河流与含水层水力耦合模型及其应用

An Integrated ModelForm ulation ofStream - aquifer Interaction System and ItsApplication

本文在分析河水与地下水相互作用规律的基础上，提出了河流－含水层相互作用水力耦合模型的建模思路、数值解法及应用实例。河流模型采用忽略河槽调蓄作用的圣维南连续方程，含水层模型为潜水二维渗流方程， 二者通过动态水量交换机制实现耦合； 模型的水量交换机制可以分别模拟含水层顶托排泄、河流压力渗漏和淋滤渗漏等不同方式的水量转换过程。河水模型和地下水模型分别用欧拉法和三角网格差分法来求解。实际应用表明耦合模型能较准确地模拟河流－地下水系统的水量平衡与动态变化过程，能有效避免地表水和地下水水量的重复计算，可作为河水与地下水相互作用地区水资源评价、规划与管理以及地表水。

Based on theanalysisofhydraulicm echanism ofstream - aquiferinteraction sys- tem , an integrated m odelis developed to sim ulate the interaction process. To allow accu- rate sim ulation ofthesystem response, stream flow and ground waterflow aresim ultane- ously m odeled and a water exchange m echanism which can dealwith continuous flow and noncontinuous flow is designed to integrate the stream flow m odeland ground waterflow m odel. Mathem atically, the stream flow issim ulated by using Saint- Venant's continuouse-quation w ith stream storage neglected and Euler'sApproach isem ployed to generate solu- tions to the equations. The stream system is discretized by im posing a grid ofretangular cells that are assigned num ericalvalues for selected hydrologic conditions and hydraulic properties. Ground w aterflow m odel, w hich isin the form ofphreaticaquiferequation, is solved with finite difference m ethod ofirregular triangulated netw orks. To integrate the m odels, the stream nodes overlap the aquifernodes where stream spass. The volum e of w ater exchange betw een stream s and aquifers is sim ulated by using Darcy'slaw , w hich isbased on thedifference betw een stream stage and watertable in the cell, and theverticalhydraulicconductivity ofthestream bottom , and itreachesthem axi- m um degree when noncontinuous flow occurs beneath the stream bottom . It can be ex- pressed as: E= m in[γ·(Hr - H) ·η,Em ,qu] H < Hr γ·(Hr - H) H ≥Hr (1-3) where E(m /d) is the exchangerate, γ= kzm , k(m /d) and m (m ) are theverticalhydraulic conductivity and thethicknessofthepoorly perm eablestrataon the stream bed respective- ly, Hr(m ) is the stream stage, H (m ) is the ground w atertable, Em (m /d) is the m axi- m um perm eability capacity ofthepoorly perm eablestrata and qu= Q l·1 W, Q,land W are the stream flow , stream coordination and stream w idth respectively, and ηisa dim ension- less factorwhich isinversely proportionalto sand contentofthe stream w ater. Acasestudy showsthatthe integrated m odelcan accurately sim ulatestream flow and ground w ater m ovem ent and the calculated volum e of each stream section flow m atches properly w ith theobserved values. Thefactsprovethatthem odelresultsareaccurateand reliable.