本研究為探討臺灣山岳隧道在不同地質情況下，所產生隧道變形之行為。本文採用PLAXIS 3D 2018軟體，以三維數值模擬(Three dimensional numerical simulation)隧道頂拱(Crown)變位分析，過程中選用隧道斷面、初期支撐(Primary support)與輪進長度皆盡可能與現地(In situ)施工相同，隧道周圍之介面依岩體差異採用不同的材料組合律。以岩體組合律(Rock Mass Constitute Law)-Hoek-Brown及Mohr-Coulomb兩種不同模式分析，探討施作岩栓與未施作相較之下，所帶來的成果與效益，將分析結果比對。由三維有限元素計算得知，地質材料之強弱對於同尺寸斷面隧道變位影響極大。分析顯示，在岩體等級愈弱且隧道斷面愈大，開挖後所產生之變位量則愈高。若忽略時間產生之潛變行為，隧道產生之最大變位量約在開挖處後方2至3倍隧道直徑距離處。而開挖面變位量約為隧道最大變位量之0.31至0.57之間，此值隨著岩體等級愈弱而愈高。開挖面前方之變位量比值隨著距離增加而遞減，在開挖面前方約1至1.5倍隧道直徑處，其比值已降至約0.1左右。本研究採用岩體組合律Hoek-Brown及Mohr-Coulomb兩種模式分析岩栓施作與否，其結果顯示在良好(Goog)、中等(Medium)岩體之中，其頂拱垂直變位差異並不明顯，而在碎弱(Poor)及大隧道斷面，此效果更加顯著，最大變位折減率可達5%左右。

The study was aimed to investigate the displacements in mountain tunnels in Taiwan under various geological conditions. The vertical displacements of crown arch were analyzed using the program, PLAXIS 3D 2018, for three-dimensional numerical simulation. Tunnel cross sections, primary supports and advancing length were selected as close to those of in-situ constructions. Various constitute laws were introduced according to the rock mass in the interfaces around the tunnels. Two rock mass constitute laws, Hoek-Brown and Mohr-Coulomb models, were used to study the results and effects of rock bolts in comparison to the lack of them. It is learned from the 3D finite element analysis that the strength of geological materials has significant influence on the displacements in tunnels of the same cross section. The analysis showed that the weaker the rock mass was and the larger the cross section was, the greater the displacements were produced behind tunnel excavation. The maximum displacement in tunnel was located 2 to 3 times of tunnel diameter behind the cutting face if the creep behavior generated over time was ignored. The displacement at the cutting face, however, fell between 31% and 57% of the maximum displacement and increased as the rock mass became weaker. The ratio for the displacement in front of the cutting face increased with distance. The ratio dropped to roughly 10% at 1 to 1.5 times of the tunnel diameter in front of the cutting face. The Hoek-Brown and Mohr-Coulomb models were used to analyze the effects of rock bolts and the absence of them. The results indicated that the vertical displacement of crown arch was not significantly different in good or medium rock mass. The effects, however, were significant in poor rock mass and tunnels with large cross section. The maximum displacement reduction ratio could reach as much as 5%.

摘　要 i
ABSTRACT iii
誌 謝 v
目　錄 vi
表目錄 ix
圖目錄 xi
第一章　緒論 1
1.1研究動機 1
1.2研究目的 2
1.3研究方法與流程 3
1.4論文架構範圍與限制 4
第二章　文獻回顧 5
2.1隧道變形行為影響 5
2.1.1隧道開挖之變形 5
2.1.2隧道塑性區影響 16
2.2岩石材料性質 17
2.2.1 岩石強度 18
第三章　分析案例工程概述 26
3.1 臺灣快速公路隧道簡介 26
3.1.1岩體分類原則 30
3.2山岳隧道開挖施工及支撐 33
3.3監測方法 33
第四章　數值分析方法與模式介紹 39
4.1 PLAXIS 3D程式簡介 39
4.2 PLAXIS之大地工程應用 41
4.2 有限元素分析方法 42
4.3土壤模式之應用 43
4.3.1 Linear-elastic應力-應變關係 43
4.3.2 Mohr-Coulomb模式 44
4.3.3 Hoek-Brown模式 48
4.3.4 Mohr-Coulomb與Hoek-Brown之參數轉換 57
4.4山岳隧道分析流程概述 59
第五章　山岳隧道開挖分析及探討 69
5.1材料參數選用 69
5.1.1 Mohr-Coulomb模式材料參數 70
5.1.2 Hoek-Brown模式材料參數 71
5.1.3隧道襯砌、岩栓、輪進、網格參數 72
5.2隧道頂拱垂直變位量 75
5.3 Mohr-Coulomb與Hoek-Brown分析比較 84
5.4施作岩栓之效益分析 87
5.5 正規化後之隧道變位量分析 90
5.6 與文獻資料-Unlu and Gercek公式比對 97
5.6.1 良好岩體 98
5.6.2 中等岩體 99
5.6.3 碎弱岩體 101
第六章　結論與建議 104
6.1結論 105
6.2建議 107
參考文獻 108

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