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研究生:蔡易豐
研究生(外文):Yi-Feng Tsai
論文名稱:變分法於擋土牆土壓力,淺基礎承載力及邊坡穩定分析等理論之研究
指導教授:吳賴雲
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:土木工程學研究所
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:188
中文關鍵詞:變分法最小位能原理虛左k
外文關鍵詞:variational methodminimum potential energyvirtua
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  • 被引用被引用:0
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摘要
本文分別以最小勢能法及虛平麮z推導出邊坡上滑動土體勢能及擋土牆土壓力之泛函數,再利用變分法求極值之方式求取邊坡及擋土牆背填土臨界破壞面之控制方程式,進而求取該破壞面所對應之安全因數、土壓力,而無需假設多組破壞面去進行冗長繁複之計算。本文亦利用基礎底部破壞土楔上水平力平衡之觀念求取淺基礎之極限承載力。其結果與其他理論相比顯示出本文建議方法之可行性。
在求取邊坡之破壞面時,基於控制方程式之特性,本文利用主動土楔、中央土楔、被動土楔間水平力平衡之關係,推導出邊坡安全因數及破壞面右端點水平座標之合理猜測值,使破壞面快速的被求取,此克服了以往因邊坡破壞面為非線性方程式,而引起數值收斂不易的問題,更以簡單之幾何範例說明了變分法求極值之充分條件,及所求之安全因數是為相對極小或絕對極小,而不需引用複雜的Jacobi condition,而切片間側力之引進,亦解釋了以往所求破壞面不合理之現象。本文亦利用退化型邊界積分方程式推導出黏土邊坡之安全因數,及破壞面左右端點水平座標之關係式,而大幅減少數值分析時未知數之個數,此外更證明緩坡時,坡趾破壞為黏土邊坡之臨界破壞面。在求取擋土牆土壓力時,本文所推導之方法可含誚h種土壓力理論,藉由切片間側力之適當選取可充分解釋Rankine theory、Coulomb theory 及Mononobe-Okabe theory,在考慮牆摩擦力遞減效應後,本文亦可以求取合理之被動土壓力,而無需像傳統方法般,去假設釵h破壞面,並進行冗長之計算。在求取淺基礎承載力方面,發現適當的界定中央土楔之範圍,利用其破壞土楔上水平力平衡之關係,亦可求得合理之極限承載力。
目錄
誌謝 一
摘要 二
目錄 四
表目錄 七
圖目錄 一二
一、緒論
1-1緣起 1
1-2研究內容 2
二、文獻回顧
2-1邊坡穩定分析 4
2-2擋土牆土壓力之求取 17
2-3極限承載力之求取 19
三、變分法數學模式之推導
3-1一般型式泛函數 22
3-2移動式邊界條件 24
3-3分數型泛函數 26
四、變分法於邊坡穩定分析中之研究
4-1前言 29
4-2公式推導 30
4-3數值程序 40
4-4數值範例 42
4-5結果及討論 45
4-6結論 52
五、退化型邊界積分方程式於黏土邊坡穩定分析之研究
5-1前言 54
5-2退化形邊界積分方程式之推導
5-2-1坡底破壞 54
5-2-2坡面-坡頂破壞 57
5-2-3坡底-坡面破壞 57
5-2-4坡面-坡面破壞 58
5-3數值分析 59
5-4數值範例 60
5-5結果與討論 61
5-6結論 64
六、變分法於擋土牆土壓力、淺基礎承載力及動態邊坡穩定分析之研究
6-1前言 65
6-2公式推導 66
6-2-1主動土壓力之研究 66
6-2-2被動土壓力之研究 71
6-3數值程序 72
6-4極限承載力因子之分析 74
6-5邊坡於動態載重下之穩定分析 75
6-6數值範例 77
6-7結果與討論 80
6-8結論 85
七、總結與建議
7-1總結 87
7-2建議 89
參考文獻 91
附表 100
附圖 124
附錄 165
符號說明 185
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