Mathematical modeling of consolidation in unsaturated poroelastic soils under fluid flux boundary conditions

The spatiotemporal variability in precipitation could have a significant impact on ground subsidence. In this paper, we utilize a previously developed one-dimensional theory of consolidation for a two-fluid system, the generalization of Biot's theory, to investigate the impact of a time-dependent fluid flux across the surface of an unsaturated soil on the solid deformation and pore pressure responses. We consider three prescribed fluid flux patterns and the associated gradient of pore water pressure: constant, periodic, and exponential flux patterns. We employ a Fourier series representation and Laplace transformation in the space and time domains to derive a complete set of closed-form analytical solutions, including the complementary and particular solutions, describing both transient and steady-state excess pore water and pore air pressure responses as well as the total settlement induced by the fluid flux. Using two different types of soil, i.e. clay and sand, we demonstrate the dependence of the solution on the initial water saturation and hydraulic conductivity in the saturated and unsaturated regimes. Results of this study reveal that the fluid flux across the surface could have a significant impact on the dissipation of excess pore water pressure and the time evolution of the total settlement of the ground surface. The effect on the pore water pressure is more significant for sand than for clay irrespective of moisture content, mainly because of the much higher hydraulic conductivity of sand. Finally, we show that the hydraulic conductivity has a dominant effect on the consolidation behaviors of saturated and unsaturated soils subjected to surface fluid flux.