Modeling three-dimensional deformation in response to pumping of unconsolidated aquifers

A mathematical model and a corresponding coupled numerical model that incor porate the concepts of three dimensional poroelasticity based on plot's con solidation theory are developed for simulating the displacement field of so lids within unconsolidated aquifers in response to induced changes in water pressure, The granular displacement model (or GDM) is incorporated into MO DFLOW, a U.S. Geological Survey's finite-difference program, and uses an ef ficient row-indexed storage mode and biconjugate gradient solver, so that i t is tractable at the field scale. The application to three dimensions is a n improvement over two-dimensional axisymmetric models incorporating Blot's equations and over the commonly used one-dimensional subsidence models bas ed on Terzaghi's method of effective stress. Most subsidence due to ground- water withdrawal occurs in the inelastic range of specific storage within c lay interbeds or confining units, However, most horizontal deformation occu rs within coarser aquifer units, The GDM program uses both elastic and inel astic storage and Poisson's ratio as key parameters. Conversion from elasti c to inelastic specific storage occurs when the previous maximum volume str ain for a particular cell is exceeded, Model outputs are compared with a cu rrently available one-dimensional subsidence model (IBS1) developed for MOD FLOW and an axisymmetric finite-element Blot program, The results indicate that under traction free conditions subsidence is a three-dimensional probl em and one-dimensional subsidence models tend to focus excessive amounts of vertical deformation near the pumped well. The magnitude of vertical defor mation in one-dimensional subsidence models is exacerbated as the grid size becomes smaller in the vicinity of the pumping well. This is due to increa sed calculated drawdown in the vicinity of the well for more finely-spaced grids.