Poroelastic theory of consolidation in unsaturated soils

Poroelasticity is the coupling between applied stress and pore fluid pressure that occurs when a soils is compressed. The classic Biot model applies this concept to the consolidation of saturated soils, but a self-consistent poroelastic theory of unsaturated soil consolidation is not available. Here, we generalize the Biot model of consolidation to unsaturated soils, including a natural formulation of effective stress, presenting a set of governing partial differential equations with their analytical solutions applicable to both permeable and semipermeable drainage boundary conditions. The theory of poroelastic behavior in a deformable porous medium containing two immiscible, viscous, compressible fluids was applied to the three-dimensional consolidation of unsaturated soils. Three coupled partial differential equations were developed that feature the displacement vector of the solid phase and the excess pore water and air pressures as dependent variables. These equations generalize the classic Biot consolidation model, which applies to saturated soils, with effective stress emerging naturally from a pure compliance formulation of the relation between stress and strain. Under uniaxial strain and constant total compaction stress, the equations simplify to two coupled diffusion equations for the excess pore water and air pressures. Analytical solutions describing the response to instantaneous compression under both permeable and semipermeable boundary drainage conditions were obtained using the Laplace transform. Numerical calculations of pore water pressure, effective stress, and total settlement were made for a soil with clay texture as a representative example. The results show that excess pore water pressure dissipates faster at higher initial water content, leading to higher effective stress. The loading efficiency also was found to be highly sensitive to initial water saturation.