Semi-analytical solution of groundwater flow in a leaky aquifer system subject to bending effect

The bending of aquitard like a plate due to aquifer pumping and compression is often encountered in many practical problems of subsurface flow. This reaction will have large influence on the release of the volume of water from the aquifer, which is essential for the planning and management of groundwater resources in aquifers. However, the groundwater flow induced by pumping in a leaky aquifer system is often assumed that the total stress of aquifer maintains constant all the time and the mechanical behavior of the aquitard formation is negligible. Therefore, this paper devotes to the investigation of the effect of aquitard bending on the drawdown distribution in a leaky aquifer system, which is obviously of interest in groundwater hydrology. Based on the work of Wang et al. (2004) this study develops a mathematical model for investigating the impacts of aquitard bending and leakage rate on the drawdown of the confined aquifer due to a constant-rate pumping in the leaky aquifer system. This model contains three equations; two flow equations delineate the transient drawdown distributions in the aquitard and the confined aquifer, while the other describes the vertical displacement in response to the aquitard bending. For the case of no aquitard bending, this new solution can reduce to the Hantush Laplace-domain solution (Hantush, 1960). On the other hand, this solution without the leakage effect can reduce to the time domain solution of Wang et al. (2004). The results show that the aquifer drawdown is influenced by the bending effect at early time and by the leakage effect at late time. The results of sensitivity analysis indicate that the aquifer compaction is sensitive only at early time, causing less amount of water released from the pumped aquifer than that predicted by the traditional groundwater theory. The dimensionless drawdown is rather sensitive to aquitard's hydraulic conductivity at late time. Additionally, both the hydraulic conductivity and thickness of the aquifer are the most sensitive parameters in influencing the predicted dimensionless drawdown.