Bridging effective stress and soil water retention equations in deforming unsaturated porous media: a thermodynamic approach

The finite deformation of an unsaturated porous medium is analysed from first principles of mixture theory. An expression for Bishop’s effective stress is derived from (1) the deformation-dependent Brooks and Corey’s water retention curve and (2) the restrictions on the constitutive relationships of an unsaturated medium subject to finite deformation. The resulting expression for the effective stress parameter χ is reasonably consistent with experimental data from the literature. Hence, it is shown that Bishop’s equation is constitutively linked to water retention curves in deforming media