CONSIDERING THE EFFECT OF BODY FORCE FOR REGIONAL LAND DISPLACEMENTS

Abstract

In this study, a general mathematical model was developed for land displacements that occur as a result of the pressure decline in confined and/or phreatic aquifers. Two equations were developed by employing the equilibrium (force balance) equation and the flow equation in a deforming aquifer system. Both of these equations were integrated over the thickness of the aquifer system once a regional model had been formulated. The change of the body force in saturated and unsaturated zones of aquifers was considered in the derivation of the equilibrium equation. It was assumed that no external loading or force acting on the aquifer system was present. Two coupled equations expressed in terms of the averaged dilation and pressure were then obtained. The pumping data sets given in the papers of Bear and Corapcioglu1,2 in 1981 and 1983 were analysed. Drawdown and displacements in a confined aquifer were demonstrated to be identical to those estimated by Bear and Corapcioglu.1 In the case of a phreatic aquifer, however, the results estimated by the present approach were slightly different from those obtained by Corapcioglu and Bear.2 The discrepancies in the results are possibly due to errors in the equations presented by Corapcioglu and Bear.2 The present approach was able to avoid several assumptions and complex procedures used by Bear and Corapcioglu,1,2 especially in the case of a phreatic aquifer, by taking into account the change in the body force.