河渠水位线性变化条件下河渠-潜水非稳定流模型及其解
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摘要
在河渠水位迅速变化后再缓慢变化的条件下,建立了河渠半无限潜水含水层中非稳定渗流模型.利用Boussinesq第一线性化方法及Laplace变换,并注意应用Laplace变换中的"积分性质",给出形式相对简单、由常用函数表达的解,阐述特定解及其相应的物理意义.由解所揭示的潜水位变化规律表明,含水层任一点处潜水位变动速度的时间变化曲线形态是固定的,与河渠边界水位变动速率λ无关;潜水最大变速发生的时间,随λ呈非线性位移.依据潜水位变化规律,建立利用潜水位变动速度求含水层参数的方法,并用实例演示了拐点法求参数的过程.
Based on the first linearized Boussinesq equation,the analytical solution of the transient groundwater model for description of phreatic flow in a semi-infinite aquifer bordered by a linear stream with linearly varying stream water levels,was derived through the Laplace transform and in view of the integral property of the Laplace transform. The solution is composed of some common functions and its expression form is relatively simple. According to the mathematical characteristics of the solution,its corresponding physical meaning was discussed. The variation rule of the phreatic level revealed by the solution shows that the temporal variation curve of the aquifer at any point is fixed and has nothing to do with the change rate of the water level of the river channel. The time of the maximum speed change of the phreatic aquifer nonlinearly varies with λ. Based on the variation rule of the phreatic level,the method determining the aquifer parameters with the changing velocity of the phreatic level was established,and the process of obtaining the parameter with the inflection point method was demonstrated through an example.
Based on the first linearized Boussinesq equation,the analytical solution of the transient groundwater model for description of phreatic flow in a semi-infinite aquifer bordered by a linear stream with linearly varying stream water levels,was derived through the Laplace transform and in view of the integral property of the Laplace transform. The solution is composed of some common functions and its expression form is relatively simple. According to the mathematical characteristics of the solution,its corresponding physical meaning was discussed. The variation rule of the phreatic level revealed by the solution shows that the temporal variation curve of the aquifer at any point is fixed and has nothing to do with the change rate of the water level of the river channel. The time of the maximum speed change of the phreatic aquifer nonlinearly varies with λ. Based on the variation rule of the phreatic level,the method determining the aquifer parameters with the changing velocity of the phreatic level was established,and the process of obtaining the parameter with the inflection point method was demonstrated through an example.
引文
[1]张蔚榛.地下水非稳定流计算和地下水资源评价[M].北京:科学出版社,1983.(ZHANGWeizhen.Calculation of Unsteady Flow of Groundwater and Evaluation of Groundwater Resources[M].Beijing:Science Press,1983.(in Chinese))
[2]BEAR J.多孔介质流体力学[M].李竞生,陈崇希,译.北京:中国建筑工业出版社,1983.(BEAR J.Dynamics of Fluids in Porous Media[M].LI Jingsheng,CHEN Chongxi,transl.Beijing:China Architecture&Building Press,1983.(Chinese version))
[3]束龙仓,陶月赞.地下水水文学[M].北京:中国水利水电出版社,2009.(SHU Longcang,T AOYuezan.Groundwater Hydrology[M].Beijing:China Water&Power Press,2009.(in Chinese))
[4]陶月赞,姚梅,张炳峰.时变垂向入渗影响下河渠-潜水非稳定渗流模型的解及应用[J].应用数学和力学,2007,28(9):1047-1053.(T AO Yuezan,YAO Mei,ZHANG Bingfeng.Solution and its application of transient stream/groundwater model subjected to time-dependent vertical seepage[J].Applied Mathematics and Mechanics,2007,28(9):1047-1053.(in Chinese))
[5]MAHDAVI A.T ransient-state analytical solution for groundwater recharge in anisotropic sloping aquifer[J].Water Resources Management,2015,29(10):3735-3748.
[6]Bansal R K.Approximation of surface-groundwater interaction mediated by vertical stream bank in sloping terrains[J].Journal of Ocean Engineering and Science,2017,2(1):18-27.
[7]HUANG F K,CHUANG M H,WANG G S,et al.T ide-induced groundwater level fluctuation in a U-shaped coastal aquifer[J].Journal of Hydrology,2015,530(1):291-305.
[8]MUNUSAMY S B,DHAR A.Homotopy perturbation method-based analytical solution for tide-induced groundwater fluctuations[J].Groundwater,2016,54(3):440-447.
[9]SU N H.T he fractional Boussinesq equation of groundwater flow and its applications[J].Journal of Hydrology,2017,547(2):403-412.
[10]DAVID P V,SAHUQUILLO A,ANDREU J,et al.A general methodology to simulate groundwater flow of unconfined aquifers with a reduced computational cost[J].Journal of Hydrology,2007,38(1/2):42-56.
[11]KIM K Y,KIM T,KIM Y,et al.A semi-analytical solution for groundwater responses to streamstage variations and tidal fluctuations in a coastal aquifer[J].Hydrological Processes,2007,21(5):665-674.
[12]SERRANO S E,WORKMAN S R,SRIVAST AVA K,et al.Models of nonlinear stream aquifer transients[J].Journal of Hydrology,2007,336(1):199-205.
[13]陶月赞,曹彭强,席道瑛.垂向入渗与河渠边界影响下潜水非稳定流参数的求解[J].水利学报,2006,37(8):913-917.(T AO Yuezan,CAO Pengqiang,XI Daoying.Parameter estimation for semi-infinite phreatic aquifer subjected to vertical seepage and bounded by channel[J].Journal of Hydraulic Engineering,2006,37(8):913-917.(in Chinese))
[14]MIZUMURA K.Approximate solution of nonlinear Boussinesq equation[J].Journal of Hydrologic Engineering,2009,14(10):1156-1164.
[15]YOUNGS E G,RUSHTON K R.Dupuit-forchheimer analyses of steady-state water-table heights due to accretion in drained lands overlying undulating sloping impermeable beds[J].Journal of Irrigation and Drainage Engineering,2009,135(4):467-473.
[2]BEAR J.多孔介质流体力学[M].李竞生,陈崇希,译.北京:中国建筑工业出版社,1983.(BEAR J.Dynamics of Fluids in Porous Media[M].LI Jingsheng,CHEN Chongxi,transl.Beijing:China Architecture&Building Press,1983.(Chinese version))
[3]束龙仓,陶月赞.地下水水文学[M].北京:中国水利水电出版社,2009.(SHU Longcang,T AOYuezan.Groundwater Hydrology[M].Beijing:China Water&Power Press,2009.(in Chinese))
[4]陶月赞,姚梅,张炳峰.时变垂向入渗影响下河渠-潜水非稳定渗流模型的解及应用[J].应用数学和力学,2007,28(9):1047-1053.(T AO Yuezan,YAO Mei,ZHANG Bingfeng.Solution and its application of transient stream/groundwater model subjected to time-dependent vertical seepage[J].Applied Mathematics and Mechanics,2007,28(9):1047-1053.(in Chinese))
[5]MAHDAVI A.T ransient-state analytical solution for groundwater recharge in anisotropic sloping aquifer[J].Water Resources Management,2015,29(10):3735-3748.
[6]Bansal R K.Approximation of surface-groundwater interaction mediated by vertical stream bank in sloping terrains[J].Journal of Ocean Engineering and Science,2017,2(1):18-27.
[7]HUANG F K,CHUANG M H,WANG G S,et al.T ide-induced groundwater level fluctuation in a U-shaped coastal aquifer[J].Journal of Hydrology,2015,530(1):291-305.
[8]MUNUSAMY S B,DHAR A.Homotopy perturbation method-based analytical solution for tide-induced groundwater fluctuations[J].Groundwater,2016,54(3):440-447.
[9]SU N H.T he fractional Boussinesq equation of groundwater flow and its applications[J].Journal of Hydrology,2017,547(2):403-412.
[10]DAVID P V,SAHUQUILLO A,ANDREU J,et al.A general methodology to simulate groundwater flow of unconfined aquifers with a reduced computational cost[J].Journal of Hydrology,2007,38(1/2):42-56.
[11]KIM K Y,KIM T,KIM Y,et al.A semi-analytical solution for groundwater responses to streamstage variations and tidal fluctuations in a coastal aquifer[J].Hydrological Processes,2007,21(5):665-674.
[12]SERRANO S E,WORKMAN S R,SRIVAST AVA K,et al.Models of nonlinear stream aquifer transients[J].Journal of Hydrology,2007,336(1):199-205.
[13]陶月赞,曹彭强,席道瑛.垂向入渗与河渠边界影响下潜水非稳定流参数的求解[J].水利学报,2006,37(8):913-917.(T AO Yuezan,CAO Pengqiang,XI Daoying.Parameter estimation for semi-infinite phreatic aquifer subjected to vertical seepage and bounded by channel[J].Journal of Hydraulic Engineering,2006,37(8):913-917.(in Chinese))
[14]MIZUMURA K.Approximate solution of nonlinear Boussinesq equation[J].Journal of Hydrologic Engineering,2009,14(10):1156-1164.
[15]YOUNGS E G,RUSHTON K R.Dupuit-forchheimer analyses of steady-state water-table heights due to accretion in drained lands overlying undulating sloping impermeable beds[J].Journal of Irrigation and Drainage Engineering,2009,135(4):467-473.