Variational Slope Stability Analysis of Materials with Nonlinear Failure Criterion



Rafael Baker

Associate Professor, Faculty of Civil and Environmental Engineering,
Technion - Israel Institute of Technology, Technion City, Haifa, Israel


A rigorous variational slope stability analysis for materials with a non-linear failure criterion is presented. The main advantage of the variational framework over classical slope stability procedures is that it does not introduce any geometrical or static assumptions. The present paper introduces general approuch, results, and the solution procedure associated with the variational methodology. Specific results (stability charts and failure modes) based on this methodology, and discussion of their engineering significance, are presented in a separate publication. Various properties of critical slip surfaces and normal strength functions are established. In particular it is shown that: a) Critical slip surfaces possess the characteristic property of log spirals, namely the angle between the normal and the radius vector is equal to the local value of the mobilized friction angle (which is not constant when non-linear strength functions are considered). b) Critical normal stress distributions are convex functions possessing a single maximum in their range of definition. c) Critical slip surfaces are singular at points where normal stresses approach the tensile strength of the material, and this singularity has a major effect on the solution of the problem. Inspection of particular solutions illustrates that common static assumptions employed in classical limiting equilibrium procedures are not justified in the sense that they are not associated with the critical conditions. More important however, the present work shows that such static assumptions are not only unjustified; being in fact unnecessary.

Keywords: Non-linear failure criteria, Slope stability computations, Variational analysis.

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