Kinematic limit analysis for clays with anisotropy and different strengths in compression and tension

Abstract

While performing the upper bound limit analysis, using an associated flow rule, the expressions for the power dissipation function corresponding to different forms of yield criteria for clays exhibiting shear strength anisotropy and transversely asymmetric properties (implying different strengths in compression and tension), have been derived in terms of velocities, strain rates and shear strength parameters without involving stress variables by using the concept of duality in an optimization theory. The optimization has been performed in an efficient manner by using the second order cone programming (SOCP). The problems of strip and square footings have been dealt with. The lower bound solutions have also been established for the plane strain problems, and the two bound solutions have been found to match very closely with each other. The results also match well with the different solutions reported in literature. The variations of the power dissipation function and nodal velocity patterns in the problem domain have also been studied. The proposed formulation(s) will be useful for solving different two and three-dimensional geomechanics problems in clays to account for shear strength anisotropy as well as transversely asymmetric properties.