Geotechnical stability analysis

TLDR

The paper presents recent advances in stability analysis that merge classical plasticity limit theorems with finite elements to provide rigorous upper and lower bounds on failure load. Finite‑element limit analysis methods avoid failure‑mode assumptions, rely on simple strength parameters, and accommodate heterogeneous, anisotropic, fissured soils, discontinuities, complex boundaries, and loading in two and three dimensions. The bounding properties enable accurate limit loads through exact error estimates and adaptive meshing, and a new development incorporating pore‑water pressures is described, with stability solutions for foundations, anchors, slopes, excavations, and tunnels.

Abstract

This paper describes recent advances in stability analysis that combine the limit theorems of classical plasticity with finite elements to give rigorous upper and lower bounds on the failure load. These methods, known as finite-element limit analysis, do not require assumptions to be made about the mode of failure, and use only simple strength parameters that are familiar to geotechnical engineers. The bounding properties of the solutions are invaluable in practice, and enable accurate limit loads to be obtained through the use of an exact error estimate and automatic adaptive meshing procedures. The methods are very general, and can deal with heterogeneous soil profiles, anisotropic strength characteristics, fissured soils, discontinuities, complicated boundary conditions, and complex loading in both two and three dimensions. A new development, which incorporates pore water pressures in finite-element limit analysis, is also described. Following a brief outline of the new techniques, stability solutions are given for several practical problems, including foundations, anchors, slopes, excavations and tunnels.