博碩士論文 103322021 詳細資訊




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姓名 李尚達(Shang-Ta Lee)  查詢紙本館藏   畢業系所 土木工程學系
論文名稱 混凝土之三維等效單軸應變材料組成模型
(3-D Equivalent Uniaxial Strain of Concrete Material Constitutive Model)
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摘要(中) 本研究主要研究混凝土材料之非線性行為,透過Darwin & Pecknold提出的等效單軸應變概念與Balan所提出的混凝土亞塑性模型(Hypo-plastic Model),將混凝土材料中多軸互制行為轉化為多個單軸行為,簡化了混凝土在塑性行為分析中許多積分及複雜的數學計算,且也能得到相當好的結果。在傳統的塑性力學中,流動法則(Flow Rule)及硬化法則(Hardening Rule)為塑性材料模型中常用到的兩個法則,在亞塑性模型中雖然此兩個法則無使用,但其造成的影響卻直接表現於材料行為中。本研究使用之分析方式有別於傳統做法,使用塑性力學處理材料非線性問題,提出一個方法處理混凝土非線性行為。混凝土之亞塑性材料模型中主要分為兩個部分,分別為材料破壞曲面(Ultimate Surface),及等效單軸應力應變曲線。本研究選用由Menetrey & Willam 修正 Willam-Warnke 之模型,成為Menetrey-Willam模型。同時,考慮到材料之三維壓力強度極限(Ultimate Strength),加入帽蓋模型修正且提出封閉Menetrey-Willam模型,包含了子午線與帽蓋模型。在混凝土等效單軸應力應變曲線則是使用Saenz所提出的曲線公式,此公式僅需以一條方程式即可描述混凝土行為中之硬化段與軟化段,在數值模擬的使用上相當簡潔且方便。本研究之數值算例分別驗證了混凝土單軸、雙軸、三軸及高強度混凝土之三軸行為,在混凝土的三軸試驗中,因三個方向的應力加載,導致混凝土的強度提高,在研究中也提出修正破壞曲面的方式預測混凝土在三軸試驗的應力應變走向。
摘要(英) In this research, focus on non-linear behavior of concrete by using concept of “Equivalent Uniaxial Strain” proposed by Darwin & Pecknold and concept of “Hypo-plastic Model” proposed by Balan, concept of “Equivalent uniaxial strain” degenerate muti-axial which react upon each other into multiple uniaxial, also simplify mathematic calculation. Though, in traditional plastic mechanics, flow rule and hardening rule commonly use plastic material model, those rules are not used in hypo-plastic model. Method of this research is different from traditional way. Hypo-plastic model can be classified into two parts, one is “Ultimate Surface”, the other one is “Equivalent uniaxial strain envelope”. In regard of using ultimate surface model, choose Willam-Warnke which revised by Menetrey & Willam and named Menetrey-Willam Model. Meanwhile, in consideration of ultimate strength in tri-axial compress, we adding “Cap Model” to revise and named this model “Closed Menetrey-Willam” model, this contain both meridian and cap model. Second part of hypo- plastic model is using Equivalent uniaxial strain envelope of concrete proposed by Saenz. In this study, uniaxial, biaxial, tri-axial experiments are applied to verify analysis. Especially tri-axial loading test, because of loading path along three principal directions, strength of concrete will be lifted up to another level, in order to solve this, propose a method of revising failure surface to predict ultimate state in tri-axial loading test.
關鍵字(中) ★ 等效單軸應變
★ 破壞曲面
★ 非線性分析
★ 高強度混凝土
★ 亞塑性材料模型
關鍵字(英) ★ Equivalent uniaxial strain
★ failure surface
★ non-linear analysis
★ high strength concrete
★ hypo-plastic model
論文目次 第一章 前言 1
1.1研究動機與目的 1
1.2文獻回顧 2
1.3研究方法與內容 3
第二章 混凝土破壞準則與模型 8
2.1 Haigh-Westergaard座標軸系統 8
2.1.1 偏平面(Deviatoric Plane)與Rendulic平面 16
2.2 Ottosen 4-Parameter Model 18
2.3 Hsieh-Ting-Chen 4-Parameter Model 20
2.4 Willam-Warnke Five-Parameter Model 21
第三章 混凝土材料之等效三軸模型 25
3.1 混凝土材料本構關係(Constitutive Equivalent) 26
3.2 等效單軸應變(Equivalent Uniaxial Strain) 27
3.3 單軸包絡曲線(Uniaxial Envelope) 29
3.4 應力空間與等效單軸應變空間(Closed) Mentrey Willam 破壞曲面 30
3.4.1橢圓函數(Ellipse Function) 33
3.4.2子午線(Meridians) 36
3.4.3廣義帽蓋模型(Generalized Cap Model) 37
3.4.4結合子午線模型與帽蓋模型 38
3.5應力路徑(Stress Path) 40
3.6極限強度曲面修正(三軸實驗曲線建立極限強度包絡面) 41
3.7 數值計算流程 51
第四章 數值算例與驗證 58
4.1 混凝土模型橢圓函數討論與單軸及雙軸實驗與數值分析比對 58
4.1.1 橢圓函數討論 58
4.1.2單軸及雙軸實驗與數值分析比對 61
4.2 一般強度混凝土三軸實驗與數值分析比對 66
4.3 高強度混凝土三軸實驗與數值分析比對 74
4.4 高強度混凝土實驗與修正等效單軸包絡線分析比對 83
第五章 結論與建議 89
5.1結論 89
5.2 建議 92
參考文獻 94
附錄A 應力三向對稱性 97
附錄B 橢圓函數 100
附錄C 實驗數據整理 107
附錄D 程式流程圖 109
參考文獻 [1] Balan T. A., Spacone E., Kwon M., A 3D hypoplasticmodel for cyclic analysis of concrete structures, Computers & Structures, 23, 2001, pp 333-342.
[2] Li T, Crouch R. A C2 plasticity model for structural concrete. Computers &Structure 2010; 88: 1322–32.
[3] 張鈴菀, “向量式有限元分析法於鋼筋混凝土結構非線性行為之應用,” 臺灣國立中央大學碩士論文, 2009.

[4] 賴昱儒, “混凝土結構分析之三維等效單軸應變組成材料模型”, 臺灣國立
中央大學碩士論文,2014.
[5] 王國昌,”混凝土結構之非線性不連續變形分析” 臺灣國立中央大學博士 論文, 2004.

[6] Xiaobin Lu, ”Uniaxial and tri-axial behavior of high strength concrete with and without steel fibers” New Jersey Institute of Technology in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Civil Engineering, 2005.
[7] Chen, W. F. , “Plasticity for structural Engineers”, 1988.
[8] Willam, K, J and Warnke, E. P. , “Constitutive Model for the Tri-axial Behavior of Concrete,” Concrete Structures Subjected to Tri-axial Stresses, International Association for Bridges and Structural Engineering, Bergamo, Italy, 1974.
[9] Menetrey, P. H. , and Willam, K. J. , “Tri-axial Failure Criterion for Concrete and Its Generalization”, ACI Structural Journal, 1995;92:311-8
[10] Klisinski, M., ”Degradation and Plastic Deformation of Concrete,” IFTR Report 38, PhD
thesis, Polish Academy of Science, 1985
[11] Kolymbas, D. ”An outline of hypo-plasticity” Arch Appl Mech 1991:6;143-51
[12] Mordini, A., “Three Dimension Numerical Modeling of RC Behavior,” PhD thesis,
University of Parma, Italy, 2006.
[13] Pisano, A.A., Fuschi, P., and De Domenico, D., “A Kinematic Approach for Peak Load
Evaluation of Concrete Elements,” Computers and Structures, 2013; 119:125-139.
[14] Kupfer, H.B., and Gerstle, K.H., 1973, “Behavior of Concrete under Biaxial Stresses,” Journal of the Engineering Mechanics Division, Vol.99, pp. 853-866.
[15] Ottosen, N.S., “Constitutive Model for Short-Time Loading of Concrete,” Journal of the Engineering Mechanics Division, 1979;105(1):127-141
[16] Darwin, D., and Pecknold, D.A., “Nonlinear Biaxial Stress-Strain Law for Concrete,” ASCE, 1977;103(2):229-241.
[17] Bazant, Z.P., and Kim S.S., “Plastic-Fracturing Theory for Concrete,” Journal of the Engineering Mechanics Division, 1979;105(3):407-428.
[18] Saenz, I.P., ”Discussion of equation for the stress-strain curve of concrete, by P. Desay and S. Krishan” ACI Journal:61(9):1229-35.
[19] Saenz, I.P., “Equation for stress-strain Curve of Concrete,” Journal Proceeding ACI, Vol.66, No.9, pp.1229-1235, 1964.

[20] Ottosen N. S. and Ristinmaa M. , “The Mechanics of Constitutive Modeling, Elsevier, 2005.
[21] Hoek, E., and Brown, E. T., "Empirical Strength Criterion for Rock Masses," Journal of the Geotechnical Engineering Division, V. 106, No. GT9, 1980, pp. 1013-1035.
[22] Linse, D., and H. Aschl,“ Versuche zum Verhalten von Beton unter mehrachsiger Beanspruchung,“ test report, TU München, 1976
[23] Bazant, Z. P. and Shieh, C.L., ”Endochronic Model for Nonlinear Triaxial Behavior of Concrete,” Nuclear Engineering and Design, Vol. 47, pp. 305-315, 1978.
指導教授 王仲宇(Chung-Yue Wang) 審核日期 2016-8-11
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