臺灣博碩士論文加值系統

本研究利用Trefftz配點法求解飽和土層之地下水滲流問題，研究方法採用不須建置網格且不須對邊界進行積分的Trefftz配點法，該法利用近似解表示成線性函數組合使其滿足控制方程式之方式進而求解，與傳統數值方法相比Trefftz配點法求解精度高，且對於不規則邊界問題、不連續邊界問題與對角邊邊界問題的求解較傳統數值方法更具優勢。為解決Trefftz配點法僅應用於單連通問題之限制，本研究另採用多源點Trefftz配點法透過選用多個源點處理複雜之多連通問題，此外本研究利用區域分解法搭配Trefftz配點法進行互層土壤滲流問題之求解。為使本研究發展之模式更適切的模擬真實工程問題，本研究進一步利用Trefftz配點法求解土壩地下水滲流問題，考慮均質土壩、均質土壩含排水孔洞、互層土壩等問題進行分析。結果顯示，本研究以Trefftz配點法所開發之數值模式可分析均質與互層土層地下水滲流問題並獲得良好的應用成果。

This study presents the the numerical solutions for seepage flow in layered soil using the Trefftz collocation method. The Trefftz collocation method is a meshless numerical method with very high accuracy for solving boundary value problems where approximate solutions are expressed as a linear combination of functions automatically satisfy governing equations. To deal with complicated problems for multiply connected domain, the generalized multiple source point boundary collocation Trefftz method which allows many source points in the Trefftz formulation was adopted. In addition, the domain decomposition method which decomposes the problem domain into several simply connected subdomains and to use the Trefftz method in each one was also adopted to solve the seepage flow in layered soil. The validity of of the proposed method is established by conducting several numerical examples in a simply connected domain and a doubly connected domain. Application examples were also carried out using the proposed numerical model. Furthermore, the seepage problems of a vertically layered earth dam with the phreatic surface were also studied. The results revealed that the proposed method can not only obtain numerical solutions for seepage flow in layered soil but also can achieve very high accuracy result in numerical solutions to that of the conventional numerical method.

摘要 I
ABSTRACT II
圖目次 V
表目次 VII
一、緒論 1
1-1前言 1
1-2研究目的與動機 1
1-3研究內容 2
二、文獻回顧 4
2-1地下水滲流數值方法之發展與研究 4
2-2Trefftz配點法之發展與應用 8
三、飽和土層之地下水滲流理論介紹 10
3-1飽和土層地下水之定義與介紹 10
3-2達西定律 12
3-2.1白努利定律 12
3-2.2達西定律 13
3-3飽和土壤地下水滲流之控制方程式 14
四、飽和土層地下水滲流理論推導 20
4-1二維Trefftz配點法基底推導 20
4-2二維Trefftz配點法 27
4-2.1Trefftz配點法介紹 27
4-2.2特徵長度 33
4-2.3Trefftz法之收斂性分析 38
4-2.4Trefftz配點法求解滲流問題流程 39
4-3自由液面問題 45
4-3.1自由液面描述 45
4-3.2自由液面求解流程 46
4-4互層問題 53
4-4.1互層問題描述 53
4-4-2區域分解法 54
五、飽和土層滲流數值模式之驗證 59
5-1驗證案例一(規則型單連通問題) 59
5-2驗證案例二(規則型單連通問題) 63
5-3驗證案例三(規則型單連通問題) 66
5-4驗證案例四(不規則型單連通問題) 70
5-5驗證案例五(不規則型雙連通問題) 74
5-6驗證案例六(自由液面問題) 78
5-7驗證案例七(互層問題) 82
六、飽和土層滲流問題應用案例 86
6-1應用案例一 86
6-2應用案例二 90
6-3應用案例三 94
6-4應用案例四 98
七、結論與建議 102
7-1結論 102
7-2建議 103
參考文獻 104

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