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Mathematical model for regional land subsidence due to pumping: 1. Integrated aquifer subsidence equations based on vertical displacement only
Author(s) -
Bear Jacob,
Corapcioglu M. Yavuz
Publication year - 1981
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr017i004p00937
Subject(s) - aquifer , geology , phreatic , terzaghi's principle , specific storage , cone of depression , subsidence , compressibility , geotechnical engineering , groundwater flow equation , head (geology) , hydraulic head , aquifer properties , groundwater , aquifer test , groundwater flow , geomorphology , mechanics , pore water pressure , groundwater recharge , structural basin , physics
A mathematical model for regional land subsidence has been developed by employing Terzaghi's concept of effective stress and assuming vertical solid compressibility only. First the groundwater mass conservation equation in a compressible aquifer is developed for a three‐dimensional space. Assuming that the problem justifies an assumption of a thin aquifer, relative to horizontal lengths of interest, this equation is then integrated over the aquifer's thickness, taking into account the conditions on top and bottom surfaces bounding the aquifer. The result is the commonly used aquifer flow equation in terms of averaged piezometric head. By introducing a relationship between changes in averaged piezometric head and corresponding changes in aquifer thickness, a single equation is obtained in terms of land subsidence. The development is carried out for a single and a multi‐layered confined aquifer and for a phreatic one. An example is given of the application of the equation in radial coordinates describing land subsidence in a hypothetical six‐layered aquifer.