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.

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.

Earthquake Impact Analyses on Slopes Using Finite Element and Limit Equilibrium Methods

2010 ◽  
Vol 163-167 ◽  
pp. 3868-3871
Author(s):  
Yu Hwang Ong ◽  
Anuar Kasa ◽  
Zamri Chik ◽  
Taha Mohd Raihan
Keyword(s):  
Finite Element ◽  
Factor Of Safety ◽  
Limit Equilibrium ◽  
Friction Angle ◽  
Determine Factor ◽  
Earthquake Activity ◽  
Limit Equilibrium Methods ◽  
Dynamic Analyses ◽  
Cut Slopes ◽  
Steep Slopes

The objective of this research is to determine factor of safety for various cut slopes under the influence of earthquake activity. Finite element method was used to generate initial static stress condition and run dynamic analyses of the cut slopes. Factor of safety was then calculated using limit equilibrium method. Both sand and clay were analyzed in this study. The results show that steep slopes with initial safety factor of 1.5 are capable to sustain earthquake magnitude of 0.25g due to high shear strength of the soil. However, slopes with friction angle less than 21º for sand and cohesion value less than 38 kPa for clay are not stable. This shows that earthquake loading should be considered in the design of cut slopes in Malaysia.

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.

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.

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.

Some difficulties associated with the limit equilibrium method of slices

1983 ◽  
Vol 20 (4) ◽  
pp. 661-672 ◽  
Author(s):  
R. K. H. Ching ◽  
D. G. Fredlund
Keyword(s):  
Slope Stability ◽  
Factor Of Safety ◽  
Limit Equilibrium ◽  
Stability Limit ◽  
Limit Equilibrium Method ◽  
Soil Conditions ◽  
Side Force ◽  
Limit Equilibrium Methods ◽  
Equilibrium Method ◽  
The Stability

Several commonly encountered problems associated with the limit equilibrium methods of slices are discussed. These problems are primarily related to the assumptions used to render the inherently indeterminate analysis determinate. When these problems occur in the stability computations, unreasonable solutions are often obtained. It appears that problems occur mainly in situations where the assumption to render the analysis determinate seriously departs from realistic soil conditions. These problems should not, in general, discourage the use of the method of slices. Example problems are presented to illustrate these difficulties and suggestions are proposed to resolve these problems. Keywords: slope stability, limit equilibrium, method of slices, factor of safety, side force function.

Factor of safety of slope stability from deformation energy

2018 ◽  
Vol 55 (2) ◽  
pp. 296-302 ◽  
Author(s):  
Shiguo Xiao ◽  
Wei Dong Guo ◽  
Jinxiu Zeng
Keyword(s):  
Shear Strength ◽  
Factor Of Safety ◽  
Plastic Material ◽  
Limit Equilibrium ◽  
Deformation Energy ◽  
Simple Expression ◽  
Shear Stresses ◽  
Limit Equilibrium Methods ◽  
Coulomb Failure Criterion ◽  
Elastic Plastic Material

The factor of safety of a slope (Fs) is invariably assessed using methods underpinned by moment, force, and (or) shear strength equilibrium concerning slip surfaces. Each method inherently embeds some form of limitations, despite being popularly adopted in practice. In this paper, a new Fs is devised using the ratio of ultimate energy (eu, upon sliding) over accumulated “elastic” energy. The Fs is then reduced to a simple expression of the power to shear stress and shear strength, by taking soil as an elastic–plastic material obeying the Mohr–Coulomb failure criterion. This expression empowers significant efficacy in gaining the factor of safety (without involving energy or directions of shear stresses). The Fs values were calculated for three typical slopes concerning various mechanical properties (dilation, Poisson’s ratio, and shear modulus) and effective computational strategies. All of the Fs values (to a congruous accuracy of available methods) were obtained in less than 1% the time of conventional numerical analyses. The proposed Fs, equally applicable to limit equilibrium methods, may be utilized in practice to expedite slope design.

scholarly journals Factor of Safety Reduction Factors for Accounting for Progressive Failure for Earthen Levees with Underlying Thin Layers of Sensitive Soils

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Adam J. Lobbestael ◽  
Adda Athanasopoulos-Zekkos ◽  
Josh Colley
Keyword(s):  
Finite Element ◽  
Strain Softening ◽  
Progressive Failure ◽  
Limit Equilibrium ◽  
Thin Layers ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Limit Equilibrium Methods ◽  
The Stability ◽  
Reduction Factors

The effects of progressive failure on flood embankments with underlying thin layers of soft, sensitive soils are investigated. Finite element analysis allows for investigation of strain-softening effects and progressive failure in soft and sensitive soils. However, limit equilibrium methods for slope stability analysis, widely used in industry, cannot capture these effects and may result in unconservative factors of safety. A parametric analysis was conducted to investigate the effect of thin layers of soft sensitive soils on the stability of flood embankments. A flood embankment was modeled using both the limit equilibrium method and the finite element method. The foundation profile was altered to determine the extent to which varying soft and sensitive soils affected the stability of the embankment, with respect to progressive failure. The results from the two methods were compared to determine reduction factors that can be applied towards factors of safety computed using limit equilibrium methods, in order to capture progressive failure.

Stresses and deformations in a reinforced soil slope

1990 ◽  
Vol 27 (2) ◽  
pp. 224-232 ◽  
Author(s):  
R. J. Chalaturnyk ◽  
J. D. Scott ◽  
D. H. K. Chan ◽  
E. A. Richards
Keyword(s):  
Finite Element ◽  
Slip Surface ◽  
Limit Equilibrium ◽  
Maximum Load ◽  
Reinforced Soil ◽  
Soil Reinforcement ◽  
Soil Slope ◽  
Element Analysis ◽  
Reinforced Slope ◽  
Reinforcing Layer

Nonlinear finite element analyses were performed on a nonreinforced embankment and a polymeric reinforced embankment, with 1:1 side slopes, constructed on competent foundations. The nonreinforced and reinforced embankment analyses are compared to examine the influence of polymeric reinforcement within a soil slope. It is shown that significant reductions in the shearing, horizontal, and vertical strains within the slope occur because of the presence of the reinforcement.The finite element analysis of the reinforced embankment construction gives the magnitude and distribution of load within the reinforcement. For all embankment heights, the maximum reinforcement load did not occur in the lowest reinforcing layer but in the reinforcing layer placed 0.4H above the foundation, where H is the height of the slope. The displacement patterns and surface deformations of the nonreinforced and reinforced slopes are compared to show the marked reduction in slope movements resulting from the presence of the reinforcement.The location and shape of potential shear surfaces within the homogeneous reinforced slope are examined. The position of the maximum load in each reinforcing layer within the reinforced slope indicates that, for the example studied, a circular-shaped slip surface represents a probable failure mechanism within the slope. Key words: soil reinforcement, geotextiles, finite element, slope stability, geogrids, limit equilibrium, reinforced slope.

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