Dilatancy is a special material property of soil; and it is important for sand to describe its dilatancy accurately in the constitutive modeling. Through a large number of triaxial tests

it has been found that dense sand and loose sand show different dilatancies and stress-strain relation characteristics under the same loading condition

which indicate that the dilatancy of sand is not only related with the stress condition

but also with its physical state. The state parameter theory explains the combined effects of stress condition and physical state on the dilatancy of sand successfully. Hollow cylindrical torsional shear apparatus can be used to perform monotonic shear tests in different principal stress directions. Through such experimental tests

the difference in the dilatancy of sand in different principal stress directions is examined even under the same initial stress condition and physical state

which shows that the principal stress direction is also important to the dilatancy of sand. A state parameter including the principal stress direction is proposed by analyzing the effects of principal stress direction on the dilatancy of sand in the tests; and a dilatancy equation considering the principal stress direction is established. Compared with the experimental results

the method is proved to be correct and accurate.