Tide-induced Beach Groundwater Overheight: The Equivalent Seaward Boundary Condition

Beach groundwater table fluctuates with tidal oscillations in coastal unconfined aquifer. The period-averaged water table height is higher than the steady-state water table with the neglect of tidal effects. That is, there exists an overheight between the two. Besides, the overheight is profound while the beach slope is gentle. However, such tidal overheight is often ignored in the current regional numerical simulation due to intensive computational requirement. Only the mean sea level is used as the fixed seaward boundary, which may wrongly predict the groundwater table position. Therefore, we aim to determine an equivalent seaward boundary through numerical modeling. The equivalent seaward boundary takes into account the tide-induced overheight effects. On the other hand, it could be incorporated in the current numerical models without increasing the computational cost.Based on the governing equation and boundary conditions that describe the tide-induced groundwater fluctuation, we developed a numerical model of groundwater flow subject to tidal oscillations. Non-dimensionalisation was applied to the model, resulting in two controlling dimensionless parameters: α and ε. With the definition of overheight, we derived an empirical formula based on a large number of numerical experiments and regression analysis. The formula is described as followwith A denoting tidal amplitude and Ov for the groundwater table overheight:Ov = A × [1 - (0.11 × α + 1.33)× exp(-0.89 × ε^0.46)]. Laboratory experimentswere also carried out to validate the numerical modeling results. At last, we demonstrated how to apply the empirical formula to the equivalent seaward boundary condition through an example.Furthermore, we also investigated two interrelated problems and drew conclusions as follows: (1) The fluctuations of tide-induced coastal groundwater table exhibit three characteristics: amplitude attenuation, phase lag and asymmetry;(2) The dimensionless seepage face length shows good correlation with the dimensionless parameter α and ε. Besides, the effects of ε on dimensionless seepage face length are much larger than those of α and the dimensionless seepage face length enlargesequivalent seaward boundary, numerical model, overheight, non-dimensionalisation, seepage face length...