NUMERICAL SIMULATION OF SUBSIDENCE DUE TO PUMPING WITH HYSTERESIS EFFECT INCLUDED Carlos Cruickshank-Villanueva Institute of Engineering, National University of Mexico Mexico, D.F. Abstract Highly compressible impermeable, materials have in general different com- pressibility indexes in the effective stress ranges above and below the preconsolidation stress; this is traduced in different specific storage co- efficients. I. Herrera and coworkers (see references) developped a numerical method to simulate the flow in a system of aquifers separated by aquitards which includes a boundary solution for the flow in the confining layers and which proved to be accurate and more efficient than a numerical integration over a discretization grid of the aquitard. Yet, it cannot be directly applied to cyclic head variations because of the afore mentioned hysteresis effect. An approximate solution is presented here which extends the boundary method to such situations. The solution was tested against finite differ- ences results, which in general take much more computational effort and storage allocation, obtaining very good approximation in all situations tested. It was also tested against field measurements of subsidence with equally good coincidence. Introduction It is a well known property of clayey deposits to have a larger vertical compressibility index when the effective stress (total minus pore water pressure) acting on the solid structure is above the preconsolidation stress (maximum preconsolidation stress occurred in the history of the ma- terial) than when it is below it. This larger compressibility corresponds to the so called "virgin" state of the deposit in which its internal struc- ture is weak to external pressures and deforms rapidly; when the effective pressure is relieved, the structure does not recover its original state but yet behaves elastically to changes in stress with a much lower strain- stress ratio; when the preconsolidation stress in surpassed, the material regains its higher compressibility. The compressibility of the material in the virgin state is in general one to two orders of magnitude larger than in the preconsolidated state. This is shown schematically in Fig 1 with typical results from a drained, vertical consolidation test. This behaviour translates into geohydrological terms as a larger specif- ic storage coefficient when the pore water pressure drops below the hysto- rical minimum (which, keeping total pressure constant, corresponds to a maximum effective vertical stress) than when it is above it. In aquifers which are in contact with compressible, low permeability deposits there is an important amount of water released to the aquifer from these deposits when the pressure drops due to pumping or to a natural decline in recharge to the aquifer. This water comes from the destroyed internal structure of the fine grain materials and does not return back to it as easily as it went out. This behaviour has to be taken into account in order to explain and predict water flow and land subsidence in aquifer systems consisting of 79