混凝土結構之非線性不連續變形分析

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王國昌(Kuo-Chang Wang) 查詢紙本館藏

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土木工程學系

論文名稱

混凝土結構之非線性不連續變形分析
(Nonlinear Discontinuous Deformation Analysis of Concrete Structures)

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摘要(中)

摘要
本論文提出一新的混凝土塑性模型─雙荷載函數混凝土模型，以兩個不同的函數形式分別考慮了混凝土因微裂縫拓展所造成的體積改變，以及因錯動所造成的形狀變化，同時將混凝土進入塑性後的硬化法則，亦分別依形狀改變與體積改變分開，並在隨動式硬化法則移動後的應力空間中，建立起硬化參數和應力函數的關係。將此兩個荷載函數經過適當的組合後，可以證明與體積變化相關的材料塑性行為，符合非相關性流動法則，而其相對應的塑性勢能函數(plastic potential)恰是兩個荷載函數之和。
將此一雙荷載函數混凝土模型與向量式有限元結合，將混凝土結構的分析以宏觀裂縫的形成為分界，區分為宏觀裂縫形成前的連續體行為，與宏觀裂縫形成後的不連續體行為兩部分。前者主要的工作在處理混凝土材料的彈塑性與不可逆的非線性行為﹔後者因裂縫的形成，材料變成非等向性，計算上著重在單一連體碎裂成多個連體，各個連體之間接觸判斷與接觸力等互致作用的處理。
以此一程序分析混凝土結構在承受靜載重和動態載重下的行為。首先，以一考慮因裂縫造成混凝土體積變化效應雙荷載函數模型，與現有單軸、雙軸和三軸實驗結果比較，驗證本方法在模擬混凝土宏觀裂縫形成前的連續體行為上，是目前最適用的材料模型。同時在重複加卸載的情況下，此一雙荷載函數模型可模擬材料非線性與不可逆的特性，可作為分析混凝土動態行為的基礎。其次，在靜荷載作用下，以本方法模擬混凝土結構承受剪力的行為，驗證了混凝土宏觀裂縫發生後本文所提的混凝土開裂模式，與單一連體碎裂成多連體後的開裂計算法、多連體間的碰撞互制等現象的計算方法，已經具備分析混凝土結構物的基礎。
在混凝土的動態行為模擬方面，首先以一維的混凝土桿承受衝擊荷載之分析，驗證本文所發展的材料模型與計算方法適用於混凝土承受衝擊載重下的行為。接著驗證本方法在模擬混凝版承受高速衝擊的穿孔現象，承受中速衝擊的彈坑現象與承受低速衝擊的剝離現象的效果。在確立了本方法在定性分析上，可以模擬混凝土結構受衝擊載重下的行為之後，再分別以混凝土版承受撞擊試驗以及鋼筋混凝梁承受撞擊試驗結果和計算結果比較，顯示本論文所提之計算方法，在混凝土結構承受衝擊載重下的定量分析上，也已經有初步理想的結果。

摘要(英)

Nonlinear Discontinuous Deformation Analysis of Concrete Structures
ABSTRACT
In this thesis, a dual loading functions plasticity (DLFP) model that is capable to characterize the elastic-plastic behaviors of concrete material under various multi-axial stress state is proposed. The dilatation effect due to the formation of micro cracks and the shape change effect due to dislocation are taken into account by individual loading function to guide the plastic behavior of concrete. The hardening parameter of each loading function is determined based on series of worldwide-recognized experimental data. It is shown that the presented dual loading functions model can predict the plastic behavior of concrete material at various stress state. This incremental type model can be adapted into numerical code to simulate the irreversible behavior of concrete material during any loading –unloading process. The numerical algorithm for applying this DLFP model is also presented. Although associated flow rule is applied to individual loading function during the derivation, but it is proved that the overall format of the flow rule within this concrete plasticity model is non-associated.
We combine DLFP with Vector Form Intrinsic Finite Element, VFIFE, to analysis concrete structures. The procedure is mainly divided into two major parts by the formation of macro crack: the continuum behavior before macro crack forming and multi-bodies behavior after macro crack forming. The major work of the former is to establish a concrete constitutive relation. In this thesis, DLFP is adapted. The major work of the latter is to handle crack of concrete, which contains new nodes generation, detection of contact and contact force.
With such procedure, we analyze concrete structure under static and dynamic load. Comparing with uni-axial, bi-axial and tri-axial experiment data, DLFP represent a better choice of all the concrete models. This DLFP can handle cyclic behavior of concrete without difficulties. We also analyze a concrete structure that is under shear to verify the procedure of post failure behavior of concrete. Finally, we use this tool to analyze the concrete structure under dynamic loading. In qualitative analysis, we analyze the concrete slab under impact of low, medium and high velocities to verify the procedure. The results show the trends are admit with experiments though quantitative analysis still needs more efforts to put on.

關鍵字(中)

★ 雙荷載函數
★ 不連續
★ 非線性
★ 混凝土

關鍵字(英)

★ dual loading functions
★ discontinuous
★ nonlinear
★ concrete

論文目次

目錄
第一章緒論 10
1.1 研究背景 10
1.2 研究目的 12
1.3 論文章節內容 13
第二章混凝土材料特性和破壞機理 15
2.1混凝土材料的特性 15
2.1.1非均質，非等向性的多相混合材料 15
2.1.2複雜的微觀內應力變形狀態 16
2.1.3變形的多元組成 17
2.1.4應力狀態和途徑對力學行為的影響 18
2.1.5時間和環境對力學行為的影響 18
2.2混凝土的宏觀受力行為和破壞機理 19
2.2.1受碎裂和裂縫所導控的材料行為 20
2.2.2混凝土受壓後的變形與破損關係 22
2.2.3混凝土橫向軸向應變與體積變形和混凝土強度的關係 22
2.2.4混凝土泊松比與破損的關係 23
2.3混凝土典型破壞型態 23
2.4小結 23
第三章向量式有限元 26
3.1物理模式與數學模式 28
3.2剛體運動與疊加原理 29
3.3平面固體元的推導 31
3.3.1轉動與共轉座標 …….. 31
3.3.1.1共轉座標 34
3.3.2變形位移的計算 34
3.3.3節點內力的計算 36
3.3.3.1三節點常應變元 37
3.3.3.2四節點同參數有限元 43
3.3.4節點作用力的計算 49
3.3.4.1三節點常應變元 50
3.3.4.2四節點同參數有限元 54
3.3.5節點質量的計算與運動方程式 57
3.3.5.1節點質量 57
3.3.5.2運動方程式 58
3.3.6討論 59
第四章混凝土宏觀裂縫形成前的行為模擬…………………………………………65
4.1前言 65
4.2現行的混凝土塑性模式回顧 65
4.3雙荷載函數混凝土塑性模型 68
4.3.1混凝土破壞準則 69
4.3.2初始降伏函數與荷載函數 70
4.3.3硬化法則 72
4.3.4流動性法則 74
4.3.5增量塑性應力應變關係 75
4.3.6一致性條件 76
4.4非關連性流動率混凝土塑性模型 79
4.4.1整體降服函數 79
4.4.2整體塑性勢能函數 81
4.5計算流程 84
第五章混凝土宏觀裂縫形成後的不連續體行為模擬………………………………95
5.1 前言 95
5.2現行混凝土裂縫模型回顧 96
5.3混凝土破壞模式 100
5.3.1純粹裂縫破壞 102
5.3.2純粹碎裂破壞 103
5.3.3混合型破壞 103
5.4撞擊接觸分析處理方法 104
5.4.1流體動力學法 105
5.4.2懲罰法 105
5.4.3撞擊接觸判斷 108
5.4.4懲罰法的穩定條件 109
5.4.5圓球法 110
5.5程式之資料結構 112
第六章實例分析 120
6.1混凝土靜載重試驗結果驗證 120
6.2循環荷載 124
6.3混凝土承受剪力下的斷裂分析 126
6.4 一維混凝土桿承受衝擊壓力試驗 126
6.5混凝版承受高速衝擊的穿孔現象 ………………………… 127
6.6混凝土版承受中速衝擊的彈坑現象 127
6.7混凝土版承受低速衝擊的剝離現象 128
6.8混凝土板撞擊試驗 128
6.9鋼筋混凝土梁撞擊試驗 129
第七章結論與建議 157
7.1 結論 157
7.2 進一步的研究方向 160
參考文獻 162
附錄A 混凝土材料模型推解過程 172
附錄B 考慮溫度變化之混凝土雙荷載函數模型 176
圖目錄
圖2.1 混凝土受單軸壓力下軸向橫向應變與體積變化的關係 25
圖2.2 混凝土在不同應力組合下的破壞型態 25
圖3.1A 簡單三角形元變形示意圖 61
圖3.1B 簡單三角形元之變形位移示意圖……………………………………………… 61
圖3.2 簡單三角形元之剛體位移表示法 62
圖3.3 簡單三角形元內一點之位移 62
圖3.4 四節點同參數平面固體元 63
圖3.5A 三節點常應變元節點力 63
圖3.5B三節點常應變元節點力等效力臂 64
圖4.1 混凝土材料受力後的體積變化 89
圖4.2 混凝土單軸拉壓應力應變關係 89
圖4.3 混凝土二維應力空間表示 90
圖4.4 HTC混凝土模型破壞面 90
圖4.5 偏應力空間降服面的變形 91
圖4.6 擴展式應變硬化法則 91
圖4.7 隨動式應變硬化法則 92
圖4.8 混合式應變硬化法則 92
圖4.9 雙荷函數模型的整體降服函數 93
圖4.10 混凝土雙荷載函數計算流程 94
圖5.1A離散裂縫模型 113
圖5.1B 改進後的離散裂縫模型 113
圖5.2A 尖端裂縫模型 113
圖5.2B 鈍裂縫模型 113
圖5.3 (a)斷裂前與(b)斷裂後之網格 114
圖5.4 二維有限元素斷裂模式 114
圖5.5 判斷開裂模式之應力分瓣圖應力面 115
圖5.6 元素重疊之現象：(a)t=0；(b)t=t1 115
圖5.7 主元素與徒元素：(a)處理前；(b)處理後 116
圖5.8 元素穿透示意圖 116
圖5.9 主元素與徒元素示意圖 117
圖5.10 內插函數 117
圖5.11 節點與元素之穿透判斷示意圖 118
圖5.12 元素撞擊垂直剛性牆之示意圖 118
圖5.13 圓球法 118
圖5.14 連結陣列之連結方向示意圖 119
圖6.1 混凝土形狀改變相關以及體積改變相關的硬化參數雙軸實驗結果 130
圖6.2 單軸與雙軸壓力計算結果與實驗比較 131
圖6.3 雙軸拉-壓計算結果與實驗比較 132
圖6.4 單軸與雙軸拉力計算結果實驗比較 133
圖6.5 混凝土形狀改變相關以及體積改變相關的硬化參數三軸實驗結果 134
圖6.6 三軸圍壓計算結果與實驗比較 135
圖6.7 循環荷載問題有限元分析模型 136
圖6.8 加載歷時圖：(a)循環荷載-A；循環荷載-B 136
圖6.9 循環荷載-A之降服面變化示意圖 136
圖6.10 循環荷載-B之降服面變化示意圖 137
圖6.11 雙荷載塑性準則分析結果：循環荷載-A 137
圖6.12 雙荷載塑性準則分析結果：循環荷載-B 137
圖6.13 HTC塑性準則分析結果：循環荷載-A 138
圖6.14 HTC塑性準則分析結果：循環荷載-B 138
圖6.15混凝土加卸載路徑相關不可逆現象模擬 139
圖6.16混凝土承受剪力下的斷裂分析 139
圖6.17 混凝土承受剪力下的斷裂分析歷時圖 142
圖6.19一維混凝土桿承受衝擊壓力加載歷時圖 143
圖6.20 例題 3分析結果：t = (a)0.3、(b)1.5、(c)2.7、(d)3.9、(e)4.5、(f)5.1、(g)5.7、(h)6.3、(i)45、(j)60、(k)90、(l)120毫秒 149
圖6.21 高速撞擊下混凝土板受穿透破壞之有限元素網格；t=：(a) 0.125、(b)1.00、(c)1.50與(d)2.25毫秒 150
圖6.22 中速撞擊下混凝土板受彈坑破壞之有限元素網格；t=：(a) 0.0125、(b)0.025、(c)0.0375與(d)0.125毫秒6-15 151
圖6.23 低速撞擊下混凝土板產生剝離現象之破壞圖；t=：(a) 0.18、(b)0.45、(c)0.65與(d)1.0毫秒 152
圖6.24 混凝土板背面疤落情形(周承劉，2001) 153
圖6.25 混凝土板撞擊問題之撞擊力歷時圖 153
圖6.26 混凝土板破壞歷時圖 154
圖6.27 鋼筋混凝土梁斷面圖(Kishi，2002) 155
圖6.28 鋼筋混凝土梁撞擊試驗設備(Kishi，2002) 155
圖6.29 混凝土梁破壞圖(Kishi，2002) 155
圖6.30 鋼筋混凝土梁破壞圖：V = 5 m/s 156
表目錄
表1.1 鋼筋混凝土結構數值分析發展之階段及重點內容 12
表2.1 水泥沙漿和粗骨材的物理性質比較 16
表2.2 混凝土內部的微裂縫在荷載作用下的幾個拓展階段 24

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指導教授

丁承先、王仲宇
(E.C. Ting、C.Y. Wang)

審核日期

2004-1-16

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