Dilatant Nature of Sand Shear Strength

Many shear strength criteria have been proposed for soils. The Mohr–Coulomb, Matsuoka–Nakai, and Lade–Duncan criteria are more frequently used for sands. For sands sheared in drained conditions, the general stress–dilatancy relationship is obtained from the frictional state concept. It is shown that, in failure states, the dilatancy for triaxial compression, the plane strain condition (biaxial compression), triaxial extension, and general states can be expressed by the ratio of the volumetric and axial strain increments for triaxial compression. By using the frictional state concept, the shear strength of sand for general states can be expressed by the critical state angle and the dilatancy for drained triaxial compression. It is shown that the calculated shear strength of the sand is similar to that obtained by using the Mohr–Coulomb, Matsuoka–Nakai, and Lade–Duncan criteria for the non-dilative, moderate-dilative, and high-dilative behaviors of sand, respectively. Therefore, the shear strength of sand has a purely dilative nature for deformations without breakage effects.