混凝土非穩態氯離子擴散分析與壽命預測模型｜國立臺灣科技大學博碩士論文系統

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研究生：	孫詠明 Yung-Ming Sun
論文名稱：	混凝土非穩態氯離子擴散分析與壽命預測模型 Non-Steady State Chloride Diffusion and Service Life Prediction Model for Concrete
指導教授：	張大鵬 Ta-Peng Chang
口試委員:	黃忠信 J.S. Huang 黃然 R. Huang 梁明德 M.T. Te 楊仲家 C.C. Yang 林英俊 I.J. Lin 陳君弢 C.T. Chen
學位類別：	博士 Doctor
系所名稱：	工程學院 - 營建工程系 Department of Civil and Construction Engineering
論文出版年：	2009
畢業學年度：	97
語文別：	英文
論文頁數：	139
中文關鍵詞：	混凝土、氯離子擴散係數、壽命預測、耐久性、數值分析
外文關鍵詞：	concrete, chloride diffusion coefficient, service life prediction, Kirchhoff transformation
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為模擬混凝土結構物暴露於海水侵蝕環境，本論文以Kirchhoff 轉換法，求出Fick第二定律於非穩定狀態之一維擴散方程式之正確解析解，並稱之為 KHF解析解，其中假設氯離子濃度為氯離子擴散係數之函數D(C)，擴散時間及擴散深度又為濃度之函數C(x,t)。同時也利用數值分析方法求解一維擴散式在D(x)、D(t)、D(x,t) 及D(C) 四種擴散係數模型，數值解可用來了解使用不同變數時對模擬氯離子擴散物理過程的影響，研究發現使用D(t)、D(x,t) 及D(C) 模型進行壽命預測較假設D為常數之壽命為長。並將KHF解析解與數值解比較,發現兩者相當符合，證實KHF解析解的可用性及可靠性。並利用微分敏感度分析方法，討論KHF解析解中時間、深度、表面氯離子濃度及參考點濃度對氯離子擴散係數之敏感度分析。本研究又利用KHF解析解發展出兩種應用方式：
1. 簡化混凝土結構物之時間距離相依氯離子擴散係數檢測方法
利用KHF數學預測模型，本文發展出兩種氯離子擴散實驗之簡化方法，並分別以例題示範。其一為「單一時間長試體法」，只需要在某一固定時間，鑽孔測試少量較長試體之固定間距氯離子濃度。其二為「長時間短試體法」，在連續並固定間隔時間內，只需要較短的鑽孔試體測試某一固定深度氯離子濃度。
2. 預測暴露於海蝕環境之混凝土結構物壽命
利用KHF解析解修正 LightCon的海蝕混凝土壽命預測模型，可以得到一個更符合與時間距離相依的數學假設的理論壽命預測模型。對海蝕環境結構物的耐久性評估時，利用這個預測模型可由至少兩次鑽孔檢測結果，預測混凝土結構物之服務壽命。論文中說明計算步驟及舉例證實預測模型的可行性，並且將預測結果和LightCon模型結果對照，比較兩者之預測值。
但是，鋼筋混凝土結構物是經常受到險峻多變的環境影響如：濕度、風力、降雨和降雪等，還有混凝土品質逐漸的退化像是有裂縫、碎裂、崩解等；為了改進數學模型並且達到更合理的混凝土結構物壽命預測，長期實驗和實地的調查仍然是必需繼續進行研究的。

To simulate a concrete exposed to chloride environment, this study uses the Kirchhoff transformation method to solve a non-steady one-dimensional diffusion equation, named the KHF analytical solution, in which the apparent diffusion coefficient D is a function of the concentration of chloride C(x,t). A numerical solution for same one-dimensional diffusion equation was also carried out considering four different diffusion coefficients D(x), D(t), D(x,t) and D(C). These numerical results served as a handy tool to understand the actual influences of different types of diffusion coefficients on the physical diffusion process with chloride. And we found the result of service life prediction by D(t), D(x,t) and D(C) will be longer than by D is assumed as a constant. The KHF analytical solution is verified by the numerical analysis and is proved suitable to model the concentration dependent diffusion problem. The sensitivity analysis of four parameters of KHF analytical solution, i.e., the time of exposure, reference depth, surface chloride concentration, and chloride concentration of reference point, was studied by the analytical differentiation techniques.
Two major applications were developed by the KHF analytical solution:
1. Simplify the inspection of time-depth dependent diffusion coefficients of real concrete structures
Two new simple methods to effectively process the experimental results from the natural diffusion test are proposed: one is called the long-specimen-at-one-specific-time method using fewer drilled cylindrical concrete specimens at one time and the other the short-specimen-at-long-elapsed-time method using short drilled cylindrical concrete specimens at various service times.
2. Service life prediction model for existing concrete structures exposed to a chloride environment
This part uses the KHF analytical results to modify an existing service life prediction model of concrete structures exposed to a chloride environment– the LightCon model. Two examples calculated from both two models based on a set of laboratory test data were compared. Practically, the proposed service life prediction model is more reasonable on mathematical logics in that chloride diffusion coefficient is treated as a variable dependent on time, depth, as well as chloride content of concrete, rather than as a constant as normally assumed. However, the study also reveals that more long-term laboratory and field studies on this subject are definitively necessary to improve the mathematical models for a more reliable estimation on the service life of concrete structures in chloride environment.

Abstract	I
Chinese Abstract	III
Dedication	V
Acknowledgements	VI
Table of Contents	VII
List of Tables	XII
List of Figures	XIV
List of Symbols	XVIII


 Introduction	1
1 Background	1
2 Objectives and scopes	2
3 Thesis organization	3

 Literature Review	6
1 Introduction	6
1.1 Chloride transport mechanisms	6
1.2 Interaction of chloride and hardened concrete	7
2 Mathematical models of diffusion	9
2.1 Fick’s first law	9
2.2 Fick’s second law	10
3 Experiment of diffusion	12
3.1 Steady state test methods	13
3.2 Non-steady state test methods	14
3.3 Electrical test methods	15
 Mathematical Model for Time-depth Dependent Diffusion Coefficient by Kirchhoff Transformation Analysis                                              21
1 Introduction	21
2 Solution of time-depth dependent diffusion equation	21
2.1 The process of chloride ingress	21
2.2 The solution of the differential equation of diffusion	22
3 Discussion – The physical phenomena	25
4 Conclusions	27
 Sensitivity Analysis of Time-Depth Dependent Chloride Diffusion Coefficient in Concrete	30
1 Introduction	30
2 Time-depth dependent chloride diffusion model	32
3 Differential sensitivity analysis of time-depth dependent chloride diffusion coefficient	33
4 Results of sensitivity analysis of chloride diffusion coefficient	37
4.1 Sensitivity of chloride diffusion coefficient to time of exposure	37
4.2 Sensitivity of chloride diffusion coefficient to inspecting concrete depth	38
4.3 Sensitivity of chloride diffusion coefficient to surface chloride concentration
	39
4.4 Sensitivity of chloride diffusion coefficient to chloride concentration of inspecting point	40
5 Conclusions	41

 Determining Time-depth Dependent Chloride Diffusion Coefficient in Concrete
46
1 Introduction............................................................................................................	46
2 Verification of the proposed mathematical model	47
2.1 Relationship between apparent chloride diffusion coefficient D and time t 	48
2.2 Relationship between apparent chloride diffusion coefficient D and depth x 	48
3 Discussion	50
3.1 Two new methods to determine time-depth dependent apparent chloride diffusion coefficient	50
3.2 Illustrations for proposed methods	52
4 Conclusions	54

 Non-steady State Service Life Prediction Model for Existing Concrete Structures Exposed to a Chloride Environment                                    65
1 Introduction	65
2 Proposed mathematical modeling for service life prediction	68
3 Service life prediction procedures of the proposed model	71
4 Illustrated examples and discussion	75
5 Conclusions	79

 Effects on Chloride Diffusion Coefficient with Numerical Method 	89
1 Introduction	89
2 Theoretical background of explicit method	90
3 The finite differential equations of diffusion equation	91
3.1 Diffusion coefficient is constant	91
3.2 Diffusion coefficient is depth dependent D(x) 	92
3.3 Diffusion coefficient is time dependent D(t) 	93
3.4 Diffusion coefficient is time-depth dependent D(x,t) 	93
3.5 Diffusion coefficient is concentration dependent D(C) 	94
4 Comparison of the simple analytical solution and the numerical solutions 	95
4.1 The analysis of constant diffusion coefficient Dc	95
4.2 The analysis of depth dependent diffusion coefficient D(x) 	96
4.3 The analysis of time dependent diffusion coefficient D(t) 	97
4.4 The analysis of time-depth dependent diffusion coefficient D(x,t) 	99
4.5 The analysis of concentration dependent diffusion coefficient D(C) 	100
5 Comparison of the KHF analytical solution and the numerical solution of D(C)	102
6 Conclusions	103

 Conclusions and Recommendations	115
1 Conclusions	115
2 Recommendation for future researches	118

References	120
Appendix I.  Experimental Data from Tumidajski, 1995   	130
Appendix II.  Experimental Data from Dhir, 1998 	133
Appendix III.  Experimental Data from Nokken, 2004	134
作者簡介	136
授權書	139

                                

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