Consolidation of Elastic Porous Media Saturated by Two Immiscible Fluids

Abstract

A theory is presented to simulate the consolidation of elastic porous media saturated by two immiscible Newtonian fluids. The macroscopic equations, including mass and momentum balance equations and constitutive relations, are obtained by volume averaging the microscale equations. The theory is based on the small deformation assumption. In the microscale, the grains are assumed to be linearly elastic and the fluids are Newtonian. The bulk and shear moduli of the solid matrix are introduced to obtain the macroscopic constitutive equations. Momentum transfer terms are expressed in terms of intrinsic and relative permeabilities assuming the validity of Darcy's law. In one dimension, the governing equations reduce to two coupled diffusion equations in terms of the pore pressures of the fluid phases. An analytical solution is obtained for a column with a fixed impervious base and a free drainage surface. Results are presented for cases of practical interest, Le., columns saturated by oil-water and air-water phases. Results indicate that the presence of a second fluid phase affects pore water pressure and total settlement.

Poroelastic theory of consolidation in unsaturated soils incorporating gravitational body forces

“…For instance, the relative saturation of air S 1 in the current configuration is determined by where S 1 0 is the relative saturation of air in the reference configuration and Δ S 1 = S 1 − S 1 0 is the difference in the relative saturation of air evaluated between the current and reference configurations. The latter, of course, is a function of capillary pressure (Tuncay and Corapcioglu 1996; Lo et al, 2005): where p c = p 1 − p 2 is the capillary pressure; d S 1 /d p c expresses the slope (evaluated in the reference configuration) of the curve relating capillary pressure to the relative saturation of air (or water since S 1 = 1 − S 2 ), i.e., the water retention curve. As shown in the appendix, the elasticity coefficients a ij depend on this slope.…”

“…This kind of diffusive coupling also appears in the consolidation theories developed by Fredlund et al (2012, Eq. [16.17] and [16.36]) using continuity equations and by Tuncay and Corapcioglu (1996, Eq. [74] and [75]) using the technique of volume averaging.…”

Influence of pore water pressure change on consolidation behavior of saturated poroelastic medium

“…This conceptual breakthrough was achieved later by Biot (1941), who brought the role of the solid and fluid constituents on equal footing to formulate a pair of coupled equilibrium equations of motion using the displacement vector of solid and fluid pore pressure as dependent vari-ables, now known as poroelasticity. Tuncay and Corapcioglu (1996) used volume-average theory to simulate the consolidation problem of poroelastic media saturated by two immiscible Newtonian fluids. In addition, Luo and Zeng (2011) constructed a coupled three-dimensional model of consolidation and groundwater extraction based on the viscoelasticplastic constitutive relation and rheological theory of Biot's poroelasticity, and used finite element method to simulate and compare groundwater level changes and soil compression.…”