Application of lower bound limit analysis with second-order cone programming for plane strain and axisymmetric geomechanics problems

Abstract

The present thesis illustrates the application of the lower bound limit analysis with finite elements and second-order cone programming for various geotechnical stability analyses. For the plane strain case, we firstly investigate the bearing capacity of shallow foundations on sand subjected to combined loading. The results are represented as load interaction diagrams. Secondly, the effect of seismic forces on the stability of inclined anchors embedded in frictional soils and the passive earth pressure on a rigid retaining structure is established. For the axisymmetric case, the Mohr-Coulomb yield criterion is formulated as a set of second-order cones, which gives rise to a second-order programming problem, which provides computationally more efficient method for numerical lower bound limit analyses of an axisymmetric problem compared with previous studies. This method is then applied to the bearing capacity of circular foundations and anchors/or multi-plate anchors.