Abstract: The previous studies show that there exists a steady stress state,defined as asymptotic state,when sand is loaded along constant strain increment ratio paths.Asymptotic states varies with the strain increment ratio.And asymptotic state is a more common concept than critical state,which is a particular case when volumetric strain increment equals zero.In this study,based on the observation of a series of strain path tests,the reason why asymptotic states change varing with the strain increment ratio was revealed as that the proportion of deformation due to the variation of effective mean principal stress and shear stress changes during a loading process.The mechanical behavior that the deformation due to compression and that due to stress-dilatancy occurred simultaneously and varied together during a loading process was defined as compression-dilatancy coupling effect.On this basis,two-and three-dimensional asymptotic state criteria were formulated to determine the relation between the mobilized stress ratio of asymptotic states and the strain increment ratio.In addition,the effectiveness of the criteria was proved by the test results.