Three-dimensional lower bound finite element limit analysis of an anisotropic undrained strength criterion using second-order cone programming

This paper describes a formulation of second-order cone programming for three-dimensional lower bound finite element limit analysis considering a cross-anisotropic undrained strength criterion. A three-dimensional generalized yield criterion accounting for the cross-anisotropic undrained strength of clay is proposed and requires four input shear strengths in triaxial compression and extension, direct simple shear, and pressuremeter tests. The proposed formulation is verified through the predictions of various compressions of anisotropic soil blocks while the importance of undrained strength anisotropy is demonstrated by analyses of undrained bearing capacity of strip, circular and square footings on anisotropic clays.