L型邊界且為非均質非等向水層的半解析解

Abstract

瞭解地下水層的水位空間分佈與水文地質參數，是評估地下水資源的開發量或整治地下水污染的重要課題。以新竹含水層為案例，此含水層被斷層及河流圍繞，其形狀近似為L形。本研究係建立數學模型，在定水頭邊界(河流)及不透水邊界(斷層)侷限下的L形含水層，模擬地下水經多口井抽水後的暫態水力水頭分佈，此模型將考慮含水層的異質性和非等向性。首先透過區域分割法建立數學模型，將該含水層分割成兩個子區域。此模式考慮每個子區域各有不同的水力傳導係數，且各區域含水層皆具非等向性。藉由分離變數法及考慮子區域間水位與流通量的連續條件，推導出Laplace域的半解析解。所求得的解用來模擬L形含水層在抽水下的暫態水力水頭分佈；若L形含水層受汙染時，此解可提供地下水流況資料，協助規劃地下水汙染物控制。此半解析解可更進一步描述梯形含水層經抽水後的洩降分佈，本解亦可作為數值模式的驗核工具，分析數值模式在L形凹角邊界處計算上可能產生的水位誤差。

Understanding groundwater flow distribution is important for evaluating groundwater resource and dealing with groundwater pollution problems. This study considers an aquifer bounded by faults and rivers in Hsinchu, Taiwan, and the aquifer can be approximately to have an L-shaped domain. A mathematical model is developed to describe the transient groundwater flow due to multiple pumping in an anisotropic, heterogeneous aquifer with an L-shaped domain with impermeable boundary and constant-head boundary representing the fault and the river, respectively. Method of domain decomposition is used to handle such an irregular boundary by dividing the aquifer into two sub-regions with different hydraulic conductivities. Taking into account the continuity conditions of hydraulic head and flux at the boundary between two sub-regions, the solution of the model in Laplace domain is then derived by the method of separation of variables. The semi-analytical solution can be used to assess the groundwater resources in transient pumping effect and provide flow information for pump-and-treat design if the aquifer has contamination. The solution can also be applied to delineate the hydraulic head distributions in aquifers with trapezoid boundary and to verify the numerical solutions which might give inaccurate results at the corner of the irregular boundary.