Angle of dilation

The angle of dilation controls an amount of plastic volumetric strain developed during plastic shearing and is assumed constant during plastic yielding. The value of ψ=0 corresponds to the volume preserving deformation while in shear.

Clays (regardless of overconsolidated layers) are characterized by a very low amount of dilation (ψ≈0). As for sands, the angle of dilation depends on the angle of internal friction. For non-cohesive soils (sand, gravel) with the angle of internal friction φ>30° the value of dilation angle can be estimated as ψ=φ-30°. A negative value of dilation angle is acceptable only for rather loose sands. In most cases, however, the assumption of ψ = 0 can be adopted.

Unlike the modified linear model the nonlinear models require to specify only the elastic modulus. A drop in the material stiffness is a result of evolution of plastic strains and corresponding redistribution of stresses. This consequently yields an instantaneous tangent material stiffness as a function of the current state of stress represented in the figure belowby an instantaneous tangent modulus E_T.