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Land Subsidence — B. A Regional Mathematical Model for Land Subsidence due to Pumping

Corapcioglu, M. Yavuz / Bear, Jacob

Abstract A regional mathematical model for land subsidence and horizontal displacement resulting from pumping from an aquifer is developed on the basis of the works of Biot and Verruijt on consolidation. The regional mathematical model is obtained by integrating the equations that describe soil deformation in a three-dimensional space over the aquifer’s thickness, assuming conditions of plane excess total stress. These equations involve coupling between the equations of equilibrium of the porous medium and those of mass conservation. The resulting model yields both the aquifer compaction and the horizontal displacements, as functions of space coordinates and of time, for confined, leaky and phreatic aquifers. An analytical solution is presented for the special case of a well pumping from an infinite homogeneous isotropic aquifer. The solution provides estimates of drawdown (of averaged piezometric head), vertical land subsidence and horizontal displacement as functions of distance from the well and time. The results indicate that approximately half the volume strain is produced by vertical subsidence, while the other half is produced by the horizontal displacement. Hence, vertical subsidence is overestimated by noncoupled models. We also study the case for a phreatic aquifer where the total stress changes due to water table fluctuations and averaged land subsidence equations for a single-fluid geothermal reservoir.