Three dimensional analytical study of landsubsidence due to groundwater overpumping

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。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。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。關本研究成果可歸納臚列如下：、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。、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。、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。、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。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. s 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.his 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.his research entails the following breakthroughs in providing solutions for 3-D land subsidence problem:.A model that finds the fast solution for normal land subsidence problem..The proof for land subsidence control equation can be deduced to the form of Stokes’ flow.Water being pumped out of the aquifer can be regarded as a stokeslet in the laminar flow with no Reynold’s Number.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).誌謝 Ⅰ文摘要 ⅡBSTRACT Ⅳ錄 Ⅵ目錄 Ⅷ圖目錄 ⅩⅠ號說明 ⅩⅡ一章 導論 1.1 前言 1.2 研究動機與目的 3.3 文獻回顧 4.4 研究方法與步驟 8.5 章節介紹 10二章 三維耦合抽水引致地層下陷模式之建立 11.1 以多孔彈性介質理論建立地層下陷基本方程式 11.2 三維耦合地層下陷控制方程式推導 13.2.1 質量守恆控制方程式推導 13.2.2 動量守恆控制方程式推導 14.2.3三維耦合地層下陷控制方程式彙整 15三章 三維非耦合抽水引致地層下陷模式之建立 17.1 三維非耦合地層下陷控制方程式推導 17.2 非耦合地層下陷控制方程式與Stokes’Flow型式相似性探討19.3 多孔彈性介質控制方程式解之充分邊界條件 20四章 三維非耦合抽水引致地層下陷之點抽水源 24.1點抽水源為何不是Mass Source 24.2 點抽水源為什麼是Radial-Stokeslet 27.3 抽水量與點抽水源強度之關係 30五章 抽水引致之地層下陷問題案例及解析 33.1 模式應用之基本條件 33.1.1 應用映射方法求解問題及探討 33.1.2 座標轉換及已知係數之建置 38.2 應用案例說明 41.2.1非拘限無限深含水層瞬時點源抽水案例 41.2.2拘限無限深含水層瞬時點源抽水案例 42.2.3非拘限有限深含水層瞬時點源抽水案例(近似解) 44.2.4拘限有限深含水層瞬時點源抽水案例(近似解) 46.3 結果分析探討 49六章 結論與建議 50.1 結論 50.2 建議 52考文獻 53錄A 質量守恆方程式之推導 89錄B 動量守恆方程式之推導 96錄C 以Lamb理論推導流速與壓力之相關式 101錄D 點抽水源與Stokeslet關係 104錄E 以邊界積分法推導位移場與壓力場 107錄F 對靜止無滑動邊界之映射式推導 111者簡歷 12