Mathematical modelling of groundwater flow in shallow aquifer containing a cavity of arbitrary form bounded by a partially permeable contour [articol]

Abstract

Groundwater flow in shallow aquifer (i.e. groundwater reservoir with large plane extension in relation to the depth) containing lake, pond, groundwater recharge or drainage pit, foundation pit etc., referred further as groundwater extraction/recharge cavity or cavern represent a very important practice-oriented topics. In this regard in a former paper a general mathematical representation of groundwater flow in shallow aquifer is deduced, considering a cavity of arbitrary form bounded by a permeable contour, using the theory of the analytical functions of a complex variable. In the present paper an extension of this problem will be presented, considering a cavity of arbitrary form bounded by a partially permeable contour. This extension allows approach of new aspects and issues of groundwater management. The mathematical representations consider asymptotic conditions determined by a pre-existing initial uniform groundwater flow which has an important influence on the flow processes especially in neighbourhood of cavity. It will be deduced formulas which allow a rapid analysis of the groundwater balance in the modelled region considering the dependence of the recharge/discharge rate of the cavity from and the extension of the impermeable part of the contour and from the preexisting uniform groundwater flow. The obtained mathematical representations and formulas can be applied for cavities of different shape using conformal mapping defined through analytical functions of a complex variable.