in geotechnical engineering. A new Green-Ampt model for describing the two-stage infiltration in slopes based on fractional derivatives was proposed in this paper. The Green and Ampt (1911)’s model, and Chen and Young (2006)’s model are two special cases of the proposed model. A 1D loess soil column test in the literature as well as a laboratory rainfall test of loess slope were used to validate the proposed model. The travel curve of wetting front obtained by the proposed model was obviously closer to the actual test value than that obtained by the Chen and Young’s model, indicating that the performance of the proposed model is superior to the Chen and Young’s model due to the use of fractional derivatives. The proposed Green-Ampt model was combined with a rigorous 3D limit equilibrium method to obtain the real-time safety factor of the slope during rainfall. The calculated failure time of the loess slope by the proposed method is close to the actual failure time of the laboratory test, while the corresponding of Chen and Young’s model is obviously shorter than the actual status. Six parameters are included in the proposed model, and sensitivity analysis shows that the fractional derivative has the most significant impact on the wetting front depth, followed by the permeability coefficient, moisture content difference, suction head, rainfall intensity, and slope angle.

Three-Dimensional Stability Analysis of Bank Slopes with Reservoir Drawdown Based on Rigorous Limit Equilibrium Method

Abstract The fluctuation of reservoir water levels has significant impact on bank slope stability near a reservoir. Therefore, it is necessary to analyze the stability of bank slopes with reservoir...

Failure Mechanism and Factor of Safety for Spatially Variable Undrained Soil Slope

This paper aims to investigate the differences in factor of safety (FS) and failure mechanism (FM) for spatially variable undrained soil slope between using finite element method (FEM) , finite difference method (FDM), and limit equilibrium method (LEM). The undrained shear strength of cohesive soil slope is modeled by a one-dimensional random field in the vertical direction. The FS and FM for a specific realization of random field are determined by SRT embedded in FEM- and FDM-based software (e.g., Phase26.0 and FLAC) and LEM, respectively. The comparative study has demonstrated that the bishop method (with circular failure surface) exhibits performance as fairly good as that of SRT both in FS and FM for the undrained slope cases where no preferable controlling surfaces such as hydraulic tension crack and inclined weak seams dominate the failure mechanism. It is, however, worthwhile to point out that unconservative FM is provided by the Bishop method from the aspect of failure consequence (i.e., the failure consequence indicated by the FM from the Bishop method is smaller than that from SRT). The rigorous LEM (e.g., M-P and Spencer method with noncircular failure surface) is not recommended in the stability analysis of spatially variable soil slopes before the local minima and failure to converge issues are fully addressed. The SRT in combination with FEM and/or FDM provides a rigorous and powerful tool and is highly preferable for slope reliability of spatially variable undrained slope.

Three-dimensional stability analysis of seismically induced landslides using the displacement-based rigorous limit equilibrium method

Previously, the stability analysis of seismically induced landslides was investigated by the factor of safety of the entire sliding body, which provided no information on the displacements of the analyzed seismically induced landslides. The landslides are assessed to be dangerous when the minimum value of the factor of safety (Fs) is less than a critical value. However, unlike the landslides subjected to static loads, the dynamic safety factors of seismically induced landslides vary with time. The minimum value of the dynamic safety factors being less than the critical value does not necessarily imply failure of the seismically induced landslides. In this paper, the three-dimensional displacement-based rigorous limit equilibrium method is proposed to study the displacements of seismically induced landslides. The relationship between the shear stresses acting on the base of the columns and the shear displacements is established based on the hyperbolic soil model. By introducing the strength reduction technique, the relationship between the reduction factor (RF) and the accumulated vertical displacement can be obtained. According to the definition of the strength reduction method, the safety factors of seismically induced landslides are determined, which do not vary with time. Then, the landslides can be assessed to be dangerous when the minimum value of Fs is less than a critical value.

Three-dimensional reliability analysis of seismic slopes using the copula-based sampling method

Geotechnical parameters are often considered to be independent variables in the reliability analysis of slopes, however, some variables are correlated. In this study, the copula-based sampling method is first applied to study 3D reliability of seismic slopes as well as the cross correlation between the geotechnical parameters. The safety factors and the failure probability of seismic slopes are investigated using the copula-based sampling method in the framework of the 3D rigorous limit equilibrium method. Moreover, the effects of geotechnical parameters on reliability analysis of seismic slopes are studied. Two cases are considered to illustrate the efficiency of the copula-based sampling method. It is found that the results obtained using the copula-based sampling method are in good agreement with those obtained by a Monte Carlo simulation.

Reliability analysis of slopes using UD-based response surface methods combined with LASSO

The selection of experimental data points in response surface methods (RSMs) is still not based on precise guidelines or theory, and multicollinearity—defined as the presence of linear correlations among the uncertain variables—hinders the estimation of the regression coefficients. As a result, a local optimal solution may be obtained. Uniform experimental design (UD) is a quasi Monte Carlo simulations (MCS) method, which has the advantage of coverage of all the experimental points, and is used to analyze the reliability of slopes in this framework. Least absolute shrinkage and selection operator (LASSO) is a regression method that is employed to estimate the regression coefficients. It involves the penalize the absolute size of the regression coefficients so that the coefficients can be estimated even if the variables are multicollinear. In this paper, a new approach is proposed in which a UD-based RSM is combined with LASSO. The response variable, namely, the factor of safety (Fs), is calculated using a 3D rigorous limit equilibrium method (3D RLEM). Two examples are used to demonstrate the validity and capability of the proposed approach. Notably, the probability of failure (Pf) obtained by the UD-based RSM is larger than that for other reliability methods without multicollinearity. Ignoring the influence of multicollinearity may lead to a nonconservative estimation of slope failure probability.

A novel displacement-based rigorous limit equilibrium method for three-dimensional landslide stability analysis

Conventional stability analysis of landslides is investigated using the factor of safety of the entire sliding body, which provides no information concerning displacements of the analyzed landslides. In this paper, a novel displacement-based rigorous limit equilibrium method is proposed to investigate the displacements and stabilities of three-dimensional landslides. The relationship between the shear stresses acting on the base of the columns and the shear displacements is established based on the hyperbolic soil model, which can be directly obtained from direct shear tests. According to the displacement compatibility among the columns, the shear displacements of all columns can be determined by the vertical and horizontal displacements at a key point. Combining the six equilibrium conditions of the discretized columns with the nonlinear constitutive relation between stress and displacement of soils, the vertical displacement at the key point can be determined. By introducing the strength reduction technique into the displacement-based rigorous limit equilibrium method, the relationship between the reduction factor and the vertical displacement can be obtained. The displacement and the safety factor of three-dimensional landslides can be defined. Moreover, two cases are given to verify the robustness and precision of the present method in detail.

Huangtupo landslide stability under water level fluctuations of the Three Gorges reservoir

The Huangtupo riverside slope, which extends an area of 1.35 × 106 m2 and has a total volume of 6.934 × 107 m3, is one of the most noted large-scale landslides with great concern about the safety of immigrants in the Three Gorges reservoir area of China. During the normal operation, the reservoir water level fluctuates periodically. Water level fluctuation will soften the strength of the geologic materials on the banks, induce underground water fluctuation, and in turn affect the slope stability. On the basis of the thorough engineering geological survey, the analysis of engineering geological conditions and deformation mechanism is conducted primarily. Then, the Huangtupo landslide is divided into four minor landslides, all of which have typical three-dimensional characteristics. To these landslides, a three-dimensional rigorous limit equilibrium method is proposed, which can accommodate failure surfaces of any shape, and satisfies all the equilibrium conditions. In terms of the strength parameters of geologic materials, the stability evolution of the four minor landslides at the Huangtupo landslide under periodical water level fluctuation is investigated in detail. From the results, the 3D safety factors turned out to be somewhat bigger than the 2D results even though they displayed the same trends. The differences between 2D and 3D results are about 2.92–6.11 %. The maximum reduction in safety factors with the rapid down of water level is 0.11. It is suggested that the safety margin of the two minor landslides near the riverside is insufficient and might become instable under periodical water level fluctuation.

The long-term stability analysis of 3D creeping slopes using the displacement-based rigorous limit equilibrium method

The conventional limit equilibrium method is hardly applied to investigate the stability and the displacement of creeping slopes. In this paper, a novel displacement-based rigorous limit equilibrium method is proposed to analyze the stability and the displacement of three-dimensional (3D) creeping slopes. The relationship between the shear displacements of the slopes and the creep time is obtained based on the visco-elastoplastic creep model. According to the displacement compatibility among the columns, the shear displacements of all columns can be described by the vertical displacements at the key point. Combining the six equilibrium conditions of the discretized columns with the visco-elastoplastic creep model, the vertical displacement at the key point can be determined. With increase of creep time, the vertical displacement at the key point converges to a constant value. By introducing the concept of strength reduction technique into the displacement-based rigorous limit equilibrium method, the relationship between the reduction factor (RF) and the long-term displacement at the key point can be obtained. Then, the long-term factor of safety of 3D creeping slope is equal to the value of the reduction factor at the point of sharp increment of displacement. Two case studies are given to verify the robustness and precision of the proposed method.

Stability analysis of three-dimensional seismic landslides using the rigorous limit equilibrium method

In this paper, a new method combining the rigorous limit equilibrium method and the pseudo-dynamic method is proposed to investigate stability of 3D seismic landslides, in which the force equilibrium conditions along three coordinate axes and the overall moment equilibrium conditions around three coordinate axes are all strictly satisfied. Moreover, sinusoidal–cosinusoidal wave is applied to simulate earthquake displacement and an amplification factor of peak seismic acceleration is referred to as the amplification of seismic wave when it propagates from the bottom to the top of landslides. The pseudo-dynamic factor of safety of 3D seismic landslides is determined using trust-region-reflective iterative algorithm. The effects of the parameters of the seismic landslides on the stability are analyzed by the BP neural network algorithm, in which a database to investigate the stability of 3D seismic landslides is established. In addition, the stability of Donghekou landslide is studied to verify the accuracy and precision of the present method.

Analysis of stability of three-dimensional slopes using the rigorous limit equilibrium method

Previously, quasi-rigorous limit equilibrium methods were applied to analyze the stability of three-dimensional slopes or landslides, which only satisfy three direction force equilibrium, and one or two direction moment equilibrium. In this paper, the rigorous limit equilibrium column method, in which inter-column forces are taken into account, is established based on six equilibrium conditions which include three direction force equilibrium conditions along coordinate axes and three direction moment equilibrium conditions around three coordinate axes. The relationship between the width of sliding body and factor of safety is determined using trust-region-reflective iterative algorithm. The value of the factor of safety is obtained using Levenberg–Marquardt least square method. Moreover, the present method can be applied to automatically search slip surface of three-dimensional landslides and to determine the factor of safety of three-dimensional landslides with the known arbitrary slip surface. Three examples are discussed to verify the robustness and precision of the present method in detail. Comparing with quasi-rigorous limit equilibrium methods which only considered four or five equilibrium conditions, the present method is more accurate and rigorous.

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.

A comparative assessment of slope stability of New Orleans I-wall with partial gap between the wall and layered cohesive backfill

Following Hurricane Katrina, the study of cantilevered sheet pile I-wall with gap or partial gap has become one of the central elements of the ongoing investigation pertaining to the re-building of hurricane protection systems in New Orleans, LA. Historically, the US Army Corps of Engineers (USACE) had mostly relied upon the Method of Planes (MOP) analysis procedure for slope stability analysis of I-wall systems. However MOP is a simplified procedure which does not satisfy total equilibrium. Nevertheless, MOP is still considered by USACE as a popular analysis tool because of its simplicity and ease of use in slope stability analysis. This paper demonstrates the applicability and suitability of MOP as a viable analysis tool for the analysis of New Orleans I-wall founded on layered cohesive backfill subjected to partial gap condition. The results of MOP analyses are compared with those of rigorous limit equilibrium method. Design recommendations regarding the choice of proper analysis tool for the I-wall partial gap analysis are made based on the findings of this investigation. Relative estimates of the design factors of safety recommended in the Hurricane and Strom Damage Risk Reduction System Design Guidelines (HSDRRSDG, 2007) are also presented.

Rigorous Limit Equilibrium Method for Pile Design against Landslide

Rigorous Limit Equilibrium Method for Pile Design against Landslide

Three-Dimensional Slope Stability Analysis Using an Extended Spencer Method

A search procedure is presented to locate 3D critical slip surfaces by combining dynamic programming with a column method extended from the Spencer safety factor equation for 2D analysis. The procedure was applied to typical 3D problems (conical heaps) in order to make a meaningful comparison with variational approaches. Both minimum safety factors and their associated slip surfaces predicted using the two analyses agreed well for all cases investigated. As variational analysis is a rigorous limit equilibrium method without priori statical assumptions, this good agreement adds confidence to the simplifying assumptions of intercolumn forces for the 3D Spencer method. The comparative study presented in this paper strongly supports a recommendation of the use of a statically rigorous limit equilibrium approach satisfying both force and moment equilibrium for a realistic 3D analysis of the slope stability.