區域性地下水超抽導致地層下陷模式之發展與應用

Abstract

本研究之目的即在於發展並應用一套準確且高效率的地層下陷預測數值計算模式，以作為利用與管理地下水資源的重要工具。本研究首先根據飽和地下水及土體變形皆三維之耦合地層下陷控制方程式的量階分析結果，提出當地下水流流況為類似水平流或垂直流時，適用土體變形一維之非耦合地層下陷理論的重要結論。依據此結論，本研究以飽和地下水流方程式三維，及土體變形方程式一維之非耦合模式，模擬區域性地下水超抽引致之地層下陷，再結合以三維耦合模式，計算局部嚴重地層下陷區域。 對於一維非耦合模式之地下水流計算，提出分層三維水流之概念。亦即首先依據土壤之導水性質，將土體作垂直分層或虛擬分層，在假設每個土層之孔隙水壓於垂向深度上皆為二次多項式函數分布下，引用分層垂向積分技巧，層與層間之垂直介面邊界，再以孔隙水壓及水流通量連續之條件加以連接。結果顯示，本研究提出之分層三維水流概念，不但能模擬阻水層與含水層之水流分別為垂直流以及水平流的擬三維水流現象，更因為沒有傳統擬三維水流概念之限制，也可以模擬出僅能使用三維水流模式才能模擬之三維水流現象，如抽水井附近或複雜土層分布之地下水流況，並且能保有傳統擬三維水流概念比三維水流模式計算效率高之特點。 三維耦合地層下陷模式之建立亦引用分層垂向積分概念，並且假設孔隙水壓及水平與垂向位移，在每個土層之垂向深度方向上皆為二次多項式函數分布。而層與層間之介面邊界，與一維非耦合模式相同，除了需滿足流體之孔隙水壓與水流通量連續外，因為多加入土體靜力平衡方程式之求解，所以亦需滿足土體之位移與有效應力連續。此外，因為土壤之參數可能差異甚大，為了避免可能發生之計算不穩定，研究中以無因次化控制方程式來建立數值模式。 研究中，一維非耦合與三維耦合地層下陷模式，皆引用具有局部解析解以及無條件穩定收斂，並可以在卡式座標下處理不規則邊界等多項特點的有限解析法來建立。模式驗證完後，分別將其應用於濁水溪沖積扇之區域性地層下陷模擬，以及雲林縣口湖會水附近嚴重下陷地區之三維土體變形計算。模擬結果顯示，分層地下水位與地層下陷量之模擬結果，其量階與趨勢大致與實測資料相吻合。

In this study an accurate and efficient landsubsidence model due to groundwater overpumping which is a basic tool for application and management of groundwater resources has been developed and applied to practical case. First of all the analysis of order of magnitude for governing equations of three-dimensional coupled landsubsidence model shows that one-dimensional uncouple landsubsidence model is applicable when the flow pattern of groundwater is approximately horizontal or vertical. Based on the results, the concept of one-dimensional uncoupled model for modeling regional landsubsidence is proposed. The local severe landsubsidence can be zoomed and solved with a combination of three-dimensional coupled model. In the one-dimensional uncoupled landsubsidence model, the concept of layered three-dimensional groundwater flow simulation is proposed. The governing equation for every layer is vertically integrated with an assumption that the pore pressure in the vertical direction is assumed to satisfy quadratic polynomial function. At the interface between two layers the continuity of pore pressure and flux has to be satisfied. The layered three-dimensional flow concept is able to efficiently simulate the fully three-dimensional flow pattern and the quasi three-dimensional flow pattern in which the groundwater flow of the aquifers and aquitard are horizontal and vertical, respectively. The proposed three-dimensional coupled landsubsidence model is developed by using the technique of vertical integration as well. The pore pressure and displacements in the horizontal and vertical directions for every layer are assumed to satisfy quadratic polynomial function. Like the one-dimensional uncoupled model, at the interface between two layers the continuity not only of pore pressure and flux but also of displacement and stress has to be satisfied. In addition, to avoid the computational instability due to the large differences of soil parameters, the governing equations are non-dimensionalized. Both one-dimensional uncoupled and three-dimensional coupled models are developed by using finite analytic method which is locally analytic and unconditionally stable and can deal with irregular boundary problems with the Cartesian coordinate system. After the two models are verified, they are applied to Tzuo-Suei River Basin for regional simulation and Kou-Hu for local modeling, respectively. The simulated results agree with the measured data quite well.