Extended yield condition of soils with tensile yield strength and rotational hardening

An extended yield condition of soils applicable to the range of negative pressure is proposed. A closed surface is formulated in a simple mathematical form not limited to the range of positive pressure. A hardening function of plastic volumetric strain is adopted, based on the linear relation of both logarithms of volume and pressure extended to the negative range of pressure for the isotropic consolidation. Isotropic softening, due to the deviatoric plastic strain rate, and anisotropic hardening, due to rotation of yield surface (rotational hardening) are also incorporated into the extended yield condition.