Gravity effect on consolidation in poroelastic soils under saturated and unsaturated conditions

A rigorous mathematical framework is presented for the development of a set of coupled partial differential equations to describe the consolidation of saturated soils under the simultaneous action of external static loads and gravity forces. These equations generalize the Biot model of poroelasticity in a systematic manner to well account for additional momentum exchange arising from the physical mechanisms involved in gravitational compaction due to changes in volumetric fraction and material density of each constituent. A boundary-value problem is then formulated as a representative example to quantitatively examine gravity effect on the dissipation of excess pore fluid pressure and settlement magnitude, and is solved numerically in a finite difference scheme. In the current study, the boundary conditions have been directly calculated in numerical scheme, which improves previous studies to avoid using the approximation of the trapezoidal rule. A physically-consistent parameter, derived fundamentally from the first principle, balance of momentum, is proposed for the first time, which provides an exact measure of the degree to which variations in final total settlement occur due to the presence of gravity effect. This dimensionless parameter takes a closed-form expression that refines our foregoing works, and is quite general since it is applicable to both saturated and variably-saturated soils. Our studies show that the variations are essentially controlled by soil elasticity modulus and height, as well as a derived gravity factor. This factor underlines the importance of the dependency between consolidation behaviors and distinct physical properties of pore fluids. Lastly, a comparative study is carried out, indicating that gravity forces yield more significant impact on unsaturated soils than saturated soils we examined, leading to more relative increment in the final total settlement.