Unconfined aquifer

An unconfined aquifer has a free groundwater table. In a shallow aquifer of thickness $h(x,t)$, hydrostatic pressure and Darcy's law give horizontal flux proportional to $-h{h}_x$.

For pore fraction $n$, permeability $k$, liquid density $\rho$, viscosity $\mu$, rainfall recharge $R$, and a shallow groundwater thickness $h$,This is a nonlinear diffusion equation with diffusivity proportional to the local thickness.

After recharge stops on a finite aquifer connected to a river, the late solution of the Boussinesq equation for an unconfined aquifer has the form $h\sim t^{-1}F(x/L)$. The profile solves a nonlinear eigenvalue problem, and river discharge decays as $t^{-2}$.

A poroelastic aquifer couples pore-fluid storage and flow to elastic compaction of its solid skeleton. Changes in gravity, surface loading, or pore pressure can therefore change groundwater discharge even without changing rainfall.

For a skeleton with Young modulus $E$, undeformed solid fraction ${\varphi }_0$, grain-fluid density difference ${\rho }_s-\rho$, and reference gravity $g_0$, the hydrostatic poroelastic compaction length isIt is the depth over which self-weight changes the solid fraction appreciably.