考量地層下陷之地下水管理模式建立與應用

Abstract

地下水為相當重要且可靠的水資源，然而地下水超抽將導致地層下陷災害之發生，因此如何合理地利用地下水資源兼且避免地層下陷危害，實為重要研究課題之一。地下水管理模式已廣泛地應用於地下水資源開發或汙染整治之規劃中，然一般地下水管理模式常僅以地下水位為限制條件來推求最大可抽水量(Optimal Total Pumpage)，鮮少考慮地層下陷之影響，因此可能高估最大可抽水量，導致非預期地層下陷災害之發生。本研究之主要目的即在建立可定量考量地層下陷影響之地下水管理模式。 本研究首先以Simulation-Optimization方法為基礎，分別利用響應矩陣法與一維土體壓密方程式建立水頭洩降量與地層下陷量之限制式，以發展同時考量水頭洩降與地層下陷影響之定率地下水管理模式，並利用二進位變數將屬於Non-smooth Optimization之管理模式轉換為混合整數線性規劃之型態以增進求解之效率。 在定率管理模式建立完成後，本研究進一步考慮地質參數(水力傳導係數與拉梅常數)空間變異性之影響，首先利用LHS (Latin Hypercubic Sampling)與蒙地卡羅模擬分析單位響應係數之不確定性，再以一階變異數分析法(First Order Variance Estimation, FOVE)推導水頭洩降量與地層下陷量之統計特性與各抽水井抽水量之關係式，最後以Chance Constrained Programming (CCP)建立考慮地質參數不確定性，並以水頭洩降量與地層下陷量需求可靠度(Compliance Reliability)為決策考量之序率地下水管理模式。 模式建置完成後，本研究以虛擬之案例驗證其正確性及適用性。定率模式驗證結果顯示無論是在穩態、動態或多層地下水系統之條件，定率模式皆能提供在滿足水頭洩降量與地層下陷量限制條件下，地下水系統之最大可抽水量與各井抽水量最佳之時空分布，且當管理問題為穩態時，模式更具有決定抽水井設計最大抽水能力(Maximum Pumping Capacity)與最佳設井位置之功能。 在序率管理模式驗證方面，本研究蒐集過往地質參數相關之調查資料，共設計了五個不同方案以期能涵蓋地質參數可能之變異程度。驗證結果顯示在地質參數變異程度不高時，以一階變異數分析法計算地層下陷量統計特性能得相當良好之結果，而無論地質參數變異程度如何，序率模式計算之最大可抽水量皆能滿足需求可靠度之限制，且驗證過程中亦顯示Active Constraints會同時發生在水頭洩降量與地層下陷量可靠度之限制式，顯示若不考慮地層下陷之影響而僅以水頭洩降為限制條件，可能會高估最大可抽水量。 模式驗證後，本研究將定率與序率管理模式應用於台灣西部之濁水溪沖積扇地區，並依據政策、地層下陷概況與地下水需求量擬訂不同之地下水管理方案，以求得不同方案下之最大可抽水量。應用結果顯示，無論有無考慮參數不確定性之影響，濁水溪沖積扇地區並無法同時滿足地下水需求量以及避免或減緩地層下陷危害發生之目標，而其亦正面臨地下水嚴重超抽導致地層下陷災害嚴重之情形，由此顯示本研究發展之模式能正確反應濁水溪沖積扇地下水系統之特徵以及模式於實務應用之價值。

Groundwater is one of the major water resources in the world. Today, many groundwater aquifer systems are over-developed resulting in serious hazards of land subsidence. Although groundwater management models have been extensively applied to establish the optimal groundwater development or remediation strategies, only a few studies explicitly considered the land subsidence effect. This study presents a groundwater management model explicitly considering land subsidence. From the simulation-optimization approach, the response matrix technique and one-dimensional consolidation equation are adopted to develop a deterministic management model. Due to the phenomenon that soil is hardly swelled, the nature of groundwater management considering subsidence is a non-smooth optimization problem. To improve the efficiency of solution technique, the non-smooth optimization is transferred into mixed-integer linear programming (MILP) by introducing the binary variables. By Latin Hypercubic Sampling (LHS) technique, along with numerical subsurface flow simulation, statistical features of unit response coefficients due to random hydrogeologic parameters, including hydraulic conductivity (K) and Lame constants (μ and λ), are quantified. The first-order-variance-estimation (FOVE) method is adopted to analyze the uncertainties of drawdown and land subsidence based on which the concept of chance-constrained programming (CCP) is applied to transfer the original deterministic management model into its stochastic form. The stochastic management model enables the determination of optimal total pumpage subject to the constraints that drawdown and land subsidence do not exceed the allowable values with stipulated compliance reliability. Hypothetical examples are utilized to verify the developed management model. The verification is using numerical model simulation by trial-and-error. The results indicate that the deterministic model can provide accurate optimal total pumpage in steady, transient state or multi-layer aquifer system. Besides, the deterministic model also enables the determination of maximum pumping capacity and optimal allocation of pumping wells. A hypothetical example is utilized to demonstrate the applicability of the stochastic model to five scenarios in which various levels of parameter uncertainty are considered. The results indicate that joint consideration of drawdown and land subsidence is essential, and the proposed stochastic management model can be generally applied for regional groundwater resources management in conjunction with controlling land subsidence. After the proposed management model have been verified, it is applied to Choshui alluvial fan located in mid-west Taiwan which is facing serious land subsidence hazard due to groundwater over-pumping. Several management strategies have been considered based on the policy, groundwater demand, and profile of land subsidence. The optimal solutions to all management strategies considered, whether deterministically or stochastically, indicate that the groundwater demand and land subsidence controlling cannot be satisfied simultaneously. The application considers present situation of Choshui alluvial fan which shows that the proposed management model is applicable to real world problems.