Modeling of Structural Damage of Older Reinforced Concrete Components Catherine Ann Pagni A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering University of Washington 2003 Program Authorized to Offer Degree: Department of Civil and Environmental Engineering Table of Contents List of Figures.................................................................................................................v List of Tables................................................................................................................vii Chapter One: Introduction..................................................................................................1 1.1 Background and Research Impetus...........................................................................1 1.2 Research Objectives..................................................................................................1 1.3 Thesis Organization..................................................................................................3 Chapter Two: Literature Review........................................................................................6 2.1 Introduction...............................................................................................................6 2.2 Damage Measures.....................................................................................................6 2.3 Experimental Data....................................................................................................7 2.3.1 Specimen Design Details...................................................................................7 2.3.2 Interior Joint Specimens....................................................................................9 2.3.3 Exterior Joint Specimens.................................................................................11 2.3.4 Influence Factors for Behavior Variation........................................................13 2.4 Methods of Repair...................................................................................................15 2.5 Predicting Damage as a Function of Demand.........................................................17 2.5.1 Fragility Curves...............................................................................................17 2.5.2 Testing goodness-of-fit....................................................................................18 2.5.3 Distribution Selection......................................................................................19 2.5.4 Method of Maximum Likelihood.....................................................................23 2.6 Loss Estimation.......................................................................................................24 Chapter Three: Damage Measures....................................................................................26 3.1 Introduction.............................................................................................................26 3.2 Damage Measures...................................................................................................26 3.2.1 Progression of Damage....................................................................................27 3.2.2 Damage States..................................................................................................27 i 3.3 Cracking..................................................................................................................28 3.3.1 Damage State 0................................................................................................28 3.3.2 Damage State 1................................................................................................29 3.3.3 Damage States 2, 3, and 5................................................................................29 3.3.4 Damage State 9................................................................................................30 3.4 Concrete Spalling and Crushing.............................................................................31 3.4.1 Damage State 6................................................................................................31 3.4.2 Damage State 8................................................................................................32 3.4.3 Damage State 10..............................................................................................33 3.4.4 Damage State 11..............................................................................................33 3.5 Joint Failure Mechanisms.......................................................................................34 3.5.1 Damage State 12(a)..........................................................................................34 3.5.2 Damage State 12(b)..........................................................................................35 3.5.3 Damage State 12(c)..........................................................................................35 3.6 Strength-based Damage Measures..........................................................................35 3.6.1 Damage State 4................................................................................................36 3.6.2 Damage State 7................................................................................................36 3.7 Conclusion..............................................................................................................38 Chapter Four: Engineering Demand Parameters and Experimental Data........................40 4.1 Introduction.............................................................................................................40 4.2 Experimental Data..................................................................................................40 4.2.1 Type of Joint....................................................................................................40 4.2.2 Identify Data Points.........................................................................................41 4.3 Engineering Demand Parameters............................................................................41 4.3.1 Drift Ratio........................................................................................................42 4.3.2 Number of Cycles............................................................................................43 4.3.3 Nonlinear Function of the Drift and Cycles.....................................................44 4.3.4 Joint Strain.......................................................................................................45 4.4 Conclusion..............................................................................................................46 ii Chapter Five: Methods of Repair......................................................................................47 5.1 Introduction.............................................................................................................47 5.2 Repair of Damage Measures...................................................................................47 5.3 Method of Repair 0: Cosmetic Repair....................................................................48 5.3.1 Demolition.......................................................................................................48 5.3.2 Finish Work.....................................................................................................48 5.4 Method of Repair 1: Epoxy Resin Injection of Cracked Concrete.........................49 5.4.1 Epoxy Resin.....................................................................................................49 5.4.2 Advantages and Disadvantages........................................................................50 5.5 Method of Repair 2: Patching of Spalled Concrete................................................50 5.5.1Cementitious Material.......................................................................................50 5.5.2 Advantages and Disadvantages........................................................................51 5.6 Method of Repair 3: Removal and Replacement of Damaged Concrete................51 5.6.1 New Concrete and Formwork..........................................................................51 5.6.2 Shoring.............................................................................................................51 5.6.3 Advantages and Disadvantages........................................................................51 5.7 Method of Repair 4: Removal and Replacement of Damaged Rebar.....................52 5.7.1 New Rebar.......................................................................................................52 5.7.2 Shoring.............................................................................................................52 5.7.3 Advantages and Disadvantages........................................................................52 Chapter Six: Predicting Damage as a Function of Demand.............................................54 6.1 Introduction.............................................................................................................54 6.2 Data Sets.................................................................................................................54 6.2.1 Data Set One....................................................................................................55 6.2.2 Data Set Two....................................................................................................56 6.2.3 Data Set Three..................................................................................................56 6.2.4 Comparison of Data Sets.................................................................................56 iii 6.3 Distribution Selection.............................................................................................57 6.3.1 Step-wise CDF.................................................................................................57 6.3.2 Normal Distribution.........................................................................................59 6.3.3 Lognormal Distribution...................................................................................59 6.3.4 Weibull.............................................................................................................60 6.3.5 Beta..................................................................................................................61 6.3.6 Best Distribution..............................................................................................62 6.4 Method of Maximum Likelihood............................................................................64 6.5 Fragility Curves for Selected EPDs........................................................................67 6.5.1 Number of Cycles............................................................................................68 6.5.2 Nonlinear function of drift and cycles.............................................................69 6.5.3 Joint Strain.......................................................................................................70 6.5.4 Nonlinear function o f Joint Strain and Cycles................................................71 6.5.5 Comparison of the EDPs..................................................................................71 6.6 Uncertainty..............................................................................................................72 6.7 Conclusion..............................................................................................................74 Chapter Seven: Loss Estimation.......................................................................................75 7.1 Introduction............................................................................................................75 7.2 Cost Framework.....................................................................................................75 7.2.1 Labor................................................................................................................75 7.2.2 Equipment........................................................................................................77 7.2.3 Repair Materials...............................................................................................78 7.3 Markups.................................................................................................................79 7.3.1 Labor Conditions.............................................................................................79 7.3.2 Mobilization.....................................................................................................80 7.3.3 Delays due to the Earthquake..........................................................................80 7.3.4 Overhead and Profit.........................................................................................80 7.3.5 Uncertainty.......................................................................................................80 iv 7.4 Unit Cost per Method of Repair.............................................................................81 7.4.1 Method of Repair 0..........................................................................................81 7.4.2 Method of Repair 1..........................................................................................82 7.4.3 Method of Repair 2..........................................................................................82 7.4.4 Method of Repair 3..........................................................................................83 7.4.5 Method of Repair 4..........................................................................................83 7.5 Downtime per Method of Repair...........................................................................84 Chapter Eight: Example....................................................................................................91 8.1 Introduction.............................................................................................................91 8.2 Example Building...................................................................................................91 8.2.1 Building Dimensions.......................................................................................92 8.2.2 Joint Dimensions..............................................................................................92 8.3 Demand Parameter..................................................................................................92 8.4 Earthquake Loss Assessment..................................................................................93 8.4.1 Predicting Damage for Given Demand............................................................93 8.4.2 Markups...........................................................................................................94 8.5 Moderate Earthquake Demand...............................................................................95 8.5.1 Contract Price...................................................................................................96 8.5.2 Downtime.........................................................................................................97 8.6 Severe Earthquake Demand....................................................................................97 8.6.1 Contract Price...................................................................................................98 8.6.2 Downtime.........................................................................................................99 8.7 Uncertainty..............................................................................................................99 8.8 Conclusion..............................................................................................................99 Chapter Nine: Conclusions.............................................................................................101 9.1 Summary...............................................................................................................101 9.2 Conclusions...........................................................................................................102 9.3 Improvements of the Prediction of the Economic Impact....................................104 9.4 Projected Use of Model........................................................................................105 v List of References.......................................................................................................106 Appendix A Design Details of Joint Specimens.........................................................110 Appendix B Joint Strain from Curvature Measurements............................................113 Appendix C Best Engineering Demand Parameter.....................................................115 Appendix D Questions and Answers from Interviews...............................................118 Appendix E Best Distribution ....................................................................................122 Appendix F Modeling of Beam-Column Joints in OpenSEES...................................124 vi List of Figures Figure 1.1: Flowchart identifies the link between the traditional concerns of the engineer with the traditional concerns of the owner..................................................................2 Figure 2.1: (a) Exterior joint detail demonstrates anchorage of beam rebar bent into the joint. (b) The same joint exhibits shear failure of the beam. (Hakuto 2000)............13 Figure 2.2: Detail of exterior joint specimen O7 demonstrates anchorage of beam rebar bent into the column. (Hakuto 2000)........................................................................13 Figure 2.3: The proper labeling of the width and depth of the beam-column joint..........15 (Adapted from Pessiki 1990)............................................................................................15 Figure 2.4: Probability density functions of the Lognormal and Normal distributions. (Haldar and Mahadevan, 2000).................................................................................21 Figure 2.5: Probability density functions for the Beta distribution for varying values of the beta function parameters. (Haldar and Mahadevan, 2000).................................23 Figure 3.1: Interior joint specimen PEER 22 exhibits Damage State 1 partially hidden by instrumentation and Damage State 0 from the previous load cycle. (Walker 2001) 29 Figure 3.2: Interior joint specimen CD30 22 exhibits Damage State 5. (Walker 2001)...30 Figure 3.3: Exterior joint specimen 07 exhibits Damage State 9. (Hakuto 2000)............31 Figure 3.4: Interior joint specimen PEER 22 exhibits Damage State 6. (Walker 2001)..32 Figure 3.5: Interior joint specimen PEER 14 exhibits Damage State 8. (Walker 2001)..33 Figure 3.6: Interior joint specimen C15 14 exhibits Damage State 11. (Walker 2001)...34 Figure 3.7: An existing joint in Caracas, Venezuela exhibits Damage State 12 after an earthquake. (Portland Cement Association, 1967)...................................................35 Figure 3.8: Response hysteresis for specimen P8 (Pessiki 1990).....................................37 Figure 3.9: (a) Response hysteresis of specimen P4 (b) Response hysteresis of specimen P7 (Pessiki 1990)......................................................................................................38 Figure 4.1: The damage states are identified on the response hysteresis of specimen PEER 22. (Adapted from Walker 2001)...................................................................41 Figure 4.1: Typical loading set-up of beam-column joint sub-assemblage......................42 Figure 4.2: Number of cycles counted for the load history of specimen PADH 14. (Walker 2001)...........................................................................................................44 Figure 4.3: Joint strain is measured by the large shear rig (Alire 2002)...........................45 Figure: 6.1: Scatter plots showing the demand at which each damage state (0-12) occurs for all 25 specimens. (a)Drift Ratio (%) (b)Number of cycles (c) Nonlinear Function of drift and cycles (d) Joint strain.............................................................................55 Figure 6.2: Results of Kolmogorov-Smirnov test applied to the three data sets..............56 Figure 6.3: The probability of exceeding each of the five repair groups evaluated using the Stepwise CDF.....................................................................................................58 vii Figure 6.4: Fragility curves for the repair methods 0-4 evaluated using the normal distribution................................................................................................................59 Figure 6.5: Fragility curves for the repair methods 0-4 evaluated using the lognormal distribution................................................................................................................60 Figure 6.6: Fragility curves for the repair methods evaluated using the Weibull distribution................................................................................................................61 Figure 6.7: Fragility curves for the repair methods evaluated using the Beta distribution. ...................................................................................................................................62 Figure 6.8: Kolmogorov-Smirnov test results. (a)Comparison of the test parameters for each distribution and the critical value. (b)Comparison of the probability of the test parameters being less than the critical value.............................................................63 Figure 6.9: Probability of exceeding the repair method evaluated using the method of maximum likelihood to determine the lognormal parameters..................................66 Figure 6.10: Chi-Square test results show that the method of maximum likelihood yields a smaller error and thus will be used to determine the fragility curves....................67 Figure 6.11: Prediction of the method of repair given the number of cycles...................68 Figure 6.12: Prediction of the method of repair for a nonlinear function of drift ratio and number of cycles.......................................................................................................69 Figure 6.13: Prediction of the method of repair given the demand in terms joint strain..70 Figure 6.14: Predication of the method of repair given the demand in terms of nonlinear function of joint strain and number of cycles...........................................................71 Figure 6.15: Results of the Kolmogorov-Smirnov test applied to the selected EDPs for data set two...............................................................................................................72 Figure 8.1: The joint demand is linked to a probability of requiring a specific method of repair using the fragility curves................................................................................81 viii List of Tables Table 5.1: Damage states assigned to each repair technique............................................47 Table 6.1: Stepwise CDF for Method of Repair 0............................................................58 Table 6.2: The results of the Chi-Square test for Method of Repair 0..............................64 Table 6.3: Evaluating the confidence parameters of data set one.....................................73 Table 7.1: Approximate downtime per joint using the time allotted to each method of repair according to the 2003 National Renovation and Insurance Repair Estimator cost book...................................................................................................................90 Table A.1: Design details for interior joint specimens...................................................110 Table A.2: Design details for exterior joint specimens...................................................111 Table A.3: Variation of behavior due to 3 factors..........................................................112 Table C.1: Best EDP.......................................................................................................115 Table C.2: Best EDP.......................................................................................................116 Table C.3: Best EDP.......................................................................................................117 Table E.1: Best Distribution...........................................................................................122 Table E.2: Best Distribution...........................................................................................122 Table E.3: Best Method..................................................................................................123 ix