Convergence aspect of limit equilibrium methods for slopes

1990 ◽  
Vol 27 (1) ◽  
pp. 145-151 ◽  
Author(s):  
R. N. Chowdhury ◽  
S. Zhang
Keyword(s):  
Factor Of Safety ◽  
Slip Surface ◽  
Limit Equilibrium ◽  
Solution Process ◽  
Iterative Solution ◽  
Friction Angle ◽  
Equilibrium Analysis ◽  
Negative Slope ◽  
Slip Surfaces ◽  
Geological Discontinuity

This note is concerned with the multiplicity of solutions for the factor of safety that may be obtained on the basis of the method of slices. Discontinuities in the function for the factor of safety are discussed and the reasons for false convergence in any iterative solution process are explored, with particular reference to the well-known Bishop simplified method (circular slip surfaces) and Janbu simplified or generalized method (slip surfaces of arbitrary shape). The note emphasizes that both the solution method and the method of searching for the critical slip surface must be considered in assessing the potential for numerical difficulties and false convergence. Direct search methods for optimization (e.g., the simplex reflection method) appear to be superior to the grid search or repeated trial methods in this respect. To avoid false convergence, the initially assumed value of factor of safety F0 should be greater than β1(=−tan α1 tan [Formula: see text]) where α1 and [Formula: see text] are respectively the base inclination and internal friction angle of the first slice near the toe of a slope, the slice with the largest negative reverse inclination. A value of F0 = 1 + β1, is recommended on the basis of experience. If there is no slice with a negative slope for any of the slip surfaces generated in the automatic, search process, then any positive value of F0 will lead to true convergence for F. It is necessary to emphasize that no slip surface needs to be rejected for computational reasons except for Sarma's methods and similarly no artificial changes need to be made to the value of [Formula: see text] except for Sarma's methods. Key words: slope stability, convergence, limit equilibrium, analysis, optimization, slip surfaces, geological discontinuity, simplex reflection technique.

Pseudo-Static Analysis of Slope Considering Circular Rupture Surface

2014 ◽  
Vol 5 (2) ◽  
pp. 37-43 ◽  
Author(s):  
Sima Ghosh
Keyword(s):  
Factor Of Safety ◽  
Limit Equilibrium ◽  
Slope Angle ◽  
Failure Surface ◽  
Friction Angle ◽  
Equilibrium Analysis ◽  
Seismic Slope Stability ◽  
Slide Mass ◽  
Critical Circle ◽  
Seismic Forces

In this present paper, a circular failure surface passing through the toe is assumed for a homogeneous soil, and the Fellenius line is used to locate the centre of the most critical circle. Using limit equilibrium analysis under the influence of static forces such as weight of potential slide mass and surcharge along with the pseudo-static seismic forces are considered to obtain the factor of safety of the slopes. Factor of safety is found through the application of force equilibrium. The effects of variation of different parameters like slope angle (i), soil friction angle (F) and seismic acceleration coefficients both in the horizontal and vertical directions (kh and kv respectively) on the factor of safety are presented. Finally, the present results are compared to the existing solutions available in literature and found to give minimum values of factor of safety using the present approach for seismic slope stability analysis.

Search for critical slip surfaces based on finite element method

1995 ◽  
Vol 32 (2) ◽  
pp. 233-246 ◽  
Author(s):  
Jin-Zhang Zou ◽  
David J. Williams ◽  
Wen-Lin Xiong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Programming ◽  
Factor Of Safety ◽  
Slip Surface ◽  
Limit Equilibrium ◽  
Dynamic Programming Method ◽  
Critical Slip Surface ◽  
Slip Surfaces ◽  
Element Method

In this paper, finite element methods (FEM) are used to determine local shear strength mobilization ratios within a slope and to indicate the probable location of the critical slip surface. To locate the critical slip surface and hence determine the minimum factor of safety, an improved dynamic programming method (IDPM) is employed, in which possible slip surfaces, which must pass between state points, may pass both between and along stages. The IDPM is coupled with an expression for the factor of safety for which the stresses are obtained from the FEM. The results obtained using the FEM–IDPM, for a homogeneous slope and for a test embankment on soft Bangkok clay, have been compared with those observed and obtained using the traditional finite element method and the generalized limit equilibrium wedge method. The FEM–IDPM has the advantage over limit equilibrium methods that the strain- and time-dependent behaviour of soil and the staged construction of the slope can be modelled. Key words : critical slip surface, dynamic programming, factor of safety, finite element method, limit equilibrium method, slope stability.

scholarly journals A limit equilibrium analysis of progressive failure in the stability of slopes

1978 ◽  
Vol 15 (1) ◽  
pp. 113-122 ◽  
Author(s):  
K. Tim Law ◽  
Peter Lumb
Keyword(s):  
Slip Surface ◽  
Progressive Failure ◽  
Limit Equilibrium ◽  
Friction Angle ◽  
Soil Mass ◽  
Local Failure ◽  
Equilibrium Analysis ◽  
Stability Of Slopes ◽  
The Stability ◽  
Definition Of

A limit equilibrium method of analysis is proposed for the study of progressive failure in slope stability under a long-term condition. Based on effective stresses, the formulation of the method is derived from consideration of force and moment equilibrium within the soil mass above a prospective slip surface. By dividing the soil mass into a number of vertical slices, recognition of local failure can be made. Once local failure takes place, post-peak strength is assumed to be operative. This then initiates a redistribution of interslice forces and leads to some further local failure. Thus realistic available strengths along the slip surface can be evaluated. This permits the definition of a final safety factor, which is expressed in terms of the actual available reserve of strength. The proposed method has been applied to three well documented case records and encouraging results have been obtained. Based on the assumption that post-peak strengths are given by a friction angle equal to the peak value and a zero cohesion, stability charts have been prepared for design purposes.

Effect of the axis of moment equilibrium in slope stability analysis

1992 ◽  
Vol 29 (3) ◽  
pp. 456-465 ◽  
Author(s):  
D. G. Fredlund ◽  
Z. M. Zhang ◽  
L. Lam
Keyword(s):  
Slope Stability ◽  
Factor Of Safety ◽  
Slip Surface ◽  
Limit Equilibrium ◽  
Stability Limit ◽  
Slip Surfaces ◽  
Moment Equilibrium ◽  
Simplified Method ◽  
General Limit ◽  
The Moment

Some of the methods of slices satisfying moment equilibrium derived for circular slip surfaces have been extended to accommodate noncircular (or composite) type slip surfaces. A question arises regarding the point about which moment equilibrium should be taken and whether varying the center for moment equilibrium has a significant effect upon the computed factor of safety. This paper addresses the question of the effect of the center for moment equilibrium as it pertains to noncircular (or composite) slip surfaces. In particular, extensions of the Ordinary, Bishop's simplified, and the General Limit Equilibrium (GLE) methods are examined. The results show that considerable variations in the factor of safety can occur when using the extended Ordinary method. The extended Bishop's simplified method shows varying factors of safety as the moment axis moves vertically. Variations in the computed factor of safety can generally be expected to be less than 12%. The GLE, Morgerstern–Price, and Spencer methods are independent of the axis for moment equilibrium. Key words : slope stability, limit equilibrium, moment equilibrium, factor of safety, noncircular slip surface.

Potential Slip Surfaces of Slope with Strength Parameters

2011 ◽  
Vol 243-249 ◽  
pp. 3315-3318 ◽  
Author(s):  
Hang Lin ◽  
Ping Cao
Keyword(s):  
Shear Strength ◽  
Numerical Analysis ◽  
Factor Of Safety ◽  
Slip Surface ◽  
Friction Angle ◽  
Shear Strength Parameters ◽  
Strength Parameters ◽  
Slip Surfaces ◽  
Stability Of Slope ◽  
The Stability

The cohesion c and friction angle φ are the main strength parameters influencing the stability of slope. Any of them changes, the factor of safety of slope will change, but it has seldom been considered in the literature how the potential slip surface will change at the same time. In the present paper, the analytical deduction and numerical analysis are done to find out the effect of shear strength parameters c and φ to the distribution of potential slip surface. The study shows that, the potential slip surface is affected by the combination of c and φ, whose function is λ=c/(γhtanφ).

The Hepburn landslide: an interactive slope-stability and seepage analysis

1991 ◽  
Vol 28 (4) ◽  
pp. 556-573 ◽  
Author(s):  
G. A. Misfeldt ◽  
E. Karl Sauer ◽  
E. A. Christiansen
Keyword(s):  
Factor Of Safety ◽  
Slope Failure ◽  
Slip Surface ◽  
Friction Angle ◽  
Seepage Analysis ◽  
Continuous Processes ◽  
Valley Slope ◽  
Slip Surfaces ◽  
Artesian Aquifer ◽  
Saline Springs

Mechanisms of active landslides are continuous processes involving the dynamics of slope failure interacting with the groundwater regime. This process is simulated in phases by combining stability calculations interactively with a seepage analysis to determine the factor of safety for a dormant landslide near Hepburn, Saskatchewan. The landslide is a multiple retrogressive failure with two parallel slip surfaces at different elevations. The slip surfaces are in originally overconsolidated Cretaceous and Tertiary clays softened by shear from glaciation. An artesian aquifer is present at the base of the slip surface, causing saline springs at the base of the valley slope. A residual effective friction angle of 6.7° with zero cohesion was found to best characterize the shear strength of the clays in the failure zone. Potential nets and head profiles from the seepage analysis illustrate the strong influence of changing topography on the groundwater flow system. The present-day factor of safety for the dormant landslide was estimated to be 1.10. Key words: multiple retrogressive landslides, dormant landslide, seepage modelling, residual strength, artesian conditions, glacial drift, Cretaceous clays.

Progressive failure of the Carsington Dam: a numerical study

1992 ◽  
Vol 29 (6) ◽  
pp. 971-988 ◽  
Author(s):  
Z. Chen ◽  
N. R. Morgenstern ◽  
D. H. Chan
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Factor Of Safety ◽  
Progressive Failure ◽  
Limit Equilibrium ◽  
Equilibrium Analysis ◽  
Element Analysis ◽  
Limit Equilibrium Analysis ◽  
The Finite Element Analysis ◽  
Yellow Clay

The mechanism of progressive failure is well understood as one which involves nonuniform straining of a strain-weakening material. Traditional limit equilibrium analysis cannot be used alone to obtain a rational solution for progressive failure problems because the deformation of the structure must be taken into account in the analysis. The failure of the Carsington Dam during construction in 1984 has been attributed to progressive failure of the underlying yellow clay and the dam core materials. The dam was monitored extensively prior to failure, and an elaborate geotechnical investigation was undertaken after failure. The limit equilibrium analysis indicated that the factors of safety were over 1.4 using peak strength of intact clay material or 1.2 based on reduced strength accounting for preshearing of the yellow clay layer. Factors of safety were found to be less than unity if residual strengths were used. The actual factor of safety at failure was, of course, equal to one. By using the finite element analysis with strain-weakening models, the extent and degree of weakening along the potential slip surface were calculated. The calculated shear strength was then used in the limit equilibrium analysis, and the factor of safety was found to be 1.05, which is very close to the actual value of 1.0. More importantly, the mechanism of failure and the initiation and propagation of the shear zones were captured in the finite element analysis. It was also found that accounting explicitly for pore-water pressure effects using the effective stress approach in the finite element and limit equilibrium analyses provides more realistic simulations of the failure process of the structure than analyses based on total stresses. Key words : progressive failure, strain softening, finite element analysis, dams.

Landslide Simulation Using Limit Equilibrium and Finite Element Method

2016 ◽  
Vol 857 ◽  
pp. 555-559 ◽  
Author(s):  
Zuhayr Md Ghazaly ◽  
Mustaqqim Abdul Rahim ◽  
Kok Alfred Chee Jee ◽  
Nur Fitriah Isa ◽  
Liyana Ahmad Sofri
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Factor Of Safety ◽  
Slip Surface ◽  
Limit Equilibrium ◽  
Main Concern ◽  
Analysis Method ◽  
Stability Of Slope ◽  
The Stability ◽  
Element Method

Slope stability analysis is one of the ancient tasks in the geotechnical engineering. There are two major methods; limit equilibrium method (LEM) and finite element method (FEM) that were used to analyze the factor of safety (FOS) to determine the stability of slope. The factor of safety will affect the remediation method to be underdesign or overdesign if the analysis method was not well chosen. This can lead to safety and costing problems which are the main concern. Furthermore, there were no statement that issued one of the analysis methods was more preferred than another. To achieve the objective of this research, the soil sample collected from landslide at Wang Kelian were tested to obtain the parameters of the soils. Then, those results were inserted into Plaxis and Slope/W software for modeling to obtain the factor of safety based on different cases such as geometry and homogenous of slope. The FOS obtained by FEM was generally lower compared to LEM but LEM can provide an obvious critical slip surface. This can be explained by their principles. Overall, the analysis method chosen must be based on the purpose of the analysis.

scholarly journals Stability estimation of slopes with determined slip surface by the MSTAB-3D method based on sliding body limit equilibrium analysis

2019 ◽  
Vol 262 ◽  
pp. 04004
Author(s):  
Janusz Ukleja
Keyword(s):  
Cross Sections ◽  
Slip Surface ◽  
Limit Equilibrium ◽  
Equilibrium Analysis ◽  
Limit Equilibrium Analysis ◽  
Modified Method ◽  
3D Elements ◽  
Resultant Forces ◽  
The Impact ◽  
Section Analysis

The method developed for this study, established on the premises of the limit equilibrium flat analysis for a spatial solution, is a modification of the STAB-3D method, previously described by the author. It combines the analyses methods of 2D slices of flat cross–sections with the spatial analyses methodology rooted in a specific breakdown of a landslide sliding body into 3D elements assuming some simplifying solution. However, this method is solely applicable in case of a landslide failure with a stipulated slip surface and with a consistent decline of a determined slide direction. Such a method was developed in the article published earlier, which provided then its basic assumptions and the equilibrium formulations. The following publication thereof, presents overall suppositions for this method as well as its modification involving the resultant forces brought to the equilibrium with the generalized slide direction. Apart from that, a comparative analysis was carried out on the impact of this modification applicability of the obtained results with regard to the STAB-3D method. The algorithm was also presented concerning the modified method with its results being compared to a couple of selected methods LEM (limit equilibrium method). The undertaken analysis reveals that the modified MSTAB-3D method determines stability indicators that are very similar to its earlier version. Moreover, the results occur to be also approximating the values obtained in the course of other methods with regard to the flat cross-section analysis.

The 2001 R.M. Hardy Lecture: The limits of limit equilibrium analyses

2003 ◽  
Vol 40 (3) ◽  
pp. 643-660 ◽  
Author(s):  
John Krahn
Keyword(s):  
Finite Element ◽  
Factor Of Safety ◽  
Slip Surface ◽  
Limit Equilibrium ◽  
Geotechnical Engineering ◽  
Software Tools ◽  
Great Promise ◽  
Engineering Practice ◽  
Stability Factor ◽  
Limit Equilibrium Methods

Limit equilibrium types of analysis have been in use in geotechnical engineering for a long time and are now used routinely in geotechnical engineering practice. Modern graphical software tools have made it possible to gain a much better understanding of the inner numerical details of the method. A closer look at the details reveals that the limit equilibrium method of slices has some serious limitations. The fundamental shortcoming of limit equilibrium methods, which only satisfy equations of statics, is that they do not consider strain and displacement compatibility. This limitation can be overcome by using finite element computed stresses inside a conventional limit equilibrium framework. From the finite element stresses both the total shear resistance and the total mobilized shear stress on a slip surface can be computed and used to determine the factor of safety. Software tools that make this feasible and practical are now available, and they hold great promise for advancing the technology of analyzing the stability of earth structures.Key words: limit equilibrium, stability, factor of safety, finite element, ground stresses, slip surface.

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