地下水超抽引致地層下陷之三維解析研究

Three dimensional analytical study of landsubsidence due to groundwater overpumping

曾鈞敏(Chung-Min Tseng)

指導教授 ： 黃良雄

共同指導教授 ： 楊錦釧(Jinn-Chuang Yang)

國立臺灣大學/工學院/土木工程學研究所/博士(2009年)

https://doi.org/10.6342/NTU.2009.03142

摘要

台灣地層下陷問題嚴重，致相關研究發展，已成為防治地層下陷之重要決策方向之一，惟台灣地區地下水含水層地質錯縱複雜，致數值模擬耗時而無法即時提供決策者所需之答案。故本研究方向乃發展一個簡捷之解析模式，俾供使用者能快速求解地下水超抽引致之地層下陷量，以預為地下水資源管理及水土資源保育分析之重要工具。
根據相關文獻分析，了解目前對於水流耦合土體之模式尚未臻完整外，且多為數值解法，對於現實地層狀況諸多參數難以獲取及校定情況下，除模擬複雜困難外，模擬結果亦難以符合真實狀況。
本研究目的依據台灣地層下陷防治之現況需求為導向，除藉由多孔彈性理論推導出土體變形與水體流動之三維耦合地層下陷方程式外，並尋求合理簡化分析方法，再推導出土體變形量與水壓非耦合方程式，以迅速反應計算地層下陷量。並藉由抽水行為探討與案例說明，使模式更臻完善。
有關本研究成果可歸納臚列如下：
一、成功推導出三維水流與土體耦合方程式，並再接續完成含孔隙水壓力與土體位移項之非耦合控制方程式，便於解決複雜問題及做為大型計算程式撰寫之支援。
二、另研究成果於尋求一個可即時反應計算地層下陷量之簡化分析方法時，獲得一重大發現，即所得控制方程式型式與Stokes Flow相同，對於求解大區域三維之地層下陷問題係一突破。且相較於數值模擬可快速求得結果。另本研究除建立控制方程式外，對於含水層交界面之各類邊界條件，亦探討完成，極利於後續引申加值應用。
三、含水層內之點抽水源，由本研究證明可藉由流體力學中無雷諾數黏流之Stokeslet現象來描述。並利用邊界積分法再次佐證為Radial-Stokeslet。
四、地層內之水力傳導係數經由達西定律與本研究結果比對，顯現其非為定值，為距離之函數，其值將因土體位移而隨之改變，而改變值隨遠距離至抽水點之距離成反比現象。另因水力傳導係數值極小，乘上距離後，其改變值微小，惟已反應抽水後實際顆粒組成改變之物理意義。

關鍵字

地層下陷 ； 地下水超抽 ； 耦合 ； 非耦合 ； Stokes Flow ； Radial-Stokeslet

並列摘要

Besides regulating and reducing the pumping of groundwater, the Taiwan government has also been conducting related researches, such as developing and using new models to better understand potential landsubsidence areas. Because the simulation results do provide valuable trend information for the implementation of prevention measures, these models play vital roles in the decision-making process.
As abovementioned, not only these models which couple groundwater flow with soil body are not yet perfected, most models still use the time-consuming and highly complex numerical methods to find the solution. However, such method still cannot output realistic data because land conditions and other key parameters still cannot be quantified. As results, the research in this paper aims to develop a practical and easy-to-use model which can find the fast solution for the value of landsubsidence due to groundwater overpumping in large land area. Consequently, the model will become helpful in managing groundwater resources and conservation of land and water.
This research first coupled the 3D water flow with the soil control equation, and then deduces the complete uncoupled equation using only pore water pressure and soil displacement. Furthermore the research uses the compressibility of solids and obtains the simplified analytical method for calculating the value of land subsidence in real time. The results show that the control equation is very similar to Stokes flow, which means singularity of the flow with no Reynold’s Number can be introduced into the equation to find the condition of landsubsidence when groundwater is over-pumped. Validated by using the boundary integral method, water being pumped underground is a stokeslet. In the end, the research looks into confined and unconfined aquifers, analyzes and validates the model using different case studies, and demonstrates that the model is both practical and easy-to-use.
This research entails the following breakthroughs in providing solutions for 3-D land subsidence problem:
1.A model that finds the fast solution for normal land subsidence problem.
2.The proof for land subsidence control equation can be deduced to the form of Stokes’ flow
3.Water being pumped out of the aquifer can be regarded as a stokeslet in the laminar flow with no Reynold’s Number
4.Water conductivity in the ground, K, is not a constant. It changes as the displacement of soil body changes. As observed, the variation of K is inversely proportional to distance (r).

並列關鍵字

landsubsidence ； overpumping ； coupled ； uncoupled ； Stokes Flow ； Radial-Stokeslet

參考文獻

1.Batchelor G. K., “An Introduction to Fluid Dynamics” Cambridge Univ. Press, 1967.

2.Bear J. and Bachmat Y., “Introduction to Modeling of Transport Phenomena in Porous Media”, Kluwer Academic Publishers, 1990.

3.Bear J. and Corapcioglu M.Y., “Mathmatical Model for Regional Land Subsidence due to Pumping. I. Integrated Aquifer Subsidence Equations based on Vertical Displacement only “, Water Resources Research, VOL. 17, No. 4, pp.937-946, 1981a.

4.Bear J. and Corapcioglu M.Y., “Mathmatical Model for Regional Land Subsidence due to Pumping. II. Integrated Aquifer Subsidence Equations based on Vertical and Horizontal Displacement “, Water Resources Research, 17 pp947-958, 1981b.

5.Blake J. R., “A note on the image system for a stokeslet in a no-slip boundary”,Proc. Camb. Phil. Soc., 70, pp.303-310, 1971.