Modeling poroelastic response of an unsaturated, multi-layer soil with gravity effect to time-invariant stress loading

In contrast to homogeneous soil deposits, stratified layering introduces vertical heterogeneity, resulting in not only greater spatial variability but also more complex structural responses. This complexity is further exacerbated by gravitational compaction, which gives rise to distinct fluid flow and solid deformation mechanics within each variably saturated layer and at the interfaces between layers—markedly differing from those observed in homogeneous, single-layer soils.

The current study systematically addresses these key issues by developing a comprehensive flow-deformation formulation of poroelasticity that rigorously captures the conservation of mass and momentum within and between phases in a system of unsaturated, multi-layer unconsolidated sediments under time-invariant loading. A key innovation of this formulation is its robust incorporation of gravitational body forces, enabling the establishment of a physically-consistent boundary-value problem that ensures continuity-preserving conditions at layer interfaces. Furthermore, we derive two novel closed-form analytical expressions that, for the first time, quantify the final total stress and total settlement in such a soil system under the influence of gravitational body forces. To characterize the extent of this impact, we introduce a dimensionless parameter that provides a quantitative measure of gravitational effects.

To further enhance our understanding of the theory, we conduct a series of numerical simulations on a dual-layer soil system comprising sand overlying clay, with varying levels of water saturation. Our results demonstrate that, irrespective of the saturation levels examined, gravitational body forces exert a significantly greater influence on the lower clay layer than on the upper sand layer, particularly at lower water saturations. Neglecting gravitational body forces in a layered soil model leads to an underestimation of both the dissipation rate of excess pore water pressure and the total settlement. Notably, the discrepancy in final total settlement between models that include and exclude gravitational forces exhibits an approximately linear dependence on soil thickness.