Mathematical model for regional land subsidence due to pumping: 2. Integrated aquifer subsidence equations for vertical and horizontal displacements

A mathematical model for regional subsidence due to pumping from an aquifer is developed on the basis of Biot's work on coupled three‐dimensional consolidation. Following Biot's work on threedimensional consolidation, with coupling between mass conservation and equilibrium equations, a mathematical model for regional subsidence due to pumping from an aquifer is developed by averaging the three‐dimensional model over the thickness of the aquifer and assuming conditions of plane stress. Both (vertical) land subsidence and horizontal displacements, as functions of plane coordinates and time, can be estimated by solving the model equations for a given confined or leaky confined aquifer. An analytical solution is presented for the special case of a single well pumping from an infinite homogeneous isotropic aquifer. The solution provides estimates of changes in averaged (over the vertical) values of piezometric head, vertical subsidence, and horizontal displacement. The results indicate that under the conditions of the studied case of radial flow the solution for piezometric head is identical to the one obtained by noncoupled models. Furthermore, half the volume strain is produced by vertical subsidence while the other half by the horizontal displacement. Hence the vertical subsidence is only approximately half the value obtained in noncoupled models which neglect horizontal displacement. A numerical example demonstrates these conclusions.