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Slope Stability Analysis with the Shear Strength Reduction Method

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Slope Stability Analysis with the Shear Strength Reduction Method Ready for Prime Time: Slope Stability Analysis with the Shear Strength Reduction Method We believe that the SSR method, facilitated by its implementation in software, is ready for prime time, the point at which it can be applied to the practical, routine analysis of slopes. This article provides reasons why this is so, as well as providing practical guidelines for SSR modelling. Prime time generally refers to the Due to its ability to realistically model a evening hours between 7 and 11 p.m. very broad range of problems, the Finite when the largest audience watches Element Method (FEM) has become television. Because of what stands to be tremendously popular since it was first gained, TV networks fiercely compete applied to geotechnical engineering in for the attention of these viewers. Ad- 1966. For various reasons that will be vertising during this period is powerful. outlined in this article, its primary ap- A well executed ad can create positive plication in geotechnical engineering, brand recognition while a bad ad will though, had been restricted to stress turn customers off. Networks and ad- and deformation analysis of excavations vertisers go to great lengths to ensure and support. Recent refinements to the that shows and ads stand up to the SSR method, and advances in comput- scrutiny of discerning buyers, and it’s ing technology have now altered this in this sense that we believe the Shear landscape. Strength Reduction (SSR) method of slope stability analysis is ready for prime time: it will stand up to the scrutiny of the discerning geotechnical audience, and is therefore ready for routine slope analysis. Brief Description of SSR The central concept of the SSR method As was discussed in an article in the is very simple. Similar to limit-equi- Summer 2004 issue of RocNews, librium analysis, it involves successive Will Finite Elements Replace reductions (by some factors) in the shear Limit-Equilibrium in Slope Design? strengths of slope materials until failure powerful programs, which enable rou- occurs. Failure is indicated when the tine geotechnical finite element analysis, finite element model does not converge are available today. Phase2, Rocscience’s to a solution, because equilibrium can- two-dimensional FEM program, is a not be maintained. The critical factor at leader in this market. The program which failure occurs is taken to be the significantly reduces the amount of time factor of safety. required to build, compute and inter- pret models. Recent Advances in the Version 6 of Phase2 highly automates the SSR Method SSR procedure for calculating a factor of safety. In some cases, it is even easier to In the past, a number of factors limited use than conventional limit-equilibrium application of the SSR technique for analysis. In addition, the new Phase2 can routine slope stability analysis. These read Slide (Rocscience’s limit-equilib- included: rium slope stability program) files, and Lengthy modelling, compute, automatically convert them into fully and results analysis times meshed, finite element equivalents. The Lack of automated tools for perform- version includes algorithms, which make ing the successive changes to shear it possible to perform SSR analysis for strength non-linear material strength models, a A perceived hunger for material capability missing in practically all the input data, which were not collected other competing products. For more in routine site investigations, at least detail, see the article: not with reasonable accuracy Stability Analysis of Rock Slopes Restriction to linear material strength using the Finite Element Method (Mohr-Coulomb model), and Unproven reliability of SSR results The previous article explained that the additional data required for the SSR method is routinely collected for other forms of geotechnical analysis. As a Guidelines for SSR Modelling result the need for additional data does not overly complicate finite element In the course of verifying the reliability slope stability analysis. of the SSR method, we studied various aspects of finite element slope stability The Summer 2004 RocNews article also analysis and compiled a set of modelling addressed the question of the reliabil- guidelines. These guidelines are espe- ity of SSR results, and listed references, cially useful, since FEM slope stability which report good agreement between analysis is still new to many geotechni- SSR and limit-equilibrium results. To cal engineers, and generally requires further increase confidence in the SSR more modelling know-how than limit- technique, we tested the method on 33 equilibrium analysis. benchmark slope examples. These cases, which cover a broad range of material We studied the impact of Young’s mod- and slope behaviours, have been used ulus, Poisson’s ratio, and dilation angle to verify the results of slope stability pro- on computed factor of safety values. grams, including Slide. Because the SSR factor of safety is deter- mined based on the occurrence of non- The results of our study were published convergence, aspects of finite element in a paper, modelling such as stopping rules (con- A Comparison of Finite Element Slope vergence criteria), number of iterations Stability Analysis with Conventional and tolerance, which influence solution Limit-Equilibrium Investigation convergence, were also investigated. presented at the recently concluded Although the compiled set of guidelines 58th conference of the Canadian Geo- is by no means an exhaustive list of how technical Society (CGS) in Saskatoon. to perform SSR analysis, it is still very The study confirmed what had been helpful to both experienced users and previously reported; in all the cases, the novices. SSR gave answers that agreed very well with limit-equilibrium results. The rules of thumb for replicating limit- are therefore required in addition to fac- equilibrium slope analysis with the SSR tor of safety values, then effort must be method can be summarized as follows: made to specify the right estimates of these properties. Assume a single Young’s modulus and a single Poisson’s ratio for slope In addition, for multiple material slope materials models the ratios of the different Assume a zero dilation angle Young’s moduli can affect deforma- tion patterns. In some instances differ- Assign all materials elastic-perfectly ent stiffness ratios can produce failure plastic behaviour mechanisms that differ from limit equi- Use six-noded triangular or other librium solutions. The images on the higher-order elements. For a given following page show the different shear number of nodes higher-order ele- deformation contours at failure that ments are generally more efficient arise in a slope for two different sets of (produce results that are closer to Young’s moduli for the material layers. the ‘true’ solution) Although the factor of safety values are Begin with smaller number of el- very similar for the two cases, the failure ements. Refine model (increase mechanisms differ. number of elements) once you’ve obtained a good handle on a slope This has implications for the design (lo- problem, and cation and capacity) of support or other remedial measures for multiple material Check the sensitivity of results to slopes. For example, if support deforma- number of elements tions are required, then it is important We would like to note that the defor- to assign adequate estimates of Young’s mation parameters (Young’s modulus, moduli and Poisson’s ratios. Poission’s ratio and dilation angle) in- fluence the magnitudes of computed deformations. If deformations at failure These contours of maximum shear strain indicate two different failure mechanisms for a multi-material slope. The difference in failure mode is caused by changing the Young’s moduli of the material layers. Prime Time Ready We believe that SSR technology has The SSR method has been found to improved to the point where it is ready work in cases in which limit-equilibrium for prime time use, the practical, routine analysis either produces misleading analysis of slopes. As has been reported results or does not work well. One such by others and as confirmed by our tests example involves analysis of the stability on several slope cases, the SSR method of slopes in which excavations such as produces reliable and consistent results tunnels and caverns have been made. over a wide range of slope problems. Whereas limit-equilibrium methods, due It matches powerful limit-equilibrium to their inability to model stress-strain features such as the ability to model behaviour, encounter difficulties on such non-linear strength, and accommodate problems, the SSR method smoothly multiple slope materials and support analyzes these cases. types. In programs like Phase2, the SSR We advocate for greater use of the SSR, has been automated to the same levels since it powerfully complements con- as those found in premier slope stability ventional limit-equilibrium analysis. The programs. tools for performing such slope analysis The SSR enjoys several advantages over are available. Why not use them? conventional limit-equilibrium analysis. Among many desirable attributes, SSR slope analysis can produce insights into We encourage readers to send failure mechanisms, and their formation, their comments and views on this topic to RocNews Feedback. in ways that may not be as evident in limit-equilibrium analysis. SSR analysis can better model the behaviour of sup- port elements, the interactions caused by the relative stiffnesses of slope ma- terials and support elements, and can indicate deformations at failure..
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