Nonlinear models

The basic nonlinear models can be again divided into two groups.

The first class of models originates from the classical Mohr-Coulomb failure criterion. In particular, the Drucker-Prager, Mohr-Coulomb and Modified Mohr-Coulomb models fall in this category. A common feature to these models is the evolution of unbounded elastic strains when loaded along the hydrostatic axis. This is evident from the figure below that shows projections of the yield surfaces into deviatoric and meridian planes, respectively. An example of the effect of the selected model is given here.

The second group of basic material models is represented by the Modified Cam-clay model employing the concept of the critical state of soil. 

Projection of yield surfaces into (a) deviatoric, (b) meridian plane

Employing nonlinear models allows us to capture the typical nonlinear response of soils.

These models describe evolution of permanent (plastic) deformation of a soil material. The onset of plastic deformation is controlled by so-called yield surface. The yield surface can be either constant (elastic-rigid plastic material), or it can depend on the current state of stress (material with hardening/softening).

Stress-strain diagram for nonlinear models

In addition to basic material parameters decribed in section "Elastic model" the nonlinear models call for the introduction of certain strength characteristics of the soil needed in the definition of a given yield surface.  With reference to the first group of materials the following parameters must be specified.

The angle of internal friction and cohesion determine the onset of plastic deformation. The angle of dilation controls an evolution of plastic volumetric strain (dilation).

The angle of dilation controls an amount of plastic volumetric strain developed during plastic shearing and is assumed constant during plastic yielding.