Modeling and Monitoring the Long-Term Behavior of Post-Tensioned Concrete Bridges Catherine E.W. French, Principal Investigator Department of Civil, Environmental and Geo- Engineering University of Minnesota November 2014 Research Project Final Report 2014-39 To request this document in an alternative format call 651-366-4718 or 1-800-657-3774 (Greater Minnesota) or email your request to [email protected]. Please request at least one week in advance. Technical Report Documentation Page 1. Report No. 2. 3. Recipients Accession No. MN/RC 2014-39 4. Title and Subtitle 5. Report Date Modeling and Monitoring the Long-Term Behavior of November 2014 Post-Tensioned Concrete Bridges 6. 7. Author(s) 8. Performing Organization Report No. Catherine E.W. French, Carol K. Shield, Brock D. Hedegaard 9. Performing Organization Name and Address 10. Project/Task/Work Unit No. Department of Civil, Environmental and Geo- Engineering CTS Project # 2013008 University of Minnesota 11. Contract (C) or Grant (G) No. 500 Pillsbury Drive SE Minneapolis, MN 55455 (C) 99008, (wo) 42 12. Sponsoring Organization Name and Address 13. Type of Report and Period Covered Minnesota Department of Transportation Final Report Research Services & Library 14. Sponsoring Agency Code 395 John Ireland Boulevard, MS 330 St. Paul, MN 55155 15. Supplementary Notes http://www.lrrb.org/pdf/201439.pdf 16. Abstract (Limit: 250 words) The time-dependent and temperature-dependent behavior of post-tensioned concrete bridges were investigated through a case study of the St. Anthony Falls Bridge, consisting of laboratory testing of concrete time-dependent behaviors (i.e., creep and shrinkage), examination of data from the in situ instrumented bridge, and time-dependent finite element models. Laboratory results for creep and shrinkage were measured for 3.5 years after casting, and the data were best predicted by the 1978 CEB/FIP Model Code provisions. To compare the in situ readings to constant- temperature finite element models, the time-dependent behavior was extracted from the measurements using linear regression. The creep and shrinkage rates of the in situ bridge were found to depend on temperature. An adjusted age using the Arrhenius equation was used to account for the interactions between temperature and time-dependent behavior in the measured data. Results from the time-dependent finite element models incorporating the full construction sequence revealed that the 1990 CEB/FIP Model Code and ACI-209 models best predicted the in situ behavior. Finite element analysis also revealed that problems associated with excessive deflections or development of tension over the lifetime of the bridge would be unlikely. The interactions between temperature and time- dependent behavior were further investigated using a simplified finite element model, which indicated that vertical deflections and stresses can be affected by the cyclic application of thermal gradients. The findings from this study were used to develop an anomaly detection routine for the linear potentiometer data, which was successfully used to identify short-term and long-term artificial anomalies in the data. 17. Document Analysis/Descriptors 18. Availability Statement Bridges, Monitoring, Finite element method, Time dependence No restrictions. Document available from: National Technical Information Services, Alexandria, Virginia 22312 19. Security Class (this report) 20. Security Class (this page) 21. No. of Pages 22. Price Unclassified Unclassified 309 Modeling and Monitoring the Long-Term Behavior of Post-Tensioned Concrete Bridges Final Report Prepared by: Catherine E.W. French, Carol K. Shield, Brock D. Hedegaard Department of Civil, Environmental and Geo- Engineering University of Minnesota November 2014 Published by: Minnesota Department of Transportation Research Services & Library 395 John Ireland Boulevard, MS 330 St. Paul, MN 55155 This report represents the results of research conducted by the authors and does not necessarily represent the views or policies of the Minnesota Department of Transportation or the University of Minnesota. This report does not contain a standard or specified technique. The authors, the Minnesota Department of Transportation, and/or the University of Minnesota do not endorse products or manufacturers. Trade or manufacturers’ names appear herein solely because they are considered essential to this report. Acknowledgements Numerical computations were performed using resources provided by the University of Minnesota Supercomputing Institute. Table of Contents Chapter 1: Introduction ................................................................................................................................. 1 1.1 Problem Statement .............................................................................................................................. 1 1.2 Research Approach and Outline ......................................................................................................... 1 1.3 Bridge Description .............................................................................................................................. 2 Chapter 2: Instrumentation ........................................................................................................................... 4 2.1 Overview ............................................................................................................................................ 4 2.2 Static System: VWSGs and Thermistors ............................................................................................ 4 2.2.1 Superstructure VWSGs ............................................................................................................... 4 2.2.2 Superstructure Thermistors ......................................................................................................... 6 2.2.3 Data Collection for the Static System ......................................................................................... 8 2.3 Dynamic System: Linear Potentiometers ........................................................................................... 9 2.3.1 Linear Potentiometers .................................................................................................................. 9 2.3.2 Data Collection for the Dynamic System .................................................................................. 10 Chapter 3: Concrete Material Testing ......................................................................................................... 14 3.1 Compressive Strength and Modulus of Elasticity ............................................................................ 14 3.1.1 MnDOT Testing ........................................................................................................................ 14 3.1.2 UMN Testing ............................................................................................................................. 15 3.1.3 Cemstone Testing ...................................................................................................................... 15 3.2 Tensile Strength ................................................................................................................................ 16 3.3 Creep and Shrinkage ......................................................................................................................... 16 3.4 Coefficient of Thermal Expansion ................................................................................................... 17 3.4.1 UMN Laboratory Testing .......................................................................................................... 17 3.4.2 In Situ Testing ........................................................................................................................... 17 3.4.3 Results Summary ....................................................................................................................... 23 3.5 Unit Weight ...................................................................................................................................... 23 3.5.1 Sample Preparation.................................................................................................................... 23 3.5.2 Testing Procedure ...................................................................................................................... 24 3.5.3 Results ....................................................................................................................................... 24 Chapter 4: Time-Dependent Behavior of Concrete .................................................................................... 25 4.1 Phenomena of Creep and Shrinkage ................................................................................................. 25 4.1.1 Concrete Creep .......................................................................................................................... 25 4.1.2 Concrete Shrinkage ................................................................................................................... 27 4.1.3 Review of Time-Dependent Studies on Existing Structures ..................................................... 27 4.2 Material Parameters for Time-Dependent Models ........................................................................... 28 4.3 ACI Committee 209 ......................................................................................................................... 31 4.3.1 Creep ......................................................................................................................................... 31 4.3.2 Shrinkage ................................................................................................................................... 33 4.3.3 Comments on Original Calibration of the ACI-209 Time-Dependent Model ........................... 34 4.3.4 Derived Material Properties for FEM Input .............................................................................. 35 4.4 B3 ..................................................................................................................................................... 35 4.4.1 Creep ......................................................................................................................................... 35 4.4.2 Shrinkage ................................................................................................................................... 38 4.4.3 Comments on Original Calibration of the B3 Time-Dependent Model .................................... 38 4.4.4 Derived Material Properties for FEM Input .............................................................................. 39 4.5 CEB/FIP Model Code 1978 .............................................................................................................. 39 4.5.1 Creep ......................................................................................................................................... 39 4.5.2 Shrinkage ................................................................................................................................... 41 4.5.3 Comments on Original Calibration of the 1978 CEB/FIP Time-Dependent Model ................. 42 4.5.4 Derived Material Properties for FEM Input .............................................................................. 42 4.6 CEB/FIP Model Code 1990 .............................................................................................................. 43 4.6.1 Creep ......................................................................................................................................... 43 4.6.2 Shrinkage ................................................................................................................................... 45 4.6.3 Comments on Original Calibration of the 1990 CEB/FIP Time-Dependent Model ................. 46 4.6.4 Derived Material Properties for FEM Input .............................................................................. 46 4.7 GL2000 ............................................................................................................................................. 47 4.7.1 Creep ......................................................................................................................................... 47 4.7.2 Shrinkage ................................................................................................................................... 48 4.7.3 Comments on Original Calibration of the GL2000 Time-Dependent Model ............................ 48 4.7.4 Derived Material Properties for FEM Input .............................................................................. 49 4.8 AASHTO LRFD Bridge Design Specifications ............................................................................... 49 4.8.1 Creep ......................................................................................................................................... 50 4.8.2 Shrinkage ................................................................................................................................... 52 4.8.3 Comments on Original Calibration of AASHTO Time-Dependent Provisions ........................ 53 4.8.4 Derived Material Properties for FEM Input .............................................................................. 54 4.9 Summary........................................................................................................................................... 54 4.9.1 Discussion of Basic and Drying Creep ...................................................................................... 55 4.9.2 Discussion of Shrinkage ............................................................................................................ 55 4.9.3 Discussion of Volume-to-Surface Ratio and Predrying ............................................................ 56 4.9.4 Applicability and Usability of Models ...................................................................................... 57 Chapter 5: Validation of Time-Dependent Properties ................................................................................ 58 5.1 Aging Compressive Strength ............................................................................................................ 58 5.2 Aging Elastic Modulus ..................................................................................................................... 59 5.3 Shrinkage .......................................................................................................................................... 59 5.4 Creep................................................................................................................................................. 60 5.5 Summary and Conclusions ............................................................................................................... 62 Chapter 6: Time-Dependent Finite Element Modeling ............................................................................... 64 6.1 Time-Dependent Finite Element Model Overview .......................................................................... 64 6.1.1 Geometry and Mesh .................................................................................................................. 64 6.1.2 Material Properties .................................................................................................................... 67 6.1.3 Construction Staging Sequence ................................................................................................. 67 6.1.4 Loading ...................................................................................................................................... 71 6.2 Modeling Time-Dependent Behavior of Viscoelastic Materials ...................................................... 72 6.2.1 Kelvin Chain Model for Viscoelastic Materials ........................................................................ 73 6.2.2 Post-Widder Theorem and Curve Fitting the Compliance Function ......................................... 74 6.2.3 Rate-Type Creep Model in Elastic Finite Element Analysis ..................................................... 77 6.2.4 Implementation of Shrinkage Strains ........................................................................................ 79 6.2.5 Relaxation of Post-Tensioning Steel ......................................................................................... 79 6.2.6 Summary of Kelvin Chain Approximation in Finite Element Implementation ........................ 80 6.2.7 Exceptions to Kelvin Chain Model Methodology ..................................................................... 83 6.2.8 Validation of Kelvin Chain Approximation .............................................................................. 88 6.3 Modeling Time-Dependent Behavior of Composite Materials ........................................................ 90 6.3.1 Effects of Mild Steel on Concrete Time-Dependent Behavior .................................................. 90 6.3.2 Adjustment of Kelvin Chain Creep Methodology for Composites ........................................... 91 6.3.3 Summary of Kelvin Chain Approximation for Composite Materials ....................................... 95 6.3.4 Validation of Time-Dependent Modeling of Composite Materials ........................................... 96 6.3.5 Summary and Conclusions ........................................................................................................ 98 Chapter 7: Examining Measured Data for Time-Dependent Behaviors ................................................... 100 7.1 Extraction of Time-Dependent Behavior using Linear Regression ................................................ 100 7.2 Temperature Dependence of Time-Dependent Phenomena ........................................................... 103 7.2.1 Temperature Dependence of Concrete Aging ......................................................................... 103 7.2.2 Temperature Dependence of Basic Creep ............................................................................... 104 7.2.3 Temperature Dependence of Shrinkage and Drying Creep ..................................................... 106 7.3 Time-Dependent Behavior in Measured Data ................................................................................ 106 7.3.1 Evidence Showing Temperature Dependence of Time-Dependent Behavior ......................... 106 7.3.2 Temperature Correction of Time-Dependent Behavior in Measured Data ............................. 109 Chapter 8: FEM Results for Time-Dependent Behavior........................................................................... 112 8.1 Comparison of Finite Element Model with Measured Data ........................................................... 112 8.1.1 Longitudinal Deflections ......................................................................................................... 112 8.1.2 Concrete Strains ...................................................................................................................... 115 8.1.3 Vertical Deflections ................................................................................................................. 116 8.1.4 Longitudinal Concrete Stresses ............................................................................................... 118 8.2 Uncertainty in Estimating Time-Dependent Behavior ................................................................... 121 8.2.1 Discussion of Creep and Shrinkage Uncertainty ..................................................................... 121 8.2.2 Investigating Time-Dependent Uncertainty using FEM ......................................................... 123 8.2.3 Accounting for Uncertainty of Time-Dependent Behavior in Design .................................... 124 8.3 Summary and Conclusions ............................................................................................................. 125 Chapter 9: FEM Investigation of Thermal Effects on Time-Dependent Behavior ................................... 127 9.1 Methodology................................................................................................................................... 127 9.2 Validation of Temperature-Dependent FEM .................................................................................. 129 9.3 Effects of Cyclic Thermal Input on Time-Dependent Behavior..................................................... 130 9.3.1 FEM Model Construction ........................................................................................................ 130 9.3.2 Investigated Thermal Variations ............................................................................................. 132 9.3.3 Results ..................................................................................................................................... 134 9.4 Summary and Conclusions ............................................................................................................. 138 Chapter 10: Protocol for Long-Term Monitoring System ........................................................................ 142 10.1 Extrapolation of Time-Dependent Data ....................................................................................... 143 10.1.1 Bayes’ Theorem .................................................................................................................... 143 10.1.2 Bayesian Regression .............................................................................................................. 144 10.1.3 Bayesian Prediction ............................................................................................................... 146 10.1.4 Long-Term Bayesian Predictions on Linear Potentiometer Data .......................................... 147 10.2 Short-Term Anomaly Detection ................................................................................................... 149 10.2.1 Criteria for Short-Term Anomaly Detection Algorithm........................................................ 149 10.2.2 Summary of Short-Term Check Method ............................................................................... 150 10.2.3 Validating Short-Term Check Methodology on Existing Data ............................................. 151 10.2.4 Validating Short-Term Check with Artificially Induced Perturbations ................................ 152 10.3 Long-Term Anomaly Detection ................................................................................................... 154 10.3.1 Criteria for Long-Term Anomaly Detection Algorithm ........................................................ 154 10.3.2 Summary of Long-Term Check Method ............................................................................... 158 10.3.3 Validating Long-Term Check on Existing Data .................................................................... 158 10.3.4 Validating Long-Term Check for Artificially Induced Perturbations ................................... 159 10.4 Summary and Conclusions ........................................................................................................... 160 Chapter 11: Summary and Conclusions .................................................................................................... 163 11.1 Interactions between Temperature and Time-Dependent Behavior ............................................. 163 11.1.1 Method for Separating Time- and Temperature-Dependent Behavior .................................. 163 11.1.2 Temperature-Dependent Rates of Time-Dependent Phenomena .......................................... 164 11.1.3 Impact of Cyclic Temperatures on Time-Dependent Behavior ............................................. 165 11.2 Long-Term Behavior of St. Anthony Falls Bridge ....................................................................... 167 11.3 Anomaly Detection Routine for Structural Monitoring ................................................................ 168 11.3.1 Detecting Short-Term Anomalies.......................................................................................... 168 11.3.2 Detecting Long-Term Anomalies .......................................................................................... 169 11.3.3 Present Drawbacks and Topics for Future Study .................................................................. 170 11.4 Efficacy of Investigated Time-Dependent Models ....................................................................... 171 References ................................................................................................................................................. 173 Tables ........................................................................................................................................................ 177 Figures ...................................................................................................................................................... 202 Appendix A: Proof of Rate-Type Creep Methodology Appendix B: Validation of Time-Dependent FEM of St. Anthony Falls Bridge Appendix C: Investigation of Simplified Construction Staging Procedure List of Tables Table 1.1: Casting dates of CIP spans ....................................................................................................... 177 Table 1.2: Casting and erection dates of the precast segments ................................................................. 178 Table 1.3: Load stages during construction .............................................................................................. 179 Table 2.1: Summary of gage types and locations ..................................................................................... 180 Table 2.2: VWSG and thermistor labeling, locations, and connections ................................................... 181 Table 2.3: Channel configuration for CR10 data collection during construction ..................................... 185 Table 2.4: Linear potentiometer labeling and locations ............................................................................ 186 Table 3.1: MnDOT test results for superstructure concrete compressive strength ................................... 187 Table 3.2: UMN test results for superstructure concrete compressive strength and modulus of elasticity ................................................................................................................................................. 187 Table 3.3: Cemstone test results for superstructure concrete compressive strength and modulus of elasticity ................................................................................................................................................. 188 Table 3.4: Superstructure concrete tensile strength measured by UMN ................................................... 188 Table 3.5: Creep sample loading and unloading ....................................................................................... 189 Table 3.6: Summary of coefficient of thermal expansion using UMN laboratory specimens .................. 189 Table 3.7: Averaged coefficient of thermal expansion by location using VWSG data ............................ 190 Table 3.8: Average superstructure coefficient of thermal expansion using LP data ................................. 190 Table 3.9: Summary of concrete coefficient of thermal expansion .......................................................... 190 Table 4.1: Mix design for superstructure and pier concrete ...................................................................... 190 Table 4.2: Volume-to-surface and reinforcement ratios for concrete elements in Span 1 ........................ 191 Table 4.3: Volume-to-surface and reinforcement ratios for concrete elements in Span 2 ........................ 192 Table 4.4: Volume-to-surface and reinforcement ratios for concrete elements in Span 3 ........................ 193 Table 4.5: Volume-to-surface and reinforcement ratios for concrete elements in piers and barrier rails ........................................................................................................................................................ 194 Table 4.6: Coefficients for increase in concrete strength with time (ACI 209R-92, Table 2.2.1) ............ 194 Table 4.7: Ultimate shrinkage correction for duration of curing (ACI 209R-92, Table 2.5.3) ................. 194 Table 4.8: Summary of model inputs required for time-dependent behavior of superstructure concrete .................................................................................................................................................. 195 Table 4.9: Summary of model inputs required for time-dependent behavior of pier and barrier rail concrete .................................................................................................................................................. 196 Table 4.10: Humidity dependent coefficients φ , λ, and ε from 1978 CEB/FIP Model Code ............... 197 f1 s1 Table 6.1: Analysis Steps for Erection Procedure .................................................................................... 198 Table 6.2: Summary of post-tensioning stresses ....................................................................................... 199 Table 6.3: Approximation coefficients for creep terms β (t – t ) and β(t) of 1978 CEB/FIP Model d 0 f Code ....................................................................................................................................................... 199 Table 6.4: Approximation coefficients for shrinkage term β(t) of 1978 CEB/FIP Model Code ............. 199 s Table 7.1: Fit parameters for Northbound Span 1 LP data using unadjusted time ................................... 200 Table 7.2: Fit parameters for Northbound Span 3 LP data using unadjusted time ................................... 200 Table 7.3: Fit parameters for Southbound Span 1 LP data using unadjusted time ................................... 200 Table 7.4: Fit parameters for Southbound Span 3 LP data using unadjusted time ................................... 200 Table 8.1: Load cases and corresponding multiple presence factors used for investigation of critical Service I and Service III vehicular live loading ........................................................................ 201