A fractal model for volume change dependency of the water retention curve

A fractal-based approach for volume change dependency of the water retention curve in a deformable unsaturated soil is presented. Conservation laws of solid mass and solid surface for uncrushable grains and Eshelby's classical theory for load-deformation of a single elastic ellipsoidal void embedded in an infinite isotropic elastic matrix are exploited to derive analytical expressions for the evolution of pore size distribution fractal dimension, air entry suction and hence water retention curve with void ratio. The applicability of the model to two experimental data sets from the literature is investigated.