Here we have the effective stress, the constitutive relationship, the incremental strain and the partial saturation relationship.
Since the capillary pressure is dependent on the size of soil void, for a given granular material with specific void ratio and under isothermal conditions we can assume that a unique function defines the capillary pressure relationship. Further if water flow occurs, the permeability coefficient "k" will be again a unique function.
The above system of equations is the generalised Biot formulation for dynamic behaviour of saturated-unsaturated porous media. It can be solved incrementally for most problems with appropriate boundary and initial conditions.