Gradient dependent dilatancy and its implications in shear banding and liquefaction

A gradient dependent dilatancy condition is assumed in order to capture the heterogeneous character of deformation in granular soils. This assumption is incorporated into the structure of classical deformation and flow theories of plasticity and its implications in two interesting examples of patterning instability, that is shear banding and liquefaction, are examined. Shear banding is considered within a modified gradient dependent deformation theory, while liquefaction is studied within a modified gradient dependent flow theory of plasticity. In both cases a deformation induced length scale is obtained near the instability, and this is identified with the thickness of the shear band or the spacing of the liquefying strips