Analytical Solution Of Tidal Wave Propagation In A Coastal Aquifer

Various coastal hydrogeological, engineering geological, ecological and environmental problems related to tidal dynamics are emerging endlessly with the social and economic development in coastal areas, e.g., seawater intrusion, stability of coastal engineering and marine retaining structures, beach dewatering for construction purposes, and deterioration of the marine environment. In order to solve these problems, the coastal hydrogeological conditions need to be identified including the aquifer parameter estimation and the interaction process between groundwater and seawater. The traditional and standard methods for identifying coastal hydrogeological conditions are well-documented in many text books such as pumping test or slug-test data analysis, numerical modeling, Guelph permeameter test and floodwave-response technique. However, these methods are either expensive or very site-specific. Pumping-test, for example, is very popular and is deemed as the standard method to date, but it is very costly, time-consuming and not always advisable for coastal aquifer systems. In addition, it may accelerate seawater intrusion and/or aggravate intrusion problems, and the conventional analysis of pumping-test data is cumbersome and quite subjective.In coastal aquifers, the groundwater level (hydraulic head or water table) in coastal aquifer fluctuates with time in response to the water level fluctuations of the tidal water body (sea or river or lagoon), which is referred to as tidal effects. Jacob [1950] derived an equation for the tidal groundwater fluctuation in a single coastal confined aquifer. Since then, the theoretical research and field investigation of groundwater flow and salinity distribution in the coastal aquifer systems have been conducted by many hydrogeologists. These studies indicate that the natural phenomenon of tidal effect has the potential to provide a convenient, economic and reliable way of identifying coastal hydrogeological conditions in large scale. They also provide a strong theoretical guide and technical support for solving various coastal hydrogeological, engineering geological, ecological and environmental problems related to tidal dynamics. How to estimate aquifer parameters including the extending length of the confined aquifer under the sea, and how to identify the existence of aquifer's submarine outlet-capping, via the analysis of the tidal effect data from observation wells in coastal areas, are important and interesting tasks of hydrogeologists.This paper focuses on the analytical solution of the tidal wave propagation in a coastal aquifer system and its application in a case study in a coastal area. The main results are as follows.1. General conceptual model for coastal aquifer systems was given.This paper made an attempt to consider a coastal aquifer system comprising a shallow unconfined aquifer, a confined aquifer, and a semipermeable layer (the confined aquifer's roof) between them. The unconfined aquifer terminates at the coastline, the confined aquifer and its roof extend under the sea for a certain distance. The aquifer's submarine outlet is covered by a thin, vertical layer of sediment (referred to as the "outlet-capping" hereafter) with properties dissimilar to the aquifer. The joint actions of the leakage effects of the aquifer's offshore roof and the submarine outlet-capping on the tide-induced head fluctuation in a coastal aquifer system are took into account. However, tide-induced water table fluctuations in the unconfined aquifer and the elastic storages of the aquifer's roof and the aquifer's submarine outlet-capping are neglected.2. An analytical solution to describe the tide-induced head fluctuation in a generalized coastal confined aquifer system was derived.Based above-mentioned assumptions, the mathematical model for this coastal aquifer system was given, and the analytical solution to the model was derived using the theories of Fourier transform and complex variable functions. For aquifers with zero or infinite offshore length, or with impermeable roof or outlet-capping, or without the outlet-capping, existing solutions in the literature are obtained, indicating that the solutions by many previous researchers are the special cases of our new solution.3. Threshold value of the offshore aquifer length was discussed.Most existing studies show that the confined aquifer, especially the deep confined aquifer may extend under the sea with a considerable distance from the coastline. This fact, however, is lack of quantitative description and examination. According to our analytical solution, a formula of the threshold value of the offshore extending length is obtained. Given the typical values of the model parameters contained in the formula and the simplicity of the formula, the threshold value for the offshore aquifer length was found to be less than 5 km for typical coastal aquifer systems. And the threshold value can also be regarded as the maximum offshore distance within which the hydrogeological information of the offshore seabed, aquifer and the submarine outlet-capping are able to be explored via tidal effect data observed inland.4. The sensitivity analysis of the parameters on the analytical solution.The influences of the leakage and length of the aquifer's offshore roof, the outlet-capping's leakance, and the tidal loading efficiency on the tidal wave propagation in inland aquifer are discussed. For an aquifer with its offshore length greater than the threshold, the inland head fluctuation becomes insensitive to variations of this length and the outlet-capping's leakance. The leakage through the offshore roof decreases the threshold value. When the offshore confined aquifer is short, the inland head fluctuation increases with the outlet-capping's leakance. In this case negative phase shift occurs near the coastline only for aquifers with small leakages through the offshore roof and the outlet-capping. In general, the combined actions of the tidal loading, the leakage and length of the offshore roof, and the leakage of the outlet-capping lead to complex, non-monotonic dependency of the inland head fluctuation on the aquifer parameters.5. A case study was conducted in a coastal area in Beihai Peninsula, Guangxi Province, P R China.The tidal and piezometer data in a coastal aquifer in the Beihai Peninsula, Guangxi Autonomous Region, P R China are used to estimate the aquifer parameters based on least-squares penalty method with the analytical solution derived here. The fitting result suggests that the model is suitable to describe the reality, and the characteristics of the tidal wave propagation in the confined aquifer are able to be well described. The results strongly indicated a weak-hydraulic outlet-capping covering the aquifer's submarine outlet and a considerable leakage through the aquifer roof.6. Three real situations consistent with our model were described.The real world cases represented by our model and solution can be summarized as the following three cases which could be illustrate the feasibility of our model in settling the related issues emerging in the coastal groundwater system. The first case is a slope coastal confined aquifer's submarine outcrop covered by seabed sediments, another two situations are a coastal confined aquifer's submarine outcrop covered by vertical sand filter layer behind a retaining structure of coarse material, and a leaky confined aquifer extending under a tidal river.7. Some suggestions and remarks were given.Finally, some shortages were discussed in point of this model and case study. Meanwhile, some proposals and arguments or remarks for future work are presented. The thread and direction of these suggestions could be put in to the theoretical pursuit and/or field survey in the field of (submarine) groundwater and solute transport in coastal aquifers.In summary, this paper made an attempt to fill some gaps in the research of coastal tidal dynamics by considering a more general coastal aquifer system. A new analytical solution is derived, discussed and used for estimating aquifer parameters and hydrogeologic conditions in a case study.