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Seismic structural health monitoring of bridges Mirza, Kian 2006

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SEISMIC STRUCTURAL HEALTH MONITORING OF BRIDGES by KIAN MIRZA B.Sc, The University of Shaihd Chamran, 1990 M.Sc, The Azad University-South Branch, 1994 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF T H E REQUIRMENTS FOR T H E DEGREE OF DOCTOR OF PHILOSOPHY in T H E FACULTY OF GRADUTE STUDIES (Civil Engineering) T H E UNIVERSITY OF BRITISH COLUMBIA June 2006 © Kian Mirza, 2006 ABSTRACT Seismic Structural Health Monitoring (SSHM) is defined here as the process to determine the status of serviceability of a structure immediately after an earthquake. This can be done remotely via the Internet or any suitable communication link. In this study, a procedure was introduced for SSHM of bridges with limited strong motion instrumentation. This procedure is developed and presented in a flowchart format, which can be easily implemented as a user-friendly software. The SSHM Procedure is able to analyze the recorded motions by the sensors installed on a bridge after an earthquake and determine the serviceability status of the structure. The level of serviceability can be easily determined by the procedure as Safe, Limited or Out of Service. It can also determine the location and severity of the damages sustained, i f any. This procedure is a combination of the results of two main components: those from the use of a structural health monitoring (SHM) technique and those from a series of nonlinear structural analyses. This combination can minimize the errors and misinterpretation of results, which may arise from the independent implementation of each component. The Damage Index Method (DIM) is the S H M method used in this study, and has been critically reviewed. This is the first time the DIM has been used on a real bridge with very limited number of sensors. A n actual bridge (the Painter Street Overpass Bridge located in California), which has been instrumented and has experienced more than ten earthquakes of different intensities was selected as a case study. The proposed SSHM was implemented to assess the status of the bridge for selected earthquakes. Complementary strong motion records were generated to induce artificial levels of damage to a well calibrated finite element model of the bridge, and the results from these analyses were used to further assess the effectiveness of the proposed procedure. The proposed SSHM procedure is shown to be accurate, rational and relatively easy to implement in engineering practice. Table of Contents ABSTRACT II T A B L E OF CONTENTS Ill LIST OF FIGURES VII LIST OF ABBREVIATIONS & SYMBOLS XIII PREFACE XIV ACKNOWLEDGEMENTS XVII CHAPTER 1 1 LITERATURE REVIEW AND OBJECTIVES 1.1 INTRODUCTION 1 1.2 DEFINITION OF DAMAGE 1 1.3 STRUCTURAL H E A L T H MONITORING PROCESS 2 1.4 PAST PROJECTS ON BRIDGES 3 1.4.1 Doebling, Farrar, & Cornwell (1997) 3 1.4.2 Wang, Satpathi, and Heo (1997) 4 1.4.3 Nigbor & Diehl (1997) 4 1.4.4 Kwonetal. (1998) 5 1.4.5 Maeck & De Roeck (1999) 5 1.4.6 Stubbs et al. (1999) 6 1.4.7 Wangetal. (1999) 6 1.4.8 Koetal. (1999) 7 1.4.9 Feng & Baling (1999) 8 1.4.10 Enright et al. (1999) 8 1.4.11 Peeters and De Roeck (2000) 9 1.4.12 Bergmeister & Santa (2000) 9 1.4.13 Feng et al. (2000) 10 1.4.14 Choi & Kwon (2000) / / 1.4.15 Park, Kim, & Stubbs (2002) / / 1.4.16 Zabel (2004) 12 1.4.17 Bernal & Hernandez (2004) 12 1.4.18 Park, Stubbs, & Bolton (2005) 12 1.5 RESEARCH NEEDS 13 1.6 SCOPE AND OBJECTIVES 14 1.7 THESIS OUTLINE 15 CHAPTER 2 16 APPLIED METHODOLOGY 2.1 INTRODUCTION 16 2.2 FINITE ELEMENT UPDATING 16 2.3 NONLINEAR ANALYSES 17 2.4 SYSTEM IDENTIFICATION AND DAMAGE DETECTION 18 2.4.1 Damage Index Method (DIM) 19 2.4.2 Damage Severity Estimation 22 2.4.3 Shear Beam Theory of DIM 22 2.4.4 Illustrative Example of DIM Application 23 2.5 COMBINATION OF NONLINEAR ANALYSIS & DAMAGE INDEX RESULTS 27 2.6 BRIDGE SEISMIC STRUCTURAL H E A L T H MONITORING PROCEDURE '. 28 CHAPTER 3 29 CASE STUDY, FINITE E L E M E N T MODELLING AND MODEL CALIBRATION 3.1 INTRODUCTION 29 3.2 DESCRIPTION OF THE BRIDGE 29 3.3 AMBIENT VIBRATION TEST 36 3.4 FINITE ELEMENT MODEL 42 3.4.1 Soil-Structure Interaction 42 3.5 MODEL CALIBRATION 43 3.5.1 Trinidad Offshore Earthquake 48 3.5.2 Cape Mendocino 86-1 51 3.5.3 Petrolia 92 51 3.6 CONCLUSION 58 CHAPTER 4 59 NON-LINEAR STATIC AND DYNAMIC ANALYSES 4.1 INTRODUCTION 59 4.2 STATIC NON-LINEAR ANALYSIS (PUSHOVER) 59 4.2.1 Bent's Hinges 61 4.2.2 Soil Links 64 4.2.3 Pushover Analysis Results 65 4.3 NONLINEAR DYNAMIC ANALYSIS (TIME HISTORY) 72 4.3.1. Scaling 73 4.3.3 Trinidad 11.9 80 4.3.5 Cape Mendocino 86-6.5 90 4.3.6 Petrolia 92-3.0 95 4.3.7Petrolia 92-3.5 100 4.4 CONCLUSION 105 CHAPTER 5 106 SYSTEM IDENTIFICATION AND DAMAGE DETECTION 5.1 INTRODUCTION 106 5.2 SYSTEM IDENTIFICATION 106 5.2.1 Trinidad 9.8 107 5.2.2 Trinidad 11.9 108 5.2.3 CM86 4.6 108 5.2.4 CM86 6.5 '. 108 5.2.5 P92-3.0 109 5.2.6 P92-3.5 109 5.2.7 Discussion on Mode Shapes 109 5.3 DAMAGE DETECTION : 114 5.3.1 Artificial Earthquakes' Damage Indices 117 5.4 CONCLUSION 122 CHAPTER 6 123 A PROCEDURE FOR BRIDGES SEISMIC STRUCTURAL H E A L T H MONITORING.. 6.1 INTRODUCTION 123 6.2 GENERAL IDEA OF THE PROCEDURE 123 6.3 PROCEDURE FOR SEISMIC STRUCTURAL H E A L T H MONITORING (SSHM) 125 6.4 PROCEDURE ELEMENTS 128 6.4.1 Acceleration Comparison (AC) 129 6.4.2 Displacement Comparison (DC) /30 6.4.3 Damage Index & Frequencies Comparison 133 6.5 PREREQUISITE FOR SEISMIC STRUCTURAL H E A L T H MONITORING 135 6.6 PROCEDURE VERIFICATION AND APPLICATION 136 6.6.1 Verification 136 6.6.2 Application 140 6.7 RECOMMENDATIONS 141 CHAPTER 7 143 SUMMARY, CONTRIBUTION, AND FUTURE WORK 7.1 SUMMARY 143 7.2 CONTRIBUTIONS 144 7.2.1 Critical Review of DIM 144 7.2.2 Introducing the SSHM Procedure 145 7.3 FUTURE WORK 147 REFERENCES 148 APPENDIX A 154 APPENDIX B 161 List of Tables T A B L E 3-1: SIGNIFICANT EARTHQUAKES RECORDED AT PAINTER STREET OVERPASS (1977-1992) 32 T A B L E 3-2: AMBIENT VIBRATION RESULTS FOR P S O BRIDGE 37 TABLE 3-3: SYSTEM IDENTIFICATION USING RECORDED EARTHQUAKES (WITHOUT BASE MOVEMENT). . 40 T A B L E 3-4: SPRING AND DASHPOT V A L U E S FOR SOIL-STRUCTURE INTERACTION 44 T A B L E 3-5: COMPARISON BETWEEN THE AMBIENT VIBRATION AND THE F E MODEL RESULTS 45 T A B L E 3-6: COMPARISON BETWEEN ACCELERATIONS A N D DISPLACEMENTS FROM ANALYSIS AND RECORD 58 T A B L E 4-1: PUSHOVER STEPS RESULT 68 T A B L E 4-2: NONLINEAR ANALYSES COMPARISON 74 T A B L E 5-1: FREQUENCIES COMPARISON FOR THE ARTIFICIAL EARTHQUAKES 114 T A B L E 5-2: MODE SHAPES COORDINATES 118 TABLE 6-1: M A X I M U M ACCELERATION V A L U E S FOR THE FREE-FIELD AND THE STRUCTURE 129 T A B L E 6-2: COMPARISON BETWEEN THE DISPLACEMENTS FROM NONLINEAR A N A L Y S E S 132 List of Figures FIGURE 2-1 : U B C TEST F R A M E IN U B C (COURTESY OF C . E . V E N T U R A ) 25 FIGURE 2-2: L O C A T I O N OF SENSORS 26 FIGURE 2-3: D A M A G E DETECTION M O D E L FOR U B C TEST F R A M E ( A F T E R P A R K ' S P A P E R , 2004) 2 6 FIGURE 2-4: RESULTS OF D A M A G E L O C A L I Z A T I O N FOR C A S E 3 ( A F T E R P A R K ' S PAPER, 2004) 2 7 FIGURE 3-1: P S O B R I D G E (COURTESY OF C . E . V E N T U R A ) 3 0 FIGURE 3-2: P S O B R I D G E SENSOR L A Y O U T (COURTESY OF C . E . V E N T U R A ) 31 FIGURE 3-3: L O C A L G E O G R A P H I C A L L O C A T I O N OF THE B R I D G E A L O N G WITH THE EPICENTRE OF THE E A R T H Q U A K E S ( C O U R T E S Y OF C . E . V E N T U R A ) 32 FIGURE 3-4: G L O B A L G E O G R A P H I C A L L O C A T I O N OF B R I D G E IN U S A , (COURTESY OF Y A H O O WEBSITE) 33 FIGURE 3-5: IDEALIZED SOIL PROFILES THAT EMERGED FROM REFRACTION SURVEYS 35 FIGURE 3-6: L O C A T I O N OF THE SENSORS FOR THE A M B I E N T V I B R A T I O N TEST (COURTESY OF C . E . V E N T U R A ) 37 FIGURE 3-7: T H E M O D E SHAPES DERIVED B Y THE A M B I E N T V I B R A T I O N TEST, 1992 3 9 FIGURE 3-8: N O R M A L I Z E D V / H R A T I O VS. F R E Q U E N C Y ( H Z ) FOR A M B I E N T V I B R A T I O N TEST A N D THE E A R T H Q U A K E S 41 FIGURE 3-9: PAINTER STREET O V E R P A S S B R I D G E F E M O D E L 45 FIGURE 3-10: FIRST M O D E ( V E R T I C A L ) - B Y S A P 2 0 0 0 & A R T E M I S 46 FIGURE 3-11: S E C O N D M O D E ( T R A N S V E R S E ) - B Y S A P 2 0 0 0 & A R T E M I S 46 FIGURE 3-12: THIRD M O D E ( V E R T I C A L ) - B Y S A P 2 0 0 0 & A R T E M I S 4 6 FIGURE 3-13: F O U R T H M O D E ( V E R T I C A L ) - B Y S A P 2 0 0 0 & A R T E M I S 4 7 FIGURE 3-14: FIFTH M O D E ( T R A N S V E R S E ) - B Y S A P 2 0 0 0 & A R T E M I S 47 FIGURE 3-15: SIXTH M O D E ( V E R T I C A L ) - B Y S A P 2 0 0 0 & A R T E M I S 47 FIGURE 3-16: COMPARISON BETWEEN R E C O R D A N D A N A L Y S I S - V E R T I C A L A C C E L E R A T I O N (CM/S 2 ) VS. T I M E (SEC)-TRINIDAD OFFSHORE E A R T H Q U A K E 4 9 FIGURE 3-17: COMPARISON BETWEEN R E C O R D A N D A N A L Y S I S - T R A N S V E R S E , V E R T I C A L A N D LONGITUDINAL A C C E L E R A T I O N ( C M / S 2 ) VS. T I M E (SEC) RESPECTIVELY-TRINIDAD OFFSHORE E A R T H Q U A K E 50 FIGURE 3-18: C O M P A R I S O N BETWEEN RECORD A N D A N A L Y S I S - T R A N S V E R S E A C C E L E R A T I O N ( C M / S 2 ) VS. T I M E ( S E C ) - C A P E M E N D O C I N O 86-1 E A R T H Q U A K E 52 FIGURE 3-19: COMPARISON BETWEEN R E C O R D A N D A N A L Y S I S - V E R T I C A L A C C E L E R A T I O N ( C M / S 2 ) VS. T I M E (SEC) -CAPE M E N D O C I N O 86-1 E A R T H Q U A K E 53 FIGURE 3-20: COMPARISON BETWEEN R E C O R D A N D A N A L Y S I S - V E R T I C A L A N D LONGITUDINAL A C C E L E R A T I O N ( C M / S 2 ) VS . T I M E (SEC) R E S P E C T I V E L Y - C A P E M E N D O C I N O 86-1 E A R T H Q U A K E . . . . 54 FIGURE 3-21: C O M P A R I S O N BETWEEN R E C O R D A N D A N A L Y S I S - T R A N S V E R S E A C C E L E R A T I O N ( C M / S 2 ) VS . T I M E (SEC)-PETROLIA 92 E A R T H Q U A K E .- 55 FIGURE 3-22: COMPARISON BETWEEN R E C O R D A N D A N A L Y S I S - V E R T I C A L A C C E L E R A T I O N ( C M / S 2 ) VS. T I M E (SEC)-PETROLIA 92 E A R T H Q U A K E 5 6 FIGURE 3-23: COMPARISON BETWEEN RECORD A N D A N A L Y S I S - V E R T I C A L A N D LONGITUDINAL A C C E L E R A T I O N ( C M / S 2 ) VS . TIME (SEC) RESPECTIVELY-PETROLIA 92 E A R T H Q U A K E 5 7 FIGURE 4 -1 : C O L L A P S E OF CONTINUOUS D E C K S IN THE H Y O G O - K E N E A R T H Q U A K E 1995(AFTER C H E N & D U A N , 2000) 61 FIGURE 4-2 : F A I L U R E OF F L A R E D C O L U M N IN NORTHRIDGE E A R T H Q U A K E 1994 ( A F T E R C H E N & D U A N , 2000) 6 2 FIGURE 4-3 : T Y P E & L O C A T I O N OF S T R U C T U R A L HINGES FOR PUSHOVER A N A L Y S I S 62 FIGURE 4-4: A - A CROSS SECTION OF THE C O L U M N 63 FIGURE 4-5: B - B CROSS SECTION OF THE B E A M 63 FIGURE 4-6: M O M E N T - C U R V A T U R E D I A G R A M OF B E N T E L E M E N T S 64 FIGURE 4-7: N O N L I N E A R B E H A V I O U R OF PILES IN THE B E N T A N D THE A B U T M E N T S 66 FIGURE 4-8: PUSHOVER R E S U L T 67 FIGURE 4-9: FORMATION OF HINGES IN THE B E N T F R A M E 69 FIGURE 4-10: F O R M A T I O N OF HINGES IN THE B E N T F R A M E - C O N T I N U E D 70 FIGURE 4 -11 : B E H A V I O U R OF L I N K 21 IN THE A B U T M E N T DURING PUSHOVER A N A L Y S I S 71 FIGURE 4-12: B E H A V I O U R OF L I N K 22 IN THE B E N T DURING PUSHOVER A N A L Y S I S 71 FIGURE 4-13 : F I N A L STATUS OF H I N G E F O R M I N G FOR TRINIDAD-9.8 E Q 76 FIGURE 4-14: F O R C E - D E F O R M A T I O N OF L I N K 21 AT W E S T A B U T M E N T - T R I N I D A D 9.8 76 FIGURE 4-15 : F O R C E - D E F O R M A T I O N OF L I N K 22 AT BENT-TRINIDAD 9.8 76 FIGURE 4 - 1 6 : T I M E HISTORIES OF C H A N N E L S 4 , 5 , 7 , 6 , A N D 8- A C C E L E R A T I O N ( C M / S 2 ) VS. T I M E (SEC)- 77 FIGURE 4-17: T I M E HISTORIES OF C H A N N E L S 9 , 1 0 A N D 11- A C C E L E R A T I O N ( C M / S 2 ) VS. T I M E (SEC)- 78 FIGURE 4-18: R E L A T I V E A N D A B S O L U T E D I S P L A C E M E N T ( C M ) VS. T I M E (SEC) AT C H A N N E L 7-TRINIDAD 9.8 78 FIGURE 4-19: B A S E S H E A R ( K N ) VS. T I M E (SEC) FOR X , Y A N D Z DIRECTION-TRINIDAD 9.8 79 FIGURE 4-20: F I N A L S T A T U S OF H I N G E F O R M I N G FOR TRINIDAD-1 1.9 E Q 81 FIGURE 4 -21 : F O R C E - D E F O R M A T I O N OF L I N K 21 AT W E S T A B U T M E N T - T R I N I D A D 11.9 81 FIGURE 4-22: F O R C E - D E F O R M A T I O N OF L I N K 2 2 AT B E N T - T R I N I D A D 11.9 81 FIGURE 4-23 : T I M E HISTORIES OF C H A N N E L S 4 , 5 , 6 , 7 & 8 - A C C E L E R A T I O N ( C M / S 2 ) VS. T I M E (SEC)-TRINIDAD 11.9 82 FIGURE 4-24: T I M E HISTORIES OF C H A N N E L S 9 , 1 0 & 11- A C C E L E R A T I O N ( C M / S 2 ) VS. T I M E (SEC)-TRINIDAD 11.9 83 FIGURE 4-25: R E L A T I V E A N D A B S O L U T E D I S P L A C E M E N T ( C M ) VS. T I M E (SEC) AT C H A N N E L 7-TRINIDAD 11.9 83 FIGURE 4-26: B A S E S H E A R ( K N ) VS. T I M E (SEC) FOR X , Y A N D Z DIRECTION-TRINIDAD 11.9 84 FIGURE 4-27: F I N A L S T A T U S OF H I N G E F O R M I N G FOR C M 8 6 - 4 . 6 E Q 86 FIGURE 4-28: F O R C E - D E F O R M A T I O N OF L I N K 21 AT W E S T A B U T M E N T - C M 8 6 - 4 . 6 86 FIGURE 4-29: F O R C E - D E F O R M A T I O N OF L I N K 2 2 AT B E N T - C M 8 6 - 4 . 6 86 FIGURE 4-30: T I M E HISTORIES OF C H A N N E L S 4 , 5 , 6 , 7 A N D 8- A C C E L E R A T I O N ( C M / S 2 ) VS. T I M E (SEC)- 87 FIGURE 4 -31 : T I M E HISTORIES OF C H A N N E L S 9 , 1 0 A N D 11 - A C C E L E R A T I O N ( C M / S 2 ) VS. T I M E ( S E C ) - C M 8 6 - 4 . 6 88 FIGURE 4-32: R E L A T I V E A N D A B S O L U T E D I S P L A C E M E N T ( C M ) VS. T I M E (SEC) AT C H A N N E L 7-C M 8 6 - 4 . 6 88 FIGURE 4-33: B A S E SHEAR ( K N ) VS. T I M E (SEC) FOR X , Y A N D Z D I R E C T I O N - C M 8 6 - 4 . 6 89 FIGURE 4-34: F I N A L STATUS OF H I N G E F O R M I N G FOR C M 8 6 - 6 . 5 E Q 91 FIGURE 4-35: F O R C E - D E F O R M A T I O N OF L I N K 21 AT W E S T A B U T M E N T - C M 8 6 - 6 . 5 . . . 91 FIGURE 4-36: F O R C E - D E F O R M A T I O N OF L I N K 22 AT B E N T - C M 8 6 - 6 . 5 91 FIGURE 4-37: T I M E HISTORIES OF C H A N N E L S 4 , 5 , 6 , 7 A N D 8- A C C E L E R A T I O N ( C M / S 2 ) VS. T I M E (SEC)- 92 FIGURE 4-38: T I M E HISTORIES OF C H A N N E L S 9 , 1 0 A N D 11- A C C E L E R A T I O N ( C M / S 2 ) VS. T I M E ( S E C ) - C M 8 6 - 6 . 5 93 FIGURE 4-39: R E L A T I V E A N D A B S O L U T E D I S P L A C E M E N T ( C M ) VS. T I M E (SEC) AT C H A N N E L 7-C M 8 6 - 6 . 5 93 FIGURE 4-40: B A S E SHEAR ( K N ) VS. T I M E (SEC) FOR X , Y A N D Z D I R E C T I O N - C M 8 6 - 6 . 5 94 FIGURE 4 -41 : F I N A L STATUS OF H I N G E F O R M I N G FOR P92-3 .0 E Q 96 FIGURE 4-42: F O R C E - D E F O R M A T I O N OF L I N K 21 AT W E S T A B U T M E N T - P 9 2 - 3 . 0 96 FIGURE 4-43: F O R C E - D E F O R M A T I O N OF L I N K 22 AT B E N T - P 9 2 - 3 . 0 96 FIGURE 4-44: T I M E HISTORIES OF C H A N N E L S 4 , 5 , 6 , 7 A N D 8- A C C E L E R A T I O N ( C M / S 2 ) VS. T I M E (SEC)-P92-3 .0 97 FIGURE 4-45: T I M E HISTORIES OF C H A N N E L S 9 , 1 0 A N D 11- A C C E L E R A T I O N ( C M / S 2 ) VS. T I M E (SEC)-P92-3 .0 98 FIGURE 4-46: R E L A T I V E A N D A B S O L U T E D I S P L A C E M E N T ( C M ) VS. T I M E (SEC) AT C H A N N E L 7 -P92-3.0 98 FIGURE 4-47: B A S E S H E A R ( K N ) VS. T I M E (SEC) FOR X , Y A N D Z DIRECTION-P92-3.0 9 9 FIGURE 4-48: F I N A L S T A T U S OF H I N G E F O R M I N G FOR P92-3 .5 E Q 101 FIGURE 4-49: F O R C E - D E F O R M A T I O N OF L I N K 21 AT W E S T A B U T M E N T - P 9 2 - 3 . 5 101 FIGURE 4-50: F O R C E - D E F O R M A T I O N OF L I N K 22 A T B E N T - P 9 2 - 3 . 5 101 FIGURE 4 -51 : T I M E HISTORIES OF C H A N N E L S 4 , 5 , 6 , 7 A N D 8- A C C E L E R A T I O N ( C M / S 2 ) VS . T I M E (SEC)-P92-3.5 102 FIGURE 4-52: T I M E HISTORIES OF C H A N N E L S 9 , 1 0 A N D 11- A C C E L E R A T I O N ( C M / S 2 ) VS. T I M E (SEC)-P92-3.5 103 FIGURE 4-53: R E L A T I V E A N D A B S O L U T E D I S P L A C E M E N T ( C M ) VS. T I M E (SEC) AT C H A N N E L 7 -P92-3.5 103 FIGURE 4-54: B A S E S H E A R ( K N ) VS. T I M E (SEC) FOR X , Y A N D Z DIRECTION-P92-3.5 104 FIGURE 5-1: FIRST A N D S E C O N D T R A N S V E R S E M O D E SHAPES FOR TRINIDAD-9.8 I l l FIGURE 5-2: FIRST A N D S E C O N D T R A N S V E R S E M O D E SHAPES FOR TRINIDAD-1 1.9 111 FIGURE 5-3: FIRST A N D S E C O N D T R A N S V E R S E M O D E SHAPES FOR C M 8 6 - 4 . 6 112 FIGURE 5-4: FIRST A N D S E C O N D T R A N S V E R S E M O D E SHAPES FOR C M 8 6 - 6 . 5 112 FIGURE 5-5: FIRST A N D S E C O N D T R A N S V E R S E M O D E SHAPES FOR P92-3 .0 113 FIGURE 5-6: FIRST A N D S E C O N D T R A N S V E R S E M O D E SHAPES FOR P92-3 .5 113 FIGURE 5-7: SIMPLIFIED B R I D G E M O D E L 115 FIGURE 5-8: P L A N V I E W OF THE FIRST A N D THE S E C O N D T R A N S V E R S E M O D E SHAPES 116 FIGURE 5-9: D A M A G E INDEX M O D E L 117 FIGURE 5-10: T H E E L E M E N T S D A M A G E INDEX 121 FIGURE 5-11: T H E E L E M E N T S D A M A G E SEVERITY INDEX 121 FIGURE 5-12: T H E E L E M E N T S D A M A G E INDICATOR 121 FIGURE 6-1: F L O W C H A R T OF SEISMIC STRUCTURAL H E A L T H MONITORING OF BRIDGES 127 FIGURE 6-2: SIMPLE SUPPORTED SPAN 131 FIGURE 6-3: DECISION LEVELS BASED ON DISPLACEMENTS 132 FIGURE 6-4: P S O B R I D G E - F R E Q U E N C Y C H A N G E S FOR DIFFERENT E A R T H Q U A K E C A S E S 133 FIGURE 6-5: D I S P L A C E M E N T HISTORY AT THE B E N T TOP A N D THE B A S E - C M 8 6 E A R T H Q U A K E . 1 3 7 FIGURE 6-6: D I S P L A C E M E N T HISTORY AT THE B E N T TOP A N D THE B A S E - P 9 2 E A R T H Q U A K E 137 FIGURE 6-7: T H E E L E M E N T S D A M A G E INDEX 138 FIGURE 6-8: T H E E L E M E N T S D A M A G E SEVERITY INDEX 138 FIGURE 6-9: T H E E L E M E N T S D A M A G E INDICATOR 138 FIGURE A - l : A C C E L E R A T I O N S T I M E HISTORY (CM/S2) - (TIME IN SEC)-TRINIDAD E A R T H Q U A K E . . 155 FIGURE A - 2 : A C C E L E R A T I O N S T I M E HISTORY (CM/S2) - (TIME IN SEC)-TRINIDAD E A R T H Q U A K E . . 156 FIGURE A - 3 : A C C E L E R A T I O N S T I M E HISTORY (CM/S2) - (TIME IN S E C ) - C A P E M E N D O C I N O E A R T H Q U A K E 157 FIGURE A - 4 : A C C E L E R A T I O N S T I M E HISTORY (CM/S2) - (TIME IN S E C ) - C A P E M E N D O C I N O E A R T H Q U A K E 158 FIGURE A - 5 : A C C E L E R A T I O N S T I M E HISTORY (CM/S2) - (TIME IN SEC)-PETROLIA E A R T H Q U A K E . . 159 FIGURE A - 6 : A C C E L E R A T I O N S T I M E HISTORY (CM/S2) - (TIME IN SEC)-PETROLIA E A R T H Q U A K E .. 160 List of Abbreviations & Symbols A C : Acceleration Comparison D C : Displacement Comparison F C : Frequency Comparison F E : Finite Element L C P : Logical Combined Process L S L : Limited Service Level N E : Number of elements, N M : Number of modes O S L : Out of Service Level R D : Relative Displacement S D : Structural Displacement S H M : Structural Health Monitoring S I : System Identification S S H M : Seismic Structural Health Monitoring S S L : Safe Service Level D I j : Damage Index of j t h Element th Z j : Normalized Damage Index of j Element a}: Damage Severity of j t h Element kr: r t h modal stiffness, th th C r j : Contribution of the j element to the r modal stiffness, t h S j : Normalized shear stiffness of the j element, A r j : relative shear displacement of j t h element in r t h mode, PREFACE Structural Health monitoring (SHM) is widely performed these days due to the fact that it has several applications. Owners can monitor the behaviour and the health of structures remotely with one-time financial investment. S H M can be used for structures under service loads (e.g. Wind, Temperature, Occupancy and Traffic) during their lifetime and also in the event of earthquakes, blasts and the like. S H M , compared to the traditional visual inspection, has advantages for the owners. One of them is that while visual inspection is of no help in detecting the hidden damage, S H M is capable of detecting it in any structure (e.g. the possible damage to the structural elements which are masked by non-structural elements in buildings, or the possible cracks caused by an earthquake in the core of concrete columns of retrofitted bridges which are hidden by their-steel jacket). Another advantage of S H M is that, by round-the-clock monitoring of structures and thus increasing the level of confidence in their safety, it can reduce their insurance premiums for private owners. As mentioned above, one of the functions of S H M is investigating earthquake effects on structures. In this thesis, the main focus is on this topic, which is related mainly to the bridges. Seismic Structural Health Monitoring (SSHM) herein is referred to determining the status of serviceability of a structure right after an earthquake remotely via the Internet or any other communication link. This procedure confirms whether the structure has been severely damaged, and i f so, it can be used to determine the location and severity of the damage as well as the stability of the structure. This procedure would be helpful for decision makers to check key bridges of a transportation network after an earthquake to determine which bridge is still operational and which one is out of commission. This quick decision making would be very useful for critical management of the earthquake aftermath to reduce the amount of secondary damages and casualties. Seismic instrumentation for near-real time monitoring and damage assessment can be addressed at various levels. One of them would be to utilize modern accelerometers that are now used for strong-motion instrumentation programs. When properly deployed to represent the overall bridge dynamic response, local digital processing of acceleration data can be used to indicate threshold values of displacement, which can be associated with damage levels based on prior structural analysis. There are also several methods for damage detection that can determine the location and severity of the damage by analyzing the near-real time data. Sometimes the structural and the damage detection methods may lead to erroneous conclusion or false alarm when determining the level of serviceability of a bridge; it is therefore desirable to develop a method to avoid these pitfalls. A simple system of warning lights (green, yellow, and red) can be included in the procedure to help the operator decide on the action to be taken. In this thesis, first a literature review of health monitoring studies applied to bridges from 1996 to 2005 is introduced. An extensive review of literature on structural health monitoring has been presented in " A Review of Structural Health Monitoring Literature 1996-2001" by Shon and Farrar (2001), and the highlights of this work are summarized in this thesis. The most relevant investigations reported since 2001, have been added here. The research work on S H M using vibrational methods has been limited so far to give a general idea about the damage levels and distribution, but does not provide any information about the structure's safety. Clearly, there is a need for a procedure that can directly give information about the overall status of the structure. This research is focused on responding to this need by making use of one of the most reliable damage detection methods (Damage Index), which has been used successfully on several projects and it has been demonstrated to give more reliable results than the others. A case study is presented to demonstrate the application of the method. The subject of the case study is an instrumented actual bridge (the Painter Street Overpass Bridge located in California) that has experienced more than ten earthquakes of different intensities since 1980. The bridge is analyzed using state of the art 3-D quasi-static (Pushover) and nonlinear time history analyses. The results from the nonlinear analyses are used to test and improve the effectiveness of the DIM for predicting damage locations and its severity. Finally, with the information from the analyses results, a general Seismic Structural Health Monitoring Procedure for bridges is proposed, described and implemented in flowchart format. The procedure is suitable for bridges with limited number of sensors installed to record its motions during an earthquake. This procedure is able to analyze the time earthquake histories recorded by the sensors installed on a bridge and determine the status of the structure. ACKNOWLEDGEMENTS I would like to express my gratitude to my supervisor, Professor Carlos E. Ventura, for his patience, guidance and support during my study at U B C . He influenced my scientific and social life in a way that words can not describe. I shall be always grateful to him. I would also like to thank my parents to whom this thesis is dedicated, for sacrifices they have made to help me learn. Their unconditional love, emotional support and encouragement have always been the driving force in pursuing my life goals. My special thanks to my uncle, Farid Nikain, who helped me in editing this thesis. The financial support for this project was provided by the Ministry of Transportation (MOT) of British Columbia through Professional Partnership Program. I gratefully thank Mrs. Sharlie Huffman of MOT for her motivation and support for this study. CHAPTER 1 LITERATURE REVIEW AND OBJECTIVES 1.1 INTRODUCTION In this chapter, a definition of damage and an explanation of health monitoring are given, followed by a brief literature review of health monitoring of bridges (1997-2005). A l l projects of this literature review only evaluate vibrational methods. The needs of the field of research are explained based on an evaluation on the past projects. The outline of thesis is elaborated with the title of each chapter. 1.2 DEFINITION OF DAMAGE In the most general terms, damage can be defined as changes introduced into a system that adversely affects its current or future performance. Implicit in this definition is the concept that damage is not meaningful without a comparison between two different states of the system, one of which is assumed to represent the initial, and often undamaged, state. Therefore, the definition of damage will be limited to changes to the material and/or geometric properties of these systems, including changes to the boundary conditions and system connectivity, which adversely affect the current or future performance of these systems. As an example, a crack that forms in a structure produces a change in geometry that alters the stiffness characteristics of that part. Depending on the size and location of the crack and the loads applied to the system, the adverse effects of this damage can be either immediate or may take some time before they alter the system's performance. In terms of length scales, all damage begins at the material level and then under appropriate loading scenarios progresses to component and system level damage at various rates. In terms of time scales, damage can accumulate incrementally over long periods of time such as that associated with fatigue or corrosion damage accumulation. Damage can also result from unscheduled discrete events such as an earthquake. The basic premise of most damage detection methods is that damage will alter the stiffness, mass, or energy dissipation properties of a system, which in turn alter its measured dynamic response. Although the basis for damage detection appears intuitive, its actual application poses many significant technical challenges. The most fundamental challenge is the fact that damage is typically a local phenomenon and may not significantly influence the lower frequency global response of a structure that is normally measured during vibration tests. Stated another way, this fundamental challenge is similar to that found in many engineering fields where there is a need to capture the system response on scales of widely varying length, and such system modeling has proven difficult (Shon & Farrar, 2001). 1.3 STRUCTURAL HEALTH MONITORING PROCESS The process of implementing a damage detection strategy for civil engineering infrastructure is referred to as Structural Health Monitoring (SHM). Usage Monitoring (UM) attempts to measure the inputs to and responses of a structure before damage so that regression analysis can be used to predict the onset of damage and deterioration in structural condition. Prognosis is the coupling of information from SHM, U M , current environmental and operational conditions, previous component and system level testing, and numerical modeling to estimate the remaining useful life of the system (Sohn & Farrar, 2001). The S H M process involves the observation of a system over time using periodically sampled dynamic response measurements from an array of sensors, the extraction of damage-sensitive features from these measurements, and the statistical analysis of these features to determine the current state of the system's health. For long-term SHM, the output of this process is periodically updated information regarding the ability of the structure to perform its intended function in light of the inevitable aging and degradation resulting from operational environments. After extreme events, such as earthquakes or blast loading, S H M is used for rapid condition screening and aims to provide, in near real time, reliable information regarding the integrity of the structure. 1.4 PAST PROJECTS ON BRIDGES The projects reported in here were sorted chronologically and all of them are related to damage detection techniques. 1.4.1 Doebling, Farrar, & Cornwell (1997) Doebling, Farrar, and Cornwell (1997) analyzed modal data from the Alamosa Canyon Bridge in New Mexico. This bridge has seven independent spans with a common pier between successive spans. Each span consists of a concrete deck supported by six steel girders. The roadway in each span was approximately 7.3 m wide and 15.2 m long. The beams at the pier rest on rollers, and the beams at the abutment are bolted to a half roller to approximate a pin connection. Only the first span of the bridge was instrumented. A total of 31 acceleration measurements were made on the concrete deck and on the girders below the bridge, and force time histories were measured at two points on the bridge. Temperature measurements were made at 9 locations across the bridge to track temperature effects on the test results. Modal tests were conducted every two hours for a total of 24 hours to assess the effects of environmental changes on the results. Damage was introduced by loosening the nuts on the bolted connections that hold the channel-section cross members to the girder, but no changes in the measured modal properties were detected. For this reason, damage cases were simulated using a correlated finite element model. The researchers also evaluated the uncertainties on the measured frequency response functions (FRFs), and propagate the uncertainties to obtain uncertainty bounds on the identified modal parameters using Monte Carlo simulation. In a similar study, Doebling and Farrar (1997) demonstrated how statistical confidence limits can be defined for measured modal parameters. This statistical analysis was applied to modal data from the 1-40 Bridge that was incrementally damaged prior to its demolition. The statistical analysis revealed that, in addition to damage, there.were systematic test-to-test variations in the modal parameters of this bridge. For several damage scenarios, these variations were more significant than those produced by the damage. The conclusion of this study was that statistical analysis has to be an integral part of any modal-based damage identification procedure. 1.4.2 Wang, Satpathi, and Heo (1997) An application of the damage index method can be found in Wang, Satpathi, and Heo (1997). The authors built a scaled model of a single span plate girder bridge and carried out a modal analysis of the structure. Twenty-four accelerometers were mounted on the steel beams of the structure, and a 32-channel data acquisition system was used. Excitation was provided with an impact hammer applied at a fixed point. The effects of the boundary conditions on the modal analysis were investigated. Specifically, fixed-fixed, roller-fixed, and pinned-pinned boundary conditions were considered. Damage was introduced in a girder .flange. Assuming that the damage index values were normally distributed, a normalized index was formulated as the actual feature. The first six mode shapes were used to calculate the damage index. The normalized damage index performed quite well although the simulated damage was quite severe. The authors, however, foresaw difficulties with the method when multiple damage states were present. 1.4.3 Nigbor & Diehl (1997) The Online Alerting of Structural Integrity and Safety (OASIS) system was discussed in Nigbor and Diehl (1997). That system performs four vital functions in real time. First, a remote, real time alerting feature using visual, on-screen imaging and audible alarms is employed. Second, an event-triggered, high dynamic range, high speed accelerograph, which operates in the background, is present in the system. Third, remote control and the display of system functions through direct control feedback as well as through a Windows-based graphical user interface is accomplished. Last, OASIS can incorporate different types of measurements, such as accelerations, strains, displacements, wind, and temperature. Nigbor and Diehl discussed applications of OASIS to bridges in Korea and Thailand. 1.4.4 Kwon et al. (1998) Kwon et al. (1998) developed a scaled-down laboratory model of a truss bridge to investigate structural health monitoring. The truss bridge model was constructed based on a conventional design practice frequently used for many railways in Korea. The laboratory bridge measured 4.0 x 0.6 x 0.6 m. The authors instrumented the bridge with traditional electric resistance strain gauges as well as four Michelson fiber-optic sensors. A finite element model of the laboratory bridge was also developed for comparison with the measured data. Several damage scenarios were investigated that included the simulated breakage of different combinations of selected structural members. It was found that the Michelson fiber-optic sensors could not exactly measure the structural strain because of signal noise problems. However, the finite element results did match well with the resistance strain gauge data. The authors claim that, i f the strain had been measured properly, the damage scenarios could all have been identified from the changes in the strain patterns. 1.4.5 Maeck & De Roeck (1999) Maeck and De Roeck (1999) applied a direct stiffness approach to damage detection, localization, and quantification for the Z24 prestressed concrete bridge in Switzerland. The bridge was a full-scale highway overpass consisting of three post-tensioned box cell girders of spans 14 m, 30 m, and 14 m that rest on four piers. The two central piers were rigidly connected to the girder while the two triplets of piers at both ends were connected via concrete hinges to the girder. Different damage types were introduced into the bridge ranging from concrete spalling, the failure of anchor heads, the settling of piers between 20 mm and 95 mm, and the rupture of tendons. The bridge was demolished after the tests were completed. The authors succeeded in localizing and quantifying damage in the bridge for each damage scenario using the direct stiffness approach. Keeping in mind that bending stiffness is defined as the ratio of bending moment to curvature; the direct stiffness approach uses the calculation of modal bending moments and curvatures to derive the bending stiffness at each location. The direct stiffness calculation first uses the experimental frequencies and mode shapes to compute modal curvature. Then, changes in the dynamic stiffness, given by changes in the modal curvature, indicate the presence of damage. However, they noted that curvatures were rather small for the side spans and caused numerical difficulties in calculating bending stiffnesses in these spans. 1.4.6 Stubbs et al. (1999) Stubbs et al. (1999) employed the damage index method (DIM) to non-destructively evaluate the structural integrity of bridges. This damage index method utilizes the modal strain energy stored in the undamaged and damaged conditions of a structure to detect damage in the structure. For this study, a four-lane highway bridge that spans Interstate 40 was tested. Vibration measurements were taken at 26 locations on the deck and 4 locations on the column. First, the modal parameter identification and the damage evaluation using the damage index method were conducted using field test data gathered in December 1997 and September 1998. A standard modal analysis was conducted to determine the resonant frequencies and mode shapes of the lowest five modes. Next, a baseline finite element model was constructed utilizing the data from the as-built plans of the bridge. Modal frequencies and mode shapes were calculated from this model. A comparison of the measured modal properties with those from the finite element model was made, and possible damage locations and severities were estimated using the damage index method. Finally, the diagnosis results from the 1997 and 1998 measurements were compared to the surface crack patterns of the bridge visually inspected in May 1999. It was observed that the damage locations determined with the damage index method correlate with the actual crack patterns. 1.4.7 Wang et al. (1999) Wang et al. (1999) summarized the preliminary results of the monitoring and damage assessment investigation applied to the Kishwaukee Bridge in Illinois. The bridge consists of two separate bridges each carrying two lanes of northbound and southbound traffic on 1-39. The structure is one of the first post-tensioned segmental concrete box girder bridges constructed using a balanced cantilever technique. A large number of cracks originate from the shear key during the construction phase. Diagonal cracking is also observed in interpier segments. Over the past 20-year life span of the bridge, the cracks have propagated further. A finite element analysis has been carried out in conjunction with a modal testing of the actual bridge in the field to assess the effect of these cracks to the overall structural integrity of the bridge. A baseline modal testing of the bridge was carried out about 13 years ago, and it was concluded that the differences between the newly obtained modal parameters and the baseline modal parameters were minimal. However, the finite element simulations indicated that very large localized damage could produce very small changes in the modal parameters. In addition, another numerical simulation indicated that a 30°F decrease in the temperature can result in about a 2% increase in the frequency. Experimental measurements of temperature gradients and strains showed that the temperature gradient can produce very large stains and can exceed those introduced by traffic loading. Finally, based on the identified critical damage areas close to the piers, the authors suggested that an inexpensive monitoring system based on a limited number of measurements can be deployed. 1.4.8 Ko et al. (1999) Ko et al. (1999) discussed the development of a large instrumented bridge project in Hong Kong. Three cable supported bridges, the Tsing Ma Bridge, the Kap Shui Mun Bridge, and the Ting Kau Bridge have been constructed to support the development of a new international airport nearby. A total of 900 sensors, including accelerometers, strain gauges, anemometers, temperature sensors, and displacement transducers, have been placed on the three bridges for structural health monitoring purposes. The authors discussed possible damage scenarios for each bridge and whether or not each scenario could be detected using a measurement of dynamic modal properties. The Tsing Ma Bridge is a suspension bridge with a main span of 1,377 m and an overall length of 2,160 m. The Kap Shui Mun Bridge is a cable-stayed bridge with a main span of 430 m and side spans of 160 m on either side. The Ting Kau Bridge is also a cable stayed bridge that has two main spans of 448 m and 475 m with two 127 m side spans. For both types of bridges, the main cables are the most important part for the bridge's integrity. These cables are susceptible to damage via corrosion, internal abrasion, and localized faults such as broken wires. If bending stiffness of a cable is negligible, the tension force in the cable is related to the modal frequencies of the cable. Therefore, monitoring the modal characteristics of the cable will indicate a change in tension. However, it will not reveal any reduction in a cross sectional area caused by the corrosion or breaking of wires. The authors analyzed several other types of damage possible within the three bridges. They claimed that dynamic monitoring of the system should be able to detect most forms of damage, excluding corrosion in some parts of the structure. 1.4.9 Feng & Bahng (1999) Because several bridges in California were built prior to the development of modern earthquake design standards, a major initiative to increase the structural integrity of these old bridges has been in place for some time now. A common method for seismic retrofit has been to jacket the columns of the bridges with steel or some type of composite. Although cracks often initiate near the contact surface between the original columns and the jacketing materials, this technique often prevents visual inspection of the contact surface after retrofitting. Feng and Bahng (1999) proposed, a new method for the monitoring of jacketed columns that employs the combination of vibration testing, neural network, and finite element techniques. The authors constructed a small-scale bridge model based on an old design standard, and the columns of the bridge model were retrofitted with carbon fiber composite. A finite element model was constructed to predict baseline vibration characteristics of the bridge, and the predicted responses were compared with vibration test data taken from the scale model. Damage was then introduced in the bridge model, and vibration tests were repeated for several damage cases. The data taken from the finite element model and the damaged bridge were used to train the neural network using a standard back-propagation algorithm. The trained network is then used to determine the stiffness degradation of the bridge. 1.4.10 Enright et al. (1999) Based on the knowledge that data from non-destructive' methods are difficult to interpret, Enright et al. (1999) used a Bayesian approach to evaluate the effects of corrosion on a reinforced concrete (RC) bridge in Pueblo, Colorado. The RC T-beam highway bridge consists of three simply supported spans, each with 5 girders. The main descriptors for the initial resistance and load effects are initial shear resistance, dead shear, and initial live load. The bridge was subjected to salt spray from passing traffic that causes strength loss in the cross-sectional area of the girders caused by corrosion damage near high shear locations. The resistance and corrosion variables were obtained from site-specific data and previous work (Nowak et al. 1994). The strength degradation was estimated using a probabilistic approach, and strength degradation predictions are updated using Bayesian methods. The expected value of resistance loss increased at a nonlinear rate, as determined by regression analysis. Additionally, a plot of cumulative-time failure probability showed the center girder to have the highest probability of failure. 1.4.11 Peeters and De Roeck (2000) Peeters and De Roeck (2000) compared a classical sensitivity-based updating technique with a direct stiffness calculation approach using data from a prestressed, three-span, and 60-m-long concrete bridge. The authors noted that a direct calculation of curvatures from measured mode shapes by using a central difference approximation results in oscillations and inaccurate values caused by numerical instabilities. To deal with this problem, the authors utilized a smoothing procedure where a weighted residual penalty-based technique is adopted. Damage in the bridge took the form of pier settlements between 20 mm to 95 mm and the foundation tilt. Pier settlements of 80 mm and 95 mm seemed to yield the most pronounced stiffness changes and thus the best damage resolution. With the 40-mm settlement, damage was less clearly identified, and the small curvatures at the bridge ends for this damage scenario caused numerical instabilities. The authors concluded that the direct stiffness calculation approach offers a reliable alternative to the classical sensitivity-based updating approach. 1.4.12 Bergmeister & Santa (2000) Bergmeister and Santa (2000) discussed the instrumentation of one girder box of the Colle di Sarco viaduct in Italy. A description of the various measurement methods and their physical principles as well as their applications for the global monitoring was discussed. The instrumentation included humidity sensors, wind vanes, strain gauges on the prestressing cables and reinforcements, anemometers, inclinometers, thermocouples, and electrochemical microprobes to measure corrosion. In addition, the bearings were instrumented with load cells and fiber-optic sensors, which are based on the interferometric principle for measuring long-range displacements. The authors state that interpretation of the acquired data and consecutive decision making were equally as important as the measurements. However, the details of the data interrogation and decision making were not provided in the paper. Chapter 1-Literature Review and Objectives 1.4.13 Feng et al. (2000) Feng et al. (2000) developed an electromagnetic (EM) imaging technology for detecting voids and debonding between fiber reinforced polymer (FRP) composite jackets and reinforced concrete columns. Retrofitting RC columns with FRP composite jackets has been demonstrated to enhance structural performance. However, debonding between the jacket and column caused by seismic damage or poor workmanship can considerably weaken the column, and such damage can remain visually undetected. The proposed damage detection technique was to send a continuous E M wave at the reinforced column and detect the reflected wave energy. A fraction of the wave energy was reflected at each dielectric interface between adjacent layers (e.g., between air and jacket, jacket and column, etc.). An air gap between the jacket and column will form an additional interface, and the energy reflected at this interface should be detectable as evidence of debonding damage. The technique was unsuccessful when plane E M waves were used, so a dielectric lens was used to focus the wave on the bonding interface of the jacketed column. The time gating technique was used to remove unwanted reflections caused by unavoidable obstacles different from air voids. The modified E M wave technique was successfully demonstrated in laboratory tests to detect voids and debonding in a jacketed column with no rebar. Detecting voids in the column with rebar was still under investigation at the time of publication. Seim et a\. (1999) used fiber-optic Bragg grating strain sensors for health monitoring of a historic bridge near Portland, Oregon. The Horsetail Falls Bridge is an 18.3-meter reinforced concrete slab span type bridge, consisting of three 6.1-meter spans. The bridge was built in 1914 and was not designed for the traffic loads that it is currently subjected to. To increase the load carrying capacity of the bridge, the Oregon Department of Transportation used fiber reinforced plastic composite (FRPC) strengthening. Twenty-eight fiber-grating sensors were placed on the bridge in order to monitor the performance of the FRPC additions and the existing concrete structure. After the sensors were positioned, a 26,000-pound dump truck was moved to various locations on the bridge to ensure that the sensors were functioning properly. In parallel with this activity, more rigorous laboratory tests based on this structure were scheduled. Finite element models of the FRCP-reinforced bridge were also being developed. Data taken from the bridge was used to validate the laboratory work and finite element models. 1.4.14 Choi & Kwon (2000) Choi and Kwon (2000) developed a neural network damage detection system for a steel truss bridge. The bridge, constructed in 1940, carries one rail road, and is currently healthy. A finite element model of the bridge was developed based on design drawings, and the mass and stiffness of the truss members were updated based on static and dynamic loading tests performed on the real bridge. The refined finite element (FE) model was then used to determine which truss members had the highest stresses during static analysis. This analysis identified eight truss members as most vulnerable to damage. Based on this observation, stiffness reduction in each of these eight truss members was simulated to generate eight damage cases for the subsequent neural network analysis. The first network determined which half, either the left or the right of the midpoint of the bridge, was damaged. The second network determined which of the eight truss members were damaged. The two-step neural network successfully located the damage in the FE model, and in future studies they will implement the system on the real bridge. 1.4.15 Park, Kim, & Stubbs (2002) Another investigation on damage detection was done by Park, Kim and Stubbs on 2002. Non-destructive Damage Detection (NDD) in large/complex structures was investigated via vibration monitoring of such structures. The theory of NDD for truss type structures was formulated. To examine the feasibility of the theory, a finite element model of a 3-D truss structure, which consists of sixteen bays and includes 246 elements, was developed to simulate damage. Four damage cases were simulated numerically. The cases range from the structure being damaged in one location to the structure being damaged in three locations. Next, the theory was applied to the experimental results of a 1:6 scale model of a typical hexagonal truss. These tests consist of 17 damage scenarios subjected to three different types of damage. The performance of the method on simulating experimental data was evaluated. From the results obtained, the following conclusions were drawn: (1) the non-destructive damage detection scheme proposed can be applied successfully to large and complex structures; (2) damage detection results might be better if several modes are used simultaneously; and (3) the experimental study shows that the performance of proposed method might be significantly impacted by the noise in the measurement data, especially when small amount of damage is introduced. 1.4.16 Zabel (2004) Zabel (2004) used the application of wavelet Decomposition's energy components for damage detection on the Z24 Bridge in Switzerland. This approach is described and applied to data from dynamic bridge tests. Both, relations between response and excitation signals and two different response signals were investigated. The results clearly indicate a relatively high sensitivity to some of the simulated damage scenarios. Nevertheless, further investigations with respect to situations when only response data is available are necessary. 1.4.17 Bernal & Hernandez (2004)1 A data driven methodology for the evaluation of the earthquake induced damage on civil engineering structures was presented by Brenal and Hernandez (2004). The main feature of the approach is: (1) identification of a collection mappings containing transmissibility between sets of channels for the nominally healthy state of the system and (2) computation of differences between the predicted signals at various channels and the measured ones during a potentially damaging event. The transmissibility maps are obtained in an entirely data-driven fashion using measurements obtained from non-damaging events. The technique was found effective in identifying which earthquake motions have induced damage and which have not in a 7 story concrete structure located in Van Nuys, California. 1.4.18 Park, Stubbs, & Bolton (2005)2 In a further study using the damage index method, Park, Stubbs, and Bolton (2005) detected damage in a finite element model of a four-story steel frame structure outfitted with 16 accelerometers. This frame structure model stands 3.6 m high and has a width of 2.5 m. A l l beam-column connections are rigid, and the floors are rigid in the horizontal plane. The damage took the form of removed braces or reduced vertical stiffness in floors. Frequency response functions were calculated from average cross-power spectra of each input and output pair divided by an average auto-power spectrum of the input. The input was random, and the first four ' Although this method was used for damage detection on a building, authors believe that it can be applied to any kind of structure. 2 This study is related to the building literature, but it has been quoted in here for more information about Damage Index Method, on which this thesis is concentrated. bending modes in the two orthogonal directions and the first four torsional modes were extracted. Using the damage index method, the authors were able to locate the damage. Furthermore, using the damage index, the stiffness reduction in the damaged element was also estimated. 1.5 RESEARCH NEEDS As it can be seen in the literature review related to S H M of bridges, the research done so far has focussed wholly on vibrational methods and damages resulting from fatigue, corrosion, and serviceability load. The implementation of S H M techniques for bridge damage . due to earthquakes has not been thoroughly investigated. There is a need to investigate the used of modern S H M techniques for assessing the status of bridges immediately after an earthquake. The existing methods for damage detection are fairly well developed and they are precise enough to detect major flaws in structures. For example in the 1-40 Bridge case (Farrar 1996), several damage detection algorithms were used and most of them were good enough to identify the damage area with a few centimetres. What bridge owners are typically looking for is a simple and fast procedure which can help them make a swift decision after an earthquake (Alampalli & Ettouney, 2003). Such a procedure should identify the severity and the location of damage and also show whether the structure is operational or not. Most of the available methods for damage detection are too complicated for practical implementation and are based on vibrational mechanics, which are not understandable for civil engineers. The methods only identify the damaged elements and the severity of damage, but they do not provide information about the stability and serviceability of the structure. Therefore, a procedure is needed that can provide a structural engineer with detailed and more understandable information about the status of a damaged structure. Such a procedure can be developed by combining the vibrational methods and the structural analysis. Chapter 1-Literature Review and Objectives 1.6 SCOPE AND OBJECTIVES The main objective of this thesis is to establish a quick and effective SSHM procedure that can give enough information about the status of an instrumented bridge right after an earthquake. The procedure should include the best estimate of the location of damage, its severity and the status of serviceability of the structure. The objectives of this thesis are: • Identify a reliable and effective damage detection method for post-earthquakes assessment in an instrumented bridge, • Implement an effective Internet-based SSHM procedure by developing an efficient way to combine results from advanced nonlinear structural analyses with those from damage detection techniques, and sound engineering judgement, • Assess the effectiveness of proposed procedure by applying it to an existing instrumented bridge that has been subjected to severe earthquakes. To achieve these objectives, the following aspects of Seismic Structural Health Monitoring will be investigated: • Finite Element Model Updating (Model Calibration) • Nonlinear Analyses (For Different Earthquake demands) • System Identification & Damage detection under different levels of shaking • Combination of structural analyses and damage detection results • Development of a procedure for post-earthquake damage assessment based on the above results. The calibration of the model is done based on low amplitude results of ambient vibration test. The response of the model can be checked by the real earthquake responses. Only frequency domain method is used for system identification. One of the methods in damage detection area is used for determining the location and severity of damages on the case-study bridge. Derived results from the case study are used for developing and defining the seismic structural health monitoring of bridges. Chapter 1-Literature Review and Objectives 1.7 THESIS OUTLINE This thesis consists of seven chapters, the contents of which are as follows: • Chapter 1-Introduction & Background: this chapter begins with an introduction to the health monitoring followed by literature review of SHM, and ends with the scopes and objectives along with the thesis outline. • Chapter 2-Applied Methodology: the ways of achieving the objectives of the thesis are elaborated and the continuity and relations of different functions are explained. The Damage Index Method is introduced and explained in details. An example is given for clarifying and better understanding of the method. • Chapter 3-Case Study, Finite Element Modelling and Model Calibration: a case study is introduced. Development of an FE model of this case is described. The calibration of the model is discussed and its responses are compared with the real responses to past earthquakes recorded on the site. • Chapter 4-Nonlinear Static and Dynamic Analysis: the results of pushover and nonlinear dynamic analysis, which are derived form the calibrated FE model, are presented in this chapter. The assumptions and the methods used for these analyses are explained. • Chapter 5-System Identification and Damage Detection: this chapter contains the analyses of the results of nonlinear dynamic analysis from the previous chapter. The ability of DIM to detect damages is tested by applying different levels of damage to the case-study bridge. • Chapter 6-A Procedure for Bridge Seismic Structural Health Monitoring: based on the results from the previous chapters, a procedure is introduced for determining the status of a bridge after an earthquake. The elements of this procedure are introduced and combination of them is discussed. Finally, the performance of this procedure is shown by using real examples. • Chapter 7-Summary, Contribution and Future work: a summary of this thesis along with the contributions are explained, and future work is suggested. A list of references and two appendices (records of earthquakes & detail drawings of case-study bridge) are given at the end of this thesis. CHAPTER 2 APPLIED METHODOLOGY 2.1 INTRODUCTION In this chapter, the methodology of achieving the objectives of this thesis is discussed. In each step of the methodology, the purpose of the step is clarified and the scope of activity is explained. The Damage Index Method (DIM) is discussed. Finally, development of the SSHM procedure and its relation with the steps are clarified. 2.2 FINITE ELEMENT UPDATING Finite element updating is referred to calibration of the mathematical model parameters-of an existing structure with respect to its real response to a test or a real event. Here, the first step of the calibration is done with respect to the ambient vibration results. These results are the natural frequencies and the mode shapes, which make a successful finite element updating result in a close match between natural frequencies and mode shapes of the updated FE model and those derived from the field test. Sometimes, recorded acceleration time histories of a real earthquake are available for an instrumented structure, in which case the parameter of modal damping ratio can also be calibrated for that level of shaking. This step can be done by comparing the FE model response with the real response to an earthquake. The updated FE model will help to have nonlinear analysis results close to the real behaviour of the structure, so investigation on damage detection will be precise. In this step, it is necessary to select a case, which has enough information. It means that information about the dynamic characteristics of the structure determined from ambient vibration tests and past earthquake records should be available. 2.3 NONLINEAR ANALYSES In this step the calibrated FE model will be analyzed nonlinearly for different purposes. The nonlinear analyses can be categorized as follows: 1. Nonlinear Static Analysis (Pushover) 2. Nonlinear Dynamic Analysis (Time History) The pushover analysis will provide a force-displacement diagram, which can provide information for the structural component of the Seismic Structural Health Monitoring procedure and then be combined with the damage detection component. Because of the nature of this research, it is too hard to find enough experimental data to determine the different levels of damage on a bridge. Therefore nonlinear dynamic analysis results will be used to produce the data for the system identification and damage detection methods. The time histories response of the points of the bridge on, which the sensors are mounted, will be used for the system identification and damage detection methods. The recorded or simulated time histories are used as inputs for the nonlinear analysis. By using simulated ground motions incremental, dynamic analyses can be done. This can help to monitor the behaviour of the bridge step by step for different levels of damage. The commercially available computer program SAP2000® (SAP2000 Manual, 2005) program is used for this step. 2.4 SYSTEM IDENTIFICATION AND DAMAGE DETECTION System identification of a structure means to extract the natural frequencies and the mode shapes of that structure based on field test data (Ambient or Forced Vibration) or the recorded response of the structure to an event. There are several methods for obtaining these data. The methods can be divided in two main categories: • Frequency Domain Analysis • Time Domain Analysis For this part of the thesis, ARTeMIS Extractor® (ARTeMIS Manual, 2004) program is used for system identification. The program has the ability to analyze data by two methods. A system identification of a structure can be done by these two methods and the mode shapes extracted by each method can be compared with in order to get more confidence on the analysis results. Records form the nonlinear analyses will be used for system identification to find the periods and mode shapes of equivalent linear system for different levels of damage. The points on the model selected for picking time histories correspond with the instrumented points of the bridge. The method, which will be used for damage detection is called "Damage Index". This approach has been used in several projects (e.g. Farrar et al. 1996 & Sooyong et al. 2004) and the results showed that it is good enough to locate damage and measure its severity. Finally in this step, the damage and its severity for the different levels of earthquake will be assessed. The changes in frequencies will be monitored to find the relation between them and the observed damage. Chapter 2- Applied Methodology 2.4.1 Damage Index Method (DIM) Damage Index Method (DIM) utilizes the change in mode shapes of the pre-damage and post-damage structure to detect and locate damage in a structure. Decrease in the stiffness values of a structure due to damage causes change in mode shapes. If the undamaged mode shapes are considered as base lines, the damage will be identified by the comparison between the undamaged and damaged mode shapes. DIM can identify the location of damage based on change the coordinates of mode shapes near an element. It can also determine severity of the damage by the value of damage index. This part is the main concept of Damage Index Method (DIM) which was summarized and adopted from Sooyong Park's Ph.D. dissertation, 1997. Detailed derivations of the relevant equations can be followed in this reference. In the field of non-destructive damage detection (NDD) using modal parameters, one of the more difficult problems is that of making a statement regarding the integrity of a relatively small portion of a structure when very few modal parameters are available. In such cases, inverse methods using systems of equations usually result in unsolvable underdetermined systems with few equations but many unknowns. The discipline of pattern recognition gives a way to provide practical answers for such heavily underdetermined systems (Nadler and Smith 1993). In pattern recognition, physical world data are transformed into the so-called pattern space. Using techniques of dimensionality reduction, the pattern space is reduced to a smaller dimension known as the feature space. Data in the feature space are fed to a decision algorithm and the elements of the feature space are classified into a finite number of clusters. In the problem at hand, the dynamic response of the structure in the time domain represents the physical world data and the modal parameters represent the pattern space. The feature space is represented by indicators that are a function of measurable pre-damage and post-damage modal parameters. These indicators can be selected in such a manner that they reflect unique characteristics of the data. The decision algorithm is a means by which the data space is partitioned into Dj (i=l, 2,..., n) clusters (decision spaces). The structure is partitioned into N E elements and a damage indicator, which is consistent with the physics of the problem, is developed for each element. The damage indicator (Stubbs et al. 1992), DIrj, used herein and which forms the basis of the feature space (in the pattern recognition sense), is given by DI. j _ K L jo J {O;}+{O>;}T[K]{CD;}" {0>R}T[K]{(PR} [K j oJ {<DR} + {(DR}T[K]{cPr}_ {d>;}T[K]{o;} (2-1) where the scalars Sj and Sj , respectively, are parameters representing the stiffness properties of the undamaged and damaged j t h member of the structure, {Or} is the r t h modal vector, [K] is the system stiffness matrix, and [Kj0] is the matrix containing only geometric quantities (and possibly terms containing Poisson's ratio). Note that from matrix structural analysis, the system stiffness matrix can always be separated into a matrix that contains only the stiffness properties of the structural elements and a matrix that contains the information that defines the connectivity of the structural elements. There are two important" characteristics of the indicator DIrj given by Equation 2-1: first, the expression attempts to express the changes in stiffness at a specific location in terms of measurable pre-damage and post-damage mode shapes ({® r} and {Or*}); and second, the term [Kj0] on the right hand side of Equation (1) can be determined from a knowledge of the geometry of the structure. Note that if DIrj <1, there is no damage; i f DIrj > 1, damage may exist; and i f DIrj = go , all stiffness capacity of Element j may be lost. Thus for each possible damage location j , there are as many DIrj's available as there are mode shapes. As noted above, in the context of pattern recognition, the latter values of DIrj define the feature space. The following expression is a convenient form of damage index DIj for a single location if several modes (NM) are used: DL = N M T 1 r n r n X ( { o ; } T [ K j o ] { o ; } + { c D ; } T [ K ] { o ; } ) { o r } T [ K ] { o r } j NM Z ( { ^ } T [ K J 0 K } + {O r}T[K]{O r}){O;}T[K]{O;} (2-2) r=l The final step in damage localization is damage classification. Classification analysis addresses the problem of assigning an object to one of a number of possible groups on the basis of observations made on the objects. In this study, the objects are locations in the structure with predetermined values of DIj. There are two groups of locations: undamaged locations and damaged locations. Many techniques are available to classify a location using the proposed damage index in Equation (1) as a basis. While many other approaches are available to meet this end (Garcia 1996), Hypothesis Testing (Gibson and Melsa 1975) has been selected as the classification scheme. Hypothesis testing is selected because an independent evaluation of several classification methods including Quadratic Discriminants, Linear Discriminant, and Mahalanobis Distance, shows that Hypothesis Testing performs superiorly with a significantly small amount of computational effort (Garcia 1996). The criteria for damage localization are established on the basis of statistical reasoning. Normalized values of DIi, DI2, DI3, DINE for each location and for a single mode are generated. The normalized damage index for the j t h location and r t h mode is given by % - (2-3) where L i D ] r and Oo\r represent mean and standard deviation of the damage index, DI rj, respectively. Let H 0 be the hypothesis that structure is not damaged at member j , and let Hi be the hypothesis that structure is damaged at member j . The level of significance of the test depends on the value of Z rj with respect to a prescribed value (A,). In this case X is the difference between Zrj and the mean of normalized curve, which is zero. For example, the following decision rule with a 93% confidence level may be used to assign damage to member j when A,=1.5: (1) choose Hi if Zrj > X and (2) choose H 0 i f Zrj <X. Chapter 2- Applied Methodology 2.4.2 Damage Severity Estimation Note that in Equation (2-1) the indicator of damage is the ratio of the undamaged stiffness to the damaged stiffness. Such a number exists for each potentially damaged location. The actual magnitude of damage at a given location (a) is then expressed as the fractional change in stiffness of an element: Thus if there is no damage, Oj = 0; if there is damage, cij < 0. Note that if <Xj = - 1 , the stiffness capacity is completely lost. 2.4.3 Shear Beam Theory of DIM The damage Index method can be applied for flexural, shear and axial behaviour. Expanding equation 2-2 for shear beam behaviour is discussed here. t h t h The sensitivity of the j element in the r mode, F r;, for shear beam is given by: OL -DI ; 1 - 1 (2-4) (2-5) where NE k r - ^ S j ( A . r j ) 2 : r t h modal stiffness, j=i C r : — S: (A r j ) : Contribution of the j t h element to the r t h modal stiffness, Sj: Normalized shear stiffness of the j element, A r j : relative shear displacement of j element in r mode, NE: Number of elements, NM: Number of modes Therefore, the damage index for a shear beam element can be derived from equation 2-2. The result is: D L N M z r=l f N E ANE ( A \ i ) 2 + I S i ( A * r J ) 2 £ S j ( A , ) 3 j=i N M r=l ( N E ^ N E (Ar j)2 + £ S j ( A , ) 2 I S ^ V , ) j=l J j=l (2-6) The location of potential damage in a structure can be found as follows: 1. Calculate the damage index DIj for each element using equation (2-6). - 2. Calculate the Normalized damage indicator Zj for each element using equation (2-3). 3. The element j is damaged if Zj > X and the element j is not damaged if Zj < X. As explained for equation (2-3), the level of confidence is chosen by the accuracy of calculated mode shapes which depends on the instrumentation type and the number of sensors. Better resolution of mode shapes can be achieved with more sensors installed in a structure, and the results from DIM are more reliable. Finally, a higher level of confidence can be chosen for more reliable results. 2.4.4 Illustrative Example of DIM Application An example is given here to clarify the application of damage index method. A series of blind tests on a steel frame (Figure 2-1), which were conducted by Ventura et al, 1998 at the University of British Columbia, three damage scenarios were developed for simulated blind tests: 1. Case 1: Undamaged structure 2. Case 2: Known damage to the structure (two lateral braces were removed) 3. Case 3: Location and magnitude of damage to the structure not known. The data were processed for damage detection by Park, Bolton & Stubbs. The Damage Index Method was used to ascertain the location and the severity of the damage. They did a system identification analysis for the structure and extracted the mode shapes and the natural frequencies of the frame. The location of sensors is shown in Figure 2-2. A model for damage detection was developed, which is shown in Figure 2-3. The mode shapes coordinates and the stiffness values of the members were used in the damage index method as explained in the previous section. The exact locations of damage in the blind test were revealed at the end of the X V I International Modal Analysis Conference (IMAC) by Black & Ventura in 1998. The damage was described as: • Case 2: two braces in X-direction and in the vicinity of Sensors 3 and 7, one from the first floor and the other from the second floor were, removed. • Case 3: the initial fixed connections of the three columns in the first floor, below and near Sensor 1, were changed from rigid to pinned connections. The predicted damage by DIM matched the real locations of damage. The results are summarized as follows, and those for case 3 are shown graphically in Figure 2-4. 1) In Case 2, the predicted damage is at Elements 9, 10, and 13 of the damage detection model (i.e., near Sensors 3 and 7 in the simulated frame). The damage predicted by the Damage Index Method correlates well with the simulated damage inflicted on the model structure. The estimated damage magnitudes are 17% for the first floor and 20% for the second floor. These estimates of stiffness losses are close to the stiffness losses predicted using a finite element model of the structure. 2) In Case 3, major damage is predicted to the first floor of Frame X I (the leftmost frame in Figure 2-3) near the Sensor 1 and lesser damage is predicted to the first floor of Frame Y l and Frame Y3. This prediction is consistent with the simulated damage inflicted during the blind test. The estimated magnitude of the damage is a reduction in stiffness of 24%. In this example, the results showed that the selected damage index model can accurately locate the damage and assess its severity. This case study had enough number of sensors and the response of the structure had a good resolution (the natural frequencies and modes of the structure very well identified). Figure 2-1: UBC Test Frame in UBC (Courtesy of C.E. Ventura) Sensor Number ,f y 15 >^ •er-^</r^ ^ 7 • '' 14 Direction of Motion Sensed 13 10 • • 5 3 -> _L Figure 2-2: Location of Sensors < I © 5 \ I © I© \ t I© I Ii 4 / I © A® 7 ' Sensor Number i 12t 10 ¥© |@ | © | © Element Number (a) D D M for X-direction i © 1 © t |© |© f© I© "J |© |© 6J (b) D D M for Y-direcrion Figure 2-3: Damage Detection Model for UBC Test Frame (After Park's Paper, 2004) 1 so D l 4 t and 2 n d modes in x-dir. i n i l mm H 1 & 10 n 12 A 4 Element Number t Potential Damage lu and 2 Q d modes in v-dir. 17 15 19 X Element Number Figure 2-4: Results of Damage Localization for Case 3 (After Park's Paper, 2004) 2.5 COMBINATION OF NONLINEAR ANALYSIS & DAMAGE INDEX RESULTS First, in this step the comparisons of results with "bench marks" are introduced. The comparisons are made at three levels: • Acceleration Comparison • Displacement Comparison • DIM & Frequency Comparison The "benchmarks" are the allowable displacements (by pushover analysis), undamaged mode shapes and recorded accelerations database (if there is any available). Each comparison has limitations due to the assumptions made for the analyses, which may result in errors. These errors can lead to wrong judgement (or "false alarm") on the status of the bridge after an event. The second step is to combine the comparison results in a rational way. The logic of this part is to pass the result of each comparison through another filter to confirm its accuracy. For example, i f the displacements comparison shows failure of the structure, this failure should be confirmed by the DIM and accelerations comparison. 2.6 BRIDGE SEISMIC STRUCTURAL HEALTH MONITORING PROCEDURE The target of this research is to define a general procedure for seismic structural health monitoring of bridges. This procedure should help an owner find out the status of the structure after the earthquake. The procedure can be used to indicate the threshold values of displacement that are expected to be associated with damage levels based on prior analyses. A simple system of warning lights (green, yellow, and red) could indicate to the operator what action is to be taken. A flowchart of this procedure will be presented in Chapter 6 that shows how to check the status of a bridge. This procedure can be converted to user friendly software that helps the owner to skip the processing part and deal only with inputs and outputs. Results can be printed for further engineering assessment (e.g. location of damage and its severity). This may help the owner to come up with a better decision about a bridge with minor damage as how temporarily it can be repaired or closed. As explained in the introduction, some minor damage may be hidden in which case this printed output can help the decision maker to determine whether such damage can be repaired or it may cause major subsequent secondary damage i f ignored, especially that in a key member. In this thesis, DIM will be used for an instrumented structure with the real data from the past earthquakes, even though the number of sensors is limited and it is not certain that all of the frequencies were triggered by the earthquakes. CHAPTER 3 CASE STUDY, FINITE E L E M E N T MODELLING AND MODEL CALIBRATION 3.1 INTRODUCTION In this chapter, a two span bridge located in California is selected as a study. A finite element model of this bridge was developed first using the commercially available computer program by SAP2000 V9®. The FE model was then updated using available ambient vibration test results (Ventura et al, 1993). The FE model was considered to be a reliable representation of the actual bridge structure. The responses of the calibrated model to the past earthquakes were compared with the recorded data of the real structure's responses to check the FE model at different levels of shaking. 3.2 DESCRIPTION OF THE BRIDGE The Painter Street Overpass is a two span, pre-stressed concrete box-girder bridge constructed in 1973 over the four-lane US Highway 101 in Rio Dell, Northern California. Its construction is typical of the type of California bridges used to span two or four lane highways (Figure 3-1). The bridge is 15.85 m wide and 80.79 m long. The deck is a multi-cell box girder, 1.73 m thick and is supported on monolithic abutments at each end and two-pier bent that divides the bridge into two spans of unequal length; one of the spans is 44.51 m long and the other is 36.28 m long. The abutments and piers are supported by concrete friction piles and are skewed at an angle of 38.9 degrees. Longitudinal movement of the west abutment is allowed by means of a thermal expansion joint at the foundation level. The piers are about 7.32 m high, each supported by 20 concrete friction piles. The east and west abutments are supported by 14 and 16 piles, respectively. Detailed drawings of this structure are shown in Appendix B. Figure 3-1: PSO Bridge (Courtesy of C. E. Ventura) 3.2.1 Bridge Instrumentation and Recorded Earthquakes The bridge was instrumented in 1977 as a collaborative effort between the California Strong Motion Instrumentation Program (CSMIP) of the Division of Mines and Geology (which it is now called Geological Survey of California) and C A L T R A N S to record and study strong motion records from selected bridges in California. Twenty strong motion accelerometers were installed on and off the bridge as shown in Figure 3-2. The free-field (FF) site was originally located on the median of the highway, but in 1985 it was relocated to the current position along the highway embankment. The instrumentation has recorded several earthquakes since its installation. The 10 most significant earthquakes recorded so far are summarized in Table 3-1. The table also includes the peak accelerations recorded at the free-field and on the structure during each event. The local geographical situation of the bridge and the epicentre of the recorded earthquakes are shown in Figure 3-3, and a global geographical situation (indicated with a star) is shown in Figure 3-4. Table 3-1: Significant Earthquakes Recorded at Painter Street Overpass (1977-1992) Event Code Earthquake Date Mag. ( M L ) Epic. Dist. (km) FF Accel. (g) Struct. Accel. (g) 80ML6.9 Trinidad Offshore 8 Nov 1980 6.9 88 0.15 0.17 82ML4.4 Rio Dell 16 Dec1982 4.4 15 — 0.42 83ML5.5 Eureka 24 Aug 1983 5.5 61 — 0.22 86JML5.1 Cape Mendocino-1 21 Nov 1986 5.1 32 0.43 0.40 86 2ML5.1 Cape Mendocino-2 21 Nov 1986 5.1 26 0.14 0.35 87ML5.5 Cape Mendocino 31 Jul 1987 5.5 28 0.14 0.34 92ML6.9 Cape Mendocino - Petrolia 25 Apr 1992 6.9 6.4 0.54 1.09 92ML6.2 Cape Mendocino - Petrolia (AS1) 26 Apr 1992 6.2 6.2 0.52 0.76 92ML6.5 Cape Mendocino - Petrolia (AS2) 26 Apr 1992 6.5 6.4 0.26 0.31 125.0 124.8 124 6 124.4 124 2 124.0 123.8 Long. (°W) Figure 3-3: Local Geographical Location of the Bridge along with the Epicentre of the Earthquakes (Courtesy of C. E. Ventura) I j ^— Seattle Spokane • NititnBl Pi* Portland Salem Billings Boise 13 Salt Lake City Chty«nn«, Reno Sacramento :• tumor San Francisco Natitntl San Jote P l * Denver m S3 -—-Los Angeles Santa Fe I 1200 km 1 '150mi ®20QS Yahoo! tuts Diego^QP I P Phoenix iS2O05 NAVTPQ Figure 3-4: Global Geographical Location of Bridge in USA, (Courtesy of Yahoo website) 3.2.2 Previous Studies on PSO Bridge The first reason for selecting the PSO Bridge for a case study was the availability of a rich data bank of previous earthquakes and field tests. Another reason was the previous studies carried out by several researchers. Results of these studies are helpful in some parts of this thesis. The studies conducted on this bridge are as follows: • Ambient Vibration Test & System Identification 1. Goel, 1997 2. Ventura & Felber, 1993 3. Gates & Smith, 1982 • Soil-Structure Interaction 1. Zahng & Makris, 2001 2. Goel& Chopra, 1997 3. McCallen & Romstad, 1994 4. Wilson & Tan, 1990 Goel (1997) performed a system identification of PSO Bridge to determine the natural frequencies of the structure and their variations under the past earthquakes. He and Chopra (1997) also worked on stiffness values of the soil and the piles beneath the abutments and the bent. Ventura and Felber (1993) did an ambient vibration test to determine the natural frequencies and the mode shapes of the bridge and compared their results with those of Gates & Smith in C A L T R A N S . Ventura also inspected the bridge visually after the 1992 earthquake and prepared a report about the results. Zhang and Makris (2001) worked on soil-structure interaction of the bridge and derived stiffness values for the embankments, the piles beneath the abutments, and the piles beneath the bent. They compared their results with the values derived by McCallen & Romstad (1994) and Wilson & Tan (1990). 3.2.3 Soil Profile This part is a summary of J.Zhang & N . Makris report, 2001. Soil profile: Before construction, a geotechnical exploration at the locations of the piers was con-ducted. Using standard penetration test (SPT) measurements from the ground surface down to a depth of about 10 m, moderately stiff/dense soil layers were identified, which consisted of clayey sand, sandy silt, and gravelly sand. SPT blowcounts varied from 8 near the surface to 34 at 10 m depth. The underlying stratum was very dense gravelly and silty sand, where blowcounts exceeded 100 blows/ft. In a geophysical exploration by Heuze and Swift (1991) six so-called seismic refraction surveys were reported, along from lines parallel to the highway. Four different idealized soil profiles have emerged as shown in Figure 3-5. The differences in the S-wave velocities and shear modules among these profiles are substantial, given that they are 20-30 m apart from each other. For instance, the resulting low-strain shear modulus from the data along line 2 is 1.5 times the value of that resulting from the data along line 1. It is quite possible that some of these differences merely reflected inadequacies (general and specific) of the seismic refraction technique. The soil properties used for the dynamic analysis of embankments is taken as a set of uniform values, i.e., ps=1600 kg/m , Vs=200 m/s, and V=.4 for both west and east embankments. The small-strain shear modulus is G m a x = p sV 2 s=64 MPa. The detail of soil profile can be found in Appendix A . Figure 3-5: Idealized soil profiles that emerged from refraction surveys Chapter 3- Case Study, Finite Element Modeling and Model Calibration 3.3 AMBIENT VIBRATION TEST An extensive ambient vibration study of the Painter Street Overpass was conducted by Ventura et al. 1992, and some of the most significant findings of that study are presented here. The frequencies of the fundamental modes of vibration in the vertical and transverse directions of the bridge have been identified at 3.40 Hz and 4.10 Hz, respectively (the detail results are shown in Table 3-2). The main source of dynamic excitation for the structure during this investigation was vehicle traffic. Since the vertical modes of vibration are well excited by traffic, these modes had to be clearly identified with proper measurements. A significant number of locations on and off the bridge were measured in order to evaluate the potential coupling between vertical and lateral modes, and the relative amplitude of the excitations in the vertical and lateral direction had to be accounted for during the data interpretation process. The salient features of recorded strong motions at the Painter Street Overpass bridge have been presented and compared with the recorded ambient vibration motions. The comparative analyses showed that the events investigated excited the vertical modes of vibration of the bridge more than its transverse modes of vibration. The results indicate that the superstructure exhibited a nearly elastic response for all the events and that the fundamental frequencies tended to lower values as the level of shaking increased. The mode shapes are shown in Figure 3-7. The ambient vibration results were also compared with those obtained from a series of ambient vibration tests conducted more than twenty four years ago (CALTRANS, Gates and Smith, 1982). The analysis showed that the fundamental frequencies obtained from the latter tests are lower than those determined from the earlier test, indicating perhaps some degree of structural, or overall system, degradation through the years due to the significant seismic activity in the region. The sensors layout for the ambient vibration test of 1992 is shown in Figure 3-6. 7—"S—T E-W Elevation 37 1 3 5 O 11 \% 15 17 10 2 4 0 • k 10 12 m \ r.39 Deck Plan Field | N Ambient Vibration Instrumentation 2 23«^ A 22 24 S-/V Elevation Figure 3-6: Location of the Sensors for the Ambient Vibration Test (Courtesy of C. E. Ventura) Mode 1982 Study 1993 Study Change Vertical 1 3.61 3.40 -6% Vertical 2 — 4.92 — Vertical 3 — 6.02 -3% Vertical 4 7.28* 7.10 — Transverse 1 4.49 4.10 -9% Transverse 2 — 5.98 — Transverse 3 7.42 8.60 +16% ^Identified as second vertical mode To verify the ambient vibration result, a series of system identifications were done on all the recorded earthquakes using the ARTeMIS® program to find the Natural frequencies and the mode shapes of the structure. Also by comparing the natural frequencies derived from different earthquakes, it can help to determine whether the structure has suffered any damage or not. The results can be found in Table 3-3. The table shows that the natural frequencies of the bridge have changed after Cap Mendocino-1 earthquake and the first natural frequency changed significantly during the Petrolia earthquake. Two methods, were used for extracting the results. First, the Frequency Domain Decomposition (FDD) peak picking method, which is based on a frequency domain analysis, was used. Second, the Stochastic Subspace Identification (SSI), which is based on time domain analysis and can give the values of damping ratios, was used. Each of the methods can produce different results and that is the reason for differences between the results shown in Table 3-3. The results from Trinidad earthquake are not reliable, because the channels #4 and #7 did not record any data during the event. Some of natural frequencies could not be extracted for certain earthquakes; this means the earthquakes did not have enough energy to excite the structure at certain frequencies. The results of FDD method were used for comparison and further investigation in this thesis. In addition to the earthquakes system identification analysis, a series of analysis with the aim of finding the natural frequency of the site were done by the Nakamura's method (Onur, Ventura, and Hao, 2004). The results of these analyses are shown in Figure 3-8. The results show that the first and the second natural frequencies of the site are around 0.9-1 Hz (Vertical) and 1.6-1.8 Hz (North-South) respectively. These frequencies are clearly far from the natural frequencies of PSO Bridge. Another purpose of these analyses was to clarify the results of the system identification by carried out Goel (1997), which showed that the transverse frequency of the bridge dropped from 4.10 Hz to 1.7 Hz during Petrolia 92 earthquake. These analyses (by Nakamura Method) show that the above mentioned frequency (1.7 Hz) derived by Goel, is the transverse frequency of the site. The reason of this misleading observation is that Goel identified natural frequencies without associating them to corresponding mode shapes. M O D E 6 Figure 3-7: The Mode Shapes derived by the Ambient Vibration Test, 1992 Table 3-3: System Identification using Recorded Earthquakes (Without Base Movement) Event Code Earthquake (Date) Mag. (ML) Dist. (km) Accel, (g) Method 1st Mode 2nd Mode 3rd Mode | 4th Mode 5th Mode FF Str. Freq. Hz (%) Freq. Hz (%) Freq. Hz (%) Freq. Hz (%) Freq. Hz (%) 80ML6.9 Trinidad Offshore (8 Nov 1980) 6.9 88 0.15 0.17 FDD 3.271 3.955 — 4.883 — — — — — SSI 3.194 1.17 3.864 4.65 — — — — — . . . 82ML4.4 Rio Dell (16 Dec 1982) 4.4 15 ~ .42 FDD 3.369 — 3.857 — — R — — — SSI 3.395 1.60 4.097 3.56 — — . . . — — — 86JML5.1 Cape Mendocino-1 (21 Nov 1986) 5.1 32 .43 .40 FDD 3.369 — 4.053 — 4.736 — [RT] — — — SSI 3.267 3.06 3.596 4.72 4.684 1.22 — — — — 86 2ML5.1 Cape Mendocino-2 (21 Nov 1986) 5.1 26 .14 .35 FDD 3.320 — 4.053 — 4.590 — — — — — SSI 3.375 2.10 4.021 4.12 4.779 2.24 - — — — 92ML6.9 Cape Mendocino -Petrolia (25 Apr 1992) 6.9 24 .54 1.09 FDD 3.125 — 4.05 — 4.492 — 5.859 — — — SSI 3.147 3.92 — — — — 5.468 3.39 — — 92ML6.2 Cape Mendocino -Petrolia (AS1) (26 Apr 1992) 6.2 42 .52 .76 FDD 3.027 — — — 4.590 — 5.713 — 6.396 — SSI 3.027 4.02 — — — — 5.608 1.01 6.404 3.81 92ML6.5 Cape Mendocino -Petrolia (AS2) (26 Apr 1992) 6.5 41 .26 .31 FDD 3.174 — 4.150 — 4.540 — 5.664 — 6.592 — SSI 3.060 1.471 4.013 — — — 5.970 4.87 6.573 0.63 Figure 3-8: Normalized V/H Ratio vs. Frequency (Hz) for Ambient Vibration Test and the Earthquakes Ambient Yibraiicm Test 0.01 W 1 1 II CMSfcift Earthquake 0.01 0.1 :.".'|t, t 1 i 1 . ^ —, -f i 1 0.1 p t>2aS 1 E : rihquake . _ . • t 1 ; \ (I ••••+--J l t k 1 o.oi0 p I .1 1 10 P92aft2 Earthquake 0.01 Chapter 3- Case Study, Finite Element Modeling and Model Calibration 3.4 FINITE ELEMENT MODEL The as-built detail drawings provided by C A L T R A N S on November 1973 were used for the FE modeling. A 3-D finite element model was developed using SAP2000 V9® program. The model accounted for the soil-structure interaction. The properties used for modelling are summarized as follows: • Deck: it is a continuous multi-cell box girder, 1.73 m high. Modulus of elasticity and unit ft ~) ^ weight of concrete are E=25xl0 kN/ m and 7=2.4 kN/m respectively. The deck has a stiffening beam above the bent. • Bent: this two-column single bent has a reinforced rectangular concrete beam, with dimensions: 1.73mx 1.68m. The columns of the bent are flared with the same cross-sections and approximately 7.3 meters high. The column's cross section at the bottom is an octagon with a diameter of 1.5 m. This cross-section is constant up to 4.3 m and then changes a parabolic shape. The cross-section at top is also an octagon with a diameter of 2.75 m. These columns are reinforced with standard steel bars. The foundation of each column is rectangular with 4.6 mx3.7 m dimensions. Each foundation is resting on 20 piles. The specifications of the bent's concrete are the same as those of the deck. • Abutments: the west and the east abutments of the bridge are resting on 14 and 16 piles . respectively with a diameter of 0.35 meters. The geometry and materials properties of the bridge were modeled as per the supplied drawings. The deck and the bent components were modeled by 168 shell and 5 beam elements respectively. The piles beneath the structure were modeled as translational springs. The finite element model is shown in Figure 3-9. 3.4.1 Soil-Structure Interaction Zhang and Makris studied on the stiffness of embankments and piles for this bridge, and they compared their results with previous studies. In their study, the stiffness of embankments and piles were determined separately. Shear beam theory was used for the embankments and the Makris & Gazetas (1992) method was implemented to find the stiffness of a single pile, which was then multiplied by the number of piles (Super-position rule). The soil-structure interaction of this bridge has been studied by many researchers, from among them the Zhang and Makris (2001) results were used in this study before the model calibration using the vibration data. 3.5 MODEL CALIBRATION The aim of this part was to develop a model capable of representing the actual bridge conditions. The periods and mode shapes of the structure were calibrated by the ambient vibration test results of 1993. Two main parameters were considered for model calibration. The first one was mass and the second one was stiffness of the structure, the soil and the piles. The SAP2000® program is good enough to have a mass distribution exactly like the real bridge. Also the stiffness values of the structure can be so defined to be like the real ones (e.g. rigidity of the joints and the connections), but the stiffness values of the soil and the piles (stiffness of the springs) should be calibrated. For the first guess, the stiffness values derived by Zhang & Makris were used for the embankments and the bent piles. Finally after a lot of iterations (changing the stiffness values of the soil + the piles), an FE model was developed with the same frequencies and mode shapes as the ambient vibration results which are shown in the following figures. Table 3-5 shows the comparison between the FE model and ambient Vibration results. The mode shapes comparisons are shown in Figure 3-10 to Figure 3-15. Zhang and Makris modelled the structure and determined the six natural periods and mode shapes too. Their results show a structure with longer natural periods (softer) compared to the results derived from ambient vibration test. Finally the values for the springs are shown in Table 3-4 for comparison. After matching the dynamic specifications of the model with those of the real structure, three of the recorded earthquakes (Trinidad 80, Cape Mendocino 86 and Petrolia 92) were chosen for a series of linear time history analyses. The model responses were compared with the recorded motions. These analyses can verify the calibrated FE model as well as the results from Table 3-3, which show a drop in the natural frequency values after Cape Mendocino earthquake. The recoded accelerations for these three earthquakes can be found in Appendix A . Table 3-4: Spring and Dashpot Values for Soil-Structure Interaction Parameters Mirza 2005 Zhang & Makris 2001 Goel& Chopra 1997 McCallen & Romstad 1994 Wilson & Tan 1990 Caltrans Method A (Method B) Embankment +Pile Foundations Kx (MN/m) 1633+ 137+180 146~1458+ 815+105 876+105 Embankment +Pile Foundations Ky (MN/m) 490+ 137+180 117-438+ 851+105 201* 810+105 (68+105) Embankment +Pile Foundations Kz (MN/m) oo 582+773 — oo 564* — Embankment +Pile Foundations Cx (MN.s/m) 9+9 — — — Embankment +Pile Foundations Cy (MN.s/m) 9+9 — — — Embankment +Pile Foundations Cz (MN.s/m) 17+56 — Pile Foundation of Bent Kx (MN/m) 195 321 — 140 — 140 Pile Foundation of Bent Ky (MN/m) 140 321 — 140 — 140 Pile Foundation of Bent Kr (MN.m/rad) — 5254 — — — — Pile Foundation of Bent Kxr, Kyr (MN/rad) — 354 — — — — Pile Foundation of Bent Kz (MN/m) CO 982 — CO — — Pile Foundation of Bent Cx, Cy (MN.s/M) — 5 — — — — Pile Foundation of Bent Cz (MN.s/m) — 20 — — — — ^Embankment only +Embankment and Piles Note: X-dir, Y-dir and Z-dir are longitudinal, transverse and vertical directions respectively. Figure 3-9: Painter Street Overpass Bridge FE Model Table 3-5: Comparison between the Ambient Vibration and the FE model Results Mode Frequency-(Period) by SAP2000 Hz - (Sec) Frequency-fPmW) by ARTeMIS Hz - (Sec) 1 - Vertical 3.38-(0.29<5) 3.4O-(0.294) 2-Transverse 4.\6-(0.240) 4.HH0.244) 3-Vertical 5.07-(0.197) 4.92-(0.203) 4-Vertical 5M-(0.170) 6.02-(0.166) 5-Transverse em-{o.i66) 5.91'-(0.167) 6-Vertical 7.35-(0.136) 7A0-(0.141) Figure 3-10: First Mode (Vertical)-by SAP2000 & ARTeMIS Figure 3-11: Second Mode (Transverse)-by SAP2000 & ARTeMIS Figure 3-12: Third Mode (Vertical)-by SAP2000 & ARTeMIS Figure 3-13: Fourth Mode (Vertical)-by SAP2000 & ARTeMIS Figure 3-14: Fifth Mode (Transverse)-by SAP2000 & ARTeMIS Figure 3-15: Sixth Mode (Vertical)-by SAP2000 & ARTeMIS Chapter 3- Case Study, Finite Element Modeling and Model Calibration 3.5.1 Trinidad Offshore Earthquake This earthquake occurred on November 8 t h 1980 and its magnitude was 6.9. The distance between the bridge and the epicentre was 88 km and the structure experienced an acceleration with a magnitude of 0.17g. This was the first earthquake, with a low shaking level, that the bridge experienced after the instrumentation. Sensors # 7 and # 4 malfunctioned during the event, so they were not included in the comparison. The comparison between the acceleration time histories can be seen in Figure 3-16 and Figure 3-17 (only the intense parts were plotted). The first guess for level of damping ratio of each mode was taken from the system identification in the previous step. The value chosen for the analysis is 1.5% for all modes. The reason for using the same value for damping ratio for all modes is that the system identification only identified two or three modes of the structure along with their damping ratios in each earthquake, whereas in time history analysis 20 modes were considered for calculating the precise response of the structure. Therefore damping ratios for the unidentified modes was set arbitrarily at 1.5 %. As the time history plots show, there is a good match between the recorded and analyzed results. This analysis shows the model is well calibrated for this level of shaking. The next step is to choose another earthquake with a higher level of shaking and check the model again, because the ambient vibration results are based on the low amplitude vibrations and this model was calibrated for that level only. The objective of this part is to cross-check the phase angle and the trend of analytical response against the recorded response. Matching up the analysis responses exactly with the recorded ones, requires calibration of damping ratios for each mode individually, which is beyond this study. The damping ratio changes with the level of shaking but it can not be identified through the linear analysis and be applied to nonlinear analysis, so calibration of these values for each mode is unnecessary. Therefore, there are some differences between the peak values of the analytical results and the recorded ones. -40. r -60 Channel 5 Mix 37.7 at 11.1 Record M i n •<•••«»•* Max 50.33 atfl.4 in-44.S at 10.7 -Analysis 10 12 Channel 6 300 200 100 0 -100 -200 -300 Channel 8 tx 241.9 at 11.1 •"•«»«« TtlVlll — A n a l y s i s Max 188.7 at 11.1 10 12 Channel 9 10 12 120 80 40 0 -40 -80 -120 Channel 10 Max 96.6 at 11.0 Record M l n " 7 4 5 a t 1 0 6 Max 74.7 at 11.0 <*:U>«t11.1 -Analysis 10 12 200 150 100 50 0 •50 •100 -150 -200 Channel II -Record Analysis Max 168.5 at 14.6 10 12 Figure 3-17: Comparison between Record and Analysis -Transverse, Vertical and Longitudinal Acceleration (cm/s2) vs. Time (sec) respectively-Trinidad Offshore Earthquake 3.5.2 Cape Mendocino 86-1 This earthquake happened on November 21 s t 1986. The magnitude of the earthquake was 5.1 and the epicentre's distance from the bridge was 32 kilometres. The recorded duration of this earthquake was 21.29 seconds and the maximum acceleration recorded on the structure was •40g. This earthquake was applied to the model and the results of the acceleration time histories comparison are shown in Figure 3-12, Figure 3-13 and Figure 3-14. This earthquake was selected for the analysis because of its moderate level of shaking. The results show a good level of matching between the recorded and analyzed time histories. Some plots (e.g. Channels 7 and 6) of the analysis show higher levels of acceleration compared to those of the recorded ones. This is because of considering 5% damping ratio for all modes. A better match will result i f damping ratios of all modes are calibrated individually. 3.5.3 Petrolia 92 This earthquake occurred on April 25 t h 1992. The magnitude of the earthquake was 6.9 and the event's epicentre was 24 km away from the bridge. The recorded time histories have 60 seconds duration. It should be mentioned that is the highest level of shaking that the structure has experienced since 1980, and that the maximum acceleration recorded on the bridge was 1.09g. The free-field accelerometer recorded a peak acceleration of 0.54g. This earthquake was applied to the finite element model, and the results of the comparison between the time-histories are shown in Figure 3-21, Figure 3-22 and Figure 3-23. The plots show a reasonable match of transverse and vertical motions in some channels with some differences in channels 7 and 11. There are also some differences regarding phase angle between the analytical response and the recorded one in other channels. These differences maybe due to some minor damage during the earthquake and will be investigated in the next chapters. The system identification showed a significant decrease of the first mode frequency, as shown in Table 3-3. For this analysis, 5% damping ratio was considered for all modes. Channel 4 Max 1 56 4 at 2.4 Mln-127.6 at 2.6 Max 243.6 at 2.7 Mm-206.2 »t 2.4 - Analysis 10 300 200 100 0 -100 -200 -300 Channel 9 i I if 1 1 w ad\ I Mix 1 57 5 at 2 7 J Min -210.5 at 2.6 _ , Racord • — Analysis I Max 288.7 at 2.7 ^^^j^^g*. M m -2429 a j y y H M H | M M M ^ ^ ^ 10 Channel 5 Max 68.8 at 2 4 Racord Min-80.9 at 2.. Analyst. Max 49.4 at 2.4 Min-66.0 «l 2.3 1 2 3 4 S 6 7 8 9 10 Channel 6 -400 J " ™ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ " " ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ™ ^ ~ 1 2 3 4 5 6 7 8 9 10 Channel 10 250 200 150 100 50 0 -50 -100 -150 -200 -250 _ A A / • • Max K 1.0 a . Min-100.2 at 2.6 . . Record Analysis Max 96.2 at 2 5 7 Min -QUsA $X *-* m 10 Channel II Record Max 364.6 al 2.4 Min-391.1 at 2 5 Max 362.1 at 2.4 Min -370.6 at 2.6 Analysis 10 Figure 3-20: Comparison between Record and Analysis -Vertical and Longitudinal Acceleration (cm/s2) vs. Time (sec) respectively-Cape Mendocino 86-1 Earthquake Channel 10 Figure 3-23: Comparison between Record and Analysis -Vertical and Longitudinal Acceleration (cm/s2) vs. time (sec) respectively-Petrolia 92 Earthquake Chapter 3- Case Study, Finite Element Modeling and Model Calibration 3.6 CONCLUSION In this chapter, a calibrated FE model of PSO Bridge using the ambient vibration test results was developed successfully. The natural frequencies and mode shapes of FE model matched those from field test. Soil-structure interaction was included in the FE modelling. Three linear dynamic analyses were conducted using the earthquakes that the bridge has experienced. The Trinidad, Cape Mendocino 86 and Petrolia 92 earthquakes were the lowest, the medium and the highest levels of shaking the bridge has experienced. The Trinidad and the Cape Mendocino 86 results matched up with.the real response of the structure, but the Petrolia 92 results had differences, which may be due to damage or any other environmental source (e.g. temperature). For completeness, a summary of peak acceleration and displacements of the analyzed earthquakes are shown in Table 3-6. Lastly, it can be said that the calibrated FE model is a rational representation of the actual bridge and can used for the nonlinear analyses described in the next chapter. Table 3-6: Comparison between Accelerations and Displacements from Analysis and Record Trinidad-80 Cape Mendocino-86 Petrolia-92 Sensor Analysis Record Analysis Record Analysis Record A D A D A D A D A D A D 4 158 5.4 — — 243 0.51 155 0.57 458 6.50 1067 8.92 5 50 1.6 38 1.37 66 0.13 61 0.11 169. 1.91 174 2.11 6 274 1.78 270 1.89 430 0.14 170 0.47 747 3.09 657 2.98 7 311 5.38 — — 559 0.50 240 0.90 1020 6.49 884 7.66 8 189 2.02 242 1.57 297 0.29 288 0.32 397 3.06 576 2.61 9 168 3.66 166 3.27 289 0.51 158 0.58 701 6.94 672 5.71 10 75 1.74 97 1.69 96 0.13 229 0.34 175 3.03 305 2.83 11 190 3.52 160 4.65 352 1.10 354 1.28 915 8.31 443 8.88 *A: Acceleration (cm/s ) **D: Displacement (cm) CHAPTER 4 NON-LINEAR STATIC AND DYNAMIC ANALYSES (PUSHOVER & TIME HISTORY) 4.1 I N T R O D U C T I O N In this chapter, the calibrated bridge model is analyzed using two different methods of nonlinear analysis. First, a quasi-static nonlinear analysis is done to find the lateral force vs. displacement. This analysis is a performance-based approach and provides useful information about hinge formation and the overall ductility of the structure. Second, a series of dynamic nonlinear time history analyses are done to determine the behaviour of the structure under different levels of earthquake intensity. Finally time histories of accelerations from the nonlinear dynamic analysis at the location of sensors on the bridge are taken as input for the next step (System Identification and Damage Index). 4.2 S T A T I C N O N - L I N E A R A N A L Y S I S ( P U S H O V E R ) The aim of this analysis is to assess the performance and expected damage of the structure under lateral seismic loading. There are few assumptions and facts which should be clarified before doing the pushover analysis. These are: 1. In the lateral direction, the deck provides a lateral stiffness for the system which is too high compared to the stiffness of the columns and the abutments. 2. The columns and the abutments are the key lateral load-resisting elements governing the lateral capacity of the bridge. 3. Despite the fact that the deck and the beam are a continuous piece, hinges are considered on the beam (M3 Type) to check the assumption # 1. 4. P-A effect is considered in this analysis. 5. The soil behaves nonlinearly beneath the columns and abutments. 6. The vertical loading is due to the dead load of the bridge and the dominant transverse loading is from the first and the second mode shape deformations. 7. The hinges forming on the columns are assumed to be of P - M - M 4 type. It means Axial-Flexural hinges are considered for the columns (based on a series of experimental tests on concrete columns in PEER 5 , flexural failure only happens in the columns with L/b>4.5, in which b is the width and L is the length of the column [Structural Performance Data Base, 2005]). 8. Values of the soil+piles stiffness in the linear domain are taken from the calibrated model, and the degradation of these stiffness values are based on ANSI/API for the piles (API, 1993). 9. The nonlinear effect of the pile group is ignored in this analysis for two reasons: simplification of process and the fact that SAP2000® can not handle it. For selecting the location of the hinges and the nonlinear links in the FE model, the previously mentioned elements, which provide the lateral stiffness for the structure, due to the lateral loading, are to be clarified as follows: • Deck: deck elements have a high value of lateral stiffness compared to the other members of the structure. The other elements lose their lateral stiffness firstly due to the lateral loading, so it is acceptable to consider hinges and nonlinear links in the other parts of the structure only. Figure 4-1 illustrates this aspect of bridge behaviour. 3 M3 is a type of hinge, which includes the effect of the moment about transverse axial. 4 P-M-M is a type of hinge, which includes axial force-moment (in both directions) interaction. 5 Pacific Earthquake Engineering Center (located at the UC Berkeley) • Bent: as the beam of the bent is continuous with the decks its rigidity becomes very high and its columns will be the weakest links of the structure in lateral motion. Besides, i f these columns lose their lateral capacity, the structure will lose its serviceability. Structural hinges will form at this part of the structure only. • Embankments & Piles: these elements also provide lateral stiffness, which are modeled as nonlinear links at the boundary of the structure. They are explained and discussed in the section 4.2.2. 4.2.1 Bent's Hinges The locations of hinges in the bent were chosen with regard to observed failures of bridges during past earthquakes, as can be seen in Figure 4-1 and Figure 4-2. Figure 4-1 shows the flexural failure in long columns and rigid movement of continuous decks. Figure 4-2 shows a failure below a flare in a column. Figure 4-3 shows the location and the type of hinges. Hinges on the bent beam are examined to check i f the moment exceeds the capacity of the beam. Figure 4-4 and Figure 4-5 show the cross sections of the columns and the beam respectively. Moment-curvature of the sections was calculated by the Section Designer module which is part of SAP2000® (ACI 318-02 code was considered). The interaction of axial force with the moments was considered for the column hinges. The results are shown in Figure 4-6. Figure 4-1: Collapse of Continuous Decks in the Hyogo-Ken Earthquake 1995(After Chen & Duan, 2000) Figure 4-2: Failure of Flared Column in Northridge Earthquake 1994 (After Chen & Duan, 2000) r B #11 TOT 36 44.77 cm 62.86 152.4 cm 44.77 cm Figure 4-4: A-A Cross Section of the Column 30000 25000 _^  20000 as - 15000 E o 10000 5000 | -Beam L -Columnj — I piJUl _ . : 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 Curvature (rad) 0.004 Figure 4-6: Moment-Curvature Diagram of Bent Elements 4.2.2 Soil Links As mentioned in the pervious chapter (Section 3-5), the equivalent linear values of soil stiffness (the piles group stiffness + the embankment stiffness) were found by iterative calculations. The initial values were taken from Zhang and Makris, 2001, but these values would make the structure softer (lower natural frequencies) compared to the natural frequencies obtained from ambient vibration test. The final linear values were shown in the previous chapter (Table 3-4). For this analysis, the behaviour of the soil beneath the bent and in the abutments was assumed to be nonlinear. The stiffness degradation of piles group was taken from ANSI/API 1993. The degradation of the lateral force with respect to displacement and pile depth is defined by the following equation: P = A.P .Tanh k.x.y _____ (4-1) P u = 70.D.x.y' (4-2) Where A=0.9 for cyclic loading, Pu: Ultimate bearing capacity at the depth X in unit of force per unit length, k: Initial modulus of subgrade reaction in force per volume units, (225 lb/in 3 for moderately stiff/dense) x: Depth, D: Average diameter of the pile from the surface to depth (1 ft), y': effective soil weight and y: Lateral displacement. (Units are lb & inches) Equation 4-1 was used for plotting the p-y curves. These curves were calculated for a unit of depth and then scaled up to have the initial stiffness equal to the values derived by calibration in Chapter 3 (Table 3-4). The p-y plots of the abutments and the bent are shown in Figure 4-7. P x and P y are the plots for x (longitudinal) and y (transverse) directions respectively. The approximation of this degradation does not effect the next step result significantly, because the lateral stiffness of the columns are too low, compared to that of the soil and the decks, and the columns govern the results of the pushover and nonlinear dynamic analyses. It means the columns are the weakest links in the lateral direction and they lose their capacity rapidly before the soil and the deck enter their nonlinear domain. 4.2.3 Pushover Analysis Results The pushover analysis consisted of incremental loading applied in 13 steps and the target displacement was selected at the location of sensor # 7 (tip of bent's beam). The first hinge forms at the base of the column at 2.51 cm displacement. By 9.55 cm displacement, the bridge looses approximately 95% of its lateral strength, and the piles behave non-linearly in the Y direction (step 7). In step 13, the bridge looses its global stability at 12.34 cm of displacement. A summary of hinge formation is shown in Table 4-1. Figure 4-8 shows the base shear vs. lateral displacement (at the location of sensor # 7); also the critical steps of hinge formation are shown in Figure 4-9 to Figure 4-10 respectively. Results Discussion: The results of this analysis confirms that although the decks, the soil (embankments+piles) and the columns provide the lateral stiffness for the structure during the lateral loading, the columns govern the lateral behaviour of the structure. It means that their stiffness values are too low compared to those of the other members and they lose their lateral capacity faster than the others. Also it should be mentioned that these columns are the key members for the stability of the structure and if they lose their lateral capacity, the bridge wil l lose its stability and serviceability. 7.0E+03 6.0E+03 5.0E+03 Z 4.0E+03 S 3.0E+03 2.0E+03 1.0E+03 0.0E+00 / / — Px-Ben t — P ; ('-Bent 6 8 10 Displacement (cm) 14 l(> 6.0E+04 5.0E+04 4.0E+04 3.0E+04 e Lfa 2.0E+04 1.0E+04 0.0E+00 Px-A nutmcnts Pv-AI tutments 6 8 10 Displacement (cm) 12 16 Figure 4-7: Nonlinear Behaviour of Piles in the Bent and the Abutments Table 4-1: Pushover Steps Result Step Displacement at Sensor # 7 (cm) Frame Condition Soil Situation Abutments Bent 1 2.51 Linear Linear Linear 2 2.56 First Hinge-RC* Linear Linear 3 2.86 First Hinge-LC* Linear Linear 4 5.40 — Linear Linear 5 8.93 Second Hinges-LC-RC Nonlinear- Y Direction Linear 6 9.54 — Nonlinear- Y Direction Linear 7 9.55 First Hinge collapses-RC Nonlinear- Y Direction Linear 8 10.34 l s t & 2 n d Hinges collapse-LC & RC Nonlinear- Y Direction Linear 9 10.35 — Nonlinear- Y Direction Linear 10 11.10 — Nonlinear- Y Direction Linear 11 11.70 — Nonlinear- Y Direction Linear 12 11.71 Second Hinge collapses-LC Nonlinear- Y Direction Linear 13 12.34 Structure Collapses Nonlinear- Y Direction Linear -RC: Right Column & LC: Left Column Sensor # 7, Monitored Displacement V c ' i i i n n r - 1 - 7 / \ _ L _ I _ _ I I _ L _ / / \ / \ S T E P 2 N-S Elevation I  0 S T E P 3 f mmmmmm c i D I I F _________ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ C 1 U 1 1 U i \^_DI___C_]I___7/J \ _ _ • • • • _ / \ • / \ STEP 4 • / S T E P 5 1 i • H _ _ _ _ i C 1 O 1 I K A _________ i ; i I I | E | K . <. . • • • c z *J S T E P 6 i H H _ _ _ C 1 _ _ • K • _ _ _ _ I L J \ \ U Z D \ o 0 STEP 7 P 1 ' STEP 8 Q H H H k ^ i ^ H i . i mam K - M k ^ M i ^ k ^ M L J j \ o r z o \ 0 • ( 1 / -" STEP 11 D 1 • • • L Z 1 # / \ STEP 12 • 7 • 0 Figure 4-10: Formation of Hinges in the Bent Frame-Continued Figure 4-12: Behaviour of Link 22 in the Bent during Pushover Analysis Chapter 4-Nonlinear Static and Dynamic Analyses (Pushover & Time History) 4.3 NONLINEAR DYNAMIC ANALYSIS (TIME HISTORY) The aim of the nonlinear time history analysis was to simulate different levels of damage in the bridge. The results are used as inputs for the damage index method in the next step. The acceleration time histories of the damaged bridge at the location of sensors would be fed to DIM to check this method on PSO bridge. The details of this step are explained in the next chapter. The bridge was analyzed with the nonlinear time history method at six different levels of earthquake shaking. The minimum damage, i.e. formation of only one hinge in one of the columns, is defined as "level one", and the maximum damage, i.e. the almost collapse of the structure, is defined as "level six". For the levels in between, the level of damage was determined by the number of hinges formed and their levels of ductility capacity. The ductility capacity level of a hinge can be defined as deformation of a hinged member between yielding point and failure point. The yielding point and failure point can be defined as 0% and 100% of ductility capacity level respectively. There are six steps (SAP2000® program default) between the yielding and failure points and each step represents of 16.67% of ductility capacity level. These steps are shown with different colors. These colors are defined and shown in Section 4.3.2. The Nonlinear Direct-Integration Time-History method was used for this analysis. The results of this method are extremely sensitive to time-step size, and time-step should be decreased until the step size can not affect the analysis results. The damping of the structure is modeled using a full damping matrix in this method. The program accepts two values of the damping ratio for the first and the second modes, and then two coefficients are calculated by the entered values proportional to the stiffness matrix and the mass matrix (e.g. Rayleigh Damping). The values shown in Table 4-2 are the damping ratios which were assumed for the first and the second modes. Three earthquakes with different levels of shaking, which the bridge had experienced, were selected for this purpose, i.e. Trinidad-80, Cape Mendocino-86 and Petrolia-92, which were of low, pulse and high frequency contents. Their frequency contents helped to induce different levels of damage to the bridge. Each earthquake was scaled to two different levels that could cause different levels of damage to the bridge. These scales were selected by trial and error to reach a desired level of damage. For example, Trinidad earthquake was scaled with a scale factor greater than one and it was repeatedly changed by trial and error till the analysis resulted in a minimum damage to the structure. Table 4-2 shows the earthquakes, damping ratio, scales, level of damage and their runtime. It should be pointed out that trial and error analyses were extremely time consuming. For these analyses the following assumptions were made: • Nonlinearity of material by predefined hinges in the columns, the beam and the soil links (same as pushover analysis). • Nonlinearity of geometry by considering P-A effect. • Maximum 0.002 and Minimum 0.001 seconds for time-step size. • The dead load'of the bridge (its weight) applied as initial condition. 4.3.1. Scaling The procedure of scaling used for this study is based on Engineering and Design-Time-History Dynamic Analysis of Concrete Hydraulic Structures Manual (US Army Corps of Engineers 2003). Scaling of these earthquakes means multiplying a factor by the whole accelerations of time histories in three main directions (X, Y and Z). The author recognizes that the scaled intensities of these earthquakes are not realistic, and that the scaling has some limitations; however the purpose of this step was only to inflict different levels of damage to the bridge. Scaling limits as discussed by Iervolino & Cornell (2005), concerns the design and the near field time histories only. The author followed this limitation for the near field earthquake (Petrolia 92). Scale factors used in the analyses, are shown in Table 4-2. It should be mentioned that the vertical components of the CM86-4.6, CM86-6.5 and P92-3.5 were scaled to 4.0, 4.0 and 3.2 respectively. The reason is the bridge could not tolerate more vertical acceleration than the scaled ones, and the model became numerically unstable during the analyses. This is because of the enormous axial forces induced in the columns due to the high vertical acceleration, which caused the P - M - M hinges to become unstable. Also it should be mentioned that nonlinear analyses could not be done for further than the level of damage (almost collapse-level six) of P92-3.5 earthquake, because the model would become unstable by increasing the scale factor beyond that level. Table 4-2: Nonlinear Analyses Comparison EARTHQUAKE SCALE FACTOR DAMPING L E V E L OF DAMAGE RUN TIME (HnMin) Trinidad 1980 9.8 5% 1 4:00 11.9 7% 4 4:10 Cape Mendocino 1986 4.6 5% 2 4:00 6.5 7% 5 4:05 Petrolia 1992 3.0 5% 3 9:15 3.5 7% 6 13:05 4.3.2 Trinidad 9.8 The original Trinidad earthquake, occurred in 1980, gave 0.17g acceleration to the structure. It was the lowest level of earthquake the structure has experienced. This earthquake was scaled to 9.8 times of original one; and the damping ratio was assumed 5% for the first and the second periods to calculate the proportional coefficients of damping matrix. The scaled earthquake caused the minimum level of damage (level 1). Only one hinge formed in the north bent column. As shown in Figure 4-13 (N-S Elevation), the hinged member deformation is at the yielding point. The legend of the figure can be interpreted as follows: • Pink (yielding point) • Red (failure point) The whole range of ductility capacity is indicated by 7 colors. Each color represents 16.67% of the level of ductility. So the relation between the colors and the level of ductility capacity are: Color Level of Ductility Capacity Pink 0% 16.67% Light Blue 33.34% Green 50% Yellow 66.67% Tangerine 83.35% 100% This earthquake induced 1.4g (at CI 1), 2.1 g (at C7) and 1.6g (at C6) acceleration in X , Y and Z directions respectively. The analyzed acceleration time histories at the location of sensors are shown in Figure 4-16 to Figure 4-17. The maximum relative displacement in channel 7 was calculated 2.6 cm (Figure 4-18). The maximum values of base shears are 26000 kN and 29000 kN in the X and Y directions respectively (Figure 4-19). The soil behaved linearly during the earthquake as shown in Figure 4-14 and Figure 4-15. Link 21 located in the west abutment and link 22 located in the south column were chosen for plotting. The maximum force and displacement for each link in both directions were calculated as follows: • Abutment X (link 21)- Force=2000 kN, Displ =0.7 cm • Abutment Y (link 21)- Force=2000 kN, Displ =2.2 cm • Bent X (link 22)- Force=2600 kN, Displ.=l .0 cm • Bent Y (link 22)- Force=2000 kN, Displ =1.2 cm The forces and displacements in the model's nonlinear links represent the soil behaviour, which for this analysis remained in the linear domain. Figure 4-13: Final Status of Hinge Forming for Trinidad-9.8 EQ 2500 2000 1500 1000 z 500 Z o = -500 -1000 -1500 -2000 -2500 -0 Link21-Abutment-X 2500 2000 1500 1000 z 500 r o o -500 G_ -1000 -1500 -2000 -2500 -2 Link21-Abutment-Y 80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 Displacement (cm) 20 -1.80 -1.40 -1.00 -0.60 -0.20 0.20 0.60 1.00 1.40 1.80 2.20 Displace me nt(cm) Figure 4-14: Force -Deformation of Link 21 at West Abutment-Trinidad 9.8 3000 2000 1000 z ~Z o * -1000 -2000 -3000 -1 Link22-Bent-X 20 -1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 Dis place ment(cm) 2500 2000 1500 1000 z 500 T 0 O • -500 -1000 -1500 -2000 -2500 -1 Link22-Bent-Y • 20 -1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20 Displacement (cm) C h a n n e l 4 < h a n n e l 5 C h a n n e l 7 ... t»o - — - — — — i — — \ \ C h a n n e l 8 M i n - 1 0 2 6 at 8 .16 M a x 1 4 2 8 at 1 1 . 0 4 1 C h a n n e l 9 < Ii:i iine 1 10 MPn - 1 4 3 1 at 8 .68 l M a x 1 2 2 9 at 8 . 7 0 1(> 12 Figure 4-17: Time Histories of Channels 9,10 and 11- Acceleration (cm/s ) vs. Time (sec)-Trinidad 9.8 R e l a t i v e D i s p l a c e m e n t - C 7 i.ii 4(> 2(> 0 - 2 0 - 4 0 -6(1 A b s o l u t e D i s p l a c e m e n t - C 7 ! — — 1 B _ _ B _ H _ _ i j M a x 36 67 at 9 60 Base Shear-X 12 14 16 Min-26030 at 8.58 Max 23980 at 12.40 18 20 22 Base Shear-Y Min -29080 at 10.24 . Max 28020 at 10.66 j 18 20 22 Chapter 4-Nonlinear Static and Dynamic Analyses (Pushover & Time History) 4.3.3 Trinidad 11.9 In this analysis, Trinidad earthquake was scaled up to 11.9 times of original one; and the damping ratio was assumed 7% for the first and the second periods to calculate the proportional coefficients of damping matrix. This earthquake caused damage at the level of 4, and 3 hinges formed in bent columns (Figure 4-20). Two of them (pink color) are at the yielding point and the other one loses (dark blue) 16.67% of its ductility capacity. As shown in Figure 4-20, the north column has a hinge at the base and the south column has two hinges, at the base and at the top. . This earthquake induced 1.6g (at CI 1), 2.3g (at C7) and 1.4g (at C6) acceleration in X , Y and Z directions respectively. The analyzed acceleration time histories at the location of sensors are shown in Figure 4-23 to Figure 4-24. The maximum relative displacement in channel 7 was calculated 3.1 cm (Figure 4-25). Maximum values of base shears are 30000 kN and 32000 kN in the X and Y directions respectively (Figure 4-26). The soil behaved linearly during the earthquake as shown in Figure 4-21 and Figure 4-22. Link 21 located in the west abutment and link 22 located in the bent were chosen for plotting. The maximum force and displacement for each link in both directions were calculated as follows: • Abutment X (link 21)- Force=2100 kN, Displ.=0.7 cm • Abutment Y (link 21)- Force=2500 kN, Displ.=2.5 cm • Bent X (link 22)-Force=4300kN, Displ =1.7 cm • Bent Y (link 22)- Force=3850 kN, Displ =2.1 cm The forces and displacements in the model's nonlinear links represent the soil behaviour, which for this analysis remained in the linear domain. / N-S Elevation " c ^ i r " p ^ [ _ _ F : Figure 4-20: Final Status of Hinge Forming for Trinidad-11.9 EQ 2500 2000 1500 1000 SB 500 Z o » -500 -1000 -1500 -2000 Link2l-Abutment-X Link2l-Abutment-V 2000 1500 1000 2 500 Z o • -500 -loon -1500 -2000 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 Displacement (cm) -2.80 -2.10 -1,40 -0.70 0.00 0.70 1.40 2.10 2.80 Displacement (cm) Figure 4-21: Force -Deformation of Link 21 at West Abutment-Trinidad 11.9 3000 2000 1000 Liok22-Bent-X 5 ° T-iooo Z -2000 -3000 -4000 )0 -2.00 -1.50 -1.00 -0.50 0.00 0.50 1. Displacement (cm) -1.20 -O.80 -0.40 0.00 0.40 lUO 1.20 1.60 2.00 2.40 Displacement (em) C h a n n e l 4 M i n - 1 3 7 3 at 10.22 M a x 1 4 1 8 a t 7.88 C h a n n e l 5 C h a n n e l 6 C h a n n e l 7 f M i n - 2 1 0 4 at 10 .24 M a x 2 2 8 0 at 10 .66 C ha line I 8 - 5 0 0 -UMHI -1 son M i n - 1 1 1 1 at 8.1 B I M a x 1 633 a t 11.041 C h a n n e l 9 HIM) 6 0 0 — 4 0 0 H 2 0 0 - 6 0 0 - 8 0 0 C h a n n e l JO f f U fl l/iAAAA AI\(lJl/L -AA ^w-vA/v/^ V W I fv mI m r n w r 1 ' _ i „ _ 1 » j l j M i n -614 at 10.66 M a x 662 at 11 04 2(100 1 5 0 0 I (Kill S o u n -soo -I (Kill -15IIO 2(HIO C h a n n e l 11 | Al Ii il y p A r a M W M l w ura. n N r i 1 | y t T 1 1 M i n -1678 at 8.68 j M a x 1379 at 8.70 8 : 10 12 / 14; : Sf: 16 Figure 4-24: Time Histories of Channels 9,10 & 11- Acceleration (cm/s ) vs. Time (sec)-Trinidad 11.9 R e l a t i v e D i s p l a c e m e n t - C 7 2 ;-j ; *—j : ! j— — 1  8 0 6 0 - 2 0 - 4 0 <•>» - 8 0 A b s o l u t e D i s p l a c e m e n t - C 7 1 1 1 \ M i n -62.0 at 13.46 . M a x 44.6 at 9.60 III 12 14 16 Base Shear-X 30000 20000 10000 0 -10000 -20000 -30000 -40000 Base Shear-Y 30000 25000 20000 J l! 15000 10000 5000 Base Shear-Z 12 14 16 Min 5536 at 10.40 Max 2828 at 11.08 20 22 Figure 4-26: Base Shear (kN) vs. Time (sec) for X, Y and Z direction-Trinidad 11.9 Chapter 4-Nonlinear Static and Dynamic Analyses (Pushover & Time History) 4.3.4 Cape Mendocino 86-4.6 The original Cape Mendocino earthquake occurred in 1986 which gave 0.4g acceleration to the structure. It was a medium level of earthquake which the structure has experienced. This earthquake was scaled to 4.6 times in X , Y and 4.0 times in Z directions; and the damping ratio was assumed 5% for the first and the second periods to calculate the proportional coefficients of damping matrix. This earthquake caused damage at the level of 2, and two hinges formed in both bent columns. As shown in Figure 4-27, the hinged members' deformation is at the yielding point. This earthquake induced 1.7g (at CI 1), 2.5g (at C7) and 1.8g (at C6) acceleration in X , Y and Z directions respectively. The analyzed acceleration time histories at the location of sensors are shown in Figure 4-30 to Figure 4-31. The maximum relative displacement in channel 7 was calculated 2.8 cm (Figure 4-32). The maximum values of base shears are 32500 kN and 32400 kN in the X and Y directions respectively (Figure 4-33). The soil behaved linearly during the earthquake as shown in Figure 4-28 and Figure 4-29. Link 21 located in the west abutment and link 22 located in the south column were chosen for plotting. The maximum force and displacement for each link in both directions were calculated as follows: • Abutment X (link 21)- Force=1800 kN, Displ.=0.6 cm • Abutment Y (link 21)- Force=2000 kN, Displ.=2.2 cm • Bent X (link 22)- Force=2650 kN, Displ.=l .0 cm • Bent Y (link 22)- Force=2100 kN, Displ.=1.2 cm The forces and displacements in the model's nonlinear links represent the soil behaviour, which for this analysis remained in the linear domain. 1 ^ J L 1 < ( \ N-S Elevation U [ • C | D I E 1 F 1 M B Figure 4-27: Final Status of Hinge Forming for CM86-4.6 EQ 2500 2000 1500 1000 z 500 M z 0 • -500 -1000 -1500 -2000 -2500 •0 l.ink2l-U)ulmcnlA 2500 2000 1500 1000 z 500 s 0 » -500 -1000 -1500 -2000 Link2l-Abutment-Y 1 80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 Displacement (cm) -2.80 -2.10 -1.40 -0.70 0.00 0.70 1.40 2.10 2.80 Displacement (cm) Figure 4-28: Force -Deformation of Link 21 at West Abutment-CM86-4.6 3000 2000 _ 1000 z M f 0 w e " -1000 -2000 •3000 -1 Link22-Bent-X 2500 2000 1500 1000 2 500 M t 0 • -500 -1000 -1500 -2000 -2500 Link22-Bent-Y 20 -0.80 -0.40 0.00 0.40 0.80 1.20 Displacement (cm) 40 -1.00 -0.60 -0.20 0.20 0.60 1.00 1.40 Displacement (cm) < ha it iif I 4 C h a n n e l 5 C h a n n e l 6 1 5<MI HUM) •2IIIKI - 2 5 0 0 ll m w m — . — ^ M m 1 • M i n - 1 8 2 0 at 2.96 M a x 1648 at 2 86 12 14 211 22 C h a n n e l 7 M In - 2 4 0 0 at 2.68 flax 2 6 0 6 at 2.68 12 14 C h a n n e l 8 M i n - 1 2 2 2 at 2.66 M a x 1 144 at 2.68 C h a n n e l 9 J M i n - 1 1 4 4 at 2 .68 ax 1 279 at 2 .68 21) 22 C h a n n e l IO M i n - 3 2 4 at 2 .34 M a x 391 at 2 .44 I M i n - 1 6 2 3 at 2 .34 M a x 1731 at 2 .44 Figure 4-31: Time Histories of Channels 9, 10 and 11- Acceleration (cm/s ) vs. Time (sec)-CM86-4.6 R e l a t i v e D i s p l a c e m e n t - C 7 M i n - 2 . 8 at 2 .68 M a x 2.7 at 2 68 2(1 2 2 A b s o l u t e D is p l a c e m e n t - C 7 Base Shear-X 40000 30000 20000 10000 0 •10000 -20000 -30000 -40000 j 1 |—pSpE 1 1 ; —, —1 1 Min -30000 at 2.34 Max 32560 at 2.44 j 8 II 12 14 20 22 40000 30000 20000 10000 0 -10000 -20000 -30000 -40000 Base Shear-Y 10 12 14 16 ! i 1 „ 1 Mi U i d y u W W ~-. » A A A A _. — - - An A /v. n hi " 1 Min -32370 at 2.58 Max 34640 at 2.68 20 22 30000 25000 20000 15000 10000 5000 H H H H H H H H H H H H H 1' ' f ' Min -8799 at 2.96 Max 26890 at 2.84 10 12 14 16 18 20 22 Chapter 4-Nonlinear Static and Dynamic Analyses (Pushover & Time History) 4.3.5 Cape Mendocino 86-6.5 In this analysis, Cape Mendocino earthquake was scaled up to 6.5 times in X , Y and 4.0 times in Z directions; and the damping ratio was assumed 7% for the first and the second periods to calculate the proportional coefficients of damping matrix. This earthquake caused damage at the level of 5, and 3 hinges formed in the bent columns (Figure 4-34). A hinge formed at the base of the south column (pink), which its deformation is at the yielding point. Two hinges formed in the north column at the top and at the bottom. The hinge at the top lost 33.33% of its ductility capacity and the hinge at the bottom completely lost its capacity. This earthquake induced 2.4g (at CI 1), 2.7g (at C7) and 1.3g (at C6) acceleration in X , Y and Z directions respectively. The analyzed acceleration time histories at the location of sensors are shown in Figure 4-37 to Figure 4-38. The maximum relative displacement in channel 7 was calculated 3.8 cm (Figure 4-39), and the figure clearly shows that structure is in nonlinear domain (the oscillation is not around the zero axis). The maximum values of base shears are 44000 kN and 36000 kN in the X and Y directions respectively (Figure 4-40). The soil behaved linearly during the earthquake as shown in Figure 4-35 and Figure 4-36. Link 21 located in the west abutment and link 22 located in the bent were chosen for plotting. The maximum force and displacement for each link in both directions were calculated as follows: • Abutment X (link 21)- Force=2400 kN, Displ =0.8 cm • Abutment Y (link 21)- Force=2600 kN, Displ.=2.9 cm • Bent X (link 22)- Force=2950 kN, Displ =1.2 cm • Bent Y (link 22)- Force=2700 kN, Displ =1.5 cm The forces and displacements in the model's nonlinear links represent the soil behaviour, which for this analysis remained in the linear domain. \ V ~ I • • • • 11 N-S Elevation u • C | D 1! E | F \mmm Figure 4-34: Final Status of Hinge Forming for CM86-6.5 EQ 3000 2000 1000 z j* 0 o *" -1000 -2000 -3000 -0 Link21-Abutment-X Link2l-Abutment-Y JUUU 2000 1000 z s 0 -1000 -2000 -3000 -3 80 -0.60 -0.40 -0.20 0.00 020 0.40 0.60 0.80 Displacement (cm) 20 -2.40 -1.60 -0.80 0.00 0.80 1.60 2.40 3.20 Displacement (cm) Figure 4-35: Force -Deformation of Link 21 at West Abutment-CM86-6.5 3000 2000 1000 z • 0 u e -1000 -2000 -3000 -1 Link22-Bent-X 3000 2000 _ 1 0 0 0 z M s 0 9 -1000 -2000 -3000 -1 Link22-Bent-Y 0 20 -0.80 -0.40 0.00 0.40 0.80 1.20 Displacement (cm) 80 -1.40 -1.00 -0.60 -0.20 0.20 0.60 1.00 1.40 1. Displacement (cm) < h a ii in-1 4 < 'ha ii in-1 5 1 n 1 M i n - 2 6 : M a x 19 M H M M M M M M M M M • at 2 .34 3 " 2 4 6 . i 1 SOU 1UOO SOO o -SOO -1 o o o -1 SOO < hannet 6 1 _____ i i _ H _ M i n - 1 2 2 M a x 131 — | 3 a t 2.96 ...j 9 at 2.86 j C h a n n e l 7 |\jf^/^^ N W S A ^ / V " ' M i n - 2 7 4 6 at 2.68 M a x 2 7 3 8 at 2 .68 < ha ii ne I 8 C h a n n e l 9 <> 2 4 6 H 1(1 12 14 16 IH 2(1 22 C h a n n e l I 0 () 2 4 6 K Id 12 14 16 18 2(1 22 C h a n n e l 1 1 30(>(( 2OO0 1 (IOO • — — A AA AaaaAa 1 M i n - 2 2 6 0 a t 2 .34 < M a x 2366 at 2 .44 j • • mmm () 2 4 6 8 1(1 1 2 1 4 1 6 I S 2(> 2 2 Figure 4-38: Time Histories of Channels 9,10 and 11- Acceleration (cm/s2) vs. Time (sec)-CM86-6.5 R e l a t i v e D i s p l a c e m e n t - C 7 I, ______ _______ -gy M i n - 3 . 0 at 2 .60 mmm M a x 3.9 at 2.60 n 2 4 6 K IU 12 14 16 1 8 20 22 A b s o l u t e D i s p l a c e m e n t - C 7 .. ... " ... Min -A f M a x 6.0 at 2.40 O 2 4 6 H i n 12 14 16 IS 20 22 Base Shear-X Base Shear-Y Min-35540 at 2.58 Max 35810 at 2.68 22 30000 25000 20000 15000 10000 Base Shear-/ 8 10 12 14 16 1 : | 1 flfl M h V | yjrWI 1 mm luzeu at u.34 Max 25250 at 2 84 18 20 22 Figure 4-40: Base Shear (kN) vs. Time (sec) for X, Y and Z direction-CM86-6.5 Chapter 4-Nonlinear Static and Dynamic Analyses (Pushover & Time History) 4.3.6 Petrolia 92-3.0 The original Petrolia earthquake occurred in 1992 which gave 1.09g acceleration to the structure. It was the highest level of earthquake the structure has experienced. This earthquake was scaled to 3.0 times in X , Y and Z directions; and the damping ratio was assumed 5% for the first and the second periods to calculate the proportional coefficients of damping matrix. This earthquake caused damage at the level of 3, and two hinges formed (dark blue) at the bottom of both columns. As shown in Figure 4-41, the hinges lost 16.67% of their ductility capacity. This earthquake induced 2.6g (at CI 1), 2.8g (at C7) and 2.2g (at C6) acceleration in X , Y and Z directions respectively. The analyzed acceleration time histories at the location of sensors are shown in Figure 4-44 to Figure 4-45. The maximum relative displacement at channel 7 was calculated 3.3 cm (Figure 4-46). The maximum values of base shears are 52000 kN and 39000 kN in the X and Y directions respectively (Figure 4-47). The soil behaved linearly during the earthquake as shown in Figure 4-42 and Figure 4-43. Link 21 located in the west abutment and link 22 located in the south column were chosen for plotting. The maximum force and displacement for each link in both directions were calculated as follows: • Abutment X (link 21)-Force=2700kN,Displ.=0.9 cm • Abutment Y (link 21)- Force=2850 kN, Displ.=3.2 cm • Bent X (link 22)- Force=3700 kN, Displ =1.5cm • Bent Y (link 22)- Force=2800 kN, Displ =1.6cm The forces and displacements in the model's nonlinear links represent the soil behaviour, which for this analysis remained in the linear domain. Figure 4-41: Final Status of Hinge Forming for P92-3.0 EQ 1-Abutme •3000 -1.00 -0.811 -0.60 -11,40 -0.20 (1,00 0.20 0.40 0.60 0.80 1.00 Displacement (cm) -3000 -3.20 -2.41) -1.60 -0.80 0.00 0.80 1.60 2.40 3.20 I) is place me nt (cm) Figure 4-42: Force -Deformation of Link 21 at West Abutment-P92-3.0 -1.60 -1.20 -0.80 -0.40 (1.00 0.40 0.80 1.20 1.60 Displacement (cm) 1.80 -1.40 -1.00 -0.60 -0.20 0.20 0.60 1.00 1.40 1.80 Displacement (cm) .•mill 1500 l min sou o -SOD - I 0 0 U -1 SOU -20IIII - 2 5 0 0 C h a n n e l 4 AIM P __-fe--4J-_. i ma*mwwmr L f Mir 1 - 2 2 3 S at 4 .94 X 1392 at 6.10 M a 12 16 20 24 2H 32 36 411 44 46 52 56 6(1 C h a n n c l 5 m *** - v BP • ... . m M a x 348 at 6.94 12 1 6 56 6U 2SOO 2 0 0 0 I 5(1(1 tiHHl 500 II -son . I OIK) -1 5fM» -2(MMI -25(M> C h a n n e l 6 • i T J JWI T k 1 1 r I • r M i n - 2 2 2 4 at 6.34 ~~ M a x 2 0 6 6 at 6 .42 16 2(1 28 32 3 S 411 44 48 32 56 3(1(10 2O00 1000 (I -I Odd - 2 0 0 0 .3(100 C h a n n e l 7 J mm Jr.; _ f L H I i ^ ^ ^ ^ FT _ , • i n L, 1 - 4 M a x 2786 at 6.78 12 16 24 28 32 3 6 5 2 5 6 I 51)0 I ()()() -1000 I 511(1 C h a n n e l 8 1 1 --< t t 1 1 _Jk> t -i rr FT i ' n M a x 1188 at 4.48 -12 16 2<l 24 2 8 32 3 6 40 44 48 52 56 2IMIU - < C h a n n e l 9 1 SOO lOOO ill in i i i , o - 5 0 0 -P irr -i M1 f~T ! -1SOO r 1 _ _ _ M i n - 2266 at 4 .94 M a x 1632 at 6.10 0 4 K 12 16 20 24 28 32 3 6 40 1 1 48 52 56 6(1 SOO c ha nne l 14> 3 0 0 2O0 " _L * L ______ ii w nr -20O [ m I M in - 4 6 6 a t 4 . 3 6 1 M a x 616 at 6 00 " •SIM) 0 — . — j ™ — 4 8 12 16 20 24 28 32 31. 40 4 4 48 52 56 AO c ha rmet 1 J 2 0 0 0 „ O T —V __ • 1 1 -MHit* i M i n - 2 6 3 8 at 6 .94 M a x 2 0 0 6 at 6 04 4 K 12 16 20 24 28 32 3l» 40 44 4 8 52 3 6 611 Figure 4-45: Time Histories of Channels 9,10 and 11- Acceleration (cm/s2) vs. Time (sec)-P92-3.0 R e l a t i v e D i s p l a c e m e n t ••< 7 — _ M i n - 3 . 1 6 at 4 .82 | M a x 3 .33 at 4.96 0 4 8 12 16 2 0 24 28 32 36 4 0 44 48 52 56 6 0 A b s o l u t e D i s p l a c e m e n t - C 7 n ,1 r "A 1 j / \ n M i n - 1 2 . 7 at 4 . 2 8 || M a x 1*||jBJLtfMj| II 4 8 12 16 2(1 24 28 32 36 41) 44 48 52 56 60 Base Shea r - \ 28 40000 .0000 20000 10000 0 -10000 -20000 -30000 -40000 30000 25000 20000 -15000 10000 5000 Base Shear-Y . • Min -38980 at 6.20 • Max 37490 at 5.10 i 12 16 20 24 28 32 36 40 44 Base Shear-Z 52 56 60 1 Min -5046 at 5.34 Max 29430 at 5.84 12 16 20 24 28 32 36 40 44 52 56 60 Figure 4-47: Base Shear (kN) vs. Time (sec) for X, Y and Z direction-P92-3.0 Chapter 4-Nonlinear Static and Dynamic Analyses (Pushover & Time History) 4.3.7 Petrolia 92-3.5 In this analysis, Petrolia earthquake was scaled up to 3.5 times in X , Y and 3.2 times in Z direction; and the damping ratio was assumed 7% for the first and the second periods to calculate the proportional coefficients of damping matrix. This earthquake caused damage at the level of 6, and 4 hinges formed in the columns (Figure 4-48). Two hinges formed in each column and the bottom hinges totally lost their ductility capacity and the top hinges passed 16.67% (dark blue) and 33.33% (light blue) of their ductility capacity in the south and north column respectively. Finally in this step, the structure lost its stability and collapsed. This earthquake induced 2.0g (at CI 1), 2.6g (at C7) and 2.4g (at C4) acceleration in X , Y and Z directions respectively. The analyzed acceleration time histories at the location of sensors are shown in Figure 4-51 to Figure 4-52. The maximum relative displacement at channel 7 was calculated 3.9 cm (Figure 4-53), and the figure clearly shows that structure is in nonlinear domain (the oscillation is not around the zero axis). The maximum values for base shears are 39000 kN and 40000 kN in the X and Y directions respectively (Figure 4-54). The soil behaved linearly during the earthquake as shown in Figure 4-49 and Figure 4-50. Link 21 located in the west abutment and link 22 located in the bent were chosen for plotting. The maximum force and displacement for each link in both directions were calculated as follows: • Abutment X (link 21)- Force-2800 kN, Displ.=1.0 cm • Abutment Y (link 21)- Force=2900 kN, Displ.=3.2 cm • Bent X (link 22)- Force=5000 kN, Displ.=2.0 cm • Bent Y (link 22)- Force=4300 kN, Displ.=2.4 cm The forces and displacements in the model's nonlinear links represent the soil behaviour, which for this analysis remained in the linear domain. 1 L Jk \ N-S Elevation Figure 4-48: Final Status of Hinge Forming for P92-3.5 EQ Figure 4-49: Force -Deformation of Link 21 at West Abutment-P92-3.5 I 30(1 l l l lt l l SOU II - i son -2IMIO (.Oil 400 2 lilt (> -2IX) -4tM> -(.till 2000 151111 HMMt 5 0 0 (> -5IMI -I IMMI -1 SOU -2OO0 3Of Ml 201111 1IMMI 0 -1 OOO -21IOO I 51 Ml I IMMI 500 o -soo I Hull 1 51111 I III L i l i ! M i n - 2 3 9 7 at 4 .94 __ M a x 1466 at 4.80 28 32 < hoiiiirl S : j ** L - J . _ j l a x 364 at 6 .94 : • i n ft* J _J M i n -1601 at 4 8? HnH • M a x 1683 at 4 .94 20 24 28 C h a n n e l 7 11 • • • " - -I „ i ... I i j - m M a x 2 6 9 7 at 6 .10 Channel 8 M M •:.^;f;*.;:^j<;:!;g:!f HI m ! — m l T 38 48 I • • m i n -110/ ax 4 M a x 1 21 4 at 4 I s ou . 'mm I 1 : • - — — . — — f I ' 1 M i n - 2 4 0 6 at 4 .94 M a x 1622 at 4.80 (•till I* 16 20 H • HP m • • _ J 1 — _ — M a x 6 1 4 at 6 .00 12 16 20 24 2 » 32 36 4 0 44 Figure 4-52: Time Histories of Channels 9,10 and 11- Acceleration (cm/s ) vs. Time (sec)-P92-3.5 1 • • • • • • • •.- : ..................... . . Ill u iL M i l II A In M * Win - 3 . 9 at 6.12 ! 1 M M • H i ; . WW! l/lax 3 6 at 4 96 1 | 1 M l n -14 .1 at 4.26 J t M j M j 9 J 4 « i 6 ; 0 4 > J 12 » 6 20 24 2 » 32 36 4I> 44 4S Base Shear-X -10000 .10000 0 -10000 -20000 -.10000 -40000 ' im Min -39050 at 5.96 Max 35400 at 5.52 12 16 20 24 28 32 36 40 44 48 52 S6 60 Base Shear-Y 40000 30000 0 -10000 -20000 -30000 -40000 -50000 1 1 m _ Min -39630 at 4.94 Max 37100 at 4.80 Chapter 4-Nonlinear Static and Dynamic Analyses (Pushover & Time History) 4.4 CONCLUSION In this chapter, first a pushover analysis was performed on the structure and growth of the damage to the bent and the soil elements was monitored in each step. The results from this analysis can be used as information about the overall behaviour of the structure during an event. The steps of pushover analysis produced the displacement thresholds for the different levels of damage, i.e. each step determine what displacement causes damage to the structure and what the level of damage is. The level of damage is defined by the number of hinges formed in the bent and their level of ductility capacity. This information can be used as a bench mark for comparison with the displacements caused by an earthquake. This procedure is clarified in the following chapters. The second part of this chapter included a series of nonlinear dynamic analysis. These analyses were done to produce some results (acceleration time histories) for the damage index method (just like a pseudo shaking table test). Three earthquakes, which had happened at the site of the structure before, were selected for this analysis and each one was scaled to two different levels. These analyses were designed to produce different levels of damage, which are independent of each other. Both nonlinear analyses (pseudo-static and dynamic) showed that the weakest element in the structure is the bent. The columns of the bent suffered damage and lost their lateral stiffness capacity before the other elements. Also it should be mentioned that these columns are the key elements in the stability of the structure in both the vertical and lateral directions. CHAPTER 5 SYSTEM IDENTIFICATION AND DAMAGE DETECTION 5.1 INTRODUCTION In this chapter, first, the generated time histories for the six different artificial earthquakes from the previous chapter are assumed to be actual recorded motions. Second, natural frequencies and mode shapes are derived for the structure by system identification analysis. Third, damage index method is applied to the results from previous step. The results from D I M are discussed and the capabilities of this method are verified which is main aim of this chapter. 5.2 SYSTEM IDENTIFICATION The assumption at this step is that the generated time histories belong to a linear system, and then system identification is applied to them. To remove this assumption the time histories can be taken from the end part of the records, which contain the accelerations of a stable (constant stiffness) system. The records contain three parts as follows: • Beginning part (Undamaged) • Middle part (Transitional) • End part (Damaged) Chapter 5-System Identification and Damage Detection / The structure is still undamaged in the early part of the records; and its stiffness varies within the transitional period when the structure is suffering damage. The end part contains the information about the structure, which has been damaged. Here the stiffness values do not change any more. For a better system identification, only this part should be used which is from a few seconds after the intense part to the end of the records. The natural frequencies and the mode shapes of the damaged bridge were extracted by ARTeMIS® program for the six different artificial earthquakes described in the previous chapter. Only the transverse modes were determined, because the lateral movements of the structure are directly dependent on the loss of lateral stiffness due to an earthquake. Also it should be mentioned that only two transverse modes were extracted for this analysis. As shown in Table 3-3 (Chapter 3), the system identification of real earthquakes could only extract two transverse modes of the bridge which means that the earthquakes did not have enough energy to trigger the other transverse frequencies, and that is why only two transverse modes are extracted here. The Frequency Domain Decomposition-Peak Picking method was used for the analyses, so no value for damping coefficient was determined (ARTeMIS 2004). The values of damping ratio are not usable in this chapter. The experimental model used in these analyses is not as refined as ambient vibration analysis, because the number of sensor locations is now limited 11 to instead of 40 for the ambient vibration test. Therefore mode shapes derived by this model are not as well defined as those obtained from the ambient vibration test. Removing the side effects of the rough mode shapes will be discussed in the next chapter. 5.2.1 Trinidad 9.8 For this artificial earthquake, one hinge was developed in the north column and the hinged member deformation position is at the yielding point. The transverse frequencies were not expected to change much. The frequencies were 3.96 and 5.66 Hz for the first and the second transverse modes respectively. The transverse mode shapes of the bridge are shown in Figure 5-1. The frequencies did not change significantly and they seemed rational for this level of damage. The first and the second mode frequencies decreased by 3.5% and 5.2% compared to the original ones (derived by ambient vibration test). 5.2.2 Trinidad 11.9 This artificial earthquake formed hinges in the bent's columns. The north column has a hinge, where its deformation is at the yielding point, and the south column has two hinges, which caused a lot of stiffness loss. The frequencies for the first and the second transverse modes were 2.29 and 4.74 Hz respectively. These frequencies dropped by 44% and 20.8% for the first and the second modes compared to the original frequencies. These percentages show that the bridge stiffness decreased significantly. The transverse mode shapes of the bridge are shown in Figure 5-2. 5.2.3 CM86 4.6 The bridge suffered damage that resulted in two hinges at the base of the bent's columns. These hinges are at their first stage (yielding point) and it means the bent still has a lot of stiffness. The frequencies for the first and the second modes were 3.71 and 5.08 Hz respectively. The values dropped by 9.5% and 15% of the original ones. The frequencies also show that structure has not lost a significant amount of its lateral stiffness. The transverse mode shapes of the bridge are shown in Figure 5-3. 5.2.4 CM86 6.5 This artificial earthquake caused three hinges to form as the result of which the north column lost its stiffness and the south column suffered minimum damage. This level of damage greatly reduced the bent's stiffness. The first and the second mode frequencies were 1.61 and 4.54 Hz respectively. These values dropped by 60.73% and 24% compared to the original values. These frequencies and reduction percentages show that the structure lost much of its lateral stiffness. The transverse mode shapes of the bridge are shown in Figure 5-4. 5.2.5 P92-3.0 The bridge suffered a damage that resulted in two hinges at the base of the bent's columns. These hinges were at their second stage (16.67% loss of ductility capacity) which means that the bent preserved its lateral stiffness. The frequencies for the first and the second modes were 2.39 and 4.74 Hz respectively. The values decreased by 41.7% and 20.8% of the original ones. These percentages show that the bridge stiffness reduced significantly. The transverse mode shapes of the bridge are shown in Figure 5-5. 5.2.6 P92-3.5 This artificial earthquake caused the bent to lose its lateral stiffness completely and resulted in four hinges in the columns. Two of these hinges are at their last stage (failure point) and it means the columns lost their stiffness. The frequencies for the first and the second modes were 1.27 and 3.71 Hz respectively. The values decreased by 69% and 37.9% of the original ones. These percentages show that the lateral stiffness of the bridge decreased significantly. The transverse mode shapes of the bridge are shown in Figure 5-6. The results of all earthquakes are summarized in Table 5-1. 5.2.7 Discussion on Mode Shapes • Mode Shapes obtained from A V (Base Lines): The decks of the bridge are too stiff compared to the stiffness of the embankments (this is clarified in detail in the next section), so the first transverse mode shape of the structure is a lateral movement along with lateral deflection of the embankments. The second transverse mode shape is just like a first mode shape of a simple supported beam which means that the embankments do not move at this mode shape. The plan view of the mode shapes are shown in Figure 5-8. • Mode Shapes obtained from SI (Artificial Earthquakes): The transverse mode shapes of the bridge changed without any specific trend compared to the base lines. For example the case P92-3.5 has a first mode like a simple support beam which is quite different from the original one, and the reason is the bent has lost its total lateral stiffness and it can not play the role of a support at the middle of the bridge any more. These mode shapes moved from high frequencies to low frequencies due to the damage, and started to interact with vertical mode shapes when their frequencies became close to the values of the vertical mode shapes. Lastly, it can be said the mode shapes of undamaged bridge are like a continuous beam with three flexible supports and after final state of damage (P92-3.5), which causes the collapse of the middle support (bent), the mode shapes become like those of a simple support beam. This statement can be verified by Figure 5-6. 1st Mode 3-D 1st Mode Plan 2nd Mode 3-D 2nd Mode Plan Figure 5-1: First and Second Transverse Mode Shapes for Trinidad-9.8 i l l ; . . . . Is' Mode 3-D 1st Mode Plan 2nd Mode 3-D 2nd Mode Plan Figure 5-2: First and Second Transverse Mode Shapes for Trinidad-11.9 M l I s ' Mode 3-D 1st Mode Plan 2 n d Mode 3-D 2 n d Mode Plan Figure 5-3: First and Second Transverse Mode Shapes for CM86-4.6 \ 1st Mode 3-D I s ' Mode Plan l i l r 2 n d Mode 3-D 2 n d Mode Plan Figure 5-4: First and Second Transverse Mode Shapes for CM86-6.5 1st Mode 3-D Is' Mode Plan k 2nd Mode 3-D 2nd Mode Plan Figure 5-5: First and Second Transverse Mode Shapes for P92-3.0 1st Mode 3-D 1st Mode Plan 2nd Mode 3-D 2nd Mode Plan Figure 5-6: First and Second Transverse Mode Shapes for P92-3.5 Table 5-1: Frequencies Comparison for the Artificial Earthquakes Artificial Earthquake 1st Transverse Mode Frequency Reduction % 2n d Transverse Mode Frequency Reduction % Trinidad-9.8 3.955 3.5 5.664 5.2 CM86-4.6 3.711 9.5 5.078 15 P92-3.0 2.393 41.7 4.736 20.8 Trinidad-11.9 2.295 44 4.736 20.8 CM86-6.5 1.611 60.7 4.541 .24 P92-3.5 1.27 69 3.711 37.9 5.3 DAMAGE DETECTION This part is about using the derived information from system identification analyses in damage detection method. This method should determine the existence, the location and the severity of damage. The details of the method and the derivation of related formula were explained in Chapter two. The damage index method is categorized as follows: 1. Shear beam behaviour 2. Flexural behaviour 3. Axial behaviour In chapter two, the shear beam behaviour of this method was explained in detail. The shear beam theory is used in this part, and before using the damage index method, a discussion about the bridge behaviour during lateral movements is necessary. The behaviour of lateral movements of PSO Bridge is similar to that of a shear beam and the reasons are: 1. The bent beam is too stiff compared to the columns and this is confirmed by pushover analysis result. The main reason is that the beam and the decks were casted together and the decks are too rigid, so they do not let the beam bend in lateral movements. The bent's frame acts like a shear frame (Chopra, 2002). 2. The embankment wedge acts like shear beams, because the width of them is too long compared to their heights. Figure 5-7 shows a simplified model, which helps to understand it better (Zhang & Makris 2001). 3. The decks behave like shear beams and this can be confirmed by their mode shapes. Figure 5-8 shows the plan of the first and the second transverse mode shapes. The east deck mode shapes show a pure shear beam behaviour and the west deck mode shapes have a combination of shear and flexural behaviour. This combination tends to have a more shear than a flexural behaviour. Finally the bridge can be modeled as a shear frame for lateral movements. The equation (2-6) governs the damage index method of shear frame structures. Figure 5-7: Simplified Bridge Model *4 m • -5" 3 < s o ST ft 0.8 0.6 •"1 i 5 = a n> o s — 6! S BE -1 I a x. 0.2 0 -0.2 -0.4 -0.6 -0.8 1 • Mode 1-East Deck N o r t h t Mode 2-East Deck — Mode 1-West Deck - - - - - ' Mo de 2-West Deck 1 ' ; 1 0 1 5 2 0 2 5 3 0 3 5 4 D 4 5 5 0 5 5 6 0 6 5 7 ft 7 5 8 "1 0 8 -_ _ _ _ _ _ — — - — - — ~ ~ • — — • 5* V--3 n h en i C/2 '< *. r. 3 — a n 3 EH -o s 3 -O 3 E M re D <_ n r. 13. O 3 Chapter 5-System Identification and Damage Detection 5.3.1 Artificial Earthquakes' Damage Indices The simplified model used for the DIM is shown in Figure 5-7 shows that the bridge can be modeled for damage index method as shown in Figure 5-9. The numbers in the circles are element numbers, and the small circles are locations of sensors. Theses sensors only record lateral movements. SAP2000® program was used for calculating the stiffness values of the elements 2 and 3. The method used for this part is the traditional method for finding the stiffness, i.e. finding the force values, which cause unit displacements at the desired locations (Ghali, 2003). The stiffness values of the embankments were derived from Chapter 3 for model calibration. The stiffness values are 490 MN/m, 512 MN/ra, 825 MN/m and 490 MN/m for elements # 1, #2, #3 and #4 respectively. Element #l-west embankment Element #2-west deck+one of the bent's columns Element #3-east deck+one the bent's columns Element #4-east embankment Figure 5-9: Damage Index Model The values for the mode shape coordinates were obtained using the ARTeMIS® program. These values are shown in Table 5-2 for the earthquakes. Table 5-2: Mode Shapes Coordinates e :atic Ambient Tri-9.8 Tri-11.9 CM86-4.6 CM86-6.5 P92-3.0 P92-3.5 ~ i Sensoi Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode 4 m NO o NO ON r<-> NO ON NO o m o <N CO -3- o m m o ON NO o o O o o o o o O O o o o o © 7 ON cn (N r--00 o <N C--<N r-m o <-<-> o <N r<-> r-o <n o o o CO o O o O O o o o o o o o O o © 9 ON ON o NO ON o o O in r-- o >o o o r-<n o o ON o r-o o m ON o o o o o o o o o o o o o © © *-the units is metric and the modes are transverse only. 5.3.1.1. Trinidad 9.8 Index, severity and indicator of damage were calculated for the elements by Mathcad® software. The DIj indices show that the elements #2 and #3 were probably damaged, and that their stiffness values decreased by 11% and 7% respectively. In these analyses, due to insufficient number of the sensors, 87% confidence was assigned to the damage the members sustained. Therefore, i f Zj > 1.14, the member j is damaged and if Zj<1.14, the member j is not damaged. For this earthquake, the analysis shows that the west deck element was probably damaged, but its Zj is less than 1.14. This result shows that the DIM can not definitely identify the damaged element in this case with low severity of damage; neither can it determine the level of serviceability of a structure alone, therefore its results should be checked with the other evidences. The calculation process of this method is shown below as a sample. Trinidad-9.8, Damage Indices Calculation NE := 4 Number of Elements j := i . .NE Sj := Elements Stiffness N M := 2 Number of Modes r := 1 . .NM .5939 .6206 1 .593 A r j := Relative Displacements (Base Line)/^ j := Relative Displacements (Damaged) 0.1543 0.0852 -0.1401 0.0994 0.1331 0.0535 -0.0757 0.1109 0.0641 0.1755 -0.1432 0.0964 0.3960 -0.1239 -0.2523 0.0197 DIJ := N M I r = 1 N E ( A r , j ) 2 + £ [ S j( A <i 2 ] ~ N E i- - i T J = i 1 N M I r = 1 ( A r J ) 2 + f [ S j ( A r J ) 2 ] j = l ~ N E T J = i 1 ^ Element's Damage Index u D I j := m e a r ^ D I ^ D ^ D ^ D L j ) n D i j = 0.994 a D , j := Stdev(DI, , D I 2 , D I 3 , D I 4 ) a D I j = 0.162 D I j - M D I j a j := DIj Damage Severity Zy.= Normalized Damage Index rDIj 1.01 DIj = 1.13 1.08 0.76 •6.6-10-3 a , -0.11 -0.07 0.31 0.08 0.84: 0.51 -1.43 5.3.1.2. Trinidad 11.9 DIj indices show that the element # 2 and #3 were probably damaged and their stiffness values decreased by 15% and 6% respectively. Finally, the damage indicator Zj confirms that the west deck element was damaged and the value of it is 1.14. 5.3.1.3. CM86-4.6 The DIj indices show that only the element #2 was probably damaged and its stiffness value decreased by 28%. The damage indicator Zj confirms that this element was damaged and its value is 1.43. 5.3.1.4. CM86-6.5 This analysis shows that the values of DIj indices for the elements #2 and #3 exceeded 1, and their stiffness values decreased by 25% and 3% respectively. The Zj indices confirm that only the element #2 was damaged and its value is 1.3. 5.3.1.5. P92-3.0 For this earthquake, the DIj indices show that the elements #2 and #3 were probably damaged and their stiffness values decreased by 27% and 6% respectively. The damage indicator Zj confirms that the element #2 was damaged and its value is 1.3. 5.3.1.6. P92-3.5 The last analysis shows that only the element #2 was probably damaged and its stiffness value decreased by 21%. The damage indicator Zj confirms that the element #2 was damaged and its value is equal to 1.28. For comparison, the DIj, (Xj and Zj indices were plotted for the different earthquakes scenario and are shown in Figure 5-10, Figure 5-11 and Figure 5-12 respectively. • Trinidad-9.8 • Trinidad-11.9 Q CM 86-4.6 • CM 86-6.5 • P92-3.0 • P92-3.5 West Abutment West Deck Cast Deck East Abutment (Element#l) (Element#2) (Element#3) (Element#4) Figure 5-10: The Elements Damage Index 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 • I • Trinidad-9.8 • Trinidad-11.9 • C M 86-4.6 • C M 86-6.5 • P92-3.0 • P92-3.5 West Abutment West Deck East Deck East Abutment (Elements) (Element#2) (Element#3) (Elemen«4) Figure 5-11: The Elements Damage Severity Index Chapter 5-System Identification and Damage Detection 5.4 C O N C L U S I O N The results show that the Damage Index Method (DIM) can distinguish the presence of damage in severely damaged cases, but not in the cases with low levels of damage (Trinidad-9.8). Locating the damage involves approximation, and it is not certain which member of the structure has suffered damage. These inaccuracies are due to insufficient number of sensors and the definition of the DIM elements. The elements, which are defined for this method, are a combination of several members of the structure. The beginning and the end of these elements are at the locations of sensors. So when the number of sensors is limited, these elements include several members of the structure. For example, in PSO case, the element # 2 is a combination of the west deck and one of the columns, so when this element is determined as the location of damage by DIM, it can not be concluded that it is the deck that has suffered damage or the column. DIM could not determine the presence of damage in the Trinidad-9.8 case. As explained before, the elements # 2 and # 3 are combinations of one of the decks and one of the bent's columns. The lateral stiffness values of the columns are small fractions of the decks' lateral stiffness values. Also it should be mentioned that the columns are the weakest links in the structure and they are the first members, which suffer damage due to the lateral movement. DIM compares the mode shapes and the stiffness values of the defined elements before and after the damage. When one of the columns suffers a minor damage, the change in the values of stiffness of the elements # 2 or #3 is negligible. This makes that DIM incapable of tracking the stiffness changes of the system. Also it should be mentioned that the (Xj's values (Damage Severity Index) determine the severity of damage of the defined elements in the DIM model, so these values can not be used individually forjudging the status of the structure. The damage indices show that there is no relation between the different levels of damage by artificial earthquakes and that each of them is a specific case. The above-mentioned reasons prove that this method can not be used alone for judging the serviceability status of real cases with limited number of sensors after an event. CHAPTER 6 A PROCEDURE FOR BRIDGES SEISMIC STRUCTURAL H E A L T H MONITORING 6.1 INTRODUCTION In this chapter, a procedure for seismic structural health monitoring of bridges is introduced, which can analyze the time histories recorded after an earthquake by sensors mounted on a bridge and determine the status of the serviceability of the structure. This procedure is presented in a flow chart format, and it is a combination of the damage index method and the structural analyses. The elements of this procedure are explained in detail. This chapter includes the prerequisite information and recommendations to minimize the errors inherit in the procedure. At the end the procedure is tested with real data to verify its effectiveness. 6.2 GENERAL IDEA OF THE PROCEDURE Based on the results form the previous chapter, it was found out that the method is not accurate enough to track a minor damage to the structure. The reason is that this method compares the mode shapes before and after the damage at the location of sensors along with the stiffness values of the predefined members (DIM Model), whose both ends are at the locations of the sensors. In real cases, the number of these sensors is limited which may reduce the accuracy of DIM results. To remove this type of error, the DIM results should be combined with some others and then a final decision on the safety level of the structure can be made based on the overall result. The first process, whose results can be combined with DIM results, is the tracking of natural frequencies variation before and after the damage. Actually this combination verifies the severity of damage. If natural frequencies shift after an event, the severity of damaged can be confirmed by their changes. Also it can be found out that the variation of the frequency may arise from temperature or traffic load variation. To remove this error, a method is defined in detail in recommendations section. The damage severity index calculated by DIM, which describes the severity of the damage to a specified D I M element can not directly be used for determining the status of the structure, but the above-mentioned comparison can help to better understand the DIM results. This comparison is called Frequency Comparison (FC) The second process is the pushover analysis, already performed on the structure, whose results can give threshold levels of displacement at the key points of the structure. These thresholds can be compared with the displacements derived from the data of an earthquake and determine i f there is a possibility of damage. The results from this step can be combined with the results from DIM. This combination eliminates the errors that may affect judgment about the behaviour of the structure after an event. This Comparison between displacements is called Displacement Comparison (DC). The third process, which helps to clarify the results, is the comparison of the level of accelerations with the database accelerations (if there is any). Some bridges, like PSO Bridge, have database of the past earthquakes, happened at their sites. Visual inspections of the past earthquakes show which level of shacking is significant for the structure. These findings can be used as benchmarks when comparing with the effects of future earthquakes. This comparison can verify the results of D I M and the displacement comparison. For example, i f the acceleration comparison shows the recent event is not significant compared to the previous ones and other results show that there is no damage, the final result about the behaviour of the structure will be more reliable. The details of these comparisons will be discussed in the next section. It should be mentioned that acceleration comparison provides extra results, which will not affect the overall result directly i f a database is not available for the structure. The details will be explained later in this chapter. This comparison is called Acceleration Comparison (AC). In the next section, first the procedure is introduced generally and then its elements are discussed. 6.3 PROCEDURE FOR SEISMIC STRUCTURAL H E A L T H MONITORING (SSHM) The SSHM procedure can be introduced as shown in Figure 6-1. This procedure contains all the steps and of calculations that should be done on a series of data to help make a finial decision about the serviceability level of a bridge. The first step after receiving the data is Signal Processing to calculate the corresponding values of accelerations (Light Blue Boxes). The second step is divided into two sections, which are System Identification and Acceleration & Displacement Calculation (Blue Boxes). These operations can be explained as follows: In System Identification, the bridge frequencies and mode shapes are extracted and fed to the following sections. Damage Index Method (DIM) and Frequencies Comparison (FC) are the next calculations of this part. As explained before, in DIM, the extracted mode shapes are compared with the base lines to detect possible damaged elements and to determine damage severity. The results from here are combined with the FC. In FC, it is up to the analyzer to decide with how many natural frequencies the data should be compared. Determining the values of a and p depends on the previous analyses. Finally, the combined results of DIM and FC determine the result of this step. In the other main section of this procedure, the accelerations and displacements are calculated in the required units (e.g. metrics). The acceleration values are then redirected to the Acceleration Database for comparison with the data there, i f any. These values are recorded as a new series of data in this data base for the next event. The displacements are divided into two parts, which are Relative Displacements (if there is any) and Structural Displacements. First the result of RD is calculated and then it is fed to the conditional section of SD. Finally, the result of this part is determined based on the conditional equations, which will be explained in the next section of this chapter. The result of each section can be related to one of the three levels of serviceability as follows: • Safe Service Level (SSL) • Limited Service Level (LSL) • Out of Service Level (OSL) , These service levels are determined by a conditional equation in each step. These equations and their relation to the level of serviceability will be clarified in the next section. After determining the results of above-motioned sections, the final result, which indicates the level of serviceability of the bridge after an event, is obtained based on the Logical Combined Process (LCP). This procedure can be defined by equation (6-1).. Final Result=The Displacements Comparison Result x The DIM and Frequency Comparison Result (6-1) By using the equation 6-1 the final result will be as follows: 1. SSLxSSL=SSL 2. SSLxLSL=LSL 3. SSLxOSL=LSL 4. LSLxLSL=LSL 5. LSLxOSL=OSL 6. OSLxOSL=OSL As mentioned before, the acceleration comparison can verify the accuracy of the final decision and it completes the information, but it does not directly affect the results. This statement will be clarified in the next section with an example. Finally, at the end of the procedure, the results from DIM, LCP and A C can be printed as a report for further investigations. The main parts after signal processing section in the procedure are: 1. System Identification (SI) 2. Damage Index Method (DIM) 3. Frequency Comparison (FC) 4. Acceleration & Displacement Calculations (A&D-C) • Structural Displacements (SD) • Relative Displacements (RD) • Acceleration Database (AD) Before explaining the different parts of the procedure, different levels of serviceability are defined as follows: 1. Safe Service Level (SSL): At this level, the structure is safe and undamaged, and can be used. 2. Limited Service Level (LSL): At this level, the structure has suffered damage and it should be used under supervision of the owner at his own risk. 3. Out of Service Level (OSL): At this level, the structure has lost its structural mechanism and it is out of service. These levels can be assigned to Green, Yellow and Red colors respectively (in software format). The relation of these levels to each part of procedure will be explained later in each individual part. System identification was clarified in Chapters 2 & 3. DIM was explained and studied on PSO Bridge in Chapter 5. The other parts and their relation are explained here along with their relation with DIM results and the levels of serviceability. Finally, the procedure parts can be summarized in three comparisons: 1. Acceleration 2. Displacement 3. Damage Index & Frequencies This comparison is related to the existing instrumented bridges which have experienced earthquakes and the records of them can be classified. For a newly instrumented structure the database can be updated after every recorded event. For example, this data base for PSO Bridge is classified as in Table 6-1 which shows the accelerations of the free-field and maximum accelerations of the structure in each direction. Table 6-1: Maximum Acceleration Values for the Free-field and the Structure Earthquake Mag. (ML) Epic. Dist. (km) Free-field Accel, (g) Structure Accel, (g) X Y Z X Y Z Trinidad Offshore 6.9 88 0.15 0.06 0.03 0.16 0.17 0.33 Rio Dell 4.4 15 — — • — 0.27 0.42 0.59 Eureka 5.5 61 — — — 0.14 0.21 0.27 Cape Mendocino-86-1 5.1 32 0.43 0.15 0.08 0.4 0.25 0.29 Cape Mendocino-86-2 5.1 26 0.14 0.12 0.02 0.18 0.35 0.28 Cape Mendocino-87 5.5 28 0.14 0.09 0.04 0.21 0.33 0.24 Cape Mendocino - Petrolia 6.9 6.4 0.38 0.54 0.13 0.45 1.09 0.67 Cape Mendocino - Petrolia (AS1) 6.2 6.2 0.28 0.52 0.12 0.34 0.76 0.53 Cape Mendocino - Petrolia (AS2) 6.5 6.4 0.26 0.2 0.08 0.31 0.31 0.31 *X, Y and Z are Longitudinal, Transverse and Vertical direction respectively. After an earthquake the Free-filed and the maximum accelerations on the structure can be compared with the data base. This comparison shows that the latest earthquake is a big or a small event in the history of the structure. For example, Cape Mendocino-87 earthquake data shows that this earthquake was a small event compared to the previous ones. So if the visual inspections or the other evidences show that the structure was safe and undamaged before, it can be judged that the structure is still safe and undamaged after this earthquake (Cape Mendocino-87), which was a small event. The result of comparison will be a parameter in verifying the other results (i.e. Displacements and Mode shapes Comparisons) and can confirm their accuracy. Also this comparison is valid as long as the data base includes the accelerations history of linear behaviour only. The following criterion will be used: • If Free-field & Struct. Accelerations < Accelerations in Database, SMALL EVENT (6-1) • If Free-field & Struct. Accelerations > Accelerations in Database, BIG EVENT 6.4.2 Displacement Comparison (DC) This comparison can be categorized as follows: a) Relative Displacements (RD) Relative displacements can be referred to the displacements of different components of a bridge which along with each other (e.g. deck & column or deck & abutment), but independently move during an earthquake. For example, Figure 6-2 shows a simple supported span the deck of which can move independently of the column. After an earthquake the relative displacement between the deck and the column should be checked and compared with the seat length. This displacement should be less than L which is the length of the seat. So, it can be said that: If RD< L, the structure is O.K, and if RD>L, the deck will collapse. The other sections of procedure (Structural Displacements, DIM and Frequencies) will detect the presence of damage, if RD is large enough to cause severe damage and is less than L. b) Structural Displacements (SD) Structural displacements are referred to the threshold levels of displacement which are derived from pushover analysis of the structure. A 3-D pushover analysis is performed for the bridge, and the force-displacements diagrams for all lateral stiffness systems are plotted. The hinge formation in these systems indicates the levels of displacement threshold which can be compared with the real values of displacement in an earthquake. Figure 6-2: Simple Supported Span Although the static-pushover analysis result gives a general idea about the structure's behaviour, and sometimes the dynamic behaviour of the structure is far from it, comparison of displacements can be verified with other evidences. Performance of a bridge can be assessed on the basis of structural displacements and relative displacements and for an accurate judgment they are combined with the other information (i.e. damage index and frequency changes). For displacements comparison, the level of serviceability can be assigned to Relative Displacements and Structural Displacements as follows: I. Relative Displacements: • RD < L/S.F SSL (6-2) • RD> L/S.F OSL II. Structural Displacements: based on Figure 6-3, a pushover analysis plot may be divided into three levels of service. The level of serviceability can be assigned to their mathematical expressions as follows: • SD < D,/S.F SSL • D,/S.F<SD< D2/S.F LSL • SD > D2/S.F OSL (6-3) S.F is the safety factor which is determined by the owner, considering the importance of the bridge and its instrumentation type (Mirza & Ventura, 2005), which may affect the accuracy of the results. Force Limited Service Level Out of Service Level DI D2 Displacement Figure 6-3: Decision levels based on displacements For example, the values of D i and D2 for PSO Bridge can be derived from pushover plot in Figure 4-8. The plot shows that 2.5 cm and 6 cm are appropriate values for D i and D2 respectively. Also the values derived from nonlinear analyses shown in Table 6-2 confirm the selection of D i and D 2 . Table 6-2: Comparison between the Displacements from Nonlinear Analyses  Trinidad9.8 CM86-4.6 P92-3.0 Trinidadll.9 CM86-6.5 P92-3.5 Max. Displ. 2.6 2.8 3.1 3.1 3.9 3.9 The other comparison concerns the mode shapes and frequency changes. Damage Index Method shows the difference between the mode shapes before and after the earthquake, and determines the damaged elements as well. Also frequency variations can be checked by system identification. The combination of this information with the pervious step results helps to determine the level of serviceability of the structure with a higher degree of confidence and accuracy. Figure 6-4 shows the frequency changes for the first and the second transverse modes of PSO Bridge. The results confirm that the first mode frequency is more sensitive to damage than the second one. The variation of the first and the second mode frequencies related to the level of the damage are 3.5%-70% and 5%-38% respectively. The wide range of first frequency shows that it is reliable parameter in determining the different levels of damage. Tri-9.8 CM86-4.6 P92-3.0 Tri-11.9 CM86-6.5 P92-3.5 The results of DIM from previous chapter showed that this method can determine the damage and its location precisely enough, considering the number of sensors. Then Zj (Damage Indicator) can be used as another parameter for the making a decision about the level of serviceability. The combination of frequency variation and DIM is defined as follows: • FV<ot% andZj<). SSL • FV>a% &Zj<) .orFV<%(3&Zj>^ LSL (6-4) • FV>|3%andZj>>. OSL FV is the frequency variation percentage and is determined by the difference between the first transverse frequencies of the bridge before and after the earthquake. As mentioned before, X value is selected by the confidence level in DIM results which depends on the instrumentation type of the bridge (Mirza & Ventura, 2005). Instrumentation type is related to the number of sensors. The more sensors, the more accurate the results. The instrumentation of PSO Bridge is of Type II, and the accuracy of results is not high. Therefore, the value assigned to X is 1.14 which means 87% confidence in the results. The frequency variation percentages (values of a and P) in 6-4 can be updated by the earthquake history data base of the bridge. These primary values may be obtained from a nonlinear analysis or by reducing the stiffness of the key members in a linear analysis and checking the frequency variation. For this study, a=5 and P=70 which were derived from the first and the third damages level of Nonlinear analysis and are shown in Figure 6-4. 6.5 PREREQUISITE FOR SEISMIC STRUCTURAL H E A L T H MONITORING Seismic Structural Health Monitoring of a bridge needs some prerequisite information that can be obtained through: /. Ambient Vibration Test: This test identifies and extracts the bridge natural frequencies and the mode shapes, which will be used as a base line for Damage Index Method. Also it helps to determine the key location of sensors on the bridge. 2. Finite Element Model Calibration: The natural frequencies and mode shapes of the finite element model are matched with those of the ambient vibration test. The updated model represents the real behaviour of the structure and helps to have better results for quasi-static and dynamic analyses. 3. 3-D Pushover Analysis: This quasi-static analysis provides the Force-Displacements plots for different lateral stiffness systems of the bridge, hinge formation on these systems. Finally the values for D] and D 2 can be chosen from these plots for SSHM procedure. 4. Linear or Nonlinear Analysis: Both linear and nonlinear dynamic analysis can determine the values of a and (3 for frequencies comparison. For example, in linear dynamic analysis, the frequency variation can be tracked by reducing the stiffness values of the key members and thus obtaining values of a and p\ 5. Damage Index Model: A model is needed for DIM to determine the location and severity of damage after an earthquake, so the bridge is modeled for this purpose and the information is fed to SSHM flowchart. In this section the procedure is cross-checked and demonstrated with two examples. Also an explanation of the application of this procedure is given. 6.6.1 Verification The procedure is verified with applying two real earthquakes, which PSO Bridge has experienced, to it and the results are then compared with the visual inspection results. Cape Mendocino 86 and Petrolia 92 earthquakes were chosen for this purpose. Sensors # 7 and # 4 were off during the Trinidad 80 earthquake, so this earthquake could not be used as an example because its system identification would not be accurate enough without these sensors. The system identification results of these earthquakes were shown in Table 3-3 (Chapter 3). As mentioned before following parameters were considered for this study: • DIM, 1= 1.14 for 87% level of confidence in results. • Frequencies Comparison, a=5 and P=70. • Structural Displacements Comparison, Di=2.50 cm, D2=6.0 cm and S.F=1 (Chapter 4-Table 4-1 & Figure 4-8). The structural displacement of the bent can be derived from the difference between the top and the base displacements. Figure 6-5 and Figure 6-6 show this difference for the CM86-EQ and the P92-EQ respectively. It should be mentioned that there is no Relative Displacements Comparison for this bridge, so this step is skipped (assuming SSL for this section). The damage indices can be derived by the method described in Chapter 2 and the results for DIj, aj and Zj are shown in Figure 6-7, Figure 6-8 and Figure 6-9 respectively. The DIj, aj and Zj values show that there is no damage in Cape Mendocino earthquake, but show that the west abutment of the bridge suffered damage in Petrolia 92 earthquake. The values DIj, aj and Zj of the west abutment are 1.53, 0.35 and 1.31 respectively. The damage severity index shows that the west abutment has lost 35% of its stiffness. • ICM86 I P92 West Abutment (Element#l) West Deck (£lement#2) East Deck (Element#3) East Abutment (Element#4) Figure 6-7: The Elements Damage Index 0.5 0.4 0.3 0.2 0.1 0 •0 1 -0.2 -0.3 -0.4 1 West Abutment (Element**!) West Deck (Element^) East Deck (Element#3) East Abutment (Elemcnt#4) • ( MXd • P92 Figure 6-8: The Elements Damage Severity Index 1.5 0.5 -0.5 -1.5 West Abutment (Elemcnt#l) 1 1 i — ! m West Deck (KlcmentM) East Deck (ElementW) East Abutment (Element#4) • CM 86 • P92 The routes that examples follow in the SSHM procedure after "System Identification" and "Accelerations & Displacements Calculation" sections (Purple colors in Figure 6-1) are as follows: 6.6.1 Cape Mendocino 86 • DIM: Zj (Zi=-1.06, Z2=1.01, Z3=0.68 and Z4=0.02)< 1.14=A, then go to Frequencies Comparison. • FC: FV= (4.05Hz-4.10Hz) % =5% < 5%=<x, Then select SSL for this part. • SD: SD=0.48cm< 2.5 cm=D,/S.F, Then select SSL for this part. • AC: By checking the Acceleration Data Base (Table 6-1), the Free-field and Structure accelerations > the previous earthquakes, Then write BIG EVENT in the report. • LCP: SSLxSSL=SSL, Then select SSL. The final result of the Cape Mendocino 86 Earthquake is: the Bridge is at Safe Service Level, no element has suffered any damage, and this is the biggest level of acceleration that the bridge has experienced. There is no damage reported for the bridge in this event, which is exactly compatible with the final result of SSHM procedure. 6.6.2 Petrolia 92 • DIM: Zj (Zi=1.31, Z2=-0.27, Z3=1.09 and Z4=-0.05)>1.14=A, then go to Frequencies Comparison. • FC: FV,= (4.05Hz-4.10Hz) % =5%< 5%=a, FV 2 = (5.86Hz-5.97Hz) % =11%< 70%=|3, Then select LSL for this part. • SD: SD=5.5 cm< 6 cm=Di/S.F, Then select LSL for this part. • A C : By checking the Acceleration Data Base (Table 6-1), the Free-field and Structure -accelerations > the previous earthquakes, Then write BIG EVENT in the report. • L C P : L S L x L S L = LSL, Then select LSI. The final result of the Petrolia 92 Earthquake is: the Bridge is at Limited Service Level, the west abutment has suffered moderate damage (a,j= -35%), there is a probable damage to the east abutment (DL.= 1.1, Figure 6-7), and this is the biggest level of acceleration that the bridge has experienced. It was reported that the bridge experienced settlement of the fill adjacent to the abutments and concrete sapling at joints after the Petrolia 92 earthquake, which is compatible with the final result of SSHM procedure (EERI Report, 1992). 6.6.2 Application The application of this procedure is limited, and it can not be used for the suspension and cable-stayed bridges. The reason is that the structural mechanism of such bridges is slightly different, so the structural part of the procedure needs some change. For example, the Relative Displacements part may be replaced by the Tension Stress Levels, with which the allowable stresses are checked in the cables. The concept, which is used for this procedure, can be generalized to other types of structures, but different structural mechanisms should be studied before a part related to them can be included in the procedure. There are some recommendations for a better SSHM and more accurate and reliable results. These are the result of this study and previous projects, and are as follows: • Instrumentation Type: to make a better judgment about the response of a bridge after an earthquake, extensive instrumentation (more than 18 channels) is needed. With more sensors mounted on a structure, the response and system identification result will be more precise. The detail can be found in Guidelines for Seismic Instrumentation of Bridges in British Columbia by Mirza & Ventura, 2005. • Sensor Type: It is better to use tri-axial accelerometers for each location rather than one directional ones. The reason is the information will be needed for all directions at each sensor location after occurrence of damage. For example, in PSO Bridge, only one vertical accelerometer was used for the bent's column at its base for measuring the vertical motion of its top and bottom. This will be acceptable as long as the structure has linear behaviour and the vertical response of a column is similar at its top and bottom due to high axial stiffness value. After formation of hinges in the columns, there will be a difference in the vertical motion at the top and at the bottom. This difference (damage) can be found by the accelerations comparison, which needs two vertical sensors. This can be generalized to the sensors mounted for sensing the longitudinal behaviour of the deck. • Displacement Calculation: Decision about the level of serviceability of a bridge is made partly based on displacements values. These values are derived from the accelerations time history. There are two methods of displacement calculation; one is by double-integration of acceleration time history (Time Domain) and the other is by Frequency-Domain procedure, which gives pseudo-displacement. Both procedures have errors that sometimes cause false alarm in SSHM procedure. It is strongly recommended that this calculation should be done with the highest level of accuracy. Such accuracy can be achieved by selecting finer steps in integration process (e.g. Simpson and Trapezoidal Rules) for Time Domain, and by choosing appropriate band-pass filters for low and high-frequency cut-off in Frequency Domain. • Base Line Mode Shapes: B L M S is related to mode shapes derived from ambient vibration test and used as a base line for DIM. A bridge has different values of natural frequency under variation of loading such as traffic, temperature. These different values of frequency can induce false alarm in SSHM procedure. To neutralize this effect, the following steps should be done. 1. An ambient vibration test with the required number of sensors for extracting the real mode shapes and natural frequencies. 2. A n ambient vibration test with the number of sensors same as the bridge instrumentation type program and exactly at the decided permanent locations. This test gives rough mode shapes and can be compared with the real mode shapes of step 1. 3. System identification of pre-event record6 and extracting the mode shapes related loading just before an earthquake. These mode shapes can be compared with the rough mode shapes of the previous step by M A C or C O M A C methods. The similar mode shapes and frequencies at this step can be used as a base line for DIM. This procedure can eliminate the errors that may arise different temperatures and/or loading. The present digital recorders have enough memory and capability to record 30 seconds of accelerations right before an earthquake, which is called pre-event record. CHAPTER 7 SUMMARY, CONTRIBUTION, AND FUTURE WORK 7.1 S U M M A R Y The objective of the thesis was to introduce a seismic structural-health monitoring procedure for bridges. To reach this goal, the Damage Index Method was tested on an existing bridge. The governing limits (number of sensors, etc) caused the DIM results not to be accurate enough, so other structural evaluation methods (e.g. Pushover Analysis) were used and combined with this method to overcome the DIM's deficiencies. The results from DIM, Pushover and Nonlinear Dynamic analyses showed that they are so interrelated that can not be defined in an equation, but it is possible to compare them for judging about the behaviour of a structure after an event. For example, when a bridge is damaged during an earthquake, its stiffness decreases causing its natural periods to increase, which in turn causes higher displacements under that specific event. A change in the periods causes the corresponding mode shapes to change, and all these changes are due to the acceleration level of the earthquake. With this logic, a procedure was defined for seismic structural health monitoring of bridges. The SSHM procedure was cross-checked against the earthquakes that the PSO Bridge had experienced, and its results were confirmed. This procedure, which can be implemented on a user-friendly software, makes it possible for the user to evaluate the level of serviceability of a bridge after an event without any further calculation or site visit. Chapter 7-Summary, Contribution and Future Work 7.2 CONTRIBUTIONS The main contribution of this thesis to the state of knowledge of health monitoring can be divided into two main parts as follows: 7.2.1 Critical Review of DIM The first contribution of this thesis is the critical review of the Damage Index Method (DIM) by using it for the very first time in a real bridge with very limited number of sensors. Data from recorded earthquakes, as well as, data derived from nonlinear dynamic analyses of the bridge model, were used to evaluate the effectiveness of DIM. This method has already been tested by researches but only in special conditions. These special conditions can be categorized and compared with those used in this thesis as follows: • In all previous cases, the researchers used DIM for structures in two different independent conditions: a) Undamaged Structure, b) Damaged Structure First they extracted the frequencies and mode shapes of an undamaged structure. Then they inflicted damage to the structure by reducing the stiffness of a selected member, and extracted the frequencies and mode shapes again. Finally the DIM was used for the cases a) and b). This is a comparison between two linear cases with the same geometries and equal masses, but different stiffness values. In reality, there is a transitional zone between the undamaged and the damaged conditions of a structure during an earthquake, i.e. the structure's stiffness varies during its response to an earthquake. In this thesis real nonlinear analyses were done and used in DIM. • The past projects also had a good resolution of responses. In analytical cases, the desired mode shapes and natural frequencies were derived using the finite element programs, and there was no limit to the extraction of mode shapes and natural frequencies (e.g. Park & Kim 2002). In laboratorial cases, structures were vibrated with white noise, which can trigger all modes significantly, and then the desired mode shapes could be extracted using system identification (e.g. Park, Bolton & Stubbs, 2004). As shown in Table 3-3 (Chapter 3), some of previous earthquakes did not have enough energy to trigger all natural frequencies of the PSO bridge, therefore system identification could not help to extract the frequencies and mode shapes. In this thesis, this limited information was used in DIM. • The past projects had enough measurement points in their models to define accurately the mode shapes. In the analytical cases, the coordinates of all element nodes in each mode shape were used in D I M (e.g. Park & Kim 2002). In laboratorial cases, the structures considered had enough number of sensors, whose coordinates were used in DIM (e.g. Farrar & Jauregui, 1996). In practical cases, the coordinates of mode shapes are limited to the number of sensors mounted on a structure and this thesis dealt with such coordinates. 7.2.2 Introducing the SSHM Procedure The second and the main contribution of this research is the introduction of a Seismic Structural Health Monitoring Procedure for bridges with limited instrumentation. It should be mentioned that not only does this procedure overcome the deficiencies of the DIM results (mentioned in chapter 5), but also gives the results in a way that civil engineers can interpret them without any damage detection background or further calculations. The level of serviceability of a bridge can easily be determined by the procedure as Safe, Limited or Out of serviceability, which spares the decision maker the interpretation of individual numbers and parameters derived and introduced by each included method. The most important benefit of this procedure is accurate functioning by using information from the limited number of sensors (checked in Section 6.6.1 of Chapter 6). The number of sensors can not easily be increased in a real case, because the cost of instrumentation and running cables increases nonlinearly with the number of sensors, which may make the change uneconomical. Another feature of this procedure is its more reliable final result compared to those obtained from using only one method. In this procedure, the results from different methods are double checked with each other, and then the status of the structure is determined. This helps reduce the errors, and make more reliable decision the serviceability status of the structure. Such a critical decision, which is to be made very quickly without further investigation must be based on precise results. This procedure provides the free-field and the structure accelerations of the event as a database for checking the results of future events. This database will be very useful for confirming the final result in seismically highly active areas. This procedure in the flow chart format can easily be converted into user-friendly software. Also the service levels can be assigned to the colors used in traffic lights (Green, Yellow and Red) which make instant decision making possible. If this warning system is generalized to all bridges in a transportation network, it can quickly indicate their status after an event, which helps reduce the secondary damage and casualties. It should be mentioned that this procedure can easily be used, developed or modified for the other types of the structures, as explained in Section 6.6.2 of Chapter 6. The structural part of the procedure can be modified to correspond with the intended structural system. For example, it can be used for the structures, which have frame system, without much modification, but using it for the systems, which have cables and shear walls (in buildings) demands major changes. The author believes that this is not the final but only the first step in this area. This procedure can, and hopefully will , be completed by other researches in future. The ideal procedure for the author is one in software form that can be imbedded in the future recorders enabling them to automatically analyze and evaluate the status of a bridge. The results can be sent to the owner as a report and can also inform the motorists about the serviceability of the bridge with a simple connection to traffic lights or to a message board. This can be helpful for a better critical management in a yellow or red condition, before the owner's personnel arrive at the site. The specific areas that may be found interesting for future work can be categorized as follows: • As mentioned in Section 6.7, the displacement values, derived from the accelerations, have errors in both time and frequency domain methods. It would be interesting to minimize these errors by further investigations. • The base line mode shapes recommended in Section 6.7, can be investigated in projects of real instrumented structures to check the possibility of removing the errors from this part of SSHM procedure. • A study of using combined models of DIM (i.e. shear beam, flexural and axial behaviours) in a specific case, may help to include the effects of all modes in damage detection procedure. For example, in PSO Bridge case, the effect of vertical mode shapes can be introduced to the damage index method by defining a flexural model and its results can be combined with the shear beam model results for a better outcome. • As explained in the last paragraph of the section 7.2.2, the procedure can be modified easily for the other types of structures. Development of a procedure, that can be applicable to all types of structures, will be useful. On the other hand the procedure may include all the elements of all types of structures so that the user can select the desired ones. For example in SAP2000®, frame, shell and other elements specifications can be selected by the user for a specific case. REFERENCES 1. Alampalli S. and Ettouney M . , (2003), "Proceedings of the Workshop on Engineering Structural Health", New York State Department of Transportation, N Y , USA. 2. 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Bernal D. and Hernandez E., (2004), " A Data Driven Approach to Identify Damage Induced by Earthquakes", 13th WCEE, Vancouver, BC, Paper No. 2700. 9. Caicedo J. M . , (2003), "Structural Health Monitoring of Flexible Civi l Structures", Washangton University, Civi l Engineering Department, USA. 10. Celebi M . & Sotoudeh V. , (1985), "Integrated Instrumentation Plan for Assessing the Seismic Response of Structures—A Review of the Current USGS Program", USGS, CIRC 947. 11. Celebi M . , (2000), "Seismic Instrumentation of Buildings", USGS. 12. Civi l Engineering A S C E Journal, (1995), "Kobe Shocks the World". 13. Chan, T.H., N i , Y.Q. , and Ko, J .M. (1999) "Neural Network Novelty Filtering for Anomaly Detection of Tsing Ma Bridge Cables," Structural Health Monitoring 2000, Stanford University, Palo Alto, California, pp. 430-439. 14. Chen Ed. W.-F. and Duan L. , (2000), "Bridge Engineering Handbook", Boca Raton CRC Press. 15. Choi, M . 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Farrar C. and Jauregui D., (1996), "Damage Detection Algorithms Applied to Experimental and Numerical Modal Data from the 1-40 Bridge", Los Alamos National Laboratory, L A -13074-MS, USA. 21. Farrar C. R. and Cornwell P. J., (2000), "Structural Health Monitoring Studies of the Alamosa Canyon and 1-40 Bridges", Los Alamos National Laboratory, LA-13635-MS, USA. 22. Feng, M . , and Bahng, E., (1999), "Damage Assessment of Bridges with Jacketed RC Columns Using Vibration Test," Smart Structures and Materials 1999: Smart Systems for Bridges, Structures, and Highways, Proceedings of SPIE, Vol . 3,671, pp. 316-327. 23. Feng, M.Q. , De Flaviis, F., Kim, Y.J . , and Diaz, R., (2000), "Application of Electromagnetic Waves in Damage Detection of Concrete Structures," Smart Structures and Materials 2000: Smart Systems for Bridges, Structures, and Highways, Proceedings of SPIE, Newport Beach, California, pp. 118-126. 24. Fenves G. L. , (2001), "Instrumentation for Assessment of Earthquake Performance of Bridges and Dams", Instrumental Systems for Diagnostics of Seismic Response of Bridges and Dams Seminar. 25. Gates J. H . and Escalante L. E., (1985), "Priorities for Installation of Lifeline Facilities Instrumentation", California Seismic Safety Commission Strong-Motion Instrumentation Advisory Committee. 26. Ghali A. , Neville M . and Brown T. G., (2003), "Structural Analysis-A Unified Classical and Matrix Approach", Fifth Edition, Spon Press. 27. Goel R. K. , (1997), "Earthquake Characteristics of Bridges with Integral Abutments, Journal of Structural Engineering", A S C E , P 1435-1443. 28. Hipely P., Huang M . and Shakal A. , (1998), "Bridge Instrumentation and Post-Earthquake Evaluation of Bridges", SMIP 98 Seminar on Utilization of Strong-Motion Data. 29. Housner G. W., (1994), "The Continuing Challenge-The Northridge Earthquake of January 17", 1994 Report, California Department of Transportation. 30. Iervolino I. & Cornell C. A . , (2005), "Record Selection for Nonlinear Seismic Analysis of Structures", Earthquake Spectra Journal, Vol . 21, No. 3, P 685-713. 31. Ko, J., N i , Y . , and Chan, T., (1999), "Dynamic Monitoring of Structural Health in Cable-Supported Bridges," Smart Structures and Materials 1999: Smart Systems for Bridges, Structures, and Highways, Proceedings of SPIE, Vol . 3, 671, pp. 161-172. 32. Krishnan K. , (1999), "Seismic Response of Concrete Bridges", ACI Structural Journal, 99-63795. 33. Kumar S., (2002), "Lateral Load Deflection Response of Drilled Shafts in Sand", IE(I) Journal. 34. Kwon, I., Choi, D., Choi, M . , and Moon, H. , (1998), "Real-Time Health Monitoring of a Scaled-Down Steel Truss Bridge by Passive-Quadrature 3X3 Fiber Optic Michelson Sensors," Smart Systems for Bridges, Structures, and Highway s, Proceedings of SPIE, Vol . 3,325, pp. 253-261. 35. Lee K . M . & Xiao Z.R., (2001), " A Simplified Nonlinear Approach for Pile Group Settlement Analysis in Multilayered Soils", N R C Research Press Website (http://cg.nrc.ca). 36. Maeck, J., and De Roeck, G., (1999), "Damage Detection on a Prestressed Concrete Bridge and RC Beams Using Dynamic System Identification," Damage Assessment of Structures, Proceedings of the International Conference on Damage Assessment of Structures ( D A M A S 99), Dublin, Ireland, pp. 320-327. 37. Makris N . & Zhang J., (2004), "Seismic Response Analysis of A highway Overcrossing Equipped with Elastometric Bearings and Fluid Dampers", Journal of Structural Engineering, A S C E / June 2004. 38. Mirza K. & Ventura C , (2005), "Guidelines for Seismic Instrumentation of Bridges in British Columbia", Canada, EERF Report 04-04. 39. Mosher R. & Dawkins W., (2000), "Theoretical Manual for Pile Foundations, Engineering Research and Development Center", US Army Corps of Engineers. 40. Naeim F., Hagie S. and Alimoradi A . , (2005), "Automated Post-Earthquake Damage Assessment and Safety Evaluation of Instrumented Buildings", John A. Martin and Associates. 41. National Cooperative Highway Research Program (HCHRP), (2001), Report 461, "Static and Dynamic Lateral Loading of Pile Groups". 42. Nigbor, R.L., and Diehl, J.G., (1997), "Two Years' Experience Using OASIS Real-Time Remote Condition Monitoring System on Two Large Bridges," Structural Health Monitoring, Current Status and Perspectives, Stanford University, Palo Alto, California, pp. ' 410-417. 43. Onur T., Ventura C. E. and Hao K. X.-S. , (2004), "Site Period Estimation in Fraser River Delta using Microtremor Measurements-Experimental and Analytical Studies", 13th World Conference on Earthquake Engineering, Vancouver, B.C, Canada. 44. Park S., Bolton R. W. and Stubbs N . , (2004), "Blind Test Results for Nondestructive Damage Detection in a Steel Frame". 45. Park S., K im Y . and Stubbs N . , (2002), "Non-destructive Damage Detection in Large Structures via Vibration Monitoring", Electronic Journal of Structural Engineering (eJSE). 46. Park S., (1997), "Development of a Methodology to Continuously Monitor the Safety of Complex Structures", Ph.D. Dissertation, Texas A & M University. College Station, Texas. 47. PEER, (2005), "Structural Performance Data Base", http: / / www. ce .Washington. edu/~peera 1 / 48. Peeters B. and Ventura C. E., (2003), "Comparative Study of Modal Analysis Techniques for Bridge Dynamic Characteristics", Mechanical Systems and Signal Processing, pp. 965-988. 49. Peeters, J .M.B., and De Roeck, D., (2000), "Damage Identification on the Z24-Bridge Using Vibration Monitoring," European COST F3 Conference on System Identification and Structural Health Monitoring, Madrid, Spain, pp. 233-242 50. Rojhan C. and Raggett J., (1981), "Guidelines for Strong-Motion Instrumentation of Highway Bridges", U.S. Department of Transportation, Federal Highway Administration, Report No. FHWA/RD-82/016. 51.SAP2000, (2005), "Manual, Version 9" Computers and Structure Inc., UC of Berkeley, USA. 52. Shon H. and Farrar C , (2004), " A Review of Structural Health Monitoring Literature: 1996-2001", Los Alamos National Laboratory, LA-13076-MS, USA. 53. Stubbs N . , K im T.J. and Topole K. , (1992), " A n Efficient and Robust Algorithm for Damage Localization in Offshore Platforms", A S C E 10th Structures Congress 92, San Antonio, Texas, pp. 543-546. 54. US Army Corps of Engineers, (2003), "Engineering and Design-Time-History Dynamic Analysis of Concrete Hydraulic Structures", Engineer Manual. 55. Ventura C , Brincker R. and Andersen P., (2005), "Dynamic Properties of the Painter Street Overpass at Different Levels of Vibration", International Conference on Structural Dynamics, Paris, France. 56. Ventura C.E., Finn W. D. L. and Felber A . J., (1995), "Dynamic Testing on Painter Street Overpass", Procs. of 7th Canadian Conf. on Earthquake Eng., Montreal, Canada, pp. 787-794. 57. Wang, M.L . , Satpathi, D., and Heo, G., (1997), "Damage Detection of a Model Bridge Using Modal Testing," Structural Health Monitoring, Current Status and Perspectives, Stanford University, Palo Alto, California, pp. 589-600. 58. Woods M . C. and Seiple W. R., (1995), "the Northridge, California, Earthquake of 17 January 1994", California Department of Conservation. 59. Yin Y . , Konagai K. and Hotta H. , (2003), "Single Beam Analogy for Analyzing Nonlinear Soil-Pile Group Interaction under Lateral Loading", Tokyo, Japan. 60. Zabel V. , (2005), "Application of Wavelet Decompositions' Energy Components to Damage detection, Identification and Numerical Models", International Operational Modal Analysis Conference (IOMAC), Copenhagen, Denmark. 61. Zhang J. & Makris N . , (2001), "Seismic Response Analysis of Highway Over-crossings Including Soil-Structure Interaction", Department of Civi l and Environmental Eng. Of U C B , PEER 2001/02. 62. Zhang J. & Makris N . , (2002), "Seismic Response Analysis of Highway Over-crossings Including Soil-Structure Interaction", EQ Eng. & Struct. Dyn. 2002; 31: 1967-1991. APPENDIX A EARTHQUAKES RECORD TRINIDAD 1980 : : : : J . 1 ^^Al\rV)l^ -200 J «> 2 *» rt « 1 <> 12 1** 1 <i IN 2« C A P E M E N D O C I N O 1986 CHANNIi 1^  I •v INJ r*i is i_ J < : 11 ,v » rv" i.. -7 •-• >v [ni p*i 15 • ^  : CHANN 15 • <"._' HANNIi: 1^  12 A.rM rsi ic 13 CMANN IS I - 14 CIIANNICI. 1 ? < : u ArviN i.. i <s CIIAINNKU 1 ' CITANNIC 1^  IS i A-fM rsi i : : i.. • « -v/^iu^^l^A^ ^rr?: P E T R O L I A 1992 ANNEL2 CI lAIMNKI^  J I AIVNKI.. -4 IIANNEL 7 CHANNELH C H A N N E L < : I I ,v N N IS L • o <:: i i A N N i : : i.. • • N N •-; i . i j "fiy-ittft ^g -^*-—irtr • " *n IUNVJ -*ii^ _flr*i«™'y y • r"ir — i -r* L — Cl l A N N 1-L I . 1 CI1ANIN EL *w 1 -I A N N IS • «i <:_• I-I A N IN i-: i . • -7 • AI-^ JNEt. IN «._: I I A N N K I . 19 c ••• A N r*i 1% i.. APPENDIX B DETAIL DRAWINGS £c/aras*ic4i firm TOR RE.IrxiFOfiCF-r^afsJT AJot* All rmirtfommmmn? "*7fl <jryJr^a rtotmd o K/utraders <$+ »neta of t*nr% (rtd;'ca/e dis/a^*rv /r> /ae/ from Re f e r ence //rn /"or minforc*rrt*ni and from £ Sfrucfure /"ar dc//o/n rc/Vifarcem*nt. mm. r«—T» •MM • • i f <fMI<IW Of hum tot i n | i » 1 6 S H Q PH o o 12 C O Pi t—« H Q o o DO 13 1 I 6 4 » too •. *JS? _ _ W ,.I.,'.TI^.^?.,.?.,T I ' I • I 00 9 € Paintvr Street TYPiCAL. 3££TlOM Top /anp/'/ r&/nF '5 cant, to 'S\. stirnjps P A R T - S E C T I O N •Scats '/%'-l-O" lCo«<ff(Ji"*or\e»d Chain Link, gaifing Type 7 Sorrier Hailing Typa 2G N O A S BUILT C O R R E C I * > I ASBU«J CORSfiCTIOMJ Ktt-AScfu-*.*.. cONnucr no Oi- act*-,*  • m mm. | r u n tot ->la«fN.li>i- II. Hi t t 4 WO cu DeSIOH SECTION £ »»• 2i>r£ STATE Of CAUFWNIA DEPARTMENT Of TRANSPORTATION PAINTER STREET OVER CROSSING — - — ^ , 6 r v y v TYPICAL SECTION m. 4 - 2 3 G •u 5 . 3 . 2 lea. C / O — Wi T T 1 1 l l T i " "400 '•* I'-rj .T-J •ruTrsr; i i I i 7 iJ^ lK&3ILm>pjS^ *' * I I I I 1-1, i . t . ^ h r 4Bm.^w . l . l - f c . a i^>, ^ f g g P . . 5 H Q PH -4—» o o r — I <D • —« 00 on j mm. *mm* | mmn j rr> ..jr i . 0/ XL'S . W JS bars r~G* infn ctuj^mcrJ. v9/o_» <-Cfy>r> irtr'riQ /noniverfd rtwVCV*<r/Ir»p vj" frx>*r\ face of* aba/mcn/, I Z ' - O ' * 4 /op «*W> t San / 1 a L O N G I T U D I N A L SECTIOKi *3 conr, totZ ea. gdr. Edge of deck £$Sdr Profile Grade - c in c r a •0 1 I 4H 1 «o C 8 i 3? 10 - 1. •CI M Q A S mj».T CORRECTION AS BUILT C O N T R A C T ai-aanz* PATF <»03-7C Ooes no/ include allotjancs for fb/Mmiuor/c zctllmmuni T O P LONGITUDINAL QEINFOKCFMFHT w o cu 0ESK5N~SECTIOH £ STATE OF CAUfOKNIA DEPARTMENT OF TRANSPORTATION • x u . . , — x_ PAIMTER S T R E E T O V E R C R O S S I N G — A * / * - . G 1 R 0 E R L A Y O U T "3. / r e - — V n •» 4 - 230 •ou 53.3 7 1 IO T T T -——•—«• 1'"n -mrnjiTg np-i nr TT nnn nnrM»n i m JOi»WO^TWI--atD^gNn^OltTlWtlO>u»WO,CAU»UI^ PV^ UWTTl a».|i.^,fe«%>|-'gggp a a w a . i . c i j i ^ K ^ , i b . . . - i : . . . i . . J ; . . . , , . . . T ... .-al.^ri'.g.,:T.,-:i.,j^^r.,.r.,.i, T . r , r. r , ),„^„,i,^ ,»T.rf.<.i.^ ,-i.„.i,-l i T I i i I i : i-i.. KMX l*« 40' ( Q PH o o r—I 04 r—I CO g s s s w r S T s*** ' Q PL, o (67 GO m ^2 » 2 a / 7 Paroo*.' BmdtOpron&t 3'die lap of shotl&w footing^ tot 2 A b u t s Bent Z PAY L I M I T S OF CONCRETE  S 3 Coj/ - in- oiacx Prasf-msmet Ctvicro/« I I tSfrvcruro Contzrcfa, Bri&pa E S B Structure Con era fa, Briefga Footing 00 of fo&mq STEEL PILE ANCHOR Standard Plan Sheet Nb. DeM/No. N O A S B U L T C O R R E C T I O N AS BUILT " O^Tt^iii. A3 BUILT PLANS Street N o . - ^ ^ -Date C o m p l e t e d - - ^ -Document N a - Z e ^ ^ ^ r NTtifnhfr II i n U H H L K T U OCSKW: a.i.S.H.O. tfiM 1973 with ra«Uioat *a* as twplMantl* . >i uiou »u»i«o uo O U I M M W . LUC (.UOin: aStO-aa i l l . r M l l x ninfoncto cocmrit: i, • J4.000 » i ..t.« • 70.000 Ptl' t « 11 MitfM aack \labf 1.J00 Mi. ••<•« 1.200 *•< . « <•-•• USTItSlIN* HOIlt -» j a | t • liiSQiim tatal •> ta». t, • l*ui man of atraart • t cwnt: 1, >4i(!C*> 1 s wii i t i • US&m> • 11™ ct tvmim WOK.: *1. Daaiaa if kaaat •••U><t> 0.0BH. Far airarr* as briMUJ tmd * 111 t U-«") • taajaa k' if a •ndlf i«atfM (actor n t i M tka tltoci ol «d cwvatara ah frictioa •)„, •aacHfctf ft la. jackiaa mm iKliala fraMiaa lease* «aa arariaiai r«r B.OOD o»» laaa M ilrm 2. TaMaaa ta ka Jactaal la 0.7) f, m aooaraa at aa mtaalant •acaar aa< • 1/1". WO cu DESIOM S E C T I O N £ STAR OF CAurauriA DEPARTMENT Of TRANSPORTATION at— PAINTER S T R E E T OVERCROSSING — D E C K C O N T O U R S •.•••i-nri  HI ~"~"*n-ni n nrrwum nti cAUJ-anw* m/miT rg aat j . .aB o PH o o CD 6 0 CQ r e « p _ 1;., S s f B r a w w „ .I.I.I.I...I.T.I.... • . • : . « J : > J U i 8 M - 4 n . i J . i. i i n T, • - . r a t ^ E ^KSS ' i A i f t . i. 1 « W U .{ l"« jtf WMOWUt- HOT Of CAUrOCMlA - VCMMTTBUfT <f TllWiWMlTlp^MUMfmji K m l.aCJ H 100 200 „ 500 '115 -1'...^WJ.^....I....£^.I....T....I....I i T i .1 i T i I . . . . . ! . . . I . . . I . . . I . . .L . . .1 . . . . I , . . . I . . . . , , . J I . . T . . . T . . 7 T . I . I . IT . I .T . I .T .T , I 7 . 7 , 7 . 7 . ) 0 « Oft ' * . T . I . I . 1—1—l_L_Li_L_i t' • i • 1 < t • 1 . . 1. i . 1. i . i . i . 11 • • 111 • 0, H Q PH +-> o o CO P 4 ffl Q PH ^—> o o r — f 0 3 t *4 1« f rVIAJOf/rlLL OAT A Lift) »lfl) T !«« ua filer 20 IO II 12 13 /*• r-o-rcr ra-rer to 7 7 -7 7 6 \ 22 IO / / IZ 13 14. r-o r-o r-o rc r-o 6 6 3 a & \ 24 IO II 12 li J4 r-o-r-o-r r r-r r-r 6 S B e e 2 It. 10 II IZ 12 14. r-r rr rr r-r rr 6 & i 6 <s 1 1 / 2 2 26 IO II a 13 te r-r 1 9 rr 0 rr 1 9 rr ! 9 rr 3 1 1 2 2 * 30 10 ; r-r 11 i rr a ; r r 13 ;. or t* '. rc 9 3 9 9 9 1 1 2 2 2 J2 10 it IZ 13 . r-T re re t& re 9 9 9 9 9 1 2 2 2 Z 34 10 11 12 13 14 rc r e re re re 9 3 9 10 /O 1 2 2 2 1 M. 10 It 12 13 14. re re re re re 10 K> 10 10 to 2 2 2 2 2 36 IO It 12 li 14 fi-r e re re r r IO JO JO JO 10 Z 2 1 2 2 40 IO It 12 13 I* re re r r r r r-r to 10 JO JO JO 2 2 2 2 2 AS BUILT PLANS Contract No nj.rrK/-,^/ Date Completed -Document No. Bridge Oetott 3-4 mm. Qi Hvm\ tot - St/aoor/ pot/ /o 6m rlu*4/ tevght ( r-Gt) uJ>«n amy// «-taral 10 For A10. of 4S j"LJ Ion tutor see Wingwoll Ooh Mate pile emiedrmnl • 5" far steel piles '(•rfar Timber Piles bar clearance • C for Orel Piles • 3-Or Timber PHa Increase footing depth to Z'-O" if limber PiJet ore ased. r 1 — .Niui.mhir '1,HT1 - to rat 6 r-e-s-o-SECTION C-1 P See r«cf->f> &-6 For reinforcing not \hou,n - total II f-tr c-o-Ctamler rtr U-toMz • u rj 6>i3-SECT/ON D-O 73* /bur agomrJ unditturbea material **-toM4-SECTION 5-B \ l4fel*: IVhen superstructure rs prertrerxea\ tne uenowolt must be placed -offer stress-ing is canpt'e/tot Backfill motortoJ trftt'de or' atolls must ae placed prior to placing backfill outside, of wo/is. Match deck oeernonq Hatch to snap* accommodate cone oulter at approaches, (lib nolcn if r-ir arujMMiG JJO OYCRHAUQ SECTION A-A £xr&. joint** _ aw requirmd 0"min.) Note: SJca*v9d layout- ip for Aburmenre hovinq skews of IS* or more. *<t tot. S " A B U T M E N T CORNER D E T A I L . NO AS WAT CCSREOTOM AS BUILT CORRECTIONS KY /.ASctvpcdc-CCWTRACr MT) OI-OC.-ZZ4 DATS J - 3 J - 7 6 g r ^ . / . p WO CU 6 / 7 1 DEPARTMENT OF TRANSPORTATION x s ' 4 2 9 PAINTER STREET 0\ ERCROSSMG SIMPLE SEAM WINGWALL DETAILS to 1 1 1 . T n g i x a m v o n r w n«T*«a«T^ i«CiK _ M/THOM2ATVNCT THM 0~ M 1 0 0 * raffia? •i'+-'i>*e' ^iVP • •00 - V T06 .,.« • "I* ' T«i iff^ TO *~ ' K i l f »*•«' * 1*. IOC • wwwwaBr-.iLwji aj»uw«i« ^ " w t w w y^MMwyBMacwror r a a o r * . ' ~*"r?*^"tafiAUB»t71ff ' — — a& a _5r -T *^ too _ _ 18O 0 1. MwCnM ~\e7 i l l ? I I ,I.,-t,,-,,T.r-il...-7..,-J..-.rl, S A J , • T • 7" • T • T 1 .Li..i^j...-r^.j-ij • T 7 . T , T . I 1 • 1. U . I L.L, •T-T.,T,.T..-7.,'-T ^ 7 - 2 H Q PH -t—> o o r - H GO 1—1 CO — r r -nujunm-am or t-Kwwmn or • T 1 r' ..I.I.:.-.I.I.I.I I.i • . . . . . 1 >•1•'• itl.i.i I w » JO «• | •* w t» w 1 • M JO « | w n m » p JB » •© • a p f o a e M 1 1 J . . . . l . J . .^ . 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