A New Era in Slope Stability Analysis: Shear Strength Reduction Finite Element Technique This article examines the merits of using finite element analysis versus limit-equilibrium methods for slope design and analysis Geomechanics software used worldwide by geotechnical engineers Article prepared for RocNews software tools for rock and soil Summer 2004 A New Era in Slope Stability Analysis: Shear Strength Reduction Finite Element Technique Finite Element (FE) analysis is now widely accepted in routine excavation and support design and analysis. It may also revolutionize routine slope stability analysis. Practicing engineers and mass along a slip surface. The academics alike are becoming popularity of limit-equilibrium increasingly convinced of the methods is primarily due to their benefits of the Shear Strength relative simplicity, ready ability to Reduction (SSR) technique for evaluate the sensitivity of stability “Things should be determining slope factor of to various input parameters, made as simple as safety. This method is particularly and the experience geotechnical possible, but not any useful when several different engineers have acquired over the simpler.” modes of failure are possible; it years in interpreting calculated — Albert Einstein automatically finds the critical factor of safety values. Limit- mechanism. But has the SSR equilibrium methods require technology matured to the minimal input data. The factor stage where it can be used for of safety values they output routine analysis? In this article, help engineers to guard against we will attempt to answer this uncertainties such as ignorance question, as well as offer insights about the reliability of input into today’s slope engineering parameters and loadings, and practices. the possibility that identified failure mechanisms may differ Limit-Equilibrium Slope from actual behaviour. As Stability Analysis well, recommended factor of Limit-equilibrium methods safety values for slopes and are the most commonly used excavations generally ensure approaches for analyzing that deformations are within the stability of slopes. The acceptable range. fundamental assumption at their core is that failure occurs Despite all the benefits, the through sliding of a block or limit-equilibrium approach has some important deficiencies. 2 The technique neglects stress- literature. They were mostly strain behaviour of soils and based on an approach that flows rocks. It also makes arbitrary naturally from the definition assumptions (mostly regarding of slope factor of safety, and is inter-slice forces) to ensure now commonly referred to as static determinacy. It is awkward the Shear Strength Reduction to use for analyzing stability (SSR) technique. By definition, problems, such as the failure of the factor of safety of a slope cantilever and retaining walls, in is the “ratio of actual soil shear which failure involves deformed strength to the minimum shear wedges. strength required to prevent failure,” or the factor by which The Shear Strength soil shear strength must be Since the finite Reduction Technique reduced to bring a slope to element method Rapid advances in computer the verge of failure (Duncan, was first applied technology and sustained 1996). In the SSR finite element to geotechnical development have pushed the technique elasto-plastic strength engineering in finite element method (FEM) is assumed for slope materials. 1966, it has grown and other numerical analysis The material shear strengths tremendously in approaches to the forefront of are progressively reduced until popularity. geotechnical practice. Since it collapse occurs. was first applied to geotechnical engineering in 1966, the FEM For Mohr-Coulomb material has grown tremendously in shear strength reduced by popularity, primarily due to a factor (of safety) F can be its ability to analyze a very determined from the equation broad range of problems, while yielding realistic results. It can accommodate practically all This equation can be re-written as kinds of geometry, and can model key aspects of material behaviour such as stress paths (construction sequence), and In this case, coupled stress-pore pressure variations. and In the mid 1970s, techniques are reduced Mohr-Coulomb for applying the FEM to shear strength parameters, and slope stability analysis started these values can be input into an appearing in geotechnical FE model and analyzed. 3 Basic Algorithm Advantages For Mohr-Coulomb materials, The elasto-plastic SSR FE the steps for systematically approach offers a number of searching for the critical factor significant advantages over of safety value, F, which brings traditional limit-equilibrium a previously stable slope to the analysis. First, it eliminates the verge of failure, are as follow need for a priori assumptions on failure mechanisms (the type, Step 1: Develop an FE model of a shape, and location of failure slope, using the deformation and surfaces). The SSR technique strength properties established automatically establishes the for the slope materials. critical failure mechanism. It Compute the model and record The SSR FE eliminates artificial separation the maximum total deformation technique minimizes of slope problems into those in the slope. the expertise required involving slip surface failures, in finding critical Step 2: Increase the value of F and those involving failure of failure mechanisms and calculate factored Mohr- deformed wedges. for certain slope Coulomb material parameters Although possibly more problems. as described above. Enter the demanding in other aspects, new strength properties into the the SSR FE technique minimizes slope model and re-compute. the expertise required in finding Record the maximum total critical failure mechanisms deformation. for certain slope problems. Step 3: Repeat Step 2, using At times this goes unnoticed systematic increments of F, until by slope engineers. A typical the FE model does not converge example involves the problem to a solution, i.e. continue to of identifying the critical failure reduce material strength until mechanism beneath a concrete the slope fails. The critical F value dam on a foundation that just beyond which failure occurs includes a weak layer. The search will be the slope factor of safety. for the critical limit-equilibrium mechanism, using Slide, is (For a slope that is initially described in an AVI movie in unstable, factor of safety values in steps 2 and 3 must be reduced until the FE model converges to a solution.) 4 this issue of RocNews Summer – a combination of block search 2004. Regular non-circular limit- with surface optimization – a equilibrium analysis with the more critical slip surface with a Morgernstern method produced 2.36 factor of safety value was a factor of safety of 3.0. Using located. The images of these advanced features in Slide not results are shown on Figures 1a applied by most modelers and 1b. Figure 1a. The critical failure surface and factor of safety from conventional Morgernstern limit- equilibrium analysis of a concrete dam. The thin, beige-coloured material beneath the dam is the weak layer. Figure 1b. The critical failure surface and factor of safety obtained using block search, combined with surface optimization. Notice the differences between this surface and that in Figure 1a. 5 The problem was then modeled solution), and an exaggerated in Phase2, the finite element deformed mesh. Contours of analysis program developed maximum shear strain are shown by Rocscience, using the SSR on Figure 2b. These figures technique. This yielded a factor indicate failure in the weak zone of safety value of 2.35. Figure and a critical failure surface 2a shows the contours of total similar to the non-circular limit- displacement at the modeling equilibrium surface obtained stage preceding total failure from the combination of block (non-convergence of the search and optimization. Figure 2a. Contours of total displacement calculated for the FE model of the dam, and the (exaggerated) deformed mesh. These contours indicate a critical failure mechanism similar to that obtained from advanced limit- equilibrium analysis. Figure 2b. Contours of maximum shear strain calculated for the FE model of the dam. Like the previous image, these contours indicate the critical failure mechanism as shearing, passing through the weak zone. 6 Another benefit of the SSR aspect for some embankments approach is its elimination of and excavations. Drawing on arbitrary assumptions regarding the robustness of the FEM, the inclinations and locations the technique performs very of inter-slice forces. As well, well under a wide range of the method can automatically conditions. Lastly, it can be monitor the development of more readily applied to three- failure zones, from localized dimensional slope modeling than areas all the way to total slope limit-equilibrium methods. failure. This is particularly important in the analysis of high Will Use of the SSR Technique Become Widespread? slopes such as those found in large open-pit mines, and the In the past, a number of factors impact of slope excavation on limited application of the SSR nearby structures. Given the technique for routine slope correct deformation properties stability analysis. Compute The FEM is of materials, the SSR method can times for analyses were long, able to compute predict expected deformations computing power adequate for deformations and at the stress levels found in such analysis was expensive, and quantities such as slopes. model preparation and