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UBC Theses and Dissertations

Development and implementation of a limit equilibrium procedure for the three-dimensional analysis of asymmetric landslides Burden, Justin Matthewson


Two-dimensional limit equilibrium types of analysis have been used in engineering practice for decades and are the most commonly adopted analysis technique for assessing the stability of slopes. These methods compute a factor of safety based on a comparison of available to required shear strength along a prescribed failure surface. Forces and static equilibrium conditions are only considered in the plane of movement. However, in reality, all slope failures occur in three-dimensions. Every sliding mass has a finite length and shear forces acting at the lateral extents of the mass contribute to the resistance to movement. Errors introduced by neglecting the three-dimensional character of a slide cannot be overlooked in all cases. Examples include deep narrow excavations, convex/concave slope geometries, slopes that fail by narrow localized failure and structurally controlled failures in rock. Consideration of threedimensional effects may be of particular importance where computed two-dimensional factors of safety are marginal or when back-analyzing slope failures where derived shear strengths should reflect the influence of end effects. This thesis details the development, implementation and evaluation of a general limit equilibrium method of columns procedure suitable for analyzing the three-dimensional stability of asymmetric landslides. The proposed method, termed the three-dimensional asymmetric Spencer method, uses internal force functions to satisfy the equilibrium conditions. Unlike many of its predecessors, the algorithm satisfies force and moment equilibrium in both horizontal directions. The direction of sliding is not assumed, but rather determined explicitly in the analysis. The solution scheme is implemented in the computer program J3D. A moment balancing procedure is developed and used to investigate the effect of enforcing moment equilibrium about a vertical axis of rotation on the analysis results. Analyses completed using J3D are compared with solutions derived using existing limit equilibrium methods and three-dimensional distinct element models for several asymmetric slide examples, including the Kettleman Hills Landfill case history. Preliminary results indicate that the three-dimensional asymmetric Spencer method is well suited for the analysis of general slope stability cases, including asymmetric problems. Application of the proposed moment balancing algorithm may only be suitable for problems involving specialized slope and slip surface geometries.

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