擬利用顆粒流PFC程式來模擬岩石裂隙(fissures)間的破裂連結問題：旨在利用PFC具備分辨顆粒鍵結間之張力斷裂或剪力破裂等AE紀錄的特色，首先 (1)針對不同傾角下單一條裂隙岩石之破裂發展順序與 (張裂或剪裂) 初始破裂(crack initiation)、損傷應力(damage stress)等力學特性；(2)再安排多道不同幾何排列(共線或平行排列)條件下，探討多道裂隙間岩橋(rock bridge)之微觀破裂行為的相互影響及其連結(coalescence)發展串連行為之間破裂連接差異性問題。
本文主要獲致結論如下：(1) 由PFC數值模擬利用AE訊號抓取破裂初始應力(σ_ci)，獲知σ_ci約落在0.63UCS，與一般岩石之初始破裂應力範圍(0.35 ~ 0.6UCS) 接近，可知於PFC數值模擬中可藉由AE訊號抓取之初始破裂應力(σ_ci)。(2) 從模擬含單一裂隙岩石之張裂與剪裂的AE發展順序，可知岩石之張裂破裂比剪裂破裂發展速度快，且張力裂縫的延伸是影響整體岩石之破裂行為。因此，初始張裂機制在花崗岩的破壞過程中較初始剪裂機制重要。(3) 由PFC模擬花崗岩含雙裂隙岩石之斷鍵紀錄，可觀測到於共線狀態下顯示岩橋間微觀鍵結斷鍵是由張力斷鍵與剪力斷鍵一同形成之混合式破壞。(4) 於共線、裂隙傾角(α)為45度及岩橋角(β)為45度的狀況下得知，模擬含雙裂之單軸壓縮試驗，發現岩橋長度(2b)會影響破裂順序，並可將岩橋間破裂連結順序分成三種破壞模式，分別為LTM模式(2b/2a < 0.2)、TLM模式(0.2 < 2b/2a < 0.52)及TML模式(2b/2a >0.52)。(5) 於非共線狀態下、裂隙傾角(α)為45度，當岩橋長度小於或等於裂隙長度(即2b≦2a)，並改變岩橋角(β)時，可獲知：(i) 當β< 90°時，岩橋破裂連結為張裂與剪裂的混合破裂模式(mixed shear crack & tensile crack)為主控；(ii) 當β= 90°時，岩橋由裂隙內部尖端(inner crack tips)先出現剪力破裂，再產生張力破裂形成岩橋間的破裂連結；(iii) 當β> 90°時，岩橋之破裂連接為張力破裂形成主控。

It is planned to use the PFC program to simulate the fracture coalescence problem between rock fissures: the purpose is to use PFC to distinguish the criharactestics of AE rates such as tension fracture or shear fracture between particle bonds. First of all (1) for different inclination angles the fracture development sequence of a single fissure rock and the mechanical characteristics (tension or shear) and crack initiation, damage stress and other mechanical characteristics ; (2) Arrange multiple different geometrical arrangements (collinear or parallel arrangement) Under the conditions, discuss the mutual influence of the microscopic fissure behavior of the rock bridge between multiple fissures and the difference in fracture coalescence between the development of coalescence and the series behavior, and hope that the results of this research will be useful for future research on the fissures subject to long-term external forces. It is helpful to understand that the new fracture and its extended growth trend, which increase the serial degree of the rock fracture network and increase the liquidity.
The main conclusions obtained in this paper are as follows: (1) The crack initial stress (σ_ci) is captured by the PFC numerical simulation using the AE signal, and it is found thatσ_ci falls approximately at 0.63UCS, which is close to the initial fracture stress range of ordinary rocks (0.35 ~ 0.6UCS). The crack initiation stress (σ_ci) that can be captured by the AE signal in the PFC numerical simulation. (2) From the AE development sequence of simulating the tension and shear failure of a rock with a single fracture, it can be seen that the tension fracture of the rock develops faster than the shear fracture, and the extension of the tension failure affects the fracture behavior of the whole rock. Therefore, the initial fracture mechanism is more important than the initial shear fracture mechanism in the failure process of granite. (3) Using PFC to simulate the broken bond record of granite rock with double fissures, it can be observed that the microscopic bond broken between rock bridges in the collinear state is a mixed failure formed by the tension broken bond and the shear broken bond. (4) Under the condition of collinear,fissure inclination (α) of 45 degrees and rock bridge angle (β) of 45 degrees, it is known that the uniaxial compression test with double fissures has shown that the length of the rock bridge (2b) will affect the fracture sequence , and the sequence of fracture coalescence between rock bridges can be divided into three failure modes, namely LTM mode (2b/2a <0.2), TLM mode (0.2 <2b/2a <0.52) and TML mode (2b/2a> 0.52). (5) In the non-collinear state, the fissure inclination (α) is 45 degrees, when the rock bridge distance is less than or equal to the fissure length (i.e. 2b≦2a), and the rock bridge angle (β) is changed, it can be known that: (i) When β<90°, the fracture of the rock bridge is controlled by a mixed shear failure & tensile failure; (ii) When β=90°, the rock bridge is controlled by the shear failure occurs first, followed by tension failure to form a fractured coalescence between the rock bridges; (iii) When β>90°, the fractured coalescence of the rock bridge is the main control of the tension fracture.

目錄	I
表目錄	III
圖目錄	IV
第一章 緒論	1
1.1 研究動機	1
1.2 研究目的	5
1.3研究步驟與內容	5
第二章 文獻回顧	7
2.1實驗與程式之擬合	7
2.2岩石之破裂力學理論	14
2.3 岩石材料基本性質	17
2.4 PFC 3.1.0版二維穩定性分析	21
第三章 PFC2D程式分析介紹	23
3.1 PFC2D程式概述	23
3.2 PFC建模步驟	36
第四章 參數率定	38
4.1我國離島花崗岩之基本力學性質	38
4.2花崗岩單軸壓縮破壞行為擬合	43
4.3剪向/正向鍵結強度比(σs/σn)的影響	49
4.4 綜合討論與分析	60
第五章 含單一裂隙岩石破裂行為模擬與分析	63
5.1 含單一裂隙岩石之異向性行為	63
5.2 張裂與剪裂破裂比例之影響	71
5.3 綜合分析與討論	81
第六章 含雙裂隙岩石的破裂連接行為探討	84
6.1共線狀態下之破裂連接行為	86
6.2非共線之破裂連接行為探討	103
6.3綜合討論與分析	113
第七章 結論與建議	115
7.1結論	115
7.2建議	117
參考文獻	118
附錄A-主要參數輸入圖	123
附錄B-碩士學位考試口試委員提問與回覆對照表	126

表2.3-1 初始應力與損傷應力之抓取方式(Xue et al. ,2013)	19
表4.2-1花崗岩之PFC建議輸入參數	44
表4.3-1 三種剪向/正向鍵結強度比於尖峰強度之張/剪破壞比例	52
表4.3-2含單一裂隙岩石之三種剪向/正向鍵結強度比於尖峰強度之張/剪破壞比例	59
表7-1 PFC模擬岩橋間破裂連接之發展	116

圖1.1-1 瑞典SKB公司規劃深層地質處置孔道配置概念	1
圖1.1-2 地底處置場之高壓地下水透由岩盤裂隙而噴入處置孔內的實況(Aberg, 2009)	3
圖1.1-3 地底處置孔周圍裂隙可能交接情況示意圖(Baxter et al.,2018)	4
圖1.3-1 平均楊氏模數與單壓強度定義試驗模擬範圍(吳勁頤，2017)	6
圖1.3-2 雙軸壓縮造成應力場中的Griffith裂隙產生張力裂隙(Hoek & Martin,2014)	6
圖2.1-1 既有裂隙在單壓下裂縫尖端之兩種基本破裂形式	8
圖2.1-2 不同裂隙長度對於破裂發生之應力關係(Lajtai,1971)	8
圖2.1-3 裂隙尖端破裂發展過程(Lajtai,1971)	9
圖2.1-4 不同傾角之單一裂隙在單壓下張力破壞的側翼破裂(wing crack)形態  (Lu & Lv, 2019)	9
圖2.1-5 試驗花崗岩內平行双裂隙之幾何參數定義與新生破裂類型        (Yin et al., 2014)	10
圖2.1-6花崗岩內具二平行裂隙岩橋(rock bridge)之破裂連結方式：(a)沒連結、(b)二次破裂連結、(c)張裂連結(T)、(d)張裂-剪裂混合(MTS)連結(Yin et al.,2014)	11
圖2.1-7 實際岩石實驗中觀察到之九種岩橋破裂模式(WONG & CHAU,1998)	12
圖2.1-8以石膏模型探究共線裂隙間岩橋之連結行為(蘇建彰，1994)	12
圖2.1-9 以PHASES分析單一裂隙尖端應力分布情形(蘇建彰，1994)	13
圖2.2-1 脆性材料之Mohr-Coulomb破壞包絡線示意圖	15
圖2.2-2 Jaeger建議之含單一弱面岩體異向性強度曲線(Hoek & Brown,1980)	16
圖2.3-1 初始破裂應力(σci)與破裂損傷應力(σcd)之定義(Martin & Christiansson,2009)	18
圖2.3-2 初始應力(σci)與損傷應力(σcd)之抓取示意圖(Ghazvinian,2015)	18
圖2.3-3 音射與岩石破壞機制之關係圖(Boyce, 1981)	20
圖3.1-1 PFC運算流程圖	25
圖3.1-2 PFC2D球-球與球-牆接觸式關係圖	26
圖3.1-3 球與牆之接觸模式下之法線向量判斷示意圖	26
圖3.1-4 PFC提供的三種數值模式與其所需要的微觀參數(李宏輝，2008)	28
圖3.1-5 PFC2D的接觸勁度模式、鍵結模式與滑移模式三者的並存關係圖(Lisjak & Grasselli, 2014) 與平行鍵結模式示意圖(Potyondy & Cunall, 2004；Cho et al. 2007)	29
圖3.1-6接觸鍵結模式與平行接觸模式之比較與破裂示意圖(Cho et al. 2007)	31
圖3.1-7 接觸鍵結模式下顆粒的相對位移與接觸力之關係圖	32
圖3.1-8 顆粒與鍵結系統之力位行為	33
圖3.1-9 PFC與FLAC建立離散體-連續體耦合模型(Potyondy & Cundall, 2002)	35
圖3.1-10  PFC模擬垂直壓應力作用下所引致的圓形坑道損傷：(a)微觀張力破壞(紅)與剪力破壞(藍)並存；(b)僅微觀張力破壞(紅) (Potyondy & Autio, 2001)	35
圖3.2-1  PFC應用於單軸壓縮試驗模擬之建模程序(Potyondy & Cundall, 2004)	36
圖4.1-1 離島地區花崗岩質母岩UCS之深度分布態(楊長義，2015)	39
圖4.1-2離島花崗岩之單壓應力應變曲線(楊長義，2016))	39
圖4.1-3 本土離島花崗岩數據統計(楊長義，2016)	41
圖4.1-4 離島花崗岩之三軸剪力性質應力莫耳圓(趙振宇，2005; 楊長義，2015)	42
圖4.1-5 離島花崗岩之Hoek-Brown強度參數值m(楊長義，2016))	42
圖4.2-1 以平均楊氏模數與單壓強度定義試驗模擬範圍(吳勁頤，2017)	43
圖4.2-2 PFC模擬之應力-應變曲線圖	44
圖4.2-3 數值模擬應力應變曲線圖與實驗數據之比較	45
圖4.2-4  以PFC模擬巴西人張力試驗之破壞外觀與應力-應變曲線	45
圖4.2-5 模擬岩石之破壞型態與真實花崗岩比較	46
圖4.2-6 PFC單軸壓縮模擬結果	47
圖4.2-7 完整岩石之音射AE事件紀錄與應力-應變曲線關係圖	47
圖4.2-8  以PFC模擬單軸壓縮試驗在不同應力階段下之破裂分布	48
圖4.3-1 在三種不同剪向/正向鍵結強度比下之應力-應變曲線比較	50
圖4.3-2 在3種不同剪向/正向鍵結強度比之破壞面組成差異	51
圖4.3-3 完整岩石在三種剪向/正向鍵結強度比下之破壞類型AE比較	52
圖4.3-4  PFC模擬含單一裂隙之巴西人試體於單軸壓縮試驗之結果(林冠良，2019)	53
圖4.3-5 裂縫延伸狀態於張力集中與壓力集中區之分佈比較	55
圖4.3-6 裂縫延伸狀態於張力集中與壓力集中區之分佈比較	56
圖4.3-7 裂縫延伸狀態於張力集中與壓力集中區之分佈比較	57
圖4.3-8 含單一裂隙岩石在三種剪向/正向鍵結強度比下之破壞類型AE比較	58
圖4.4-1 以傳統應力應變曲線與音射紀錄判別之初始破裂應力	60
圖4.4-2 破裂面附近顆粒之相對位移方向	61
圖5.1-1 裂隙尖端之理論分析模型	64
圖5.1-2 裂縫試體示意圖	64
圖5.1-3 裂隙長度與破裂強度(UCS)及變形模數(E)之關係圖	66
圖5.1-4 含不同裂隙傾角岩石之應力應變曲線圖	67
圖5.1-5 含不同裂隙傾角(α)試體之尖峰強度與損傷係數曲線圖	68
圖5.1-6 不同傾角節理面之應力應變曲線圖	69
圖5.1-7 不同傾角之連續節理面及既有裂隙之強度異向性分布圖	69
圖5.1-8 不同傾角之連續節理面及既有裂隙之變形異向性分布圖	70
圖5.1-9 含各傾角裂隙岩石與完整岩石之彈性模數比例	71
圖5.2-1 不同裂隙傾角(α)與完整岩石之應力應變曲線與AE鍵結斷裂總數	73
圖5.2-2 花崗岩單壓之體積應變變化與對應之損傷應力	74
圖5.2-3 本文數值模擬之初始破裂應力(σci)與破裂損傷應力(σcd)關係圖	75
圖5.2-4 初始應力(σci)、損傷應力(σcd)及尖峰強度(UCS)下之破裂外觀	77
圖5.2-5  PFC模擬岩石材料於單壓試驗下之破裂外觀	77
圖5.2-6 不同裂隙傾角之應力應變曲線圖與AE比例	78
圖5.2-7 PFC模擬分析之初始應力(σci)、損傷應力(σcd)及尖峰強度(UCS)	79
圖5.2-8 於不同應力階段下張/剪破裂量之比例	81
圖5.3-1 連續節理面與含單一裂隙岩石異向性整合	82
圖5.3-2 不同傾角裂隙之應力-應變曲線與破裂總和數趨勢圖	82
圖6-1 以ABAQUS模擬不同排列双裂隙之破裂連結機制 (Silva & Einstein, 2013)	84
圖6-2 以ABAQUS模擬双裂隙連結順序與破裂機制結果比較(Silva & Einstein,2013)	85
圖6-3雙裂隙岩橋之幾何參數定義(改繪自Robina et al.,1998)	86
圖6.1-1  裂縫岩橋透由剪力破裂連結示意圖(Wong, et al.,2001)	87
圖6.1-2 本文各類型破裂發生位置及其定義	89
圖6.1-3 含雙裂隙岩石之張力/壓力集中區域分佈	90
圖6.1-4在岩橋區域間之顆粒位移方向	91
圖6.1-5 不同型態破壞之軸向應力與裂隙間距關係	92
圖6.1-6 變形模數與裂隙間距關係變化	93
圖6.1-7  LTM模式破壞過程示意圖	94
圖6.1-8  TLM模式破壞過程示意圖	94
圖6.1-9  TML模式破壞過程示意圖	95
圖6.1-10 三種裂隙長度之破壞模式之應力-應變曲線與AE紀錄比較	96
圖6.1-11 音射紀錄下不同破壞模式之張/剪破壞比例	97
圖6.1-12 三種不同破壞模式之AE訊號紀錄	99
圖6.1-13含雙裂隙岩石之PFC模擬初始應力(σci)、損傷應力(σcd)及尖峰強度分佈	100
圖 6.1-14共線狀態下岩橋長度與之初始應力(σci)與損傷應力(σcd)分佈	101
圖6.2-1 三種不同岩橋角(β)之裂隙示意圖	103
圖6.2-2於岩橋長度2b/2a = 0.5時之破裂外觀比較	105
圖6.2-3於岩橋長度2b/2a = 1.0時之破裂外觀比較	105
圖6.2-4於岩橋長度2b/2a = 1.5時之破裂外觀比較	106
圖6.2-5於β為60度時之初始應力(σci)、損傷應力(σcd) 、變形模數及單壓強度	107
圖6.2-6於β為90度時之初始應力(σci)、損傷應力(σcd)、變形模數及單壓強度	107
圖6.2-7於β為120度時之初始應力(σci)、損傷應力(σcd) 、變形模數及單壓強度	108
圖6.2-8於β為60度時之AE事件紀錄	110
圖6.2-9於β為90度時之AE事件紀錄	111
圖6.2-10於β為120度時之AE事件紀錄	113
圖A-1 建模參數輸入圖	123
圖A-2 裂隙設置輸入圖	124
圖A-3 斷鍵紀錄輸入圖	125

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