海潮引起滨海承压含水层地下水位变化的数值模拟研究
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摘要
研究海岸带地下水的运动规律对于沿海地区地下水资源的合理开发和科学管理、沿海地区建筑物的结构稳定安全和地下工程施工以及海岸带生态环境的保护都具有十分重要的意义，其中地下水水位的确定更是研究的重点所在。潮汐海平面上下波动带动毗邻的滨海地下水水位振动，对达到动态稳定后的地下水水位作周期平均后，其位置高出不考虑潮汐作用的稳态水位，即潮汐影响下滨海地下水水位存在超高。在现有的区域地下水数学模型中，潮汐引起的海平面波动通常被忽略，其预测出的地下水水位位置与实际情况可能会有一定的误差。
本文通过数值模拟，结合物理实验对比分析，寻找一个等效的海岸边界条件的确定方法，我们在短时间序列内把海潮边界描述成正弦函数形式，在长时间序列内把海潮边界描述成有限项傅立叶级数形式，来研究潮汐作用下的沿海区域地下水水位的周期性波动特性。本文分别针对无越流和有越流两种情形，建立了描述近岸地下水运动的一维数学模型和三维数学模型，并依据实测数据对模型参数进行反演，对模型进行校正，随后运用有限差分法对模型进行离散，并编制计算程序，求得数值解，并对数值解和实测数据进行了比较，得到了滨海含水层地下水位随海潮变化的规律，结果表明，受海潮影响的滨海含水层地下水位与海潮有相似的波动特征，周期相同，周期T=24.7h；但振幅和潮汐效率随距海岸距离具有衰减效应，呈负指数函数衰减，在距离海岸500m处，振幅为1.35268m,潮汐效率为0.54107,在2000m处，振幅为0.26736m，潮汐效率为0.10694；地下水位到达波峰或波谷的时间具有滞后效应，滞后时间随距离呈线性增加，在距离海岸500m处，滞后时间为1.825h，在2000m处，滞后时间为9.825h；在无越流初始水位水平状态下，距海岸达4389m以远时可以认为地下水位不受海潮波动的影响。并且初始水位水平和线性倾斜两种状态下又有细微差别，潮汐波动影响的最远距离也不同，这些结论为正确评价地下水资源提供参考依据。
Studies of groundwater motion in coastal aquifers are of important significance inreasonable development of groundwater resources and scientific management ofcoastal areas in building safe structures and underground project construction and inthe ecological environment protection. The research focus of this paper is on thedetermination of water level. Tidal sea levels fluctuation drives adjacent coastal waterlevel to vibrate and achieve dynamic stability after the cycle of average water level.The position obtained doves not consider higher steady-state level of tidal action,namely the inshore water level under the influence of ultra high tides. In the existingregional groundwater mathematical models, the tides caused by sea level fluctuationsis often ignored. The prediction of the location of the groundwater table and the actualsituation may be somewhat different.
In this paper, numerical simulation is combined with the physical experimentcontrast analyses to find an equivalent of the coast and a method for determiningboundary condition. We described the tidal boundary within short time series into asine function form, and the tide for a long time sequence boundary is described as alimited form of Fourier series, to study the cyclical fluctuation characteristics underthe induction of tidal water level in coastal areas. This paper examines respectivelyfor the two circumstances, the no-leaky flow and the leaky flow to establish aone-dimensional mathematical model for describing the nearshore groundwatermovement. According to the inversion of the measured data of the model parameters,a three dimensional mathematical model is established and identified. The finitedifference method is used to discrete the model, and using a calculation program, thenumerical solution is obtained, and the numerical solution and the measured data arecompared. The results show that the coastal aquifer groundwater levels change withthe tide, groundwater levels affected by the tide in the coastal aquifer and the tidehave similar characteristics with the same period of T=24.7h. The amplitudeattenuation effect is obvious and the tidal efficiency decays with the distance from theshore with a negative exponent function attenuation. In the distance of500m from the coast, the amplitude is1.35268m, and tidal efficiency is0.54107. In the distance of2000m, the amplitude is0.26736m, and tidal efficiency is0.10694. Groundwaterlevels reach the peaks and valleys with a time lag effect. The time lag increaseslinearly with the distance from the caost. In the distance of500m from the coast, lagtime is1.825h, and in2000m distance, the lag time is9.825h. In the distance of4389m far from the shore, the groumdwater levels can be thought to not be affectedby the fluctuation of the tide. The initial water level and two kinds of linear tilt andnuances are considered, the tidal swings in farthest distance are also different. Theseconclusions may provide a reference basis for the reasonable evaluation ofgroundwater resources in coastal areas.
本文通过数值模拟，结合物理实验对比分析，寻找一个等效的海岸边界条件的确定方法，我们在短时间序列内把海潮边界描述成正弦函数形式，在长时间序列内把海潮边界描述成有限项傅立叶级数形式，来研究潮汐作用下的沿海区域地下水水位的周期性波动特性。本文分别针对无越流和有越流两种情形，建立了描述近岸地下水运动的一维数学模型和三维数学模型，并依据实测数据对模型参数进行反演，对模型进行校正，随后运用有限差分法对模型进行离散，并编制计算程序，求得数值解，并对数值解和实测数据进行了比较，得到了滨海含水层地下水位随海潮变化的规律，结果表明，受海潮影响的滨海含水层地下水位与海潮有相似的波动特征，周期相同，周期T=24.7h；但振幅和潮汐效率随距海岸距离具有衰减效应，呈负指数函数衰减，在距离海岸500m处，振幅为1.35268m,潮汐效率为0.54107,在2000m处，振幅为0.26736m，潮汐效率为0.10694；地下水位到达波峰或波谷的时间具有滞后效应，滞后时间随距离呈线性增加，在距离海岸500m处，滞后时间为1.825h，在2000m处，滞后时间为9.825h；在无越流初始水位水平状态下，距海岸达4389m以远时可以认为地下水位不受海潮波动的影响。并且初始水位水平和线性倾斜两种状态下又有细微差别，潮汐波动影响的最远距离也不同，这些结论为正确评价地下水资源提供参考依据。
Studies of groundwater motion in coastal aquifers are of important significance inreasonable development of groundwater resources and scientific management ofcoastal areas in building safe structures and underground project construction and inthe ecological environment protection. The research focus of this paper is on thedetermination of water level. Tidal sea levels fluctuation drives adjacent coastal waterlevel to vibrate and achieve dynamic stability after the cycle of average water level.The position obtained doves not consider higher steady-state level of tidal action,namely the inshore water level under the influence of ultra high tides. In the existingregional groundwater mathematical models, the tides caused by sea level fluctuationsis often ignored. The prediction of the location of the groundwater table and the actualsituation may be somewhat different.
In this paper, numerical simulation is combined with the physical experimentcontrast analyses to find an equivalent of the coast and a method for determiningboundary condition. We described the tidal boundary within short time series into asine function form, and the tide for a long time sequence boundary is described as alimited form of Fourier series, to study the cyclical fluctuation characteristics underthe induction of tidal water level in coastal areas. This paper examines respectivelyfor the two circumstances, the no-leaky flow and the leaky flow to establish aone-dimensional mathematical model for describing the nearshore groundwatermovement. According to the inversion of the measured data of the model parameters,a three dimensional mathematical model is established and identified. The finitedifference method is used to discrete the model, and using a calculation program, thenumerical solution is obtained, and the numerical solution and the measured data arecompared. The results show that the coastal aquifer groundwater levels change withthe tide, groundwater levels affected by the tide in the coastal aquifer and the tidehave similar characteristics with the same period of T=24.7h. The amplitudeattenuation effect is obvious and the tidal efficiency decays with the distance from theshore with a negative exponent function attenuation. In the distance of500m from the coast, the amplitude is1.35268m, and tidal efficiency is0.54107. In the distance of2000m, the amplitude is0.26736m, and tidal efficiency is0.10694. Groundwaterlevels reach the peaks and valleys with a time lag effect. The time lag increaseslinearly with the distance from the caost. In the distance of500m from the coast, lagtime is1.825h, and in2000m distance, the lag time is9.825h. In the distance of4389m far from the shore, the groumdwater levels can be thought to not be affectedby the fluctuation of the tide. The initial water level and two kinds of linear tilt andnuances are considered, the tidal swings in farthest distance are also different. Theseconclusions may provide a reference basis for the reasonable evaluation ofgroundwater resources in coastal areas.
引文
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