Theory of transient confined-unconfined flow in a confined aquifer considering delayed responses of water table

•Effects of aquifer anisotropy and unsaturated drainage above water table are considered.•Delayed unsaturated drainage is depicted by empirical coefficient corresponding with Moench’s model.•Theoretical responses of drawdown and development of unconfined region are demonstrated. A semi-analytical solution is developed for drawdown of transient confined-unconfined flow towards a fully penetrating well in a confined aquifer. The proposed solution considers the aquifer anisotropy and the drainage from the unsaturated zone above the water table in the transient unconfined region. Based on the work by Moench (1995), the parameter of γ related to vertical hydraulic conductivity, aquifer thickness, specific yield and a delayed coefficient is introduced to investigate the delayed responses of flow behaviours, i.e., drawdown and development of the transient unconfined region. The results indicate that the flow behaviours simulations by the proposed solution are identical to that by Visual-MODFLOW Flex and finite difference method. The drawdown delayed responses occur in the early and intermediate segments, and disappear at the late segment during the transient confined-unconfined conversion. The increasing of the vertical hydraulic conductivity and the delayed coefficient can decrease the drawdown and limit the development of transient unconfined region, thus, and postpone the time of transient confined-unconfined conversion in a radial distance. The release of water by gravity storage nearby the piezometer surface is quick, resulting in an obvious log–log S-shaped drawdown-time curve. As buried depth increases, the effect of artesian storage is more pronounced. This paper provides much-needed insights of drawdown delayed response during the confined-unconfined conversion.