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系統識別號 U0026-0812200915321021
論文名稱(中文) 利用邊界元素法探討異向性岩石於模態III型之應力強度因子
論文名稱(英文) Stress Intensity Factors of Tearing Fracture (Mode III) on Anisotropic Rocks Using Boundary Element Method
校院名稱 成功大學
系所名稱(中) 資源工程學系碩博士班
系所名稱(英) Department of Resources Engineering
學年度 97
學期 2
出版年 98
研究生(中文) 涂峻嘉
研究生(英文) Jiun-jia Tu
電子信箱 n4696406@ccmail.ncku.edu.tw
學號 n4696406
學位類別 碩士
語文別 中文
論文頁數 101頁
口試委員 口試委員-李德河
口試委員-廖志中
指導教授-陳昭旭
口試委員-陳家豪
中文關鍵字 對偶邊界元素法  單域邊界元素法  應力強度因子  裂縫前緣  異向性岩石  橫向等向性 
英文關鍵字 anisotropy rock  stress intensity factor (SIF)  crack front  transversely isotropy  dual-BEM  single-domain BEM 
學科別分類
中文摘要 在岩石破壞力學的工程問題中,數值技術已成為不可或缺的工具。而許多的研究也著重在發展新的數值方法來求得應力強度因子,加上現實中具有多變的工程條件,使得發展一套新的數值方法或替代技術能夠有效以及準確的解決較具複雜的問題。而現今學者研究各種試驗方法中,目前較多圍繞在模態I、II型和I+II複合型裂縫破壞展開,對於模態III型裂縫破壞的研究還處於初級階段,僅有少量的文獻報導。但是岩體地下工程和邊坡工程中往往會發生模態III型加載下的岩石破壞,故發展模態III型破壞之應力強度因子的研究有利於暸解岩石破壞行為。
本研究提出一套單域邊界元素法(或稱對偶邊界元素法),結合異向性線彈性理論,藉以Fortran語言撰寫成程式,針對異向性岩石於模態III型之破壞,探討岩石中裂縫前緣之應力強度因子。主要討論橫向等向性材料在不同裂縫長度、材料寬度、材料層面傾角以及上述情況於不同之異向性程度的影響下,其應力強度因子KI、KII、KIII的變化,並以KIII值做進一步的討論。
先利用加載裂縫位於中央的試體,發現與加載方向垂直以及平行的兩裂縫前緣,其應力強度因子KII、KIII的分佈為一拋物線。而加載裂縫位於邊緣的試體,發現當裂縫開裂的越深,或是長寬比較小的試體其應力強度因子的值(KII、KIII)較高,而結果也證明應力強度因子是一種抵抗的能力,越容易達到破壞的試體其應力強度因子越大。
最後,本研究提供各種試驗方法,其特色在於將模態I型及II型的破壞控制住,並且KI、KII值亦趨近於零,以達到接近純模態III型破壞之試驗,可供學者在進行III型試驗中做參考。
英文摘要 Numerical technique in rock fracture mechanics have become indispensable tools for solving all kinds of science and engineering problems. Extensive research has been carried out for the development of new numerical methods to determine the stress intensity factors (SIFs). Due to the varied engineering conditions in the practical area, it is imperative to develop new numerical methods or to explore alternative techniques for the purpose of solving the complicated problems and to improve the efficiency and accuracy of the existing or new numerical methods.

In recent years, scholars investigate methods of the various tests and focus on the mode-I, mode-II and mixed-mode I-II. The mode III fracture is still in the initial stage. However, the rock mass often occur in mode-III fracture under load in underground engineering and slope engineering. Thus, the development of mode-III SIF will help to study the behavior of rock fracture.

This thesis presents the dual boundary element methods (dual-BEM) or single-domain BEM to analyze anisotropic rocks in mode-III fracture and adopts the Fortran language to develop the numerical program. For anisotropic rocks of mode-III fracture, the SIF along the crack front can be discussed. The aim of these discussions are to compare the variation of SIFs (KI, KII and KIII) for different crack length, material width, material inclined angle and the anisotropic influence in transversely isotropic material. Further, the value of KIII can be discussed.

The results show that the SIFs (KII, KIII) is a parabolic distribution when the loading directs the vertical and parallel crack fronts crack in the rocks within a center crack. For the edge crack, the higher values of SIFs (KII, KIII) occur at the deeper crack or smaller ratios of length and width. The results also proved that the SIF is an ability to resist and the greater SIF occur at the easier arrives failure.

This study provides three-dimensional test method, and its characteristics is that control mode-I and mode-II fractures (i.e. KI, KII near to zero), then approximate the pure mode-III fracture test. Finally, this study can provide the reference for the mode-III test.
論文目次 目錄
摘要 I
英文摘要 III
目錄 V
表目錄 VIII
圖目錄 IX
符號表 XIII

第一章 緒論 1
1.1 研究動機與目的 1
1.2 研究內容 3
第二章 文獻回顧 5
2.1 破壞力學發展 5
2.2邊界元素法 11
2.3 應力強度因子及破壞韌度研究回顧 15
2.4 III型破壞韌度相關試驗 20
2.4.1 邊緣裂縫扭力試驗(edge crack torsion, ECT) 20
2.4.2 直接扭轉式載重系統試驗(direct torsion, DT) 23
2.4.3 反裂式平板彎曲試驗(Anti-Clastic Plate Bending, ACPB) 25
2.4.4 III型破裂韌度試驗比較 27
2.5 裂縫間距、裂縫長度、厚度等尺寸關係之影響 28
2.6 小結 30
第三章 理論模式 32
3.1 材料座標系統與基本方程式 32
3.2 三維異向彈性之格林函數(Green’s Functions) 35
3.3 邊界積分方程式 36
3.4 數值離散 38
3.5 應力強度因子 42
3.6 數值驗證 43
3.6.1 驗證異向性材料 44
3.6.2 驗證模態III型 47
3.7 小結 62
第四章 案例分析 65
4.1 中央裂縫的應力強度因子 65
4.2 邊緣裂縫的應力強度因子 68
4.2.1 裂縫長度(a)對應力強度因子的影響 68
4.2.2 長寬比(B/W)對應力強度因子的影響 72
4.2.3 材料層面傾角(y , β)對應力強度因子的影響 77
4.3 小結 82
第五章 結論與建議 85
5.1結論 85
5.2建議 87
參考文獻 88
附錄A 98


















表目錄
表2.1量測應力強度因子的各種實驗型態 16
表2.2花崗岩、大理石之III型斷裂韌度 22
表2.3 ACPB試驗數據 23
表2.4 III型試驗方式優缺點比較 24
表3.1 A點於於不同層面角度(b , y )的位移量 42
表3.2內部點於不同深度發生位移與應力的情形(b = 60°, y = 45°) 42
表3.3 C點於於不同層面角度(b , y )的位移量 43
表3.4當S = 12mm裂縫前緣的正規化應力強度因子 49
表3.5當S = 18mm裂縫前緣的正規化應力強度因子 51
表3.6當d = 30mm裂縫前緣的正規化應力強度因子 54
表3.7當d = 60mm裂縫前緣的正規化應力強度因子 56
表3.8當a = 30mm裂縫前緣的正規化應力強度因子 58
表3.9當a = 36mm裂縫前緣的正規化應力強度因子 60
表3.10裂縫中央正規化應力強度因子的比較 63





圖目錄
圖1.1研究流程圖 4
圖2.1 Kirsch的模式:無限版中的圓孔 5
圖2.2 Inglis模式:無限版上的橢圓孔洞 7
圖2.3 Westergaard模式:近裂縫尖端之應力場 8
圖2.4 Irwin尖端裂縫座標系統 9
圖2.5三種主要的裂縫破壞模式 10
圖2.6 William模式:V型刻痕尖端之平板 11
圖2.7量測應力強度因子之方法 16
圖2.8 (a)邊緣裂縫扭力試體示意圖 (b)試驗示意圖 (Lee, 1996) 21
圖2.9邊緣裂縫扭力試驗示意圖 22
圖2.10旋轉式直接扭力試驗試體示意圖 23
圖2.11旋轉式直接扭力試驗 24
圖2.12圓柱試體之旋轉式直接扭力試驗示意圖 25
圖2.13反裂式平板彎曲試驗試體示意圖 26
圖2.14反平面沖剪試體式意圖 28
圖2.15反平面沖剪試驗裂縫間距與長度對最大拉應力 28
圖2.16反平面沖剪試驗最大剪應力之影響 29
圖2.17反平面沖剪試驗厚度之影響 29
圖2.18反平面沖剪試驗最大剪應力、最大拉應力比與裂縫間距關係 30
圖3.1總體座標系統(x, y, z)、(x1, x2, x3)與本體座標系統(x′, y′, z′) 33
圖3.2未裂開的邊界被離散成九節點元素 38
圖3.3當裂縫接觸到有限體的邊界,九節點元素產生內縮的情形 39
圖3.4在三維度下四種在未裂開邊界的九節點元素排列方式 39
圖3.5在三維度下六種在裂縫表面的九節點元素排列方式 40
圖3.6裂縫開裂長度a 43
圖3.7受到上下均佈載重的異向性岩塊 44
圖3.8受到均佈載重以及重力的異向性岩塊 46
圖3.9均向性的岩塊試體 47
圖3.10岩塊試體加載 48
圖3.11依兩紅線切割後,模擬一塊體的受力 48
圖3.12 S = 12mm模態I型正規化應力強度因子FI 50
圖3.13 S = 12mm模態II型正規化應力強度因子FII 50
圖3.14 S = 12mm模態III型正規化應力強度因子FIII 51
圖3.15 S = 24mm模態I型正規化應力強度因子FI 52
圖3.16 S = 24mm模態II型正規化應力強度因子FII 52
圖3.17 S = 24mm模態III型正規化應力強度因子FIII 53
圖3.18 d = W模態I型正規化應力強度因子FI 54
圖3.19 d = W模態II型正規化應力強度因子FII 55
圖3.20 d = W模態III型正規化應力強度因子FIII 55
圖3.21 d = a模態I型正規化應力強度因子FI 56
圖3.22 d = a模態II型正規化應力強度因子FII 57
圖3.23 d = a模態III型正規化應力強度因子FIII 57
圖3.24裂縫長度a = 30mm模態I型正規化應力強度因子FI 59
圖3.25裂縫長度a = 30mm模態II型正規化應力強度因子FII 59
圖3.26裂縫長度a = 30mm模態III型正規化應力強度因子FIII 60
圖3.27裂縫長度a = 36mm模態I型正規化應力強度因子FI 61
圖3.28裂縫長度a = 36mm模態II型正規化應力強度因子FII 61
圖3.29裂縫長度a = 36mm模態III型正規化應力強度因子FIII 62
圖4.1中央裂縫III型加載 66
圖4.2四個裂縫前緣的應力強度因子變化 67
圖4.3三種不同的裂縫長度 68
圖4.4三種裂縫長度的模態I型正規化應力強度因子 69
圖4.5三種裂縫長度的模態II型正規化應力強度因子 69
圖4.6三種裂縫長度的模態III型正規化應力強度因子 70
圖4.7裂縫中央的模態III型正規化應力強度因子 70
圖4.8 FIIIM於不同異向性程度(E/E')的變化 71
圖4.9 FIIIM於不同異向性程度(E/G')的變化 72
圖4.10三種長寬比B/W的試體 73
圖4.11三種長寬比(B/W)的模態I型正規化應力強度因子 74
圖4.12三種長寬比(B/W)的模態II型正規化應力強度因子 74
圖4.13三種長寬比(B/W)的模態III型正規化應力強度因子 75
圖4.14裂縫中央的模態III型正規化應力強度因子變化 75
圖4.15 FIIIM於不同異向性程度(E/E')的變化 76
圖4.16 FIIIM於不同異向性程度(E/G')的變化 77
圖4.17層面角度(y , b)為(0°, 0°)、(45°, 45°)、(90°, 0°)的試體 78
圖4.18三種層面角度(y , b)的模態I型正規化應力強度因子 79
圖4.19三種層面角度(y , b)的模態II型正規化應力強度因子 80
圖4.20三種層面角度(y , b)的模態III型正規化應力強度因子 80
圖4.21 FIIIM於不同異向性程度(E/E')的變化 81
圖4.22 FIIIM於不同異向性程度(E/G')的變化 82
圖4.23模態III型加載下的試體 83
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