For the homogeneous and isotropic confined aquifer shown in Figure 7. 16, it is assumed that the initial groundwater level of the confined aquifer is horizontal, consistent with the average sea level, and the coastal boundary is vertical, so the fluctuation of tidal waves can be described by sine function. Select the coordinates as shown in Figure 7. 16. The origin is at the junction of mean sea level and coastline, and the inland direction is positive. The governing equations, initial conditions and boundary conditions describing the one-dimensional unsteady flow of groundwater in coastal confined aquifers can be expressed as follows.
Fig. 7. 16 schematic diagram of coastal confined aquifer
Monograph on groundwater science
Where: h is the water level elevation based on the average sea level, m; S is the water storage coefficient of confined aquifer, dimensionless; T is the permeability coefficient of confined aquifer, m2/h; X is the distance from the coast, m; T is time, h; H0 is half the amplitude of sea level (i.e. amplitude), m; T0 is the fluctuation period of sea level, and H. The solution of the above definite solution problem is (Jacob,1950; Ferris,1951; Werner et al.,1951; Ingersoll et al., 1954)
Monograph on groundwater science
Comparing formula (7.77) with formula (7.76b), it can be seen that the water level of confined aquifer from the coastline X fluctuates with the tide, which has attenuation effect and lag effect. According to formula (7.77), the fluctuation range (Hx) of confined aquifer water level at the distance from the coastline X is
Monograph on groundwater science
From equations (7.76b) and (7.78), tidal efficiency (TE) can be obtained by the following formula.
Monograph on groundwater science
It can be found from equation (7.77) that the lag time (tL) is
Monograph on groundwater science
Equation (7.79) shows that tidal efficiency decreases exponentially with distance x, and equation (7.80) shows that lag time increases linearly with distance X.
Assuming that the permeability coefficient of the confined aquifer is T=3 1.25m2/h, the storage coefficient s = 4.5×65438+500m-4, the amplitude H0 of the tide is 2.5m, and the period t0 is 24.7h, according to the formula (7.77), the variation of the groundwater level with time at different distances x can be obtained, as shown in Figure 7.65438. It can be seen that, induced by tidal fluctuation, the groundwater level of confined aquifer at any distance X along the coastal zone also fluctuates with time. With the increase of x, the amplitude of groundwater level gradually decreases, and the time of peak or valley appears gradually increases.
Fig. 7. 17 groundwater level fluctuation curve at different distances from coastal confined aquifer
7.5.3.2 has an overflow confined aquifer.
As shown in Figure 7. 18, the coastal aquifer system consists of phreatic aquifer, weakly permeable aquifer, confined aquifer and aquifuge from top to bottom. Assuming that the water supply of the phreatic aquifer is relatively large, the fluctuation of the water level of the phreatic aquifer caused by tidal effect can be ignored. Select the coordinates as shown in Figure 7. 18. The origin is at the junction of mean sea level and coastline, and the inland direction is positive. The aquifer is homogeneous and isotropic, the groundwater in the confined aquifer flows horizontally, and the groundwater in the phreatic aquifer flows vertically through the weakly permeable layer and the confined aquifer. When the initial time t=0, the water levels in confined aquifer and phreatic aquifer are equal, which is the same as the average sea level. When t > 0, the water level of the phreatic aquifer remains unchanged. The release of water from the weak permeable layer itself can be ignored, and its vertical flow is linearly related to the head difference between the phreatic aquifer and the confined aquifer. Under the above assumptions, the governing equation, initial conditions and boundary conditions of one-dimensional unsteady groundwater flow in confined aquifer can be expressed as follows
Fig. 7. 18 schematic diagram of coastal confined aquifer overflow
Monograph on groundwater science
Where: h is the water level elevation of confined aquifer based on average sea level, m; S is the water storage coefficient of confined aquifer, dimensionless; T is the permeability coefficient of confined aquifer, m2/h; B is the overflow coefficient of weak permeable layer (the ratio of permeability coefficient of weak permeable layer to its thickness); X is the distance from the coast, m; T is time, h; H0 is the amplitude of tidal fluctuation, m; T0 is the tidal fluctuation period, h; C is the tidal period.
The solution of formula (7.8 1) (Jiao et al., 1999) is as follows.
Monograph on groundwater science
From equation (7.82), the tidal efficiency TE can be obtained by the following formula
Monograph on groundwater science
The lag time (tL) is
Monograph on groundwater science
When B=0, that is, there is no overcurrent, equation (7.82) becomes
Monograph on groundwater science
Equation (7.86) and Equation (7.77) are essentially the same, but there are differences in phase.
Assume that the hydraulic conductivity of the confined aquifer is T=3 1.25m2/h, the water storage coefficient s = 4.5×65438+500m-4, the amplitude H0=2.5m, the period t0=24.7h, c=0, and b = 0.0051/d. It can also be seen that the groundwater level of the confined aquifer at any distance x along the coastal zone fluctuates with time, but it is more moderate than that without overflow. With the increase of x, the amplitude of groundwater level gradually decreases, and the time of peak or valley appears gradually increases.
Fig. 7. 19 groundwater level fluctuation curve of coastal confined aquifer with overflow at different distances from the coast.