Limit Analysis and Stability Charts for 3D Slope Failures

The kinematic approach of limit analysis is explored in three-dimensional (3D) stability analysis of slopes. A formal derivation is first shown indicating that, in a general case, the approach yields an upper bound to the critical height of the slope or an upper bound on the safety factor. A 3D failure mechanism is used to produce stability charts for slopes. The slope safety factor can be read from the charts without the need for iterations. While two-dimensional (2D) analyses of uniform slopes lead to lower safety factors than 3D analyses do, a 3D calculation is justified in cases where the width of the collapse mechanism has physical limitations, for instance, in the case of excavation slopes, or when the analysis is carried out to back-calculate the properties of the soil from 3D failure case histories. Also, a 3D failure can be triggered by a load on a portion of the surface area of the slope. Calculations indicate that for the 3D safety factor of the loaded slope to become lower than the 2D factor for the same slope (but with a load-free surface), the load has to be very significant and equal to the weight of a soil column of the order 10?1 of the slope height.     

Nonlinear Failure Criterion and Passive Thrust on Retaining Walls

The effect of nonlinearity of the failure criterion on the passive thrust on smooth and rough vertical retaining walls is studied theoretically. Limit analysis upper bound estimates based on block-type failure mechanisms are constructed. An alternative, a priori linearization, approach is discussed. It is shown that for smooth walls both approaches, as well as the Rankine-type slip line solution, yield similar results. For rough walls, however, the ambiguity in the a priori linearization makes it difficult to compare the results. This deficiency is absent in the limit analysis nonlinear solutions.     

Stability Factors for Slopes with Nonassociated Flow Rule Using Energy Consideration

From the consideration of energy balance at collapse, stability factors were computed for soil slopes with both associated and nonassociated flow rules. The effect of the pore water pressure was also incorporated. The stress variation along the rupture surface—needed to obtain the rate of dissipation of internal energy for the nonassociated flow rule—was established on the basis of the assumption of interslice forces given by Fellenius and Bishop. Both coaxial and noncoaxial nonassociated flow rules were examined. For the coaxial flow rule, the stability factors reduce quite appreciably with a decrease in the dilatancy angle (ψ). Whereas with the noncoaxial flow rule, the effect of ψ on the results was seen to be less significant. For mild slopes, the distribution of the stresses along the rupture surface on the basis of Fellenius’s method was seen to provide more conservative results as compared with Bishop’s approach; whereas the reverse was found true for steep slopes.     

Probabilistic Slope Stability Analysis by Finite Elements

In this paper we investigate the probability of failure of a cohesive slope using both simple and more advanced probabilistic analysis tools. The influence of local averaging on the probability of failure of a test problem is thoroughly investigated. In the simple approach, classical slope stability analysis techniques are used, and the shear strength is treated as a single random variable. The advanced method, called the random finite-element method (RFEM), uses elastoplasticity combined with random field theory. The RFEM method is shown to offer many advantages over traditional probabilistic slope stability techniques, because it enables slope failure to develop naturally by “seeking out” the most critical mechanism. Of particular importance in this work is the conclusion that simplified probabilistic analysis, in which spatial variability is ignored by assuming perfect correlation, can lead to unconservative estimates of the probability of failure. This contradicts the findings of other investigators who used classical slope stability analysis tools.     

Quasi-Three-Dimensional Slope Stability Analysis Method for General Sliding Bodies

A quasi-three-dimensional procedure has been developed for computing the stability of earth slopes and waste containment facilities along general slip surfaces. The procedure, termed the Resistance-Weighted procedure, is an extension of existing quasi-three-dimensional procedures, which utilize results from two-dimensional slope stability analyses to estimate three-dimensional stability. As a part of this procedure, a scheme has been developed for modeling realistic three-dimensional sites and efficiently generating input data for two-dimensional analyses. This scheme enables Resistance-Weighted calculations to be performed using existing commercial spreadsheet and two-dimensional slope stability software. The method can also be incorporated into existing two-dimensional slope stability software with relatively little development effort. The Resistance-Weighted procedure and geometric modeling scheme are presented in this paper. Application of the procedure to a case history and results of a series of analyses to validate the procedure are described. The results of the analyses show that the Resistance-Weighted procedure produces results that compare favorably with more rigorous three-dimensional procedures. Although the Resistance-Weighted procedure is approximate, it serves as a simple means for estimating the magnitude of three-dimensional effects when a more rigorous three-dimensional procedure is not available.     

Stability Charts for Uniform Slopes

While computational tools have made most graphical methods and charts obsolete, stability charts for slopes are still routinely used in practice. The charts presented here are based on the kinematic approach of limit analysis that leads to a strict lower bound on stability number c/γH or an upper bound on the safety factor. An earlier suggestion is employed in this paper to produce charts that eliminate the necessity for iterations. Charts are presented for slopes subjected to pore water pressure and also for those exposed to seismic forces.     

Probabilistic Assessment of Slope Stability That Considers the Spatial Variability of Soil Properties

In this paper, a numerical procedure for probabilistic slope stability analysis is presented. This procedure extends the traditional limit equilibrium method of slices to a probabilistic approach that accounts for the uncertainties and spatial variation of the soil strength parameters. In this study, two-dimensional random fields were generated based on a Karhunen-Loève expansion in a fashion consistent with a specified marginal distribution function and an autocorrelation function. A Monte Carlo simulation was then used to determine the statistical response based on the generated random fields. This approach makes no assumption about the critical failure surface. Rather, the critical failure surface corresponding to the input random fields of soil properties is searched during the process of analysis. A series of analyses was performed to verify the application potential of the proposed method and to study the effects of uncertainty due to the spatial heterogeneity on the stability of slope. The results show that the proposed method can efficiently consider the various failure mechanisms caused by the spatial variability of soil property in the probabilistic slope stability assessment.     

Stability Charts for 3D Failures of Steep Slopes Subjected to Seismic Excitation

Design of slopes and analysis of existing slopes subjected to seismic shaking are carried out routinely using approximations of plane strain and substitution of a quasi-static load for the seismic excitation. A three-dimensional (3D) analysis of slopes is carried out, based on the kinematic theorem of limit analysis. A rotational failure mechanism is used with the failure surface in the shape of a curvilinear cone sector passing through the slope toe, typical of steep slopes. A quasi-static approach is used to develop stability charts allowing assessment of the factor of safety of slopes without the need for an iterative procedure. The charts are of practical importance in cases of excavation slopes and whenever a slope is physically constrained, preventing a plane failure.     

Effect of Antecedent Rainfall Patterns on Rainfall-Induced Slope Failure

Rainfall-induced slope failure occurs in many parts of the world, especially in the tropics. Many rainfall-induced slope failures have been attributed to antecedent rainfalls. Although it has been identified as a cause of rainfall-induced slope failure, the pattern or distribution of the antecedent rainfall has not received adequate attention. In this study, parametric studies were performed by using three typical rainfall patterns, identified by analysis of available rainfall data for Singapore and two different soil types to represent high- and low-conductivity residual soils of Singapore. Antecedent rainfall patterns were applied on soil slopes and a transient seepage analysis was conducted. The computed pore-water pressures were used in stability analyses to calculate the safety factor of the slope. Results indicated that antecedent rainfall affected the stability of both high-conductivity (HC) and low-conductivity (LC) soil slopes. However, the stability of the LC soil slope was more significantly affected than the HC soil slope. Patterns of antecedent rainfall controlled the rate of decrease in factor of safety, the time corresponding to Fs(min) and the value of Fs(min). Delayed rainfall pattern resulted in the lowest minimum factor of safety, Fs(min), for the HC soil slope, and advanced rainfall pattern resulted in the lowest Fs(min) for the LC soil slope.     

Search for Critical Slip Surface in Slope Stability Analysis by Spline-Based GA Method

The stability of a soil slope is usually analyzed by limit equilibrium methods, in which the identification of the critical slip surface is of principal importance. In this study the spline curve in conjunction with a genetic algorithm is used to search the critical slip surface, and Spencer’s method is employed to calculate the factor of safety. Three examples are presented to illustrate the reliability and efficiency of the method. Slip surfaces defined by a series of straight lines are compared with those defined by spline curves, and the results indicate that use of spline curves renders better results for a given number of slip surface nodal points comparing with the approximation using straight line segments.     

Three-Dimensional Stability Analysis of Convex Slopes in Plan View

A method of three-dimensional slope stability analysis for convex slopes in plan view is presented here based on the upper-bound theorem of the limit analysis approach. The method can also be used to determine the bearing capacity of foundations adjacent to such slopes. A rigid-block translational collapse mechanism is considered in which energy dissipation takes place along planar velocity discontinuities. Comparing the bearing capacity of foundations, numerical results indicate that the one located near convex slopes has less capacity than the one located near straight slopes. Inversely, slopes not subjected to surcharge loads are more stable when they are convex. Concerning the bearing capacity analyses, consideration of the curvature effect of convex slopes is more significant in frictional soils whereas for slope stability analyses, mentioned effect is of prime importance in cohesive soils. Numerical results of proposed algorithm are presented in the form of nondimensional graphs.     

Generalized Method for Three-Dimensional Slope Stability Analysis

This paper describes an extension of a new three-dimensional (3D) stability analysis method, including formulation, comparative studies, and examples of new application. The new method uses “two-directional force and moment equilibrium” in the stability analysis of 3D potential failure mass with arbitrary shapes. The use of this new method has resulted in a novel situation wherein the direction of the resultant shear force (or direction of sliding) generated on the potential failure surface can now be calculated instead of the guesswork assumptions that were formerly made. It is also demonstrated that this new method eliminates the labor-intensive work for establishing local coordinate systems performed in conventional 3D analysis. Consequently, this new method facilitates a computer-aided 3D search for the critical failure surfaces in slope areas.     

GIS-Based Implementation of Three-Dimensional Limit Equilibrium Approach of Slope Stability

The growing popularity of the geographical information system (GIS), with capacities ranging from conventional data storage to complex spatial analysis and graphical presentation, means it is also becoming a powerful tool for geotechnical engineers. In this technical note, integrating the GIS grid-based data with four proposed column-based limit equilibrium models of three-dimensional (3D) slope stability analysis, new correspondent GIS grid-based 3D deterministic models have been devised in order to calculate the safety factor of the slope. Based on four GIS-based 3D slope stability analysis models, a GIS-based program, 3DSlopeGIS, has been developed to implement the algorithm where the whole of the input data is in the same form as the GIS dataset. Certain widely addressed examples have been evaluated using 3DSlopeGIS and the results show the correction and potential of this GIS-based tool as a means of assessing the 3D stability of a slope. A practical slope problem has also been evaluated using the 3DSlopeGIS system, and the results have illustrated the convenience of data management.     

Evaluation of Interslice Force Function and Discussion on Convergence in Slope Stability Analysis by the Lower Bound Method

The interslice force function f(x) is a major assumption of the limit equilibrium method, which is important but has not been adequately considered in the past. In this paper, f(x) is taken as the control variable, and the upper and lower limits of the factor of safety for a general slope will be determined by a global optimization analysis. Based on this approach, f(x) will be determined and investigated. We demonstrate that f(x) cannot be arbitrarily assigned if a set of acceptable internal forces is required. The present approach can be presented practically as a lower bound approach with the advantage that failure to converge is virtually eliminated, which is not possible with all other existing “rigorous” methods. The “present proposal” attempts to answer several important questions in the basic theory of slope stability analysis, and provides a f(x) based on the lower bound approach statically admissible forces throughout the whole failure zone. Currently, different assumptions will give different factors of safety to the same problem, and this situation will be overcome by the use of the present proposal. The present proposal is also proven to give a result equal to the slip line solution for a simple footing on clay which is not possible for other classical slope stability methods, which has demonstrated that the applicability of the “present proposal” for general difficult problems.     

Unsaturated Infinite Slope Stability Considering Surface Flux Conditions

A slope stability model is derived for an infinite slope subjected to unsaturated infiltration flow above a phreatic surface. Closed form steady state solutions are derived for the matric suction and degree of saturation profiles. Soil unit weight, consistent with the degree of saturation profile, is also directly calculated and introduced into the analyzes, resulting in closed-form solutions for typical soil parameters and an infinite series solution for arbitrary soil parameters. The solutions are coupled with the infinite slope stability equations to establish a fully realized safety factor function. In general, consideration of soil suction results in higher factor of safety. The increase in shear strength due to the inclusion of soil suction is analogous to making an addition to the cohesion, which, of course, increases the factor of safety against sliding. However, for cohesive soils, the results show lower safety factors for slip surfaces approaching the phreatic surface compared to those produced by common safety factor calculations. The lower factor of safety is due to the increased soil unit weight considered in the matric suction model but not usually accounted for in practice wherein the soil is treated as dry above the phreatic surface. The developed model is verified with a published case study, correctly predicting stability under dry conditions and correctly predicting failure for a particular storm.     

Direct Estimation of Yield Acceleration in Slope Stability Analyses

In conventional slope stability analyses, the yield acceleration is traditionally estimated by trial and error. This approach becomes unwieldy when hundreds or thousands of iterations are required in rigorous probabilistic analyses. To cut down on the computational effort, we developed direct expressions for the values of the yield acceleration for the most commonly used methods of slope stability analysis. Analyses of example problems indicate that the direct computation of yield acceleration provides a significant improvement in the efficiency over the simple trial and error approach, although the numerical difficulties inherent to the various methods of slope stability analyses are still present.     

Meta-Analysis of 301 Slope Failure Calculations. II: Database Analysis

In response to the growing need for statistical information regarding slope stability risk analysis, this work applies inferential analysis to a compiled database of 157 failed slopes and corresponding 301 safety factor (SF) calculations. As presented in the companion paper, this database also includes a number of slope stability factors, including analytical method used, stress approach (effective versus total), assumed slip surface geometry, slope type, applied correction factors, and soil Atterburg limits. Although the SF data were found to be fairly well fit by a lognormal distribution, pronounced curvature of the residuals was observed, likely related to various unaccounted slope factors. In response, inferential statistics are used in this paper to analyze the effects of analytical method, slope type, soil plasticity, and effective versus total stress analysis. ANOVA hypothesis testing indicated significant differences between analytical methods and significant interactions between slope types and pore-water stress approaches. Direct SF calculation methods, such as infinite slope, wedge, and the ordinary method of slices were found to produce SF near 1 as expected, but higher order methods in general, and force methods in particular, predicted safety factors significantly greater than 1. Clay content alone was not a discernible influence on SF calculations. A reduced factor ANOVA model was developed to predict SF, given analytical method (a main effect) and the interactions between analytical method with both slope type and pore-water pressure approach.     

Validation of a New 2D Failure Mechanism for the Stability Analysis of a Pressurized Tunnel Face in a Spatially Varying Sand

A new two-dimensional (2D) limit analysis failure mechanism is presented for the determination of the critical collapse pressure of a pressurized tunnel face in the case of a soil exhibiting spatial variability in its shear strength parameters. The proposed failure mechanism is a rotational rigid block mechanism. It is constructed in such a manner to respect the normality condition of the limit analysis theory at every point of the velocity discontinuity surfaces taking into account the spatial variation of the soil angle of internal friction. Thus, the slip surfaces of the failure mechanism are not described by standard curves such as log-spirals. Indeed, they are determined point by point using a spatial discretization technique. Though the proposed mechanism is able to deal with frictional and cohesive soils, the present paper only focuses on sands. The mathematical formulation used for the generation of the failure mechanism is first detailed. The proposed kinematical approach is then presented and validated by comparison with numerical simulations. The present failure mechanism was shown to give results (in terms of critical collapse pressure and shape of the collapse mechanism) that compare reasonably well with the numerical simulations at a significantly cheaper computational cost.     

Material Spatial Variability and Slope Stability for Weak Rock Masses

The presence of weak materials, bedding, or discontinuities at critical locations could lead to local or large-scale failures of natural or excavated slopes or tunnels. Material spatial variation of Eagle Ford Shale in Texas was established based on laboratory and field testing results. A random field model was used to characterize the material spatial variation, and the correlation distance for the Eagle Ford Shale strength variability was evaluated. Impacts of material property variability and spatial variability on slope stability were analyzed using Monte Carlo simulation with distinct element modeling using random field elements implicitly embedded in the numerical analyses. This study provides insight into the significance of material spatial variation on stability, possible failure mechanisms, and critical locations of weak materials in a shale mass.     

Stability Analysis of Strain-Softening Slope Reinforced with Stabilizing Piles

Stabilizing piles have been used extensively over the past few decades to support unstable slopes. A new simplified method is described to analyze the stability level of a strain-softening slope reinforced with stabilizing piles. An equivalent principle is proposed to account for the three-dimensional effect of the piles on the stability level of slopes. The formulation is derived on the basis of the displacement distribution assumptions of the slope by extending the simplified Bishop slice method. The parameters can be easily determined by element tests. This method is used on a real-world slope to discuss the influential factors. The results show that the slope geometry and pile layout, which includes pile spacing, pile location, and pile depth, have a significant effect on the safety factor and critical slip surface of the reinforced slope. The stability level of a strain-softening slope is dependent not only on the strength parameters but also on the stress-strain relationship of soil.