考量預壓密之地下水管理模式之建立與應用

Abstract

地下水超抽將直接導致地層下陷災害之發生，然一般地下水管理模式常僅以水頭洩降為考量因子以推求最佳抽水量，而少數研究雖有考慮地層下陷之影響並納入地下水管理模式之限制式中，但亦未定量分析土層因預壓密狀態之不同而對地下水管理造成之影響。 本研究首先依據土壤預壓密之概念，結合可同時考量彈性(elastic)與非彈性(inelastic)壓密行為之一維土體壓密方程式以及響應矩陣法，建立以最大抽水量為目標，以地層下陷量為限制條件並可考慮土壤預壓密影響之地下水管理模式。此外本研究進一步藉由導入二進位變數之技巧，將原屬於nonsmooth規劃問題之管理模式轉換為混合整數線性規劃(MILP)之型態，以增加管理模式求解之效率。 待模式建立後，本研究首先利用測試案例說明所建立模式之正確性，再利用虛擬之應用案例分析土壤預壓密對地下水管理之影響。應用結果顯示若地下水管理模式僅間接以預壓密水頭做為限制條件以控制地層下陷，則優選之最佳抽水量僅能避免土層發生非彈性壓密，仍可能會有高估抽水量之情形進而發生預期外之地層下陷災害；另外若直接以地層下陷量做為限制條件但忽略土壤預壓密之狀態，則所優選之最佳抽水量將可能有過於低估之情形，且當初始地下水位與預壓密水頭之差值越大時，最佳抽水量低估之情形將越顯著。 於模式測試後，本研究亦將所發展之管理模式應用於台灣西部之濁水溪沖積扇地區，並依據現行政策、地層下陷概況與高鐵路線分布等擬定不同之地下水管理方案，以推求不同方案下濁水溪沖積扇之最大可抽水量。應用結果顯示，本研究所設定之任何方案皆無法使最大可抽水量滿足濁水溪沖積扇地區現行之地下水需求量，由此顯示濁水溪沖積扇目前仍面臨地下水超抽之問題，而濁水溪沖積扇案例之分析成果亦顯示本研究所發展模式於實務應用之價值。

Groundwater overpumping will cause the serious hazards of land subsidence. Although the groundwater management models have been widely applied to obtain optimal pumping strategies, only a few studies explicitly incorporated the land subsidence into model’s constraints. However, the presence of preconsolidation and its influence on groundwater management had not been considered yet. In this study, to quantify the relationship between land subsidence and drawdown, the one dimensional consolidation equation is adopted which accounts for the elastic and inelastic soil consolidation simultaneously according to the preconsolidation head and drawdown. From the simulation-optimization approach, based on the response matrix technique along with one dimensional consolidation equation, a groundwater quantity management model is developed which enables the determination of maximum total pumpage subject that the land subsidence do not exceed the allowable value. The nature of developed management model belongs to non-smooth optimization problem. In order to improve the efficiency of solution technique, the non-smooth optimization is transferred into mixed-integer linear programming (MILP) by introducing the binary variables. Hypothetical examples are utilized to demonstrate the influence of preconsolidation on groundwater management after the developed management model is verified. The results indicate that the land subsidence should be explicitly incorporated into model’s constraints, otherwise the optimal total pumpage might be over-estimated. Moreover, if the presence of preconsolidation is ignored, the optimal total pumpage might be under-estimated, especially when the differences in heads between initial and preconsolidation become significantly. The proposed management model being verified 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 scenarios have been considered based on the policy, groundwater demand, locations of high speed rails, and profile of land subsidence. The application results show that the maximum total pumpage to all management scenarios considered could not achieve the annual groundwater demands while reducing the land subsidence simultaneously, which indicate that the Chuoshui River alluvial fan is still facing serious problem for groundwater overpumping.