以應力轉換法模擬橫向等向性岩石之力學行為

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葉家宏(Chia-hung Yeh) 查詢紙本館藏

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土木工程學系

論文名稱

以應力轉換法模擬橫向等向性岩石之力學行為
(Using the methodology of stress transformation to simulate mechanical behavior of the transversely isotropic rock)

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摘要(中)

過去在探討橫向等向性岩石力學行為，無論在試驗或是一般數值模擬，針對橫向等向性岩石方面，取樣後之岩石條件會不完全一致，使得不能確保在不同傾角是相同的岩石情況下來探討橫向等向性岩石力學行為，所得到的結果會是很令人質疑的，因此本研究為了克服過去在取樣後之岩石條件會不完全一致的問題，係以應力莫爾圓的觀念及應力轉換公式，來建立一套應力轉換法。應力轉換法利用FLAC有限差分程式來進行數值模擬，只需要相同模型的邊界上，來改變施加於模型邊界上正向力及剪力的應力增量，即可模擬各種傾角下的三軸試驗之過程，由於應力轉換法能夠達到模擬各種傾角下三軸試驗之過程是在相同岩石情況的目的，因此利用此方法來探討橫向等向性岩石力學行為的結果就會令人信服，所以本研究建立應力轉換法能夠提供另一種方法來探討橫向等向性岩石力學行為的研究。
本研究以應力轉換法模擬橫向等向性岩石之三軸試驗結果來做分析，並觀察多組不同橫向等向性岩石材料之模擬結果，進而認為橫向等向性岩石之性質以及岩塊含量是影響橫向等向性岩石整體工程性質的重要參數，並以合理的推估來建立有效預測各影響因素相互間的關係，最後本研究建立一套橫向等向性岩石力學行為預測模式，僅需要了解橫向等向性岩石之性質以及橫向等向性岩石內之岩塊含量，即可預測橫向等向性岩石力學行為，如此可以大幅減少試驗以及數值分析之時間，對於了解橫向等向性岩石力學行為的效率，必定大有助益。

摘要(英)

This research establishes a methodology of stress transformation by the concept of Mohr’’s stress circle as well as the formula of stress transformation. This method can overcome the problem in the past research, which the rock condition will not be selfsame after taking samples in transversely isotropic rock. The methodology of the stress transformation makes use of numerical program (FLAC) to carry on the numerical simulation, that only needs to change stress increment of normal stress and shear stress on boundaries, which can create a series of triaxial tests in the same numerical model to investigate the mechanical properties of those transversely isotropic rocks in different types of dip angle formation. Therefore, it is convinced to make use of this method to probe into the result of mechanical behavior of the transversely isotropic rock.
This research utilizes the methodology of stress transformation, and observes the numerical results of different transversely isotropic rock materials. Furthermore, the rock material properties and volumetric fraction of block are important parameters to estimate mechanical behavior of transversely isotropic rock, and used to establish the prediction model of the mechanical behavior of transversely isotropic rock. The results show that the prediction agrees with numerical results, which can largely reduce the experiment as well as the numerical analysis, showing good improvement in prediction of mechanical behavior of transversely isotropic rock.

關鍵字(中)

★ 橫向等向性岩石
★ 岩塊含量
★ 破壞準則
★ FLAC
★ 應力轉換法

關鍵字(英)

★ failure criterion
★ FLAC
★ transversely isotropic rock
★ methodology of stress transformation
★ volumetric fraction

論文目次

摘要.....................................................Ⅰ
Abstract.................................................Ⅱ
誌謝.....................................................Ⅲ
目錄.....................................................Ⅳ
圖目錄...................................................Ⅷ
表目錄..................................................ＸI
第一章敘論...............................................1
1.1 前言..................................................1
1.2 研究動機與目的........................................1
1.3 研究內容..............................................3
1.4 論文架構..............................................3
第二章文獻回顧...........................................4
2.1 橫向等向性岩石之定義..................................4
2.2 橫向等向性岩石之破壞模態..............................5
2.3 橫向等向性岩石之破壞準則.............................11
2.3.1 Jaeger (1960)破壞準則..............................12
2.3.2 McLamore and Gray (1967)破壞準則...................15
2.3.3 Hoek-Brown (1980)破壞準則..........................17
2.3.4 Tien and kuo (2001)破壞準則........................21
2.3.5 模式驗證...........................................30
2.4 微觀力學預測模式.....................................33
2.4.1 Voigt(1889)、Reuss(1929)模式.......................33
2.5 FLAC程式簡介.........................................34
2.5.1 FLAC程式之運算程序.................................34
2.5.2 組合律模式.........................................35
2.6 橫向等向性岩石數值模擬相關研究.......................36
2.6.1 網格旋轉法.........................................38
2.6.2 探討網格旋轉法之適用性.............................39
第三章應力轉換法........................................44
3.1 應力轉換法之發展.....................................44
3.2 應力轉換法及其應用...................................46
3.2.1 推導應力轉換法之應力方程式.........................49
3.2.2 範例驗證...........................................52
3.2.3 求取應變方面.......................................58
3.3 探討應力轉換法之適用性...............................60
3.4 小結.................................................63
第四章數值分析及結果....................................64
4.1 數值模擬架構之說明...................................64
4.2 參數研究.............................................66
4.2.1 數值模擬流程.......................................66
4.2.2 數值模型...........................................68
4.2.3 數值模擬結果.......................................71
4.3 橫向等向性岩石之預測模式.............................80
4.3.1 預測模式參數之決定.................................80
4.3.2 預測結果比較.......................................88
第五章結論與建議........................................97
5.1 結論.................................................97
5.2 建議.................................................99
參考文獻................................................100
附錄A ..................................................104
附錄B ..................................................109

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指導教授

田永銘(Yung-ming Tien)

審核日期

2008-1-21

推文