Three dimensional slope stability analyses for natural and manmade slopes

Slope stability analyses in practice mostly rely on limit equilibrium (LE) procedures rather than finite element (FE) or finite difference (FD) procedures. Presently, most slope stability methods are two-dimensional (2D) which assumes the failure surface is infinitely wide and therefore three dimensional (3D) shear resistance/forces are negligible when compared to the overall driving and resisting forces. Most, if not all, slopes are not infinitely wide and have a 3D geometry. Therefore, application of 2D analyses to a 3D problem is not theoretically correct but believed to be conservative/ sufficient for engineering practice. 2D analyses are conservative because the shear resistance along the two sides of the slide mass (end effects) are neglected in the analysis. This conservatism may be acceptable for slope designs, but in the case of back-analyses of landslides, 2D analyses may result in unconservative values of back-calculated shear strength by as much as 30% (Stark and Eid 1998). In addition, 3D analyses are important in slope failure causation analyses, especially in litigation, to accurately assess the relative effects of slope changes, precipitation, shear resistance and remedial measures. This study presents a LE methodology for calculating the 3D factor of safety (FS) for natural and manmade slopes and an accompanying user friendly software package. A comparison of different 2D and 3D slope stability methods e.g., LE and continuum mechanics methods, is also presented to verify the new LE methodology. Using known slope stability examples from published literature and field case histories, 2D and 3D slope stability analysis were performed by LE and continuum methods to investigate the applicability and/or limitations of each method to different slope stability problems and geometries. An inherent advantage of continuum analyses is the failure surface geometry, i.e., rotational or translational, does not have to be specified and it is located as part of the solution for the lowest FS. However in a back-analysis, the field failure surface and slide mass geometry must be used instead of searching for the failure surface that yields the lowest back-calculated strength. Because there is no provision for specifying a failure surface, current continuum mechanics procedures can be used for design of slopes and probably not for back-analysis. In addition, LE procedures are more user friendly than FD and FE procedures, consume less computational time, and are preferred for routine analysis for design. For important projects, results of LE analysis can be checked using FD or FE procedures. Based on a review of existing 3D literature, and LE, FE, and FD analyses performed in the present study, it may be concluded that the minimum 3D FS is greater than the minimum 2D FS for all conditions considered herein. If the actual shear strength is used in the design of a slope, the assumption of an infinitely wide 2D failure is conservative. However, the same assumption may lead to an overestimate of the back-calculated shear strength from a 2D analysis. The findings that 2D analyses yield lower FS values than 3D analyses is significant for design of slopes. For example, municipal solid waste (MSW) landfill design is regulated by state and federal codes that require a minimum static FS of 1.5. These codes do not specify whether this is a 2D or 3D FS. However, it is implicitly understood that state or federal regulations require a minimum 2D FS greater than 1.5. With the acceptance of 3D stability analyses in practice, some designers have used a 3D FS of greater than 1.5 to satisfy the state or federal code. However, a 3D FS of 1.5 is less stable than a 2D FS of 1.5 which results in a less stable landfill slope but more airspace for the facility. Therefore, it is recommended that regulatory codes specify “minimum 2D FS of 1.5” to achieve the current level of stability for man-made slopes. Stark and Eid (1998) show that 3D LE software does not consider the effects of shear resistance offered by the vertical sides that parallel the direction of movement of a translational landslide mass. Based on results of a parametric study conducted herein using FE and FD analysis, it was found that the use of an earth pressure coefficient (Kτ) that is in-between at-rest (KO) and active (KA) earth pressure provides a better estimate of the side shear resistance and 3D/2D FS ratios that are in agreement with FE and FD analyses. An attempt was made to update the charts provided by Arellano and Stark (2000) that show the influence of shear strength on ratios of 3D/2D FS for various slope inclinations and geometries. Charts developed herein can be used to estimate the importance of performing a 3D slope stability analysis for a translational failure. A new 3D LE methodology and program, 3DDEM-Slope, were developed as part of this study to incorporate and/or verify some of the findings of this study. The program options include input of shear strength using a stress dependent failure envelope to capture the stress dependent behavior of soils, Janbu's (1973) correction factor for 2D and 3D slope stability analysis using Janbu's (1956) simplified procedure, and improved subroutines for calculation of the vertical column base angles. The column base angles are calculated using a third-order finite difference estimator (Horn 1981) using all eight outer points of a grid node instead of using only two adjacent grid nodes so the base angle corresponds to the angle of an inclined plane instead of a line as occurs in 2D calculations. Although the program uses a 3D DEM file, 3DDEM-Slope can be used to calculate a 2D FS at any desired cross-section along the 3D failure surface. In addition, 3DDEM-Slope compares the 2D FS for a cross-section in the middle of the slide mass with the overall 3D FS. This provides the user with a warning signal that 3D/2D FS ratio is less than the reference values obtained from FD and FE analyses for same width to height ratio and slope inclination. If so, the user can select to apply external side forces that are calculated based on the findings of this study and obtain a corrected 3D FS