UNIVERSITY OF CALIFORNIA, SAN DIEGO Development of Load and Resistance Factor Design for FRP Strengthening of Reinforced Concrete Structures A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Structural Engineering by Rebecca Anne Atadero Committee in Charge: Professor Vistasp M. Karbhari, Chair Professor Gilbert A. Hegemier Professor Francesco Lanza di Scalea Professor Marc A. Meyers Professor Jeffrey M. Rabin 2006 UMI Number: 3210643 3210643 2006 UMI Microform Copyright All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, MI 48106-1346 by ProQuest Information and Learning Company. Copyright Rebecca Anne Atadero, 2006 All rights reserved. The dissertation of Rebecca Anne Atadero is approved, and it is acceptable in quality and form for publication on microfilm: __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ Chair University of California, San Diego 2006 iii DEDICATION To my husband, Todd, maybe I could have done it without you, but I am sure glad that I didn’t have to. You are my sunshine and I love you! iv TABLE OF CONTENTS Signature Page iii Dedication iv Table of Contents v List of Figures xviii List of Tables xxi Acknowledgements xxvi Vita xxvii Abstract xxviii Chapter 1. Introduction 1 1.1 Overview 1 1.2 FRPs for Strengthening of Civil Structures 1 1.2.1 Fiber Reinforced Polymer Composites 1 1.2.2 Strengthening and Repair of Civil Structures 2 1.2.3 Advantages of FRPs for Strengthening 4 1.2.4 Disadvantages of FRPs for Strengthening 5 1.3 Design Code for FRP Strengthening 5 1.3.1 Need for a Design Code 5 1.3.2 Uncertainty in Structural Design 7 1.3.3 Design Philosophies as the Basis for Design Codes 7 1.3.3.1 Working Stress Design 8 1.3.3.2 Load and Resistance Factor Design 8 1.3.3.3 Advantages of LRFD 10 1.3.4 Current Design Guidelines for FRP Strengthening 11 v 1.4 Problem Statement and Research Objectives 13 1.4.1 Problem Description 13 1.4.2 Research Objectives 15 1.4.3 Research Approach 16 1.4.4 Outline of the Dissertation 19 Chapter 2. Background for Structural Reliability, LRFD and Design Uncertainty 22 2.1 Introduction 22 2.2 Structural Reliability Methods 22 2.2.1 Uncertainty and Risk 22 2.2.2 Evaluation of Structural Reliability 24 2.2.2.1 Effect of Uncertainty 24 2.2.2.2 Deterministic Safety Factors 25 2.2.2.3 Basic Reliability Problem 26 2.2.2.4 The Reliability Index 29 2.2.2.5 Methods of Computing the Reliability Index 32 2.2.2.5.1 First-Order, Second-Moment Reliability Index 32 2.2.2.5.2 First- and Second-Order Reliability Methods (FORM and SORM)… 33 2.2.2.5.3 Monte Carlo Simulation (MCS) 34 2.2.2.5.4 Other Techniques 35 2.2.2.6 Levels of Reliability Methods 35 2.2.2.7 Component vs. System Reliability 36 2.2.2.8 Time-dependent Reliability 37 2.2.2.9 Limitations of Reliability Methods 38 vi 2.2.2.10 Reliability Methods Used for This Dissertation 39 2.3 Previous Development of LRFD 41 2.3.1 Steel 41 2.3.2 Loads 42 2.3.3 Engineered Wood 43 2.3.4 Bridges 43 2.3.5 Concrete 45 2.3.6 Aspects of Existing Codes Considered in this Work 45 2.4 Previous Work on Reliability of FRP in Civil Infrastructure 46 2.4.1 FRP for Strengthening 46 2.4.1.1 Limitations of Existing Studies 49 2.4.2 FRP for New Construction 50 2.4.2.1 General Design Standards 51 2.5 Statistical Descriptors for Resistance Variables 52 2.5.1 Concrete 53 2.5.2 Reinforcing Steel 55 2.5.3 Dimensions 56 2.5.3.1 Area of Steel 57 2.5.3.2 Slab Dimensions 57 2.5.3.3 Beam Dimensions 57 2.5.4 Modeling Uncertainty 58 2.6 Description of Load Variables 60 2.6.1 Dead Load 61 2.6.2 Live and Impact Loads 61 vii 2.7 Consideration of Continued Degradation 68 2.7.1 Modes of Reinforced Concrete Degradation 68 2.7.2 Corrosion of Steel in Concrete 69 2.7.2.1 Carbonation-Induced Corrosion 71 2.7.2.2 Chloride-Induced Corrosion 72 2.7.2.3 Rates of Corrosion 72 2.7.3 Previous Work Modeling Corrosion-Induced Degradation in Bridges 74 2.7.4 Corrosion Models Used in this Dissertation 76 2.7.4.1 Major Assumptions for Corrosion Modeling 76 2.7.4.2 Mathematical Models for Corrosion 78 2.8 Target Reliability Index 81 2.8.1 Comparison to Other Acceptable Levels of Risk 82 2.8.2 Optimization of Cost-Benefit 83 2.8.3 Empirical Approaches 83 2.8.4 Calibration to Safety Levels Implied by Existing Codes 86 2.8.4.1 Reliability Indices from Other LRFD Codes 87 2.8.5 Selection of Target β for this Work 90 2.9 Discussion of Background Data 92 Chapter 3. Characterization of Composite Properties for Reliability Analysis and Design 94 3.1 Introduction 94 3.2 Description of Data Sets 95 3.2.1 Testing Procedures 95 3.2.2 Wet Layup Composites 95 3.3 Characterization of Random Variation 98 viii 3.3.1 A Note on the Effect of Thickness 98 3.3.2 Basic Statistics 99 3.3.3 Statistical Distributions for Representing Composite Properties 104 3.3.3.1 Distributions 104 3.3.3.2 Distributions Fit to Wet Layup Composite Data 107 3.3.4 Best Fitting Distributions 111 3.3.4.1 Strength 112 3.3.4.2 Modulus 114 3.3.4.3 Thickness 116 3.3.4.4 Summary of Distributions for Reliability Analysis 118 3.3.5 Correlation between Variables 119 3.4 Design Values for Composite Materials 121 3.4.1 Current Approaches to Selection of Design Values 121 3.4.1.1 Reliability Implications of Current Design Approach 123 3.4.2 Proposed Approach to Design Values 128 3.4.2.1 Accounting for Material Variability 128 3.4.2.2 Use of the Mean as the Characteristic Value 130 3.4.2.3 Factors for Systematic Variation and Time-Dependent Behavior 131 3.4.2.4 Promoting Reliability-Based Design 131 3.5 Characterizing and Accounting for Systematic Differences between Laboratory Derived Design Values and In-Situ Properties 133 3.5.1 Currently Used Factors 133 3.5.2 Types of Systematic Variation 136 3.5.3 Proposed Set of Application Factors 137 ix [...]... of Load and Resistance Factor Design for FRP Strengthening of Reinforced Concrete Structures by Rebecca Anne Atadero Doctor of Philosophy in Structural Engineering University of California, San Diego, 2006 Professor Vistasp M Karbhari, Chair Externally bonded fiber reinforced polymer (FRP) composites are an increasingly adopted technology for the renewal of existing concrete structures In order to... Basic Description of System of Application Factors 139 Table 3-22 Properties of Fibers and Matrices for Prediction of Strength and Modulus 141 Table 3-23 Mean and COV of Ratio of Tested Values to Values Predicted Using Properties of Fiber and Matrix for Strength 142 Table 3-24 Mean and COV of Ratio of Tested Values to Values Predicted Using Properties of Fiber and Matrix for Modulus ... field manufacture, and an environment and service-life specific factor for FRP degradation Preliminary resistance factors for design of FRP strengthening are calibrated over a range of design scenarios FRP degradation is considered based on existing durability models, and continued degradation of the structure due to general corrosion of the reinforcing steel is included The girders used for calibration... 188 Table 4-6 Comparison of Distribution of Number of Girders for Selected Bridges 188 Table 4-7 Comparison of Distribution of Deck Widths for Selected Bridges 189 Table 4-8 Comparison of QConBridge™ and CT-BDS for Selected Girders 193 Table 4-9 Load Components and LRFR Factored Load for Design 196 Table 4-10 Distribution Parameters of Load for Reliability Analysis 204 Table 4-11... R.; Lee, L.; Karbhari, V.M Consideration of Material Variability in Reliability Analysis of FRP Strengthened Bridge Decks Composite Structures 2005, 7, pp 430-443 CONFERENCE PAPERS Atadero, R.A.; Karbhari, V.M Probabilistic Based Design for FRP Strengthening of Reinforced Concrete In 7th International Symposium on Fiber -Reinforced Polymer (FRP) Reinforcement for Concrete Structure; Shield, C.K., Busel,... challenges to be overcome in design code development such as the unique characteristics of FRPs, the incomplete database of material properties, and the somewhat limited understanding of the interaction between the FRP and the existing structure 1.2 FRPs for Strengthening of Civil Structures 1.2.1 Fiber Reinforced Polymer Composites A composite is a material that is composed of two or more distinct phases... 169 Chapter 4 Calibration of Resistance Factors for Flexural Strengthening of Bridge Girders 171 4.1 Introduction 171 4.2 Procedure for Calibration of Resistance Factors 171 4.3 Summary of Previous Calibration Work 175 4.3.1 4.3.2 Large Example Calibration without Corrosion (Section C.6) 176 4.3.3 4.4 Load Factors for Strengthening Design (Section C.5) 175 Example... variables of particular significance, requiring extensive further study, are the state of the existing structure when strengthening is applied and the loads acting on the structure xxix Chapter 1 Introduction 1.1 Overview Externally bonded fiber reinforced polymer composites (FRPs) are increasingly considered as a viable means of strengthening, retrofitting, and repairing existing reinforced concrete structures. .. A-2 CDF of Bias Factor for Maximum Load for Different Time Spans 270 xviii Figure A-3 Comparison of Distributions for Mean Maximum 50-Year Load Bias Factor 271 Figure C-1 β vs ψ for Material 1 Designs to Meet LRFD and LRFR Loads 290 Figure C-2 Monte Carlo Results for 20% Steel Loss, Strength COV = 0.25, Modulus COV =0.05, 0 degradation, 75 year loads 299 Figure C-3 Hybrid Results for 20%... Histogram of Deck Width 185 Figure 4-5 Plot of Convergence of Monte Carlo Results as a Function of the Number of Trials 209 Figure 4-6 Example of Plots Used to Select Calibrated Resistance Factors 210 Figure 4-7 ψ vs Strength COV for Girder 18, Corrosion Condition 4, SD, βT = 3.5, and φ = 0.85 218 Figure A-1 PDF of Bias Factor for Maximum Load for Different . UNIVERSITY OF CALIFORNIA, SAN DIEGO Development of Load and Resistance Factor Design for FRP Strengthening of Reinforced Concrete Structures A dissertation. Overview 1 1.2 FRPs for Strengthening of Civil Structures 1 1.2.1 Fiber Reinforced Polymer Composites 1 1.2.2 Strengthening and Repair of Civil Structures 2 1.2.3 Advantages of FRPs for Strengthening. Disadvantages of FRPs for Strengthening 5 1.3 Design Code for FRP Strengthening 5 1.3.1 Need for a Design Code 5 1.3.2 Uncertainty in Structural Design 7 1.3.3 Design Philosophies as the Basis for Design