Probabilistic Analysis of Concrete Fracture Mustafa Abushaala Aldalinsi University of Texas at El Paso, [email protected]
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University of Texas at El Paso DigitalCommons@UTEP Open Access Theses & Dissertations 2010-01-01 Probabilistic Analysis of Concrete Fracture Mustafa Abushaala Aldalinsi University of Texas at El Paso, [email protected] Follow this and additional works at: https://digitalcommons.utep.edu/open_etd Part of the Civil Engineering Commons Recommended Citation Aldalinsi, Mustafa Abushaala, "Probabilistic Analysis of Concrete Fracture" (2010). Open Access Theses & Dissertations. 2629. https://digitalcommons.utep.edu/open_etd/2629 This is brought to you for free and open access by DigitalCommons@UTEP. It has been accepted for inclusion in Open Access Theses & Dissertations by an authorized administrator of DigitalCommons@UTEP. For more information, please contact [email protected]. PROBABILISTIC ANALYSIS OF CONCRETE FRACTURE MUSTAFA ABUSHAALA ALDALINSI Department of Civil Engineering APPROVED: Carlos M. Ferregut, Ph.D., Chair Cesar Carrasco, Ph.D. Rafael S. Gutierrez, Ph.D. Patricia D. Witherspoon, Ph.D. Dean of the Graduate School DEDICATION To my parents My brothers My sisters My wife and My kids PROBABILISTIC ANALYSIS OF CONCRETE FRACTURE by MUSTAFA ABUSHAALA ALDALINSI, B.S.C.E. THESIS Presented to the Faculty of the Graduate School of The University of Texas at El Paso in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE Department of Civil Engineering THE UNIVERSITY OF TEXAS AT EL PASO May 2010 ACKNOWLEDGEMENTS The author wishes to express his gratitude to Dr. Carlos Ferregut, Associate Dean of College of Engineering and Professor in the Department of Civil Engineering at the University of Texas at El Paso, for his help, patience, and guidance throughout this study. His continuous encouragement brought this study into completion. Thanks are also due to Dr. Cesar Carrasco, Associate Professor and Chairman in the Department of Civil Engineering, and Dr. Rafael S. Gutierrez, Associate Professor in the Department of Industrial Engineering of UTEP, for participating in the committee of the final examination of the author. Thanks to all my family and friends for their support, and Libyan Ministry of Higher Education for giving me this opportunity to study in the US. iv TABLE OF CONTENTS ACKNOWLEGEMENT………………………………………………………………………. iv TABLE OF CONTENTS………………………………………………………………………..v LIST OF TABLES……………………………………………………………………………...ix LIST OF FIGURES……………………………………………………………………………..x Chapter 1. INTRODUCTION………………………………………………………………………..1 1.1 Introduction…………………………………………………………………………1 1.2 Objectives and Scope………………………………………………………………..4 2. LITERATURE REVIEW…………………………………………………………………5 2.1 Introduction…………………………………………………………………………5 2.2 Literature Survey…………………………………………………………………….5 2.3 Standard Review……………………………………………………………………15 2.3.1 British standard…………………………………………………………..16 2.3.2 The Canadian standard…………………………………………………...16 2.3.3 The Japanese Principal Guide……………………………………………16 2.3.4 International standard…………………………………………………….17 2.4 Service Life Prediction Methodologies…………………………………………….18 2.4.1 Probabilistic methods…………………………………………………….18 v 2.4.2 Factorial method………………………………………………………….19 2.4.3 Engineering design method………………………………………………20 2.5 Environmental impacts on building components…………………………………...21 2.6 Fatigue analysis and assessment procedure for steel structure……………………..23 2.6.1 Limitation…………………………………………………………………23 2.6.2 Fatigue assessment procedure…………………………………………….23 2.7 Conclusion…………………………………………………………………………..25 3. FRACTURE MECHANICS……………………………………………………………..26 3.1 Introduction…………………………………………………………………………26 3.2 LEFM Approach to Fatigue Crack Propagation…………………………………….26 3.2.1 Paris Law…………………………………………………………………..27 3.2.2 Forman‘s Law……………………………………………………………..28 3.2.3 Walker‘s Law……………………………………………………………...28 3.3 The Fracture Mechanics Approach to Design……………………………………….29 3.3.1 The Energy Criterion………………………………………………………30 3.3.2 Stress Intensity Factor (퐾I) Approach……………………………………..33 3.4 Conclusion…………………………………………………………………………....35 vi 4. PROPOSED MODEL……………………………………………………………………..36 4.1 Introduction………………………………………………………………………….36 4.2 Load Histories and Measurements...............................................................................38 4.3 Optimised fatigue crack propagation model for concrete............................................43 4.3.1 Crack growth rate (퐶)...................................................................................44 4.3.2 The sudden increase function (퐹).................................................................46 4.3.3 Strength of cracked plain concrete beams....................................................47 4.4 Application to compute residual life of plain concrete................................................49 4.5 The obtained results from the application....................................................................53 4.6 Conclusions…………………………………………………………………………..53 5. RELIABILITY ANALYSIS………………………………………………………………55 5.1 Introduction………………………………………………………………………….55 5.2 Reliability Analysis Methodology...............................................................................56 5.3 Reliability Analysis of the Fatigue Crack Growth......................................................63 5.4 Analysis of suggested statistical data...........................................................................64 5.5 Example Run Using COMREL-TI 8.10 Software and Assumed Data........................68 5.6 Understanding of Parameter (∆a).................................................................................71 vii 5.7 Conclusion…………………………………………………………………………...73 6. CONCLUSIONS AND RECOMMENDATIONS………………………………………..74 6.1 Conclusions………………………………………………………………………….74 6.2 Recommendations…………………………………………………………………...75 LIST OF REFERENCES……………………………………………………………………….77 TITLE OF APPENDIX…………………………………………………………………………81 CURRICULUM VITA………………………………………………………………………….92 viii LIST OF TABLES Table (4.1) Concrete mix and material properties for small and large specimen.......................38 Table (4.2) Loading history and experimental results for small specimens................................40 Table (4.3) Loading history and experimental results for large specimens.................................41 Table (4.4) Geometry and material properties of specimens.......................................................44 Table (4.5) C values and material properties...............................................................................44 Table (4.6) Calculation of proposed model (Spreadsheet)..........................................................49 Table (4.7) Parameters used in spreadsheet................................................................................50 Table (5.1) Input parameters........................................................................................................60 Table (5.2) Values obtained from Mote Carlo Simulation...........................................................60 Table (5.3) Properties of parameters used in the sample runs......................................................63 Table (5.4) Random variables used in the reliability analysis in the sample runs.......................64 Table (5.5) Resulting sensitivity factors......................................................................................66 ix TABLE OF FIGURES Figure (1.1) Fracture process zone.................................................................................................3 Figure (3.1) Comparison of fracture mechanics approach to design with the traditional strength of material approach................................................................................30 Figure (3.2) Through-Thickness crack in an infinite plate subject to remote tensile stress..........32 Figure (3.3) Three-Dimensional coordinate system for region of crack tip.................................34 Figure (4.1) Loading devices for large and small specimen..........................................................37 Figure (4.2) Specimens‘ dimensions.............................................................................................37 Figure (4.3) Simulated earthquake loading applied in experiments..............................................39 Figure (4.4) Compliance calibration curve for large specimen.....................................................42 Figure (4.5) Effective crack length vs. number of load cycles for the large specimen (G05).......48 Figure (5.1) Definition of reliability index...................................................................................55 Figure (5.2) Basic concepts for FORM........................................................................................57 Figure (5.3) 95% confidence bounds and mean values of (da) vs. number of load cycles (N)....61 Figure (5.4) Probability density function for da=50.64 by Monte Carlo Simulation...................62 Figure (5.5) Importance factors....................................................................................................64 Figure (5.6) Coefficient of variation of (∆a) vs. sensitivity factors for ∆a, KIC, and ∆KI...........66 x Chapter 1 INTRODUCTION 1.1 Introduction In recent years, monitoring, repair, and renewal of existing structures such as bridges and buildings have brought many challenges to civil engineers. It is well known to civil engineers that fatigue leads to the bulk of structural failures. In plain and reinforced concrete structures, fatigue might account for excessive deformation, excessive crack widths, de-bonding