Analytical solution for tide-induced groundwater fluctuations in a heterogeneous coastal aquifer system due to dual tides

Recently, researchers have made significant efforts to investigate tide induced groundwater fluctuation in coastal aquifers. Different methods have been adopted for developing solutions to the problems using analytical approaches, numerical techniques, and experimental studies. Although numerical solutions lack many interesting features, compared with analytical ones in providing accurate results, they are the only alternative which enables one to satisfy necessary conditions on irregular boundaries in dealing with aquifer with different geometry. To the best of our knowledge, analytical solution for a heterogeneous coastal aquifer system with finite length has not been reported in any published literature.
Coastal aquifers are usually heterogeneous due to variations in depositional and post depositional processes. In this paper, an analytical solution was developed to tide induced groundwater fluctuations in a heterogeneous coastal aquifer system with finite length. This aquifer system contains an unconfined aquifer on the top, a semi-confined aquifer at the bottom, and an aquitard between them. The storage coefficient of the aquifer is assumed to be negligible with respect to those in the unconfined and confined aquifers. All the layers have been considered to be heterogeneous. The coastal aquifer system is infinite in y direction, and it is finite in x direction. The coastal aquifer system is influenced by the tide fluctuation from both left and right hand sides. The linearized Boussinesq equation is considered for the unconfined aquifers. The flow in the unconfined aquifer can be described by the linearized Boussinesq equation when the thickness of the unconfined aquifer is much greater than the tidal amplitude. The analytical solution is developed using the method of separation, and the closed form solution is obtained for hydraulic head in both unconfined and confined aquifers.
A hypothetical example is given to illustrate and investigate the effect of inhomogeneity on the tide-induced groundwater fluctuation. To address the effect of inhomogeneity, dimensionless hydraulic parameters are defined for the unconfined, semi-confined aquifers and the aquitard, as Lm=L1/L2, Sm=S11/S12, Tm=T11/T12, SB=S21/S22, TB=T21/T22, where L1 and L2 represent the leakage of the left and right aquitards, respectively, and S11 and S12, are storativity of the left and right unconfined aquifers, respectively, T11 and T12 are the transmissivity of the left and right unconfined aquifers, respectively, and S21 and S22, are storativity of the left and right semi-confined aquifers, respectively, T21 and T22 are the transmissivity of the left and right semi-confined aquifers, respectively. The results showed that the amplitude of groundwater head fluctuation in the unconfined aquifer increase with the leakage, however, the fluctuation in the semi-confined aquifer decreases as the leakage increases. When l1=l2=100 m (l1 and l2 are the length of the left and the right aquifers), the minimum groundwater fluctuations in the unconfined aquifers occur at the x=100 m for all leakage values, while in the semi-confined aquifer, for Lm=1, Lm=0.25, and Lm=5, it occurs at x=100 m, x= 120 m, and x=90 m, respectively. Time lag decreases as Lm increases in unconfined aquifers, however, it does not change significantly with varying of Lm, in semi-confined aquifer. Also, the results show that time lag is greater in semi-confined aquifer with respect to that in semi-confined aquifer. In the left unconfined aquifer, the groundwater head fluctuation increases with increase of Tm, and in the right unconfined aquifer, for Tm>1, it increases as Tm increases. The amplitude of head fluctuation in the semi-confined aquifer increases with increase of TB, however, the rate of increasing decreases with increase of TB. The reason may be, with increasing of transmissivity the velocity increases, therefore tide propagates rapidly in the aquifer. For Lm=0.25, and for large values of TB groundwater head fluctuation is almost constant. Also, the results show that, the groundwater head fluctuation in the unconfined aquifer decreases as Sm increases, the reason seems to be, with increasing of Sm, the damping effect of the system increases, therefore the head fluctuation in the aquifers decreases, this result had been in agreement with the results of previous researchers. The groundwater head fluctuation in the semi-confined aquifer is almost constant with variations of SB, meaning that SB has less effect on the head fluctuation in the semi-confined aquifer. It is interesting to note that, previous works that they considered a coastal aquifer system with infinite length, would be a special case of this work, when l1→∞.