Modeling Three-Dimensional Deformation in Response to Pumping of Unconsolidated Aquifers

摘要

A mathematical model and a corresponding couplednumerical model that incorporate the concepts of threedimensional poroelasticity based on Biot,s consolidation theoryare developed for simulating the displacement field of solidswithin unconsolidated aquifers in response to induced changes inwater pressure. The granular displacement model (or GDM) isincorporated into MODFLOW, a U.S: Geological Survey's finite-difference program, and uses an efficient row-indexed storagemoue and biconjugate gradient solver, so that it is tractable at thefield scale. The application to three dimensions is an improvementover two-dimensional axisymmetric models incorporating Biot'sequations and over the commonly used one-dimensionalsubsidence models based on Terzaghi's method of effectives stress.Most subsidence due to ground-water withdrawal occurs in theinelastic range of specific storage within clay interbeds orconfining units. However, most horizontal deformation occurswithin coarser aquifer units. The GDM program uses both elasticand inelastic storage and Poisson's ratio as key parameters.Conversion from elastic to inelastic specific storage occurs whenthe previous maximum volume strain for a particular cell isexceeded. Model outputs are compared with a currently availableone-dimensional subsidence model (IBS1) developed forMODFLOW and an axisymmetric finite-element Biot program.The results indicate that under traction free conditions subsidenceis a three-dimensional problem and one-dimensional subsidencemodels tend to focus excessive amounts of vertical deformationnear the pumped well. The magnitude of vertical deformation inone-dimensional subsidence models is exacerbated as the grid sizebecomes smaller in the vicinity of the pumping well. This is due toincreased calculated drawdown in the vicinity of the well for morefinely-spaced grids.