Based on the analysis of the compression

shear nonlinearity and dilatancy of sand and its complicated response under the complicated stress condition including the cyclic loading

rotation of principal stress axis and deflexion of stress path; three kinds of stress-strain relation are obtained. They are described by a relationship between effective mean normal stress and compressive volume strain

a relationship between deviatoric stress and deviatoric strain and a relationship between effective stress ratio and dilatancy strain ratio respectively. Through the increasing length in deviatoric strain path determined by the component in deviatoric strain space

the positive and negative dilatancy can be obtained under rotation of principal stress axis or deflexion of stress path. Developing the essential stress-strain relations under cyclic loading

a physical state dynamic constitutive model of sand is establisbed and related to its change in physical states.