EXPERIMENTAL INVESTIGATION OF EFFECT OF TIDE ON COASTAL GROUNDWATER TABLE*

WU Long-hua

Center for Eco-Environmental Modeling, Hohai University, Nanjing 210098, China, E-mail: jxbywlh2000@yahoo.com.cn

ZHUANG Shui-ying

Pearl River Water Resources Scientific Research Institute, Guangzhou 510611, China

(Received June 18, 2009, Revised November 10, 2009)

EXPERIMENTAL INVESTIGATION OF EFFECT OF TIDE ON COASTAL GROUNDWATER TABLE*

WU Long-hua

Center for Eco-Environmental Modeling, Hohai University, Nanjing 210098, China, E-mail: jxbywlh2000@yahoo.com.cn

ZHUANG Shui-ying

Pearl River Water Resources Scientific Research Institute, Guangzhou 510611, China

(Received June 18, 2009, Revised November 10, 2009)

In this article, a tide simulation system based on a two-way water pump technique is developed. Using this system and numerical simulations, the groundwater table fluctuation characteristics, relative over height of groundwater table, and influencing factors of over height are investigated. The experimental and numerical results indicate that the groundwater table fluctuation is of periodic, and of asymmetric. The amplitude of groundwater table fluctuations decreases with the increase of the onshore distances. There are phase lags of groundwater table fluctuations for different monitoring points. The tide can bring about remarkable over height of coastal groundwater table. The dominating factors bring about over height include the tide amplitude, aquifer thickness and tide frequency. Under experimental conditions, the relative tide amplitude over height may exceeded 50% of the maximal tide amplitude, and reach about 10% of aquifer thickness.

tide simulation system, coastal aquifer, groundwater table, over height

1. Introduction

For a long time, the influence of groundwater on coastal water environment has drawn comsiderable attention. Coastal groundwater table fluctuates with the sea tide in coastal area. Firstly, the groundwater table fluctuation will directly affect beach stability. During flood tides, seawater table is higher than beach groundwater and it will intrude into the unconfined aquifer. During the ebb tide, the groundwater will expel from coastal unconfined aquifer. The seepage and inleakage face are engendered to influence the sediment transport in the beach. When the groundwater table is higher than the average sea water level, the beach is easier eroded. Contrarily, if the groundwater table is lower than the average sea level, the sediment easily silts[1,2]. Secondly, the groundwater fluctuation shall directly affect water exchange and substance movement between seawater and groundwater[3,4]. Thirdly, the coastal groundwater table fluctuation will affect the groundwater resource gross forecast in seaboard[5]. In 1997, tide-induced groundwater oscillations in coastal aquifers were modeled by the Boundary Element Method (BEM)[6], and it was found that the groundwater table fluctuation has three characteristics: asymmetry, amplitude attenuation and phase lagging, and the governing equations are the equations for two-dimensional saturated groundwater. At present, in mathematical modeling of groundwater, the sea level fluctuates of tide is usually ignored. The average sealevel is used to the boundary condition for mathematical models merely. However, some achievements show that the mean period of groundwater table in unconfined aquifers is larger than that of the still groundwater table in seacoast (abbreviated as over height). When the tide amplitude is 4 m-5 m, the over height can attain 2 m-3 m[7-9].

Li et al.[10-12]further showed that, because of the nonlinearity of the governing equations and beach gradient, tide will lead to over height in the groundwater of near-shore land. When the beach gradient is smaller, the over height is very prominence. If the over height is ignored, the error about the groundwater resource gross forecast will be brought about. It is necessary that above statement is proved in laboratory. In this article, a tide simulation system is developed. Based on the experimental observation and numerical simulations, the groundwater table fluctuation characteristics, relative over height of groundwater table and influencing factors of over height are meticulously investigated.

2. Numerical simulations

Groundwater heads in coastal aquifers fluctuate in responses to oceanic tides. Such fluctuations have been the subject of numerous recent studies[6,13-23]. In unconfined aquifers, such responses are manifested as water table fluctuations. These fluctuations are attenuated as they propagate towards inland, while the phases of the oscillations are shifted[6]. Modeling of tidal groundwater head fluctuations are often based on the Boussinesq equation with assuming negligible vertical flow[17].

2.1 Governing equations

This solution is also based on several other assumptions as listed below:

(1) The bottom of the coastal aquifer is impermeable.

(2) The aquifer is homogeneous, isotropic and has constant thickness.

(3) The groundwater flow is horizontal in the confined aquifer, and vertical flow effects can be neglected.

(4) The density difference between the groundwater and the seawater can be neglected owing to its slight impact on groundwater level fluctuation.

(5) Capillary effects can be neglected.

Using the above assumptions, in the experiment sand flume, the groundwater flow can be approximately regarded as the one-dimensional one. Then, the governing equations of the groundwater flow in the coastal aquifer system can be given as the one-dimensional non-linear Boussinesq equation

where H is the total groundwater head andthe mean groundwater head, h the groundwater head fluctuation (H-), nethe effective porosity,K thepermeability coefficient, x the inland distance from the seashore, Let the x-axis be positive landward and perpendicular to beach and the z-axis be vertical positive upward. The origin is located at the intersection of the beach and the bottom of the impermeable layer, as shown in Fig.1. t is time.β is the beach obliquity.

Fig.1 Schematic of tidal conditions at beach face and water table fluctuations in an unconfined aquifer

2.2 Boundary and Initial conditions

Two kinds of amplitudes and frequencies of signal are mixed to simulate the natural spring-neap tides. They are A1sin (ω1t ) and A2sin(ω2t-δ) respectively, where A1and A2are amplitudes,1ω and2ω are frequencies, and δ is phase lag.

(1) Boundary conditions:

The seaward and landward boundary conditions are described by Eqs.(3), (4) and (5). The seaward boundary condition of the groundwater head is defined by the tidal sea level oscillations, i.e.,

At far inland (x→∞), the gradient of h is taken to be zero (the tidal effects are diminished). At landward boundary, the groundwater table is H2, i.e.,

(2) Initial conditions:

Initial conditions are defined by the steady-state solution of the Eq.(1). The seaward and landward initial conditions are described by (6) and (7).

2.3 Solution method

Based on the finite-difference method, Less’s three-level difference scheme is used for spatial flux discretization. Thus solving nonlinear equations are avoided. Its truncation error is O(Δx+Δt2)[24]. The scheme is absolutely stabe for arbitrarily nonnegative parameters.

Fig.2 Schematic of experimental setup

3. Experimental set-up

The tide simulation system consists of a mechanical tide generating system and an automatic control system. The mechanical tide generating system includes sand flume, water tank, bidirectional water pump, direct current motor (D. C. motor), electromagnetic flowmeter, integrated butterfly valve, pipeline, overflow weir, intelligent digital water level meter and water pressure sensor, as shown in Fig.2. The automatic control system is used to control all kinds of apparatus. The system adopts serial communication between industrial control computer and controller to remotely control the test process real time. All the experimental apparatuses are under the control of the controling center with telecommunications. In the experimental set-up, the baffle retains the sand, but it is dank. Overflow weir is used to control the groundwater table of land, and its height can be automatically adjusted to keep the groundwater table constant.

The sand flume is 30 m long, 1.2 m wide and 1.5 m high. The maximal simulation amplitude of tide is 0.25 m. In the present experiments, beach obliquity is 7o. In order to measure the changing groundwater table, all sixteen pressure sensors are located at the central bottom of sand flume based on the size of sand flume, and their coordinates in the direction of the length of sand flume are shown in Table 1. The water table fluctuations of spring-neap tides is modeled under different experiment conditions by changing the amplitude and frequency of tide and the aquifers thickness of sand flume.

Table 1 Horizontal coordinates of pressure sensors

4. Results and discussions

For tide-induced groundwater oscillations in coastal aquifers, a mass of theories and methods have been achieved based on the numerical simulations method. But generally speaking, researches groundwater table over height in coastal aquifers is still in the preliminary stage. Therefore, movement characterisitcs of groundwater oscillations is onlyobserved by experiment al set-up, and these experiment results are compared with the existing numerical results. The groundwater over height is simulated and calculated by the above established mathematical model, and the simulation results are compared with the experiment results.

Fig.3(a) Spring-neap tides-induced groundwater oscillations in coastal aquifers

4.1 Fluctuations of groundwater table

Two sets of amplitudes and frequencies of signals are mixed to simulate the natural spring-neap tides. One set set is: period T1=45min and amplitude A1=90mm . The other set is: T2=60min and A2=45mmFor these experiments the aquifer thickness (Z0) is 0.765 m, the permeability coefficient (K) is 38.016 m/d, and the effective porosity (ne) is 0.442. The groundwater table fluctuation at everymonitoring point was measured experimentally in tide simulation system, in which the time evolution of three groundwater tables are plotted in Fig.3.

Fig.3(b) Asymmetry of groundwater oscillations between the rising and falling phases in coastal aquifers

It can be seen from the Fig.3 that

(1) In the seaboard, because tide energy is transferred from surface water to groundwater by tidal waves, which results in coastal groundwater table fluctuation as shown in Fig.3(a). At the same time, the spring-neap tides give rise to the asymmetry between the rising and falling phases of the groundwater table fluctuations in coastal aquifers, as shown in Fig.3(b).

(2) Because of the period influence of tide signal, the coastal groundwater tables periodically fluctuate. And it was observed that the fluctuation period is about 3 h in the experiments.

(3) The amplitude of groundwater table fluctuation decreases with the increase of the onshore distance.

Meanwhile, phase lags were observed in groundwater table fluctuations at different monitoring points. The above-mentioned experimental results accord with those in previous studies[3-10].

Fig.4 Schematic of over height

4.2 Over height of groundwater table

The schematic of over height is shown in Fig.4. In Fig.4, the dotted line shows the mean periodic groundwater table, and the solid line of curves shows still groundwater table. β is the beach obliquity. Ordinate represents the tide level, and abscissa the onshore distance. At the point of intersection of higher high tide level and the beach, the difference betweenthe mean periodic groundwater table and the mean sea level is defined as over height (Hover).

Table 2 Experimental parameter settings of over height

In order to investigate the relations among the over heights, the tide amplitude and the aquifer thickness,relative aquifer thickness of over height (HOZ), relative tide amplitude over height (HOA) and relative aquifer thickness amplitude (AAZ) are defined as follow:

where Z0is the aquifers thickness, and A is the maximal tide amplitude.

Ten experiments were conducted by changing the amplitude, frequency of tide and the aquifers thickness of sand flume. And experimental parameters are shown in Table 2, and all results are shown in Table 3. In the mathematical model, parameter settings accords with experimental ones.

Table 3 Measurement and analysis results

It can be observed from Table 3 that the over height is remarkably brought about by the spring-neap tide. The relative tide amplitude over height (HOA) is 51.98, and the relative aquifer thickness of over height (HOZ) is 9.49. Thes e results show that the relative tide amplitude over heightexceeds 50% of the maximaltide amplitude, and reaches about 10% of aquifer thickness under the experimental conditions. When the aquifer thickness and the amplitude (with difference less than 5%) and frequency of synthetic spring-neap tides signal are kept constant, at the same time, and T1, T2and phase lag are also constant, the effect of the firstamplitude(A1)and the second amplitude (A2) on groundwater over height(Hover) is analyzed. The numerical and experimental results are shown in Fig.5.

Fig.5 Relation between HOZand the amplitude of analoging tide signal

As is shown in Fig.5, the difference of relative aquifer thickness of over height (HOZ) is smaller than 3% ineach case. In other words, the over height has nothing to do with the variation of A1and A2.

The experimental and numerical results for the cases of Nos. 6, 7, 9 and 10 show that HOAincreases withAAZatthe constant tide frequency as shown in Fig.6.

Fig.6 Relation between the AAZand theHOZ

From the Figs.5 and 6, the computed over heights are larger than experimental ones under the same conditions. This situation may be mainly caused by negligible capillary effects in numerical simulation, so the groundwater table oscillations range given by numerical simulation is larger than that in the experiment.

On the other hand, based on the experimental results of cases Nos.6, 7 and.8 it could be concluded that the over height increases with increasing tide frequency, and the influence of the tide frequency on over height is much more greater than that of the tide amplitude.

5. Conclusions

According to the numerical simulations and experimental simulations, the characteristics of the coastal groundwater table fluctuations have been investigated. The main conclusions of the results of this study can be reached as follows:

(1) The groundwater table fluctuation is periodic and asymmetric due to the effect of tides. The amplitude of groundwater table fluctuations decreases with the increase of the onshore distances. Meanwhile, there are phase lags of groundwater table fluctuations at different monitoring points.

(2)The tide can cause remarkable over height of coastal groundwater table. The dominating factors includes the tide frequency, tide amplitude and aquifer thickness, while the effect of the frequency on the over height is greater than the amplitude of the tide. Under the above experimental conditions, the relative over height exceeds 50% of the maximal tide amplitude, and reaches about 10% of aquifer thickness. Hence the over height is of great importance in forecasting the groundwater resource gross.

[1] HAN Long-xi, LI Wei and LU Yong-jun et al. Impact of artificial sand excavation on hydrodynamics and water environment of Dongjiang River network[J]. Journal of Hohai University (Natural Sciences), 2005, 33(2): 123-126(in Chinese).

[2] ZHOU Nian-qing, ZHU Xue-yu and QIAN Jia-zhong et al. The effect of tidal fluctuation on the unconfined aquifer of the site in the third phase of Qinshan nuclear power engineering[J]. Journal of Hydrodynamics, Ser. A, 2002, 17(3): 327-333(in Chinese).

[3] LI Ling, BARRY D. A. and STAGNITTI F. et al. Submarine groundwater discharge and associated chemical input to a coastal sea[J]. Water Resource Research, 1999, 35(11): 3253-3259.

[4] LI Yong, WANG Chao and YANG Lin-zhang et al. Influence of seepage face obliquity on discharge of groundwater and its pollutant into lake from a typical unconfined aquifer[J]. Journal of Hydrodynamics, Ser. B, 2007, 19(6): 756-761.

[5] LI Hai-long, JIAO J. J. Tide-induced seawater groundwater circulation in a mult-layered coastal leaky aquifer system[J]. Journal of Hydrology, 2003, 274(14): 211-224.

[6] LI L., BARRY D. A. and PATTIARATCHI C. B. Numerical modeling of tide-induced beach water table fluctuations[J]. Coastal Engineering, 1997, 30(12):105-123.

[7] TURNER I. L. Simulating the influence of groundwater seepage on sediment transported by the sweep of the swash zone acrossmacro-tidal beaches[J]. Marine Geology, 1995, 125(12): 153-174.

[8] ATAIE-ASHTIANI B.,VOLKER R. E. and LOCKINGTON D. A. Tidal effects on groundwater dynamics in unconfined aquifers[J]. Hydrological Processes, 2001, 15(4): 655-669.

[9] TEO H. T., JENG D. S. and SEYMOUR B. R. et al. A new analytical solution for water table fluctuations in coastal aquifers with sloping beaches[J]. Advances in Water Resources, 2003, 26(12): 1239-1247.

[10] LI L., BARRY D. A. and STAGNITTI F. et al. Beach water table fluctuations due to spring-neap tides: Moving boundary effects[J]. Advances in Water Resources, 2000, 23(8): 817-824.

[11] SONG Zhi-yao, Li L. and NIELSEN P. et al. Quantification of tidal water table overheight in a coastal unconfined aquifer[J]. Journal of Engineering Mathematics, 2006, 56(4): 437-444.

[12] ZHUANG Shui-ying , CHEN Juan and LI Ling. Numerical modeling of groundwater table fluctuations due to spring-neap tides in a coastal unconfined aquifer[J]. Journal of Hohai University (Natural Sciences), 2006, 34(1): 10-12(in Chinese).

[13] NIELSEN P., FENTON J. D. and ASEERVATHAM R. A. et al. Water table waves in aquifers of intermediate depths[J]. Advances Water Resources, 1997, 20(1): 37-43.

[14] BAIRD A. J., HORN D. P. Monitoring and modelling groundwater behaviour in sandy beaches[J]. Coastal Research, 1996, 12(3): 630-640.

[15] ZHANG Qian-fei, LAN Shou-qi and WANG Yan-ming et al. A new numerical method for groundwater flow and solute transport using velocity field[J]. Journal of Hydrodynamics, 2008, 20(3): 356-364.

[16] MA Xiu-yuan, LI Shu-guang and ZHU Wei-shen. A new method in groundwater flow modeling[J] Journal of Hydrodynamics, 2009, 21(2): 245-254.

[17] BAIRD A. J., MASON T. and HORN D. P. Validation of a Boussinesq model of beach groundwater behaviour[J]. Marine Geology, 1998,148(12): 55-69.

[18] JENG D. S., LI Li and BARRY D. A. Analytical solution for tidal propagation in a coupled semi-confined/phreatic coastal aquifer[J], Advances in Water Resources, 2002, 25(5): 577-584.

[19] LI H. L., JIAO J. J. Analytical solutions of tidal groundwater flow in coastal two-aquifer system[J]. Advances in Water Resources, 2002, 25(4): 417-426.

[20] LI H. L., JIAO J. J. Tidal groundwater level fluctuations in L-shaped leaky coastal aquifer system[J]. Journal of Hydrology, 2002, 268(14): 234-243.

[21] LI L., BARRY D. A. and CUNNINGHAM C. et al. A two-dimensional analytical solution of groundwater responses to tidal loading in an estuary and ocean[J]. Advances in Water Resources, 2000, 23(8): 825-833.

[22] NIELSEN P., ASEERVATHAM R. and FENTON J. D. et al. Groundwater waves in aquifers of intermediate depths[J]. Advances Water Resources, 1997, 20(1): 37-43.

[23] RAUBENHEIMER B., GUZA R. T. and ELGAR S. Tidal water table fluctuations in a sandy beaches[J]. Water Resource Research, 1999, 35(8): 2313-2320.

[24] HU Jian-wei, TANG Huai-ming. The numerical methods for the differential equations[M]. Beijing: Science Press, 1998, 282-289(in Chinese).

10.1016/S1001-6058(09)60029-9

* Project supported by the Jiangsu Planned Projects for Postdoctoral Research Funds (Grant No. 0701006B).

Biography: WU Long-hua (1974- ), Male, Ph. D., Associate Professor