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This paper is focused on continuation techniques and Newton-like methodssuggested for numerical determination of safety factors within stabilityassessment. Especially, we are interested in the stability of slopes andrelated limit load and shear strength reduction methods. We build oncomputational plasticity and the finite element method, but we mainly work onan algebraic level to be the topic understandable for broader class ofscientists and our algorithms more transparent. The presented algorithms arebased on the associated plasticity to be more robust. For non-associatedmodels, we use Davis-type approximations enabling us to apply the associatedapproach. A particular attention is devoted to the Mohr-Coulombelastic-perfectly plastic constitutive problem. On this example, we explainsome important features of the presented methods which are beyond the algebraicsettings of the problems. We also summarize the Mohr-Coulomb constitutivesolution and some implementation details.

Robust algorithms for limit load and shear strength reduction methods