@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix dc: . @prefix skos: . vivo:departmentOrSchool "Applied Science, Faculty of"@en, "Civil Engineering, Department of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Khan, Saqib A."@en ; dcterms:issued "2009-08-06T00:00:00"@en, "2001"@en ; vivo:relatedDegree "Master of Applied Science - MASc"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description """With our increased knowledge about seismicity and risks related to earthquakes, there is a greater need for retrofitting deficient structures to ensure the functioning of a transportation network and to minimize the life and economic loss associated with catastrophic events. Given the scarcity of funds, the decision maker should try to determine the optimal level of retrofit for a structure and the priorities among various candidates. A decision analysis methodology is thus proposed and demonstrated through two example bridges in order to determine the most preferable level of retrofit and the retrofit order for the two candidates. The decision alternative minimizing the total cost of the structure over its life is the best retrofit strategy while the bridge with the lower cost-to- benefit ratio should be retrofitted first. Seismic assessment o f the Colquitz river south structure was performed in terms of three different levels of seismicity. Various earthquake records were scaled to match the site-specific spectra corresponding to each level of seismicity. These records were then used to drive the non-linear dynamic analysis of the bridge pier. Overall damage states for the bridge were determined based on damage index values for the pier and expert judgement for other bridge components corresponding to various pre-defined levels of retrofit. The structural damage was then translated into dollar damage and this information was used in the decision analysis algorithm as consequence costs. An expected annual cost of future damage was then calculated and converted to present worth for each retrofit level. The estimated retrofit costs and the present value of future damages were then added to find the total expected cost for each decision alternative. Sensitivity analyses were carried out to examine the variations in decision outcome due to changes in different input parameters. Also, the effectiveness of decision analysis techniques not employing probability and risk attributes was briefly examined. For the Interurban overpass, it was assumed that the safety level retrofit would be the optimal strategy. Cost-to-benefit ratios for the two structures were then calculated corresponding to the optimal retrofit decision for each, thus determining the order of retrofit."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/11811?expand=metadata"@en ; dcterms:extent "8685158 bytes"@en ; dc:format "application/pdf"@en ; skos:note "OPTIMAL RETROFIT STRATEGY DETERMINATION FOR BRIDGES USING DECISION ANALYSIS by SAQIB A. K H A N B.Sc , University of Engineering and Technology, Lahore, Pakistan, 1998 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE THE F A C U L T Y OF GRADUATE STUDIES DEPARTMENT OF CIVIL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A August 2001 © Saqib A. Khan, 2001 U B C Special Collections - Thesis Authorisation Form Page 1 of 1 In present ing t h i s thes i s i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I fur ther agree that permission for extensive copying of t h i s thes i s for s c h o l a r l y purposes may be granted by the head of my department or by his or her representat ives . It i s understood that copying or p u b l i c a t i o n of t h i s thes i s for f i n a n c i a l gain s h a l l not be allowed without my wr i t t en permiss ion. Department of tiviL F M G l M E E R l M G The U n i v e r s i t y of B r i t i s h Columbia Vancouver, Canada Date 4 • oi • i o o l ht1p://www.library.ubc.ca/spcoll/thesauth.html 7/30/01 ABSTRACT With our increased knowledge about seismicity and risks related to earthquakes, there is a greater need for retrofitting deficient structures to ensure the functioning o f a transportation network and to minimize the life and economic loss associated with catastrophic events. Given the scarcity o f funds, the decision maker should try to determine the optimal level o f retrofit for a structure and the priorities among various candidates. A decision analysis methodology is thus proposed and demonstrated through two example bridges in order to determine the most preferable level o f retrofit and the retrofit order for the two candidates. The decision alternative minimizing the total cost o f the structure over its life is the best retrofit strategy while the bridge wi th the lower cost-to-benefit ratio should be retrofitted first. Seismic assessment o f the Colquitz river south structure was performed in terms of three different levels of seismicity. Various earthquake records were scaled to match the site-specific spectra corresponding to each level o f seismicity. These records were then used to drive the non-linear dynamic analysis o f the bridge pier. Overall damage states for the bridge were determined based on damage index values for the pier and expert judgement for other bridge components corresponding to various pre-defined levels o f retrofit. The structural damage was then translated into dollar damage and this information was used in the decision analysis algorithm as consequence costs. A n expected annual cost of future damage was then calculated and converted to present worth for each retrofit level. The estimated retrofit costs and the present value o f future damages were then added to find the total expected cost for each decision alternative. Sensitivity analyses were carried out to examine the variations in decision outcome due i i to changes in different input parameters. Also, the effectiveness of decision analysis techniques not employing probability and risk attributes was briefly examined. For the Interurban overpass, it was assumed that the safety level retrofit would be the optimal strategy. Cost-to-benefit ratios for the two structures were then calculated corresponding to the optimal retrofit decision for each, thus determining the order of retrofit. iii TABLE OF CONTENTS ABSTRACT ii TABLE OF CONTENTS iv LIST OF FIGURES viii LIST OF TABLES x ACKNOWLEDGEMENTS xii CHAPTER I: INTRODUCTION 1 1.1 Background 1 1.1.1 Bridge retrofit in British Columbia 2 1.1.2 Retrofit levels for acceptable performance 3 1.2 Objectives of study 5 1.3 Scope of study 6 CHAPTER 2: GENERAL BRIDGE AND RETROFIT DESCRIPTION 9 2.1 Colquitz river south structure 9 2.1.1 Geometric and structural description 9 2.1.2 Structural deficiencies 11 2.1.2.1 Superstructure 11 2.1.2.2 Bearings 12 2.1.2.3 Pier 12 2.1.2.4 Abutments 13 2.1.2.5 Piles and foundations 13 2.1.3 Retrofit scenarios for Colquitz south bridge 14 2.1.4 Site soil conditions for Colquitz 15 2.2 Interurban overpass 16 2.2.1 Geometric and structural description 16 2.2.2 Structural deficiencies 17 2.2.2.1 Girder diaphragms 18 2.2.2.2 Anchor bolts 18 2.2.2.3 Pier and abutment piles and foundations 18 2.2.2.4 Columns in Pier No.2 19 2.2.2.5 Abutment backwall 19 2.2.3 Retrofit of Interurban overpass 19 2.2.4 Site soil conditions for Interurban 20 iv 2.3 Costs of retrofit 20 2.3.1 Colquitz river south bridge 21 2.3.2 Interurban overpass 22 CHAPTER 3: DECISION ANALYSIS METHODOLOGIES 23 3.1 Introduction 23 3.2 Basis for ranking competing alternatives 25 3.3 Determination of expected value 25 3.4 Decision tree for present study 26 3.5 Decision making with out probability values 29 CHAPTER 4: SEISMIC HAZARD EVALUATION 31 4.1 Methodologies for seismic hazard prediction 31 4.2 Synopsis of methodology for present study 32 4.3 Considered earthquake levels 33 4.3.1 Current design level earthquake 33 4.3.2 Cascadia subduction event 34 4.3.3 Future design level earthquake 35 4.4 Annual occurrence rates and earthquake probabilities 37 4.4.1 Earthquake probability determination 37 4.5 Earthquake records selected for present study 38 4.5.1 Loma Prieta earthquake 38 4.5.2 El Centra earthquake 39 4.5.3 Miyagi earthquake 40 4.6 Ground motion amplifications and site-specific design spectra 41 4.7 Site-specific record generation 46 4.7.1 Computer program SYNTH 46 4.7.2 Modified records 47 CHAPTER 5: NON-LINEAR ANALYSIS AND D A M A G E STATE ASSESSMENT 52 5.1 General aspects of the Colquitz bent modelling 53 5.2 Non-retrofitted Vs retrofitted pier 55 5.3 Moment-curvature and push over analyses for Colquitz pier 57 5.4 Damage indices 60 5.4.1 Park and Ang damage index 61 5.4.2 Residual energy damage index 62 5.4.3 Categorization and calibration of damage 64 5.4.4 Discussion 65 5.5 Non-linear dynamic analysis and damage index determination 66 5.5.1 Computer program CANNY 66 5.5.2 Analysis results 68 5.5.3 Damage index summary 72 v 5.6 Additional damage indicators for Colquitz 73 5.7 Damage indicators for Interurban overpass for safety retrofit 78 CHAPTER 6: ESTIMATION OF DAMAGE COSTS 81 6.1 Direct damage costs 81 6.1.1 Relating direct damage costs to damage states 82 6.1.1.1 Direct damage costs for Colquitz south bridge 89 6.1.1.2 Direct damage costs for Interurban overpass 91 6.2 Indirect damage costs 92 CHAPTER 7: DECISION AND SENSITIVITY ANALYSIS 95 7.1 Net present cost (NPC) criterion 95 7.2 Decision cost comparisons 97 7.3 Sensitivity analysis 99 7.4 Discussion 102 7.5 Decision making with out probability knowledge 104 7.6 Summary 108 CHAPTER 8: BRIDGE RETROFIT PRIORITIZATION PROCEDURES 109 8.1 Existing screening procedures 110 8.1.1 The ATC/FHWA methodology 110 8.1.2 The CALTRANS procedure I l l 8.1.3 TheWSDOT approach 113 8.1.4 The IDOT scheme 114 8.1.5 Methodology proposed by Basoz and Kiremidgian 115 8.1.5.1 Vulnerability assessment 116 8.1.5.1.1 Seismic hazard analysis 116 8.1.5.1.2 Classification of bridges 117 8.1.5.1.3 Fragility analysis 118 8.1.5.2 Importance assessment 119 8.1.5.3 Overall ranking 120 8.2 Proposed methodology 121 8.3 Results 121 8.4 Discussion 123 CHAPTER 9: CONCLUSIONS AND APPLICATION OF PROPOSED METHODOLOGY 125 9.1 Conclusions 125 9.2 Application of proposed methodology 128 REFERENCES 130 APPENDIX A: 135 APPENDIX B: 145 o APPENDED C: 161 APPENDIX D: 166 v i i LIST OF FIGURES CHAPTER 2 Figure 2.1: Elevation of the Colquitz south structure 10 Figure 2.2: Photograph of the Colquitz pier and superstructure looking east 11 Figure 2.3: A view of the Interurban overpass roadway 17 Figure 2.4: A view from underneath the Interurban overpass showing Pier No.2 and the steel superstructure 17 CHAPTER 3 Figure 3.1: General layout of a decision tree 24 Figure 3.2: Decision analysis tree for bridge retrofit problem 29 CHAPTER 4 Figure 4.1: Victoria 10%/50 year robust UHRS (50th percentile values) (Private correspondence, 1999) 34 Figure 4.2: Cascadia subduction earthquake scenario spectrum (84th percentile values) for Victoria (Private correspondence, 1999) 35 Figure 4.3: Victoria 2%/50 year robust UHRS (50* percentile values) (Private correspondence, 1999) 36 Figure 4.4: Loma Prieta earthquake acceleration time history 39 Figure 4.5: El Centro earthquake acceleration time history 40 Figure 4.6: Miyagi subduction earthquake acceleration time history 41 Figure 4.7: Design spectra for bridge sites with soil amplification effects 45 Figure 4.8: Firm ground and site-specific design spectra 45 Figure 4.9: Target and computed spectra for level-1 earthquake 48 Figure 4.10: Target and computed spectra for level-2 earthquake 48 Figure 4.11: Target and computed spectra for level-3 earthquake 48 Figure 4.12: Acceleration time histories for level-1 earthquake 49 Figure 4.13: Acceleration time histories for level-2 earthquake 50 Figure 4.14: Acceleration time histories for level-3 earthquake 51 CHAPTER 5 Figure 5.1: (a) Colquitz bridge prototype pier (b) SDOF lumped-parameter model.... 54 Figure 5.2: Simplified bi-linear moment-curvature for non-retrofitted Colquitz pier.. 58 Figure 5.3: Simplified bi-linear moment-curvature for retrofitted Colquitz pier 58 Figure 5.4: Push over curve for non-retrofitted Colquitz pier 59 Figure 5.5: Push over curve for retrofitted Colquitz pier 59 Figure 5.6: Residual energy index model elaboration 63 Figure 5.7: CANNY sophisticated bilinear/trilinear hysteresis model (From CANNY-E technical manual, 1996) 67 Figure 5.8: Analysis results for level-1 earthquake 69 Figure 5.9: Analysis results for level-2 earthquake... 70 Figure 5.10: Analysis results for Ievel-3 earthquake 71 CHAPTER 6 Figure 6.1: Deterministic mapping for direct damage estimation (From Gunturi and Shan, 1993) 83 Figure 6.2: DDI Vs damage state plots for various bridge components 85 CHAPTER 7 Figure 7.1: Hurwicz rule results for different values of a 106 CHAPTER 8 Figure 8.1: Hierarchical order for primary structural attributes (From Basoz and Kiremidgian, 1996) 117 Figure 8.2: A generic fragility curve 118 LIST OF TABLES C H A P T E R 2 Table 2.1: Retrofit strategies for Colquitz south structure 15 Table 2.2: Retrofit activity costs for Colquitz south structure 21 Table 2.3: Costs for different retrofit levels as defined for Colquitz south structure... 22 Table 2.4: Break down of safety retrofit costs for Interurban overpass 22 C H A P T E R 4 Table 4.1: Annual probabilities of various earthquake levels 38 Table 4.2: Description of various site classes based on soil average shear wave velocity (Private correspondence, 2000) 42 Table 4.3: Values of Fa as a function of site class and T=0.2 sec spectral acceleration (Private correspondence, 2000) 44 Table 4.4: Values of Fv as a function of site class and T=1.0 sec spectral acceleration (Private correspondence, 2000) 44 C H A P T E R 5 Table 5.1: Damage classification according to Park and Ang (1985) 64 Table 5.2: Damage classification according to Stone and Taylor (1993) 64 Table 5.3: Proposed damage classification by Hindi and Sexsmith (2001) 65 Table 5.4: Damage index values for the base scenario 72 Table 5.5: Damage index values for the upper bound damage scenario 73 Table 5.6: Damage assessment of Colquitz for retrofit A 74 Table 5.7: Damage assessment of Colquitz for retrofit B 75 Table 5.8: Damage assessment of Colquitz for retrofit C 76 Table 5.9: Damage assessment of Colquitz for retrofit D 77 Table 5.10: Damage assessment of Interurban overpass for retrofit C 79 C H A P T E R 6 Table 6.1: Assumptions for bridge component cost assessment 86 Table 6.2: Average replacement costs for various bridge types in 1995 US dollars (from Caltrans, 1995) 87 Table 6.3: Replacements costs in millions, 2001 CDN dollars 88 Table 6.4: Removal and total costs in millions, 2001 CDN dollars 88 Table 6.5: Direct damage costs for the base scenario (2001 CDN dollars) 90 Table 6.6: Direct damage costs for the upper bound damage scenario (2001 CDN dollars) 91 x Table 6.7: Direct damage costs for Interurban overpass safety retrofit (2001 C D N dollars) 92 Table 6.8: Assumed closure days and indirect costs for Colquitz (Base scenario) 93 Table 6.9: Assumed closure days and indirect costs for Colquitz (Upper bound damage scenario) 94 Table 6.10: Assumed closure days and indirect costs for Interurban overpass for safety retrofit (2001 C D N dollars) 94 CHAPTER 7 Table 7.1: N P C s for direct costs only (Base scenario) 97 Table 7.2: N P C s for direct plus indirect costs (Base scenario) , 98 Table 7.3: N P C s for direct costs only (Upper bound damage values) 98 Table 7.4: N P C s for direct plus indirect costs (Upper bound damage values) 98 Table 7.5: N P C s corresponding to different i values and direct costs only T = 100 years, F C R F / S F R F = 1.5 (Base scenario) 100 Table 7.6: N P C s corresponding to different i values and direct plus indirect costs T = 100 years, F C R F / S F R F =1.5 (Base scenario) 100 Table 7.7: N P C s for direct plus indirect costs after increasing indirect costs corresponding to base scenario T = 100 years, F C R F / S F R F = 1.5 101 Table 7.8: N P C s for direct plus indirect costs after decreasing indirect costs corresponding to upper bound damage scenario T = 100 years, F C R F / S F R F = 1.5 101 Table 7.9: N P C s for direct plus indirect costs for i=4%, T = 100 years and F C R F / S F R F =1.4 102 Table 7.10: N P C s for direct plus indirect costs for i=4%, T = 100 years and F C R F / S F R F = 1.33 102 Table 7.11: Consequence matrix for direct plus indirect cost scenario corresponding to the lower bound damage case i = 4%, F C R F / S F R F =1.5 105 Table 7.12: M in imin and Max im in rule results 105 Table 7.13: Regret matrix for the Min imax regret rule 107 Table 7.14: Min imax regret rule results 107 CHAPTER 8 Table 8.1: Priority index calculation for Colquitz and Interurban 122 Table 8.2: Priority index determination for Interurban for different percentages of estimated consequence cost 123 ACKNOWLEDGEMENTS I am immensely grateful to my supervisor, Dr Robert.G.Sexsmith for providing me with guidance, ideas and advice during this research work. I would like to thank Dr. R.O.Foschi and Dr.D.L.Anderson for their help and guidance. I also wish to express my appreciation to Mr. Peter Brett and Mr. Brock Radloff of BC MoTH for helping me in getting technical information about the bridges selected for this study. Above all, I am heavily indebted to my parents who provided me with financial and moral support and encouragement during this time. The financial support of the Natural Sciences and Engineering Research Council of Canada and the BC MoTH is gratefully acknowledged. xii Chapter 1 - Introduction CHAPTER 1 INTRODUCTION It is important for a transportation system to remain functional after an earthquake so that rescue activities can take place and long and short-term economic losses are minimized. Bridges, being an essential part of the transportation network, are a risk to the functionality of a transportation network. A great deal of effort is currently being put into retrofitting bridges in North America and other parts of the world so that they can withstand these catastrophic events while maintaining the required degree of functionality. The present study is a continuations of work aimed at obtaining the aforementioned objective. 1.1 B A C K G R O U N D : The province of British Columbia is located in one of the most earthquake prone zones in the world, the risks of getting a devastating earthquake here being greater than in any other part of Canada. This region has had earthquakes of similar magnitude and intensity in the past as the ones that have recently happened in Turkey, Taiwan, Kobe, California and India. Due to a considerable increase in population, such an earthquake could cause much more damage i f it were to happen today. This damage would not only comprise of life loss but would also have long-term economic consequences from a transportation network perspective due to increased traffic congestion and long detours resulting in lost work time, business losses and other miscellaneous indirect factors. 1 Chapter 1 - Introduction 1.1.1 BRIDGE RETROFIT IN BRITISH COLUMBIA: The British Columbia Ministry of Transportation and Highways (BC MoTH) started a program of bridge upgrading in 1989 to ensure that bridges built before the 1983 A A S H T O requirements would be as safe as possible before the next major earthquake. A brief compendium of the objectives of this program is as follows (BC MoTH, 2000): 1. To minimize the risks of bridge collapse 2. To ensure that important highway routes are preserved for disaster response and economic recovery after earthquakes 3. To reduce damage, life loss and injury during earthquakes A total of 1100 bridges in the high-risk seismic zones of western British Columbia were initially selected for screening purposes while 470 out of those were identified as potential retrofit candidates. The program decisions for the remaining bridges have been deferred at this time but they might be included in the retrofit program in future. The taxonomy of bridges for the purpose of retrofit is as below (BC MoTH, 2000): A. Lifeline Bridges, which are some of the essentially important and major structures in the Lower Mainland such as Oak Street, Mission, Pattullo, Port Mann, Second Narrows, etc and others. B. Disaster Response Route (DRR) Bridges, which are part of a system of routes in the Lower Mainland and on Vancouver Island and hence, most exposed to earthquakes. Disaster Response Routes are such corridors, which must be available for emergency vehicle response following a disastrous earthquake. 2 Chapter 1 - Introduction C. Bridges on Economic Sustainability Routes (ESR's), which are part of corridors in the Lower Mainland, and on Vancouver Island considered essential for maintaining minimum effective transportation for economic survival after a major event. D. Other Bridges, comprising of the remaining not so critical ones in terms of emergency response operations and post-earthquake economic sustainability or recovery. 1.1.2 RETROFIT L E V E L S FOR A C C E P T A B L E PERFORMANCE: Several retrofit options and scenarios could be considered for a defined performance objective for a bridge. The underlying factors for selecting a specific level of retrofit for a given structure are its seismic vulnerability, which depends on the site seismicity and structural deficiencies, and the importance of the route on which it is located. The importance attributes consist of traffic access, detour lengths, loss of time and business, expected life loss (if any), etc. The B C MoTH has defined the following retrofitting levels for recommended seismic performance criteria (BC MoTH, 2000): A. Superstructure Retrofitting, which precludes possible unseating of bridge superstructures by tying spans to supporting piers or abutments. Devices such as restrainer cables, shear keys, etc can be used for this purpose. It might also be warranted in certain cases to repair egregious deficiencies in the substructure to ensure the effectiveness of restrainers. Inadequate single column piers with lap splices etc can be cited as an example in this regard. B. Safety retrofitting which is described as the prevention of collapse during the design earthquake that has a return period of 475 years. New bridges are required by current codes to withstand this design level earthquake without collapse and hence it can be 3 Chapter 1 - Introduction assumed that Safety Retrofitting provides a safety level, which is comparable to that of ordinary new bridges designed according to the present codes. Although not guaranteed, it is expected that bridges that have undergone safety retrofit will be usable, at least for emergency vehicles, after a design level earthquake. C. Functional Retrofitting is more of a general term encompassing rigorous and more extensive retrofitting designed to provide a higher level of assurance that bridges wil l remain in service after an earthquake. Functional Retrofitting can be assumed to provide such performance levels for retrofitted bridges that are comparable to the ones specified by recent codes for important new bridges. As per the program of the BC MoTH, the Lifeline bridges and bridges on or crossing the Disaster Response Routes are being given the highest priority. These are initially being provided with Safety level retrofit. The level of protection for selected Lifeline and Disaster Response Route bridges may be upgraded in future to have a greater assurance that they will remain in service after the design level earthquake. The need for this additional work will however have to be assessed in light of the current performance of bridges in recent earthquakes to ascertain whether the additional expenditure is justified or not. Bridges carrying traffic on Economic Sustainability Routes are being provided with Safety retrofitting. Decisions regarding the less important \"Other\" bridges are being deferred at this time. It is however expected that a majority of these bridges will require some retrofit and most of these would be retrofitted with the Superstructure retrofit option initially. Selected ones may be provided with a higher level in future. It should be noted that some bridges may already meet the required seismic performance criteria or it may be more cost effective to not go for any kind of retrofit. 4 Chapter 1 - Introduct ion Hence the option of no retrofit must always be considered while exploring the effectiveness of various retrofit levels for a specific structure or a set of bridges. 1.2 OBJECTIVES OF STUDY: The primary and foremost objective of this study is to develop and illustrate a risk-based methodology so that given a number of alternatives, the optimal retrofit strategy can be determined for a structure (or a set of structures) based on decision analysis principles employing probability and risk attributes. This entails various steps such as, the identification of required information, how it can be obtained, and how it can be organized in a decision analysis algorithm. Using the decision analysis methodology was thought to be the most appropriate strategy for rational decision-making in the face of inexact or uncertain information. Another main objective of this study is to analyse the sensitivity of data and its influence on the decision outcome since the information about damage states and the corresponding \"consequences\" is quite subjective and relatively crude. A comparison for ascertaining the effectiveness of decision analysis techniques not using probability and risk attributes in structural retrofit decision-making is also carried out. Finally, a brief review of the screening procedures that are currently in use for ranking potential candidates for retrofit is given in Chapter 8. A secondary objective of devising a two-step methodology for assigning priority indices to bridges based on a cost-to-benefit ratio approach is also illustrated thereafter. 5 Chapter 1 - Introduct ion 1.3: SCOPE OF STUDY: Two bridges located on the disaster response route on Vancouver Island were selected for the purpose of this study. The two structures are located quite close to each other and therefore promised to be good candidates for the sake of comparison. The Colquitz river south structure was selected to illustrate the primary objectives of this study in detail i.e. to determine optimal retrofit strategy level for a given structure using decision analysis employing probability and risk attributes, carry out sensitivity analyses, and examine the effectiveness of decision analysis techniques that do not consider probability and risk attributes. The initial assessment of Colquitz was based on the information provided by Choukalos Woodburn Mckenzie Maranda Ltd (Choukalos Woodburn Mckenzie Maranda Ltd, 1994). This is however carried out only for the earthquake with a return period of 475 years. Due to our increased knowledge about the seismicity of B C , the Cascadia subduction scenario and the earthquake with a return period of 2500 years are now considered critically important. Hence all three levels of seismicity were considered for this study. Since Colquitz is a single-pier, single-column structure, the pier is the most vulnerable component in this bridge. The pier was therefore subjected to detailed non-linear analyses to gain insight into the physical damage states of the bridge corresponding to different levels of seismicity. In order to drive the analyses, three earthquake records were selected and scaled to site-specific response spectra corresponding to each level of seismicity. Two damage index definitions were used to predict and compare the nature and extent of damage in the bridge pier. Since the damage index approach can be used readily only for concrete bents presently, damage in other vulnerable bridge components was considered from a demand-to-6 Chapter 1 - Introduction capacity ratio point of view. The Choukalos Woodburn Mckenzie Maranda Ltd report (Choukalos Woodburn Mckenzie Maranda Ltd, 1994) outlines various deficiencies and gives demand-to-capacity ratios for different components corresponding to the earthquake with a return period of 475 years. Using this information and the likely increase in force demands for higher levels of seismicity from the site-specific spectra along with expert judgment, overall scenarios for four different levels of retrofit were considered for the bridge and the physical damage states were translated into dollar damage by deterministic mapping procedures. Indirect damage costs for this structure due to economic loss were also taken into consideration. This dollar damage information was then treated as \"consequences\" and used in an \"expected value\" decision analysis algorithm to ascertain the optimal level of retrofit. Sensitivity analyses were then carried out to see i f changes in different input parameters affected the decision outcome. The second structure, namely, the Interurban overpass, was used to have a comparison between the two bridges for retrofit priority purposes. In order to assign a priority index to a bridge, one ought to know the optimal retrofit level for the specific structure. This exercise was not carried out for this bridge and it was assumed that the \"Safety Retrofit\" (as carried out by the BC MoTH) would be the optimal strategy for this overpass. Damage for the safety level retrofit and the no retrofit scenarios for this structure was assessed on the basis of information provided by Sargent and Vaughan (Sargent and Vaughan, 1998). Priority indices were calculated for both structures to find out the order of retrofit given a hypothetical situation of paucity of funds. This methodology can be extended to set priorities for any number of structures being considered for retrofit. This is of particular importance when funds are scarce, all 7 Chapter 1 - Introduction structures cannot be retrofitted simultaneously and the goal is to make cost effective decisions to gain maximum benefits in terms of money spent and the corresponding levels of safety that can be achieved. Since the two selected structures were retrofitted in different years, the hypothetical decisions examined in his study i.e. determining the optimal retrofit level for Colquitz bridge and the correct order for retrofitting the two candidates are considered for the year 2001. 8 Chapter 2 - General bridge and retrofit description CHAPTER 2 G E N E R A L BRIDGE A N D RETROFIT DESCRIPTION 2.1 COLQUITZ RIVER SOUTH STRUCTURE: The Colquitz river south bridge is located in Victoria on Vancouver Island, and is a critical structure on the disaster response route. The bridge was constructed in 1977. 2.1.1 GEOMETRIC A N D STRUCTURAL DESCRIPTION: The Colquitz South Structure consists of two spans. It is a single bent bridge with a fixed single column. The two spans are almost equal, being 37.743m and 37.759m respectively, and the total span is 75.502 m from back to back of diaphragms. The central pier is circular in shape with an approximate diameter of 1.68m. The length from the top of the footing to the bottom of the cap beam is 6.42m. The pier supports a cap beam cantilevering on both sides of the column. The cap beam is 2.06m deep at the top of the pier and uniformly tapers off to a depth of approximately lm at the farthest points on both sides of the column. The total length of the cap beam is 9.63m and it supports 5 steel girders, which are continuous over the pier. The 200mm thick bridge deck is then supported over the steel girders. The bridge superstructure has no apparent skew. The column supporting the above-described system has 40-3 5M bars as longitudinal reinforcement while 15M spirals at a pitch of 75mm is provided as transverse or shear reinforcement and confinement. There is a 1.38m long lap splice provided at the base of the pier. The pier is founded on battered H-piles. The 9 Chapter 2 - General bridge and retrofit description superstructure is fixed to the pier but the abutments are expansion type as the connection here is through neoprene bearings. The steel girders are composite with the deck in the positive moment regions, being connected through Nelson studs. The abutments are \"push-through\" type carried by battered, concrete filled pipe piles. The girders are therefore embedded in a concrete diaphragm at their ends, bearing directly against the end fill. Short ballast wall sections project behind the diaphragm at both ends thus separating it from the fill. Figure 2.1: Elevation of the Colquitz south structure 10 Chapter 2 - General bridge and retrofit description Figure 2.2: Photograph of the Colquitz pier and superstructure looking east 2 . 1 . 2 STRUCTURAL DEFICIENCIES: Although overall problems seemed to be minimal with this structure, there were quite a few deficiencies that needed to be addressed and retrofitted. It should be kept in mind that these defects are pertinent to the design level earthquake with a return period of 475 years. The deficiencies assessed by the Choukalos Woodburn Mckenzie Maranda Ltd about this structure are summarised as follows (Choukalos Woodburn Mckenzie Maranda Ltd, 1994): 2 . 1 . 2 . 1 SUPERSTRUCTURE: The superstructure shows no noticeable deficiencies. The deck is integral with end concrete diaphragms over the abutments while the superstructure is composite with the deck and has the capability to span in case the pier forms a pin at the base. A small deficiency however does exist in transferring the loads out of the deck and into the 11 Chapter 2 - Genera l bridge and retrofit descript ion diaphragm at the pier. This is due to the fact that the steel is non-composite over the pier and the force transfer from deck to girder is through bond only which is considered to be an unreliable load path. 2.1.2.2 BEARINGS: The \"Spencer\" type fixed bearings at the pier are thought to exhibit adequate level of performance as the internal high tensile bolts and the anchor bolts have ample capacity to transfer the lateral forces given each bearing picks up its due share of load. There is good reason to believe that the load would be shared uniformly since the deck delivers load to each girder directly and also because the girders are connected transversely with cross frames. The bearings show a good deal of reserve even i f there is an \"unzippering\" effect that leads to non-uniform load sharing and hence causes the failure of one bearing. Also, the fact that the there might be column base hinging means that loads on the bearing would be further reduced. The elastomeric pads used as bearing at the abutments however show a deficiency since they do not have enough friction capacity to prevent movement transversely. The keeper angles intended to restrain the bridge transversely would therefore be grossly over loaded for the design level earthquake. 2.1.2.3 PIER: The bridge is continuous longitudinally and the longitudinal loads are primarily taken care of, by the passive resistance at the abutments. This is due to the high stiffness of the abutments relative to the pier, which limits the overall displacement in the 12 Chapter 2 - General bridge and retrofit description longitudinal direction, meaning that the pier forces in this direction are not critical. However the column does indicate a tendency of lap splice failure under transverse loading despite the 1.38m of lap provided. This is due to the presence of heavy reinforcement and thus inadequate amounts of transverse steel to confine the splice. Although the pier forms a pin or partial pin/hinge at the base, this would not amount to over all failure since the load is shed through the superstructure to the abutments, which need further assessment. Shear in the column is not thought to be a problem. 2.1.2.4 ABUTMENTS: Longitudinal loads are carried through passive resistance of the end fill bearing on the diaphragm. The bearing area in this case is equal to the height of the diaphragm and is just adequate given the Caltrans maximum recommended values for the design level earthquake forces. Since the diaphragm actually bears against the ends of the short ballast wall, these portions could potentially fail in bending. The piles carry the most of the transverse forces. The seat lengths at the abutment bearings are inadequate according to ATC6-2. It should however be noted that the predicted movements corresponding to the design level earthquake forces using multi mode spectral analysis are much less than the provided seat length. 2.1.2.5 PILES A N D FOUNDATIONS: The piles beneath the pier foundation have sufficient capacity to carry vertical loads. The dead load of the structure could easily be supported on the central piles even i f 13 Chapter 2 - General bridge and retrofit description the pier pile cap was to fail in tension at the top. There is no indication of pile capacity for the abutments under transverse loading. The pile group just appears to be adequate for the design level earthquake forces based on the nominal capacity value of 40 kips per pile as per Caltrans specifications. 2.1.3 RETROFIT SCENARIOS FOR COLQUITZ SOUTH BRIDGE: The retrofit strategies proposed for considering different retrofit levels for the Colquitz south structure are given in Table 2.1. The proposed safety retrofit is the same as was carried out by the BC MoTH for this structure as part of their retrofit program while other levels are hypothetical in nature suggested merely for the purpose of this study. The pier retrofit was considered as part of the safety retrofit since it can likely retain its axial capacity after a splice failure for a 10% in 50 years earthquake. The abutment backfill and piles are just adequate for the force levels being considered. Their retrofit is considered as a part of the functional retrofit to provide greater assurance for vehicular access after an earthquake. 14 Chapter 2 - General bridge and retrofit description TABLE 2.1: Retrofit strategies for Colquitz south structure RETROFIT A RETROFIT B RETROFIT C RETROFIT D (NO RETROFIT) (SUPERSTRUCTURE (SAFETY (FUNCTIONAL RETROFIT) RETROFIT) RETROFIT) Leave the structure 1 .Add new seat extensions 1. Include all of 1 .Include all of as it is and accept at abutments. retrofit B. retrofit C. the future 2.Add shear stud 2. Add new shear 2. Retrofit the consequences connectors to girders over keys at abutments. abutments. pier. 3. Add steel jacket 3. Retrofit the to confine column abutment diaphragms splice. and piles. 2.1.4 SITE SOIL CONDITIONS FOR COLQUITZ: The bridge site comprises of different types of soils at varying depths. The top 1.8m contain loose brown and grey sandy gravel and some traces of clay. Mottled brown silty clay and some traces of sand and some gravel to 50 mm diameter are present from a depth of 1.8m to 5.2m. From a depth of 5.2m to 16.5m, there is soft to firm silty clay along with medium plastic sand in seams. There is clayey gravel present from a depth of 16.5m to 18.6m. The average shear wave velocity based on the information given about the top 18.6m of soil is 153.72 m/s. 15 Chapter 2 - General bridge and retrofit description 2 . 2 INTERURBAN OVERPASS: The interurban overpass (Portage Creek Bridge) was constructed in 1983 and crosses the Interurban road and Colquitz river at McKenzie avenue in Victoria on the Vancouver Island. It is also a part of the DRR on the Vancouver Island like the Colquitz river south structure. 2 . 2 . 1 GEOMETRIC A N D STRUCTURAL DESCRIPTION: The Interurban overpass is three spans; double bent steel structure, which is 125.38m long having a central span of 49.85m. The two unequal end spans are 44.95m and 30.58m. Each bent comprises of two concrete piers with a cap beam while the superstructure is a concrete deck having a roadway width of 15.9m along with 1.53m wide sidewalks and aluminium railings. The concrete piers and abutments are founded on steel H piles. The only fixed bearing is at the east abutment with all other ones being expansion type. A l l columns are approximately 1.68m in diameter. The pier no.l and pier no.2 columns have 22-35M and 29-35M bars respectively as longitudinal reinforcement. A l l four columns have 15M spirals at 75mm pitch as transverse reinforcement. The cap beam is 2.14m deep and 19.11m in length with an over-hang of 3.13 m beyond each column. The height of columns from the top of the foundation to the bottom of the cap beam for pier no.l is 7.64m while that for pier no.2 is 4.13m. The superstructure comprises of an assembly of girders, floor beams and stringers. 16 Chapter 2 - General bridge and retrofit description Figure 2 .3 : A view of the Interurban overpass roadway 2.2.2 STRUCTURAL DEFICIENCIES: The following deficiencies exist in the as-built structure (Sargent and Vaughan Engineering Limited, 1999): 17 Chapter 2 - General bridge and retrofit description 2.2.2.1 GIRDER DIAPHRAGMS: The necessity to transfer large forces from the deck slab to the piers and abutments means that there would be a failure of the connections between the existing floor beams and the girders, thus leading to their instability and collapse. 2.2.2.2 ANCHOR BOLTS: The forces generated from the superstructure would grossly overload the anchor bolts at the abutments and the piers leading to insufficient transverse restraint. This is a similar problem regarding the longitudinal resistance of anchor bolts at the fixed bearing of the east abutment. 2.2.2.3 PIER A N D A B U T M E N T PILES A N D FOUNDATIONS: It is expected that the pier piles would survive the design seismic event forces in combined bending and axial load although only marginally. Pile pull out at piers is also not a big problem although the assumption of rocking motion of the pier footings does push the limits of pile capacity along with causing potential shear failure of the pile caps. Pile pull out at the east abutment is somewhat of a bigger concern due to the fixed nature of connection between the superstructure and the abutment. Also, the toe projection at the east abutment pile cap footing shows a potential for shear failure i f the piles beneath the backwall retain their anchorage. 18 Chapter 2 - General bridge and retrofit description 2.2.2.4 COLUMNS IN PIERNO.2: A redistribution of forces after the formation of plastic hinges in columns of pier no.l causes higher shear forces to be resisted by the columns in pier no.2. Since the push over analysis shows a shear failure in pier no.2 columns before forming a plastic hinge, the aforementioned redistribution would cause a sudden shear failure, which is an unacceptable mode of failure. 2.2.2.5 A B U T M E N T B A C K W A L L : The east abutment backwall could fail in bending under passive pressure due to longitudinal loads from the superstructure. 2.2.3 RETROFIT OF INTERURBAN OVERPASS: As mentioned in chapter 1, the Interurban Overpass was only considered for having a comparison of priority indices for the two structures. For the sake of illustration, it was deemed reasonable to assume that the Safety Retrofit level (as carried out by the B C M o T H for this structure) would be the optimal strategy for this bridge. Hence only the Safety Retrofit scenario is described herein for the stated bridge. A summary of the pertinent details is as follows (Sargent and Vaughan Engineering Limited, 1999): (a) Introduce diaphragm braces at the floor beams over the piers and abutments. Reinforce floor beam to exterior girder connections with welds to prevent block tear out at the end of the beam. 19 Chapter 2 - General bridge and retrofit description (b) Anchor structural steel weldments to the pier caps and abutment seats for transverse restraint. Extend abutment seats to accommodate this. Add a longitudinal restrainer to the west abutment, leaving allowance for expansion. (c) Provide FRP wraps to increase the shear capacity without altering the moment capacity in order to prevent the sudden shear failure in columns of pier no. 2. (d) Strengthen the toe projection at the east abutment pile cap in shear by a concrete thickening of the footing, dowelled into the abutment wall. 2.2.4 SITE SOIL CONDITIONS FOR INTERURBAN: This bridge site has a top layer of gravel, which is about 0.5m thick. There is soft to firm brown silty clay from a depth of 0.5m to 5.5m. Soft to firm grey silty clay is present along with traces of medium plastic fine sand from a depth of 5.5m to 15.0m along with some gravel which is 20mm to 50mm. Below this layer, there is dense gravely sand along with some silt and small gravel up to 22.25m depth. The average shear wave velocity based on the given information is 171.61m/s. 2.3 COSTS OF RETROFIT: A break down of the costs for various retrofit measures for the two structures considered for this study is given in Tables 2.2 to 2.4. The costs corresponding to different retrofit levels are given in terms of C D N dollars for both the retrofit year of the structure and 2001 assuming an inflation rate of 4% for the Colquitz bridge. 20 Chapter 2 - General bridge and retrofit description 2.3.1 COLQUITZ RIVER SOUTH BRIDGE: The costs for retrofitting various components in the Colquitz South structure are shown in Table 2.2. A l l estimates except for the last activity are based on actual numbers given in the report by Choukalos Woodburn Mckenzie Maranda Ltd (Choukalos Woodburn Mckenzie Maranda Ltd, 1994). Since an actual retrofit was not designed for the abutment piles and diaphragm, a hypothetical value had to be assumed for this activity. The cost of functional retrofit was assumed as 1.5 times that of safety retrofit. Table 2.2: Retrofit activity costs for Colquitz south structure Retrofit Activity COST (1994 C D N $) Add new shear keys at abutments 15000 Provide new seat extensions at abutments 18000 Add shear stud connectors to girders over pier 4000 Provide steel jacket to confine column splice 15000 Retrofit abutment piles and diaphragm 26000 (assumed) The total costs for different retrofit scenarios as defined in table 2.1 would therefore be as follows: 21 Chapter 2 - General bridge and retrofit description Table 2.3: Costs for different retrofit levels as defined for Colquitz south structure RETROFIT L E V E L COST (1994 C D N $) COST (2001 C D N $) No retrofit (Retrofit A) 0 0 Superstructure retrofit (Retrofit B) 22,000 29,000 Safety retrofit (Retrofit C) 52,000 68,500 Functional retrofit (Retrofit D) 68,000 102,250 2.3.2 INTERURBAN OVERPASS: The costs for safety level retrofit for the Interurban overpass are shown in table 2.4 as follows (Sargent and Vaughan Engineering Limited, 1999): Table 2.4: Break down of safety retrofit costs for Interurban overpass RETROFIT ACTIVITY COST (1999 CDN$) Cost of Mobilization 20,000 Cost of West abutment retrofit 48,106 Cost of Pier No . l retrofit 49,080 Cost of Pier No.2 retrofit 76,400 Cost of East abutment retrofit 75,910 Total cost of Safety retrofit 264,496 The safety retrofit cost in terms of 2001 C D N $ is thus 295,000 dollars for an inflation rate of 4%. 22 Chapter 3 - Decision analysis methodologies C H A P T E R 3 DECISION ANALYSIS METHODOLOGIES 3.1 INTRODUCTION: Complex decision-making involves uncertainty due to our inability to predict accurately the factors influencing future events. Decision analysis methodologies are powerful tools that enable the decision maker to take into account all of the various factors such as different courses of action available, outcomes of nature and corresponding consequences of each outcome to arrive at the optimal decision given the miscellaneous constraints and uncertainties. Since it is impossible to take all of the aforementioned factors simultaneously into account when faced with a complex problem, decision analysis entails the decomposition of the problem into a decision tree. It starts with all possible courses of action (ai,a2,.. ..an), followed by the various possible states of nature (9 i ,02 , . . . 0 n ) and their probabilities [P(0i)P(02),1....P(Gn)] and consequences (un,ui2 , . . .uim , . . .u n m)[Figure 3.1]. A decision tree therefore starts with a decision node at the left representing alternative courses of action followed by chance nodes representing chance events that comprise of the outcome of nature. The occurrence of a chance event can be considered as a random event such as an earthquake over which the decision maker has no control. The main problem is thus decomposed into a number of smaller problems that help decide the optimal course of action through the standard folding back procedure. A detailed treatment of the folding back procedure is given by Benjamin and Cornell (Benjamin and Cornell, 1970), Fabrycky and Thuesen (Fabrycky and Thuesen 1984), and many others. 23 Chapter 3 - Decision analysis methodologies e.[P(eo] U l l Figure 3.1: General layout of a decision tree It is usually convenient to ensure that the events considered in a decision problem should be mutually exclusive and collectively exhaustive i.e. they should have no overlap and should completely fill up the sample space. The sum of their probabilities wil l therefore be equal to one. 24 Chapter 3 - Decision analysis methodologies 3.2 BASIS FOR R A N K I N G COMPETING ALTERNATIVES: A n expected value for a random variable can be calculated i f its probability mass function or probability density function is known. If we use such probability distributions to describe the profit or cost of an investment as a random variable, the expected values of these parameters can be assumed as reasonable basis for the sake of comparing alternatives. This means that the expected profit or cost of an investment proposal depicts the long-term profit or cost that would be realised i f the investment were repeated a large number of times and the pertinent probability distributions remained unchanged. Since this study focuses on bridge retrofit decision-making and as bridges are structures with considerable life spans, the expected value criterion appears to be a logical basis for comparing alternatives. Also, since the retrofit decision-making has to be done by the government, the expected value criterion seems plausible, as the money to be spent on the retrofit program on a yearly basis is small as compared to the total annual budget. This leads to an effective and logical use of the taxpayer's money on a long-term basis. 3.3 DETERMINATION OF EXPECTED V A L U E : The expected value for a course of action can be determined by solving the decision tree through the use of the \"folding back\" or \"roll back\" procedure. The following two rules have to be employed while starting from the tips of the decision tree's branches and working back towards the initial nodes: 1. If the node happens to be the first chance node, calculate the expected value of that node by summing the products of the possible outcomes and their 25 Chapter 3 - Decision analysis methodologies corresponding probabilities. For the following chance nodes, determine the expected value based on the 'folded back' values on the adjacent nodes to the right of the one being considered. 2. If the node is a decision node, select the minimum cost or maximum profit from the adjacent nodes to the right of the node under consideration. The expected costs thus obtained for each alternative have then to be discounted to the present. 3.4 DECISION TREE FOR PRESENT STUDY: The current policy by the B C MoTH is to retrofit deficient bridges for various performance levels corresponding to the current design earthquake i.e. one with a return period of 475 years. The earthquakes with smaller return periods and hence less magnitude (and intensity) are likely to cause only negligible damage to the unretrofitted bridges while retrofitted structures would most likely have no damage from the lower level earthquakes. The decision would thus be sensitive to the design level earthquake and the ones that have considerably longer return periods such as the Cascadia subduction event or the crustal event with a probability of 1 in 2500 years but not so much to the lower level earthquakes. It was therefore decided to take the design earthquake, as the lowest level to be incorporated into the decision analysis, as still lower level earthquakes would not have much of a bearing on the decision. The three different earthquake levels and hence chance events identified for the decision tree for this study (Figure 3.2) are: 26 Chapter 3 - Decision analysis methodologies (a) Earth quake level-1: Design Level Earthquake abbreviated as EQ1 on the decision tree (b) Earth quake level-2: Cascadia subduction event with a probability of 1 in 2500 years, abbreviated as EQ2 on the decision tree (c) Earth quake level-3: Crustal earthquake with a return period of 1 in 2500 years, abbreviated as EQ3 on the decision tree The probabilities of occurrence of various earthquakes as shown in the decision tree of figure 3.2 are annual probabilities of these events. Also, it has been assumed that the probability of having joint events in a year e.g. two earthquakes of level-1, one earthquake each of level-1 and level-2, etc is negligibly small and hence neglected. Since there is considerable variability in the nature of earthquakes even i f they have similar magnitudes, it was decided to use three different earthquake records for each level of earthquake under consideration. This could lead to considerably different damage states and hence different consequences for each level of earthquake. The states of nature were therefore identified as different damage levels corresponding to each earthquake level. Assigning a probability of 1/3 to each damage level corresponding to the same level of seismicity was based on the \"Laplace principle\" or the \"Principle of Insufficient Reason\". It effectively means that in the absence of other information, each damage state is considered equally likely. The three earthquake records used in the present study are Loma Prieta (LP), E l Centro and Miyagi (MI) and would be referred to as record-1, record-2 and record-3 respectively in the subsequent chapters. The consequences associated with experiencing a certain type of earthquake for a given level and a given retrofit strategy are shown at the tip of the decision tree. The 27 Chapter 3 - Decision analysis methodologies letter \" C \" denotes the consequence index while the first subscript shows whether the damage corresponds to the first, second or third record used. The second subscript is for the level of earthquake and hence 1,2 and 3 show the design level earthquake, the Cascadia subduction event and the crustal event with the return period of 1 in 2500 years. The following alphabets designate the level of retrofit for which the consequences have been calculated. The possible courses of action are clearly the retrofit options available, identified as NRF (for no retrofit), SSRF (for superstructure retrofit), SFRF (for safety retrofit) and FCRF (for functional retrofit) in the decision analysis tree as shown in figure 3.1. As an example, the expected value E (per annum) of NRF would be give by: E (NRF) = S l , N R F * P l + S 2,NRF*P2 + S 3 ,NRF *P3 where, 51, N R F - C l l N R F * l / 3 +C21NRF*l/3 + C 3 i N R F * l / 3 52, N R F = C ] 2 N R F * l / 3 + C 2 2 N R F * l / 3 + C 3 2 N R F * l / 3 53, N R F = C l 3 N R F * l / 3 + C 2 3 N R F * l / 3 + C 3 3 N R F * l / 3 Si, S2 and S3 values for other retrofit scenarios can be similarly determined using the corresponding consequence indices. Expected values per annum for other alternatives can then be determined and discounted to the present for the purpose of comparison. 28 Chapter 3 - Decision analysis methodologies H3(Pi) B$(P2) H?(P3) NRF S5KF H3(Pl) XiS) Q.SSRF 03i Qgj^ IiS)— G i s w •05)— G s w GZSSSF H?(P3) -Q2L -03L -m—Qs* SEW H3(P1) KHt H?(P2) H3 (H) -Q3L H?(P2) GlFOT : - (j2FOT -G2>—Ora* ClKKF -05) G K R F SM2L- Qtsw X^ 3)— C O T F -03)— GlKPF Figure 3.2: Decision analysis event tree for bridge retrofit problem 3.5 DECISION M A K I N G WITHOUT PROBABILITY V A L U E S : A decision maker may be faced with a situation wherein he or she finds it difficult to assign probabilities to future events with a sufficient degree of confidence. When dealing with earthquakes, one may find it hard to have too much confidence in assigning probabilities to events of such nature. For example, the probability of getting a 29 Chapter 3 - Decision analysis methodologies large earthquake after having one of similar nature in the recent past could be considerably smaller. It was therefore thought appropriate to look at the proposed decision problem based on the premise that there is no rational way of assigning probabilities to the associated events. This was however done only to have a comparison between the results of the two broadly different categories of decision analysis. The various methods employed for this comparison are: (a) The Maximin and the Maximax rule, which can be termed as Minimax and Minimin rules since we are dealing with costs for our problem. The first rule is based on an extremely pessimistic view of the outcome of nature while the second one is based on an extremely optimistic view of the outcome of nature. (b) The Hurwicz rule which embraces a relative degree of optimism and pessimism through an index of optimism a, which varies between 0 and 1. (c) The Minimax Regret rule has a conservative underlying philosophy as it seeks to minimize the maximum regret for a given set of actions. The effectiveness of these techniques is examined and discussed in Chapter 7 along with sensitivity analyses. 30 Chapter 4 - Seismic hazard evaluation CHAPTER 4 SEISMIC HAZARD EVALUATION Evaluation of the nature, extent and likelihood of seismicity is an essential part of obtaining data to be used for damage state assessment and the decision analysis algorithm. This chapter discusses in detail the various aspects of seismic hazard evaluation and elucidates the methodology adopted for the purpose of this study. The determination of earthquake occurrence rates and probabilities, selection of earthquake records, ground motion amplification aspects and site-specific record generation are described herein. 4.1 METHODOLOGIES FOR SEISMIC H A Z A R D PREDICTION: The two fundamental procedures for seismic hazard prediction are the deterministic and the probabilistic approaches. The deterministic analyses make use of discrete, single-valued events to arrive at scenario-like description of earthquake hazard. The probabilistic methodology however allows the incorporation of multi-value or continuous events and models. Of most importance, the probability of different magnitude (or intensity) earthquakes occurring is included in the analysis (Reiter, 1990). The latter methodology can be used in two ways i.e. by developing the response spectrum for a specific value of peak ground acceleration or by constructing the uniform hazard response spectrum (UHRS) for the site under consideration. A thorough discussion of the 31 Chapter 4 - Seismic hazard evaluation probabilistic seismic analysis is given by the EERI committee on seismic risk (EERI committee on seismic risk, 1989). Since the bridges for this study are located in Victoria, the spectra for Victoria for various earthquake levels (with different mean return periods or probabilities of exceedence) were used as target spectra to assess the expected seismicity at the bridge sites as explained in the following section. 4.2 SYNOPSIS OF METHODOLOGY FOR PRESENT STUDY: This study employs three different levels of earthquakes for considering the effects of various seismicity levels on the extent of damage. The three levels of seismicity considered correspond to the current code design level earthquake with a return period of 475 years, the Cascadia subduction event scenario, and the future code design earthquake with a return period of 2500 years with the level of seismicity increasing from the first to the last case respectively. Since different earthquake records have different characteristics such as the number of pulses, duration, etc, three natural earthquake records were selected for the purpose of damage state assessment corresponding to each level of seismicity. These records are from the 1940 E l Centro earthquake, the 1978 Miyagi earthquake and the 1989 Loma Prieta earthquake. The soil information for the bridge sites indicated that these are overlain by soft soils and therefore the firm-ground response spectra for Victoria corresponding to each level of seismicity were increased to take the effects of soil amplification into account. Each of the selected natural earthquake records was then modified to match its response spectrum to the site-specific (target) spectra for each 32 Chapter 4 - Seismic hazard evaluation seismicity level obtained in the previous step thus leading to nine modified records. These records were then used to drive the non-linear dynamic analysis for the Colquitz south structure. 4.3 CONSIDERED E A R T H Q U A K E LEVELS: The suggested methodology relies on an integrated approach whereby the first and third levels of earthquake considered are based on probabilistic UHRS methodology while the second level corresponds to the deterministic Cascadia subduction event response spectrum. A brief background of the various earthquake levels thus considered is as follows: 4.3.1 CURRENT DESIGN L E V E L EARTHQUAKE: Since the B C MoTH is currently retrofitting bridges to achieve certain performance objectives corresponding to the current code design level earthquake with a return period of 475 years, it was deemed reasonable to incorporate this as the basic/lowest earthquake level. As discussed in Chapter 3, the still lower level earthquakes were not considered as they would most likely cause negligible damage to the existing infrastructure and hence would not have any significant bearing on the decision outcome. The UHRS spectral values correspond to the Robust 50 t h percentile with a probability of 0.0021 p.a. on firm ground for a damping of 5% as shown in figure 4.1 (Private correspondence, 1999). 33 Chapter 4 - Seismic hazard evaluation Figure 4.1: Victoria 10%/50 year robust UHRS (50th percentile values) (Private correspondence, 1999) 4.3.2 CASCADIA SUBDUCTION EVENT: The next higher-level earthquake considered is the Cascadia subduction scenario whereby the seismicity is primarily driven by the subduction of the Juan de Fuca plate under the North American plate. There is evidence that large offshore subduction earthquakes have occurred many times in the past several thousand years with moment magnitudes M w in the range of 8-9 on the thrust fault between the subducting Juan de Fuca plate and the North American plate (At Water et al., 1995; Clague et al., 1995). Hence there is a realistic threat of damage from the subduction scenario event, which was therefore included in this study. The scenario earthquake has a magnitude Mw=8.2 on the subduction zone at the depth of 25 kilometres (Private correspondence, 1999). The response spectrum values selected for this study correspond to the 84 t h percentile values (exceeded 16% of the times). The 84th percentile values were considered for this study because the spectrum so obtained lies between the 10%/50 year UHRS and the 2%/50 year UHRS for the period 34 Chapter 4 - Seismic hazard evaluation range of interest. The spectral values for the 84 t h percentile Cascadia subduction scenario correspond to the 2% chance of exceedence in 50 years. The target spectrum for this scenario event is shown in figure 4.2 as follows: 0 1 2 3 4 5 T(sec) • Figure 4.2: Cascadia subduction earthquake scenario spectrum (84th percentile values) for Victoria (Private correspondence, 1999) 4.3 .3 FUTURE DESIGN L E V E L E A R T H Q U A K E : It is now being increasingly recognised that the threat to the Vancouver metropolitan area and Victoria stems from shallow crustal earthquakes and not so much from the subduction earthquakes. There has been a greater consensus about this opinion due to extensive work conducted by structural and geotechnical engineers over the past few years. It has to be recognised that as a society becomes more and more wealthy and at the same time aware of the damage potential of earthquakes, the level of acceptable 35 Chapter 4 - Seismic hazard evaluation risk decreases. The upcoming Canadian code to be introduced in the near future therefore specifies a higher design level earthquake with a return period of 2500 years or a probability of exceedence of 2% in 50 years (0.000404 p.a.). This is being regarded as the maximum credible earthquake level and since future performance requirements are going to be based on this level of seismicity, it was thought appropriate to include this as the highest level for the present study. The UHRS spectral values thus selected correspond to the Robust 50 t h percentile with a probability of 0.000404 p.a. on firm ground for a damping of 5% (Figure 4.3). Figure 4.3: Victoria 2%/50 year Robust UHRS (50l percentile values) (Private correspondence, 1999) 36 Chapter 4 - Seismic hazard evaluation 4.4 A N N U A L OCCURRENCE RATES A N D E A R T H Q U A K E PROBABILITIES: When considering individual zones around a site, it is normal practice to use the Gutenberg-Richter relationship to relate the magnitude of earthquakes to their recurrence rate. The relationship in its simplest from is as follows: log N = a - b M Where ' M ' is the magnitude, ' N ' is the average number of earthquakes per year with magnitude more than or equal to M while 'a' and 'b' are constants which are generally obtained by regression on a database of seismicity of the source zone of interest. 4.4.1 E A R T H Q U A K E PROBABILITY DETERMINATION: It is imperative to determine the annual probabilities of encountering the aforementioned levels of earthquakes so that the element of risk can be introduced into the decision process. The occurrence rates for level 1, 2 and 3 earthquakes are 1 in 475 years, 1 in 2500 years and 1 in 2500 years respectively (Private correspondence, 1999). Since we are dealing with events having long return periods and the chance of having more than one per annum is negligible, the annual probabilities of occurrence would be approximately equal to the annual occurrence rates. Table 4.1 gives the annual probabilities of the various earthquake levels. It should be noted that the zero-level earthquake as shown in table 4.1 comprises of all events with a lower level of seismicity as compared to the current design level earthquake. It is therefore only given for the sake of completeness. 37 Chapter 4 - Seismic hazard evaluation TABLE 4.1: Annual probabilities of various earthquake levels EQ Level Recurrence interval Annual occurrence rate Annual Probability (Pi) 0 - - 0.9971 1 1 in 475 years 0.0021 0.0021 2 1 in 2500 years 0.000404 0.0004 3 1 in 2500 years 0.000404 0.0004 » 1 4.5 E A R T H Q U A K E RECORDS SELECTED FOR PRESENT STUDY: A brief discussion about the selected earthquakes and the corresponding records is as follows: 4.5.1 L O M A PRIETA EARTHQUAKE: The Loma Prieta earthquake occurred at 5:04 pm on the 17 th of October 1989 causing 62 deaths and over $ 10 Billion US in damage. The magnitude of earthquake on the Richter scale was 7.1 and it was centred about 101 K m (60 miles) south of San Francisco. The acceleration-time history for this earthquake is shown in figure 4.4. 38 Chapter 4 - Seismic hazard evaluation t(sec) Figure 4.4: Loma Prieta earthquake acceleration time history (North-South component, Capitola fire station, 2000 points at 0.02 sec) The record shows strong shaking for about 20 seconds with a number of pulses in excess of 0.4 g in the first 10 seconds. The rumbling can be seen to continue up to about 40 seconds. 4.5.2 EL CENTRO EARTHQUAKE: The Imperial Valley E l Centro earthquake occurred on the 18 th of May 1940 causing 9 deaths and about $ 6M US in damage. It had strong motion duration of about 25 seconds. The acceleration-time history of the Elcentro earthquake is shown in Figure 4.5. 39 Chapter 4 - Seismic hazard evaluation 0.4 t(sec) Figure 4.5: El Centro earthquake acceleration time history (North-South component, Japan arch centre, 1134 points at 0.02 sec) As can be seen form the record, the Elcentro record does not have as high a P G A as that of Loma Prieta. There is only one pulse in excess of 0.3g but there is a large pulse of about 0.2g around the 12-second mark after the initial high acceleration levels seem to be on the decrease. 4.5 .3 M I Y A G I EARTHQUAKE: A subduction type earthquake record was also used in this study. This is the magnitude 7.4 Miyagi event in the Pacific Ocean off the coast of Miyagi (Japan). This earthquake occurred on the 12 t h of June 1978 resulting in the death of 27 while causing injuries to about 1100 people (Fowler, 1980). The acceleration time history shown for this record in Figure 4.6 depicts a number of pulses quite close to or in excess of 0.2g while considerable intensity of shaking can be seen to last for a longer duration as compared to the first two records. 40 Chapter 4 - Seismic hazard evaluation 0.3 -0.2 : — IM ¥ -0.3 t(sec) Figure 4.6: Miyagi Subduction earthquake acceleration-time history (North-South component, 2000 points at 0.02 seconds) 4.6 GROUND MOTION AMPLIFICATIONS A N D SITE-SPECIFIC DESIGN SPECTRA: The summary logs show that the sites for bridges selected for this study are overlain by soft soils. The average shear wave velocities calculated for the Colquitz river south structure and the Interurban overpass were 153.72 m/sec and 171.16 m/sec respectively. The soil amplification effects therefore had to be taken into account. A simple procedure employing the methodology proposed for the upcoming Canadian code was used. This procedure comprises of classifying a given soil into one of six different classes based on average soil shear wave velocity and multiplying the Sa values at different periods for the firm ground conditions with suitable coefficients depending upon the range of values at periods of 0.2 and 1.0 seconds. The various site classes defined as below in table 4.3 are based on the average properties in top 30m (Private correspondence, 2000). 41 Chapter 4 - Seismic hazard evaluation Table 4.2: Description of various site classes based on soil average shear wave velocity (Private correspondence, 2000). Site Class Soil Profile Name Soil Shear Wave Average Velocity, Vs (m/sec) A Hard Rock V s > 1500 B Rock 760 < V s < 1500 C Very Dense Soil and Soft Rock 360 < Vs < 760 D Stiff Soil 180 4.0 sec where Fa is an acceleration-based site coefficient, Fv is a velocity-based site coefficient and Sa is the 5% damped spectral response acceleration for a period T. The values of Fa as a function of site class and T=0.2 sec spectral acceleration and Fv as a function of site class and T=1.0 sec spectral acceleration are given in tables 4.4 and 4.5 respectively as follows. 43 Chapter 4 - Seismic hazard evaluation Table 4.3: Values of Fa as a function of Site class and T = 0.2 sec spectral acceleration (Private correspondence, 2000). Site class Values of Fa Sa(o.2)<0.25 Sa (0.2)= 0.5 Sa (o,2) =0.75 Sa ( 0.2)=1.0 Sa(0.2) = 1-25 A 0.7 0.7 0.8 0.8 0.8 B 0.8 0.8 0.9 1.0 1.0 C 1.0 1.0 1.0 1.0 1.0 D 1.3 1.2 1.1 1.1 1.0 E 2.1 1.4 1.1 0.9 0.9 F ~ ~ Table 4.4: Values of Fv as a function of site class and T = 1.0 sec spectral acceleration (Private correspondence, 2000) Site class Values of Fv Sa ( 0.2)<0.1 Sa(0.2)= 0.2 Sa (0.2) =0.3 Sa ( 0 . 2 ) = 0.4 Sa(0.2)>0.5 A 0.5 0.5 0.5 0.6 0.6 B 0.6 0.7 0.7 0.8 0.8 C 1.0 1.0 1.0 1.0 1.0 D 1.4 1.3 1.2 1.1 1.1 E 2.1 2.0 1.9 1.7 1.7 F ~ ~ ~ 44 Chapter 4 - Seismic hazard evaluation The design spectra corresponding to the various earthquake levels considered in this study hence obtained are shown as below in figure 4.7. Figure 4.8 shows all the six spectra (modified and unmodified) for the sake of comparison. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 2%/50 year design spectrum — — Cascadia(84th perc) scenario 10%/50 year design spectrum Figure 4.7: Design spectra for bridge sites with soil amplification effects •10%/50 years spectrum for firm ground • Cascadia spectrum for firm ground •2%/50 years spectrum for firm ground -10%/50 year spectrum with soil amplification effects -Cascadia spectrum with soil amplification effects -2%/50 year spectrum with soil amplification effects Figure 4.8: Firm ground and site-specific design spectra 45 Chapter 4 - Seismic hazard evaluation It is evident from Figure 4.8 that the site-specific design spectra are much higher than their firm ground counterparts. As can be seen from tables 4.4 and 4.5, the values of Fa and Fv vary between 2.1 and 0.9 for Soil Class E. Considering 20 and 50 percent of mass contribution from the bridge structure to the pier, the elastic period of the pier for the Colquitz bridge pier lies in the range of 0.8 seconds to 1.0 seconds. Clearly, soil amplification effects for the period range of interest are considerable. 4.7 SITE-SPECIFIC RECORD GENERATION: The final step in the seismic hazard evaluation is to obtain site specific earthquake records which would then help drive the non-linear structural analyses. The selected earthquake accelerograms were therefore modified so that their response spectra matched the obtained design spectra as described in section 4.6. The computer software S Y N T H was used for this purpose. A brief discussion about the program follows. 4.7.1 COMPUTER P R O G R A M SYNTH: S Y N T H can be used to generate artificial time histories compatible with a target spectrum. The initial time history is a real accelerogram with a maximum number of values equal to 8192 (Naumoski, 1985). There are three input files where by the user inputs information such as the number of initial and generated acceleration values, the time interval between these values, PGA, etc along with initial accelerogram values at equal time intervals, and periods and pseudo acceleration spectral values for the target spectrum. The output also comprises of three different files where by information such as 46 Chapter 4 - Seismic hazard evaluation periods and spectral values of the computed spectrum are output along with acceleration values of the generated time history. 4.7.2 MODIFIED RECORDS: The site-specific spectra determined earlier were input into S Y N T H as target spectra along with time histories for the various earthquakes. Each earthquake record was changed to match its spectrum with the three different target spectra for various earthquake levels and hence 9 different site-specific records were generated for driving the non-linear dynamic analyses of the Colquitz bridge pier. A reasonable agreement was reached between the target and computed Spectra for the various time histories by using S Y N T H as evident from Figures 4.9 through 4.11. Each of the modified records (or its spectrum) is abbreviated hereinafter by two alphabets depending on the seed record followed by the level of seismicity (1,2 or 3) to which it has been matched. EC1, LP2 and MI3, etc thus show the E l Centra record matched to the earthquake level-1 spectrum, Loma Prieta record matched to earthquake level-2 spectrum and Miyagi record matched to earthquake level-3 spectrum respectively. 47 Chapter 4 - Seismic hazard evaluation • 10%/50 years EQ target spectrum -EC1 computed spectrum • LP1 computed spectrum MM computed spectrum Period,T(sec) Figure 4.9: Target and computed spectra for level-1 earthquake 1 0.8 0.6 Sa(g)04 0.2 0 Cascadia EQ target spectrum EC2 computed spectrum LP2 computed spectrum Ml2 computed spectrum Period,T(sec) Figure 4.10: Target and computed spectra for level- 2 earthquake 2 3 Period,T(sec) -2%/50yearEQ target spectrum - EC3 computed spectrum - LP3 computed spectrum MI3 computed spectrum Figure 4.11: Target and computed spectra for level-3 earthquake The various time histories corresponding to the three different earthquake levels are shown in Figures 4.12 through 4.14. 48 Chapter 4 - Seismic hazard evaluation Figure 4.12: Acceleration-time histories for level-1 earthquake The PGA's for EC1 and LP1 occur at different times in the time histories. In LP1, there is a pulse of about 0.4g around the 14-second mark while there are a number of pulses in access of 0.25g that are absent in EC1. There is more sustained shaking in M i l lasting for a longer duration. This record has a number of pulses of 0.2g to 0.25g around the 15-second mark. 49 Chapter 4 - Seismic hazard evaluation t(sec) Figure 4.13(c)-MI2 Figure 4.13: Acceleration-time histories for level-2 earthquake It can be seen from the level-2 records that the PGA for these is less as compared to the level-1 records. However, the expected displacement demand on the structure would be more due to the shape of the target spectrum for this level. Looking carefully at the records reveals that large pulses in LP2 are more scattered during the time history and it has more pulses with amplitudes around 0.3g as compared to EC2. MI2 shows more uniform shaking with only one pulse in excess of 0.3g but a large number of pulses in excess of 0.2g. 50 Chapter 4 - Seismic hazard evaluation t(sec) Figure 4.14(c)-MI3 Figure 4.14: Acceleration-time histories for level-3 earthquake It is evident from level-3 records that the PGA for these is considerably higher as compared to records for the first two levels. EC3 has one pulse each with amplitudes around 0.8g and 0.4g. In comparison, LP3 has one pulse around 0.8g, one around 0.7g and two around 0.4g amplitude levels. More yield excursions may therefore be suspected for the bridge pier when subjected to this record. MI3 is similar to M i l and MI2 inasmuch as it has sustained, uniform shaking for a longer duration. It has one pulse of about 0.8g and a number of pulses with approximately 0.4g amplitude. The strong shaking duration is longer for this record as compared to the other two. 51 Chapter 5 - Non-linear analysis and damage state assessment CHAPTER 5 NON-LINEAR ANALYSIS AND DAMAGE STATE ASSESSMENT This chapter focuses on quantifying damage for the two bridges under consideration. The Colquitz river south structure is given a more thorough treatment whereby damage in the single column pier is assessed through non-linear analyses for different earthquake levels (using various scaled records) for each retrofit scheme as defined in Chapter 2. Damage in other structural components of this structure for various retrofits is determined on the basis of the information provided by Choukalos Woodburn Mckenzie Maranda Ltd (Choukalos Woodburn Mckenzie Maranda Ltd, 1994) and expert judgment. For the Interurban overpass, no analyses were carried out and structural damage was determined on the basis of expert judgment, information provided in the report produced by Sargent and Vaughan Engineering Ltd for B C MoTH (Sargent and Vaughan, 1999) and the trends shown by the design spectra for different seismicity levels. Safety retrofit was assumed to be the optimal strategy for the Interurban overpass and hence damage has only been assessed for this scenario. This chapter therefore illustrates the application of non-linear analysis techniques to assess pier damage with the help of damage indices. Important aspects pertinent to bridge bent modelling, damage index calibration and eliciting the overall damage for various retrofits are discussed in detail in the following sections. 52 Chapter 5 - Non-linear analysis and damage state assessment 5.1 G E N E R A L ASPECTS OF THE COLQUITZ BENT MODELLING: The Colquitz bridge is a single bent, single pier structure with a fixed column and two expansion type abutments. Since this forms a relatively simple structural configuration, it was deemed suitable to employ the Lumped-Parameter model for this bridge. The bridge bent was modelled as a single degree of freedom structure with seismic mass lumped at the top node [Figure 5.1(b)]. The column length was divided into five flexural and one rigid element. The rigid element was introduced to take into account the stiffness difference between the column and the superstructure. The length of this link was determined to be 3m starting from the lower end of the cap beam. The total length of the column thus modelled was 9.42m from the base of the column to the centre of the lumped mass. The pier has piles driven to the bedrock and was thus treated as fixed at the base. Since the bridge is longitudinally continuous and the abutment stiffness is much higher than that of the pier, the pier forces in the longitudinal direction are not critical (Choukalos Woodburn Mckenzie Maranda Ltd, 1994). The longitudinal modelling of the bridge bent was thus avoided. In order to calculate the value of the lumped mass at the top of the pier, a small linear elastic model of the bridge was produced. Hand calculations showed that for an infinite stiffness of the abutments as compared to the pier, the pier would attract approximately 12.5% of a unit uniform load applied at the super structure level taking the deck stiffness into account. Since the effects of shear deformation and abutment flexibility were neglected in the calculations, the lumped mass value was determined by taking 20% of the super structural mass, half of the column mass and the mass of the 53 Chapter 5 - Non-linear analysis and damage state assessment beam to account for abutment flexibility and shear deformation. This was thought of as a reasonable estimate and was treated as the base case for this study. 0.2m 1.2m Rigid link=3m 5@ 1.28m Figure 5.1(b) Figure 5.1(a) Figure 5.1: (a) Colquitz Bridge Prototype Pier (b) SDOF Lumped-Parameter Model 54 Chapter 5 - Non-linear analysis and damage state assessment Analyses were also carried out by calculating the lumped mass by considering 50% of the super structural mass for determining an upper bound for the damage assuming a pin at the superstructure level. This would help to have an idea about the pragmatic range of values for sensitivity analyses to be carried out later. 5.2 NON-RETROFITTED VS RETROFITTED PIER: Since the Colquitz bridge has only one single column pier, it is the most critical element in the structural assembly. The pier was thus investigated in detail to have confidence in predicting its performance. The as-built or non-retrofitted column has 40-35M bars as longitudinal reinforcement while 15M spirals are provided at a pitch of 75mm. This seems to be a well-confmed column but the presence of a lap splice at the column base renders it susceptible to lap-splice failure. Calculations indicate that despite the 1.37m (54 inch) of lap splicing provided, the spiral reinforcement is not adequate to prevent a splice failure at the base. Lap splices in hinge zones, such as the base of columns should not be used, as they tend to break down under cyclic inelastic action even when very long splice lengths are provided. Another critical issue in this regard is the shortening of effective plastic hinge length due to the doubling of the effective longitudinal reinforcement ratio, thus causing an early onset of ductility failure (Priestly et al; 1997). In order to avoid the aforementioned type of failure, the column base was retrofitted with a 10mm thick steel jacket, 1.5m in height, extending upwards from the column footing. A typical gap of 50mm was provided between the jacket and the footing of the column to avoid the 55 Chapter 5 - Non- l inear analysis and damage state assessment possibility of the jacket acting as compression reinforcement by bearing against the footing thus avoiding excessive flexural strength of the plastic hinge region. A steel jacket provides passive confinement by inducing lateral confining stress in the concrete. We can consider the jacket as continuous hoop reinforcement and the level of confinement depends on the hoop strength and stiffness of the steel jacket. For assessment purposes, the jacket was assumed to have a yield strength of 248 MPa. The following equation was used to estimate the maximum effective compression strain e c m for the retrofitted pier (Priestly et al; 1997): e c m = 0.004 + 5.6 tj fyj e s m / D f c c (5-1) where tj is the jacket thickness, fyj is the jacket yield stress, £ s m is the strain at maximum stress and f c c is confined concrete compression strength. For assessing the non-retrofitted pier, an extreme fibre compression strain (ec) equal to 0.002 was used as degradation begins to happen after reaching a curvature ductility corresponding to this value of extreme fibre compression strain (Priestly at al; 1997). An appreciable increase in the ultimate strain capacity and hence the maximum lateral displacement of the pier is achieved by using the steel jacket. This makes the pier more ductile and imparts it the capability to meet much higher displacement demands. 56 Chapter 5 - Non-linear analysis and damage state assessment 5.3 M O M E N T - C U R V A T U R E A N D PUSHOVER A N A L Y S E S FOR COLQUITZ PIER: The computer program Response 2000 was used to determine the moment-curvature relationship for the non-retrofitted and the retrofitted Colquitz bridge pier. The following issues had to be addressed before the software could be used to obtain the required relationships: Confinement of concrete can cause an appreciable increase in the ultimate compression strain that can be carried. This increase was taken into account for modelling the retrofitted Colquitz pier by initially having an estimate of the enhanced f c value of concrete due to confinement from the steel jacket. Equation 5-1 was then used to determine the maximum effective compression strain that could be carried by the confined concrete. The £ c m values for confined concrete can range from 0.012 to 0.05, which is a 4-16 fold increase over the traditionally assumed value for unconfined concrete. For the given steel jacket retrofit, the f c c value was determined to be 50 MPa leading to an e c m value of 0.034. This approach not only takes into account the increase in the yield and ultimate displacement of the pier but also considers the jump in the yield moment that is caused due to the enhanced concrete stress due to confinement. This is necessary to have realistic results from the non-linear dynamic analyses. Shear was not considered to be a problem as there would be a considerable increase in the shear carrying capacity of the pier due to the jacket retrofit. Simplified bi-linear moment-curvature plots were employed to carry out the non-linear dynamic analyses of the bridge pier. These are shown in figures 5.2 and 5.3 as follows: 57 Chapter 5 - Non- l inear analysis and damage state assessment * 15000 -t Moment (KN-m) 10000-5000 -0 4 (2.3,9000) I ! I I I i I I 1 -80 -70 -60 -50 -40 -30 -20 -10 -5000 /--10006* -15000 -Figure 5.2: Simplified bi-linear momc Colquitz * i I I i i I I i ) 10 20 30 40 50 60 70 80 Curvature (rad/Km) >^ mt-curvature for non-retrofitted pier | 15000 -Moment (KN-m) | 10000 5000 -O < (10,11500) • • / (70,11500) I I I I I ! I W J -80 -70 -60 -50 -40 -30 -20 -10 / ( -5000 -10000 -• • -15000 -Figure 5.3: Simplified bi-linear momen ' I I I I i i i i ) 10 20 30 40 50 60 70 80 Curvature (rad/Km) • t-curvature for retrofitted Colquitz pier The above moment-curvature plot values were used to perform the pushover analyses (Figures 5.4, 5.5) of the Colquitz pier for the two scenarios. A large increase in 58 Chapter 5 - Non-linear analysis and damage state assessment the ultimate displacement capacity for the pier was observed after retrofit. This is due to the 17-fold increase in the ultimate strain carrying capacity for the retrofitted pier as compared to one taken to define the ultimate condition for the non-retrofitted pier. Since this is a single column pier, the Pushover curve also defines the monotonic force-displacement curve for the column to the failure state. 1400 500 600 Figure 5.4: Pushover curve for non-retrofitted Colquitz Pier 1400 600 Figure 5.5: Pushover curve for retrofitted Colquitz Pier 59 Chapter 5 - Non-linear analysis and damage state assessment It is evident form the two pushover curves that the ultimate displacement capacity of the retrofitted pier is about 7 times that of the non-retrofitted pier while there is a 1.25 times increase in the ultimate force taken by the retrofitted pier in comparison to the non-retrofitted pier. Also, the pushover curve for the non-retrofitted pier shows that the ultimate condition happens almost immediately after the yielding of the column thus indicating the propensity of the lap splices to come apart due to lateral expansion of concrete in the tension region. 5.4 D A M A G E INDICES: Damage indices are tools in the form of non-dimensional parameters that help engineers and decision makers with quantification of damage sustained in concrete structures under earthquake loading. This information is employed to have an idea about the consequences related to different levels of earthquake. The damage indices do not rely on the subjectivity of the evaluator and provide a means by which different retrofit or design options can be assessed objectively. Damage indices can quantify damage in individual structural elements, storeys or complete structures and can be obtained from non-linear dynamic analysis. They are calculated on the basis of a non-linear dynamic analysis. A number of damage index definitions have been proposed by different researchers, which mostly employ deformation and energy absorption as measure of the level of damage. A comprehensive review of damage indices is given by Williams and Sexsmith (Williams and Sexsmith, 1994). The two broad categories of damage indices are the non-cumulative and cumulative damage indices. Non-cumulative indices fail to 60 Chapter 5 - Non-linear analysis and damage state assessment take into account the accumulation of damage occurring under cyclic loading. Usage of cumulative damage indices is thus recommended for determining the state of damage due to seismic loading. 5.4.1 P A R K A N D A N G D A M A G E INDEX: The best known and most widely used of all the cumulative damage indices is that of Park and Ang (1985). This damage index is defined as follows: DI ~ 8 m + P E (5-2) 5U F y 8U where 8 m and 8U are the maximum displacement and the ultimate displacement respectively, Fy is the yield force of the structural component, E is the amount of dissipated hysteretic energy and (3 is a parameter representing the extent of strength degradation after yielding. The first term in the equation 5-2 is a simple pseudo-static displacement measure and is referred to as deformation damage, which takes no account of the cumulative damage. The second term accounts solely for the cumulative damage due to cyclic loading and is termed as the strength damage. The term p in this term can have values ranging from 0.0 to 0.5. Low values of this parameter are used for properly reinforced and well-confined columns while higher values are recommended for poorly detailed structural sections. A more recent and slightly modified form of the Park and Ang index by Stone and Taylor (1993) is based on a formulation wherein the recoverable deformation is removed from the first term, and moment and curvature are used in place of force and displacement: 61 Chapter 5 - Non-linear analysis and damage state assessment D l = (bm - (j)y (5E (5-3) + <(>„ - <)>y M y <|>u where (j)m, (j)y and (j)u represent the maximum, yield and ultimate curvatures, M y is the yield moment while E and fi have the usual meaning. 5.4.2 RESIDUAL ENERGY D A M A G E INDEX: A very recently proposed measure of damage is the Residual Energy damage index (Hindi and Sexsmith, 2001). This index is based on the predicted hysteretic behaviour of a concrete column and yields a damage index at a point in the time history for the element taking into account parameters such as stiffness degradation, strength deterioration and ultimate displacement reduction. This model primarily considers the amount of work required to fail a reinforced concrete column monotonically after it has been damaged due to cyclic loading. It takes the energy A n under a monotonic load-displacement curve up to failure as a reference capacity, and then uses the actual load-displacement history up to point n, followed by a monotonic load-displacement curve from the end of last cycle n (zero force point) to failure representing the amount of work required henceforth to fail the column, A n (figure 5.6). The damage index is then calculated by using the following expression: D l = A 0 - A n (5-4) A 0 Figure 5.6 elaborates on the model definition, graphically showing the meaning of the reference capacity An , and the residual capacity A n of the column. 62 Chapter 5 - Non-linear analysis and damage state assessment / / / / / (a) Loaded column F 7 T Failure I I I 1 A / / A° / / / / / / / A (b) Monotonic force-displacement envelope (c) Cyclic loading (n cycles) (d) Degraded monotonic energy after n cycles Figure 5.6: Residual energy index model elaboration 63 Chapter 5 - Non-linear analysis and damage state assessment 5.4.3 CATEGORIZATION A N D CALIBRATION OF D A M A G E : The various proposed damage indices are calibrated against observed damage. Each one of these correlates the specific damage index with the observed damage based on visual distress in the structure or to the repairability of the building. The Park and Ang index as described in the previous section employs the former approach while Stone and Taylor (Stone and Taylor, 1993) applied the modified index definition to 82 tests on Caltrans circular bridge columns by using the latter method. The two damage classifications are described as follows in tables 5.1 and 5.2. Table 5.1: Damage classification according to Park and Ang (1985) D <0.1 No damage or localized minor cracking 0.1 1.0 Collapse Table 5.2: Damage classification according to Stone and Taylor (1993) D<0.11 No damage or localized minor cracking 0.11 0.77 Collapse 64 Chapter 5 - Non-linear analysis and damage state assessment The residual energy model concludes the following scale from the comparison between the proposed model and the observed damage (Table 5.3). Table 5.3: Proposed damage classification by Hindi and Sexsmith (2001) D< 0.1 No damage 0.1 SFRF * P 2 + S3,SFRF * P 3 where Pi = 0.0021, P 2 = 0.000404 and P 3 = 0.000404 and hence, E(safety retrofit) = 0.2525 * 0.0021 + 0.9218 * 0.000404 + 1.4798 * 0.000404 = 0.0015M The NPC for the safety retrofit scenario is then given by, NPC(safety retrofit) = 0.0685 + 0.0015*[l-(l+0.04)100] / 0.04 = 0.10 M NPC's for other alternatives can be similarly calculated. The option with the least NPC is then the optimal retrofit strategy. 96 Chapter 7 - Decision and sensitivity analysis 7 .2 DECISION COST COMPARISONS: For carrying out the basic decision cost comparisons, a real interest rate of 4% not considering inflation was assumed. It is also realized that beyond about 100 years, the time span considered has very little effect (Nishimura, 1997). A value of T equal to 100 years was thus assumed. Tables 7.1 and 7.2 give NPC of each retrofit option for both direct and direct plus indirect cost cases corresponding to the base scenario. Tables 7.3 and 7.4 show the same information for the upper bound damage values. A l l costs are given in 2001 C D N dollars. As described in Chapter 3, the various retrofit options i.e. no retrofit, superstructure retrofit, safety retrofit and functional retrofit are abbreviated as NRF, SSRF, SFRF and FCRF respectively. Table 7.1: NPCs for direct costs only (Base scenario values) ACTION NPC (M) NRF 0.037 (Optimal) SSRF 0.066 SFRF 0.081 FCRF 0.106 97 Chapter 7 - Decision and sensitivity analysis Table 7.2: NPCs for direct plus indirect costs (Base scenario values) ACTION NPC (M) NRF 0.135 SSRF 0.164 SFRF 0.1 (Optimal) FCRF 0.108 Table 7.3: NPCs for direct costs only (Upper bound damage values) ACTION NPC (M) NRF 0.059 (OPTIMAL) SSRF 0.0877 SFRF 0.87 FCRF 0.122 Table 7.4: NPCs for direct plus indirect costs (Upper bound damage values) ACTION NPC (M) NRF 0.2024 SSRF 0.2261 SFRF 0.1273 (OPTIMAL) FCRF 0.1313 98 Chapter 7 - Decision and sensitivity analysis The results show that considering direct costs only, the no retrofit option comes out to be the optimal strategy for both base and upper bound damage considered for damage. However considering the effect of the indirect costs for these two cases changes the decision outcome as it considerably increases the NPC of the no retrofit option. The optimal decision now is to retrofit the structure to the safety level for each of the lower and upper bound damage cases. 7.3 SENSITIVITY ANALYSIS: Due to a number of assumptions and approximations in deriving the consequence costs, it is logical to examine the sensitivity of the decision to critical input parameters. It has already been shown in the previous section that the decision is not sensitive to the amount of superstructure mass assumed at the pier for realistic values of 20 and 50 percent. Since the variations in the nature and extent of seismicity were modelled thoroughly in the decision tree, no further variations were considered in this regard. However a number of other parameters were varied and their effect on decision outcome analysed. This was carried out as follows: • Taking i as 3%, 5% and 6% for the lower bound damage costs assuming the initial functional retrofit cost to safety retrofit cost ratio as 1.5 • Varying indirect costs by +10%, +20%, +25% and +50% for lower bound damage and by -10%, -20%, -25% and -50% for upper bound damage respectively (for i = 4%). • Keeping i as 4% and taking the initial functional retrofit to safety retrofit cost ratios as 1.4 and 1.33 for both upper and lower bound damage cases 99 Chapter 7 - Decision and sensitivity analysis The results for various sensitivity analyses are shown in Tables 7.5 through 7.9. Table 7.5: NPCs corresponding to various i values and direct costs only T=100, FCRF/SFRF = 1.5 (Base scenario) ACTION NPC (i = 3%) NPC (i = 5%) NPC (i = 6%) NRF 0.048 (Optimal) 0.030 (Optimal) 0.024 (Optimal) SSRF 0.0766 0.059 0.052 SFRF 0.085 0.079 0.077 FCRF 0.107 0.105 0.104 Table 7.6: NPCs corresponding to various i values for direct plus indirect costs T=100 years, FCRF/SFRF = 1.5 (Base scenario) ACTION NPC (i = 3%) NPC (i = 5%) NPC (i = 6%) NRF 0.174 0.109 0.092 SSRF 0.203 0.138 0.120 SFRF 0.109 (Optimal) 0.094 (Optimal) 0.089 (Optimal) FCRF 0.110 0.107 0.106 100 Chapter 7 - Decision and sensitivity analysis Table 7.7: NPCs for direct plus indirect costs after increasing indirect costs corresponding to base scenario T = 100 years, FCRF/SFRF = 1.5 ACTION INDIRECT COST VARIATION +10% +20% +25% +50% NPC NPC NPC NPC NRF 0.144 0.154 0.159 0.184 SSRF 0.173 0.183 0.188 0.213 SFRF 0.102 (Optimal) 0.104 (Optimal) 0.104 (Optimal) 0.109 (Optimal) FCRF 0.1090 0.1096 0.1097 0.1104 Table 7.8: NPCs for direct plus indirect costs after decreasing indirect costs corresponding to upper bound damage scenario T = 100 years, FCRF/SFRF = 1.5 ACTION INDIRECT COST VARIATION -10% -20% -25% -50% NPC NPC NPC NPC NRF 0.188 0.174 0.166 0.131 SSRF 0.212 0.198 0.191 0.157 SFRF 0.123 0.119 (Optimal) 0.117 (Optimal) 0.107 (Optimal) FCRF 0.123 0.121 0.12 0.115 101 Chapter 7 - Decision and sensitivity analysis Table 7.9: NPCs for direct plus indirect costs for i = 4 % , T =100 years and FCRF/SFRF = 1.4 ACTION NPC FOR LOWER BOUND OF D A M A G E NPC FOR UPPER BOUND OF D A M A G E SFRF 0.999 (Optimal) 0.1273 FCRF 0.102 0.1249 (Optimal) Table 7.10: NPCs for direct plus indirect costs for i = 4%, T =100 years and FCRF/SFRF = 1.33 ACTION NPC FOR LOWER BOUND OF D A M A G E NPC FOR UPPER BOUND OF D A M A G E SFRF 0.099 0.1273 FCRF 0.097 (Optimal) 0.12 (Optimal) 7.4 DISCUSSION: The decision and sensitivity analyses show that when only direct costs are considered, no retrofit option is the optimal strategy for both lower bound and upper bound damage states (for i = 4%). However accounting for the indirect costs in the decision makes the safety retrofit as the optimal course of action for both lower and upper bounds of damage. The decision is relatively insensitive to the variations in the discount rate as NRF is optimal for all direct cost scenarios while SFRF is optimal for all direct 102 Chapter 7 - Decision and sensitivity analysis plus indirect scenarios. However for i = 3%, the NPCs for SFRF and FCRF are close enough that the decision maker might be indifferent between these two strategies. Variations in indirect costs for the lower bound damage scenario do not affect the decision outcome yielding SFRF as the optimal level. For the upper bound damage values, a variation of-10% in the indirect costs make the NPCs for SFRF and FCRF equal to each other and hence the decision maker would be indifferent between the two retrofit levels for such consequence costs. However for other values of indirect costs, the SFRF is the optimal strategy. For FCRF/SFRF = 1.4 and i = 4%, SFRF is the optimal level for the lower bound damage case while FCRF is the optimal strategy for the upper bound damage case. However for FCRF/SFRF =1.33 and i = 4%, FCRF is the optimal course of action for both cases. Considering the lower bound damage values and i = 4%, the decision maker would be indifferent between SFRF and FCRF for FCRF/SFRF = 1.37 while for the upper bound case this value is 1.43. The effect of variation in T on the decision was also analysed. It was found that the decision outcome was only changed for a value of T = 25 years. The decision analysis indicated NRF as the optimal retrofit scheme for T = 25 years when both direct and indirect damage costs are taken into account for the lower bound damage case taking i = 4%. For T =50 and 75 years, there was no bearing on the decision which still yielded the SFRF as the most favourable course of action for direct plus indirect costs. 103 Chapter 7 - Decision and sensitivity analysis 7.5 DECISION-MAKING WITHOUT PROBABILITY KNOWLEDGE: In a situation where meaningful data are unavailable to assign probabilities to future events, the problem can be formulated in a structured manner and standard decision rules may be applied. For the current study, such techniques were used to ascertain their usefulness in structural retrofit decision-making. The base scenario for both direct and indirect cost cases with i = 4% was considered for this purpose. The Minimin and Minimax rules were first used. The former is based on an extremely optimistic view of nature while the latter is based on an extremely pessimistic view of nature. A compromise between these two approaches is achieved through the Horwicz rule that allows the decision maker to select an index of optimism, a. Thirdly, the Minimax Regret rule is a conservative approach with the underlying premise that the decision maker wishes to minimise his maximum regret about a decision. The application of all three rules requires the construction of a consequence matrix that exhibits the interaction of decision alternatives and the states of nature. The consequence matrix for the studied case is given in Table 7.10. For the Minimin rule, the minimum value of consequences corresponding to each retrofit level is identified. The retrofit level corresponding to the minimum of all such values would then be the required retrofit strategy. For the Minimax rule, the maximum consequence value for each retrofit level is determined and the retrofit level corresponding to the minimum of all such values is then deemed to be the preferred line of action. The results from both these methods show that the functional retrofit is the most suitable level of retrofit to be carried out (Tables 7.11 and 7.12). 104 Chapter 7 - Decision and sensitivity analysis Table 7.11: Consequence matrix for direct plus indirect cost case corresponding to base scenario, i = 4%, FCRF/SFRF = 1.5 ALTERNATIVES STATES OF N A T U R E SI S2 S3 S4 S5 S6 S7 S8 S9 NRF 0.875 0.86 0.871 2.45 2.36 2.32 6.77 6.77 6.77 SSRF 0.899 0.884 0.895 2.474 2.382 2.345 6.799 6.799 6.799 SFRF 0.252 0.252 0.252 0.923 0.856 0.856 1.508 1.465 1.465 FCRF 0.102 0.102 0.102 0.102 0.319 0.102 0.527 0.743 0.727 Table 7.12: Minimin and Maximin rule results A L T E R N A T I V E MINIMIN R U L E M I N I M A X R U L E NRF 0.86 6.77 SSRF 0.884 6.799 SFRF 0.252 1.508 FCRF 0.102 (min, optimal) 0.743 (min, optimal) The Minimin and Maximin rules have extremely pessimistic and optimistic underlying philosophies respectively. In order to achieve a compromise between optimism and pessimism, the decision maker can employ the Hurwicz rule which allows the selection of an index of optimism a such that 0 R2 >...>Rj>...> R N , and the bridge having the highest ranking R| is identified as the first candidate for seismic retrofitting. The ranking R i is related to the 115 Chapter 8 - Br idge retrofit pr ior i t izat ion procedures two main criteria of Vulnerability and Importance through the following functional relationship (Basoz and Kiremidgian, 1996): Ri = f(Vi ,I0 (8-1) 8.1.5.1 V U L N E R A B I L I T Y ASSESSMENT: The vulnerability assessment for a bridge entails the following aspects: • Seismic hazard analysis at the bridge site • Classification of bridges based on their structural characteristics • Fragility analysis The mathematical expression for Vulnerability evaluation is as follows: V = f(D,A,Cn,m) (8-2) where: D = damage state assuming values dr in D = {di,d 2,....,d z}, where Z is the total number of damage states, A = seismic hazard at the bridge site, C n = bridge class n defined based on the primary structural attributes Y , M = modifier based on the secondary structural attributes Y . 8.1.5.1.1 SEISMIC H A Z A R D ANALYSIS: The parameter A is a function of local soil conditions at the bridge site and location of the bridge relative to potential seismic hazard sources and represents either ground shaking or severity of the liquefaction. The results of seismic hazard analysis 116 Chapter 8 - Bridge retrofit prioritization procedures comprise of the probability of exceeding various levels of a site parameter over a future time period presented by a seismic hazard curve (Kiremidgian, 1992). 8.1.5.1.2 CLASSIFICATION OF BRIDGES: The classification of bridges is based on primary structural attributes, Y . Figure 8.1 shows a hierarchical scheme of these elements. The bridge attributes considered in this regard are the material and structural type and miscellaneous properties such as number of spans and span continuity, number of columns and bents, abutment type, etc. The material type Y i refers to the material of the substructure while the structural type represents the superstructure configuration of a bridge. Figure 8.1: Hierarchical Order for Primary Structural Attributes (from Basoz and Kiremidgian, 1996) 117 Chapter 8 - Bridge retrofit prioritization procedures 8 .1 .5 .1 .3 FRAGILITY ANALYSIS: The fragility analysis comprises of developing ground motion-damage relationships for computing the probability of a bridge being in a particular damage state for a given ground motion level, P (D = d r / a,Cn). A simple approach for obtaining the fragility curves is by considering the combination of all possible failure modes based on components. This information can then be used to develop the fragility curves by defining relationships between the component states and the system damage states. The authors have also proposed a set of modifiers m for modifying the fragility curves, based on secondary vulnerability attributes such as skewness, effect of seat width, etc. A modifier for a given attribute may or may not be a function of the ground motion level or the bridge class [Basoz and Kiremidgian, 1996]. A generic fragility curve is shown in Figure 8.2 where 'a' is a specific ground motion parameter. 118 Chapter 8 - Bridge retrofit prioritization procedures Performing all the above-mentioned analyses, the Vulnerability Vj of the bridge Bj can be evaluated through the use of equation (8-2). 8.1.5.2 IMPORTANCE ASSESSMENT: The Importance criterion of bridge assessment entails the appraisal of consequences arising from life safety and socio-economic aspects of bridge damage. Mathematically the bridge importance criterion can be expressed as follows: Ii = f(Si,E i ,Gi,L i ,Q i ,H i) (8-3) The various factors in equation (8.2) are explained as below: • Sj is the life safety factor for bridge Bj that depends upon route carried on and under the bridge and the corresponding ADT along with the damage level of the bridge. • Ej is the emergency response factor for bridge Bj depending on factors such as; whether or not bridge Bj belongs to an ensemble of bridges whose failure delays accessibility to a disaster area from available resource locations, travel time based on the travel times between two points before and after the failure of bridge Bj and spatial importance of bridge B i in the given highway network system. • Gi is the factor taking into account the long-term economic impact based on the A D T for the route carried on the bridge, traffic capacity of the route carried on the bridge and the origin-destination trip demands for various origin destination pairs. • Lj is a factor accounting for the interaction of other lifelines carried on bridge Bj. • Qj is the defence route factor evaluated on the basis of whether the bridge carries and/or crosses a defence route. 119 Chapter 8 - Bridge retrofit prioritization procedures • Hj is factor corresponding to the historical significance of bridge Bj. The importance assessment is thus carried out by obtaining a decision maker's values and developing utility functions and scaling factors for all importance attributes, determining lifeline network analysis attributes for a given bridge, performing network analysis (connectivity analysis for emergency response, serviceability analysis for long term economic impact) and obtaining the overall utility value for importance assessment employing equation (8-3). 8.1.5.3 O V E R A L L RANKING: The overall ranking of a structure is obtained through the integration of the Vulnerability and Importance criteria. The rank of bridge Bj as a function of these two criteria as defined by equation (8-1) can be expressed as below: U B j = k v U v i + kjU.i where U B j is the utility value for bridge B i to be used in obtaining R;, k v and kj are the scaling constants for vulnerability and importance respectively and U V i and are the utility values for vulnerability and importance respectively. Bridges in set B are then ranked by decreasing values of U B j to obtain the rank order Ri > R 2 >.. >RN-Unlike other approaches, this methodology rationally considers vulnerability as a function of site seismicity and incorporates the various pertinent parameters in a thorough fashion. Similarly, the importance assessment is carried out by considering a number of factors that have not been taken into account in other studies. The two criteria are then combined using relative weighting factors. The methodology fits well with decision analysis principles, since it attempts to quantify damage in structures along with the 120 Chapter 8 - Bridge retrofit prioritization procedures determination of consequences. It is the most comprehensive and rational approach of prioritizing bridges in a large inventory developed so far. 8.2 PROPOSED METHODOLOGY: The approach proposed herein is a systematic two-step procedure that can be summarised as follows: STEP 1: Subject the bridges under consideration to detailed decision analysis and determine the optimal course of action for each structure based on the Net Present Cost (NPC) criterion as illustrated in Chapter 7. STEP 2: Determining the opportunity loss R; for each structure, which is the difference between the present consequences of doing nothing, CNRF, and the NPC of the optimal course of action as determined in the previous step for each bridge. The logical action now is to determine the benefit-to-cost ratio yj for each bridge by dividing R with the cost of retrofit Coi corresponding to the optimal level of retrofit for each candidate (Sexsmith, 1994). Ranking can now be carried out in the decreasing order of RJ/COJ ratios for each candidate under consideration. 8.3 RESULTS: In order to assign the index y, = Rj/Coi as defined above to Colquitz for the sake of prioritization, the results obtained for this structure corresponding to the lower bound of damage for direct plus indirect costs and an i value of 4% are used. For the Interurban overpass, the optimal retrofit strategy is assumed as the safety retrofit level. For assigning the priority index to this structure, we need to determine the present consequence cost of 121 Chapter 8 - Bridge retrofit prioritization procedures the no retrofit option. Given the deficiencies in the unretrofitted structure, it is reasonable to assume that the overpass would have to be replaced for all earthquake levels. This leads to a total consequence cost of C D N $15.25 million and hence a NPC of $1,085 million. The priority index values are given in Table 8.1 for the two structures. Table 8.1: Priority index calculations for Colquitz and Interurban BRIDGE OPTIMAL RETROFIT CNRF NPC Ri Coi Yi= Ri/Coi COLQUITZ SFRF 0.135 0.1 0.035 0.0685 0.51 I N T E R U R B A N SFRF 1.085 0.398 0.687 0.295 2.33 The priority index values clearly show that the Interurban overpass should be retrofitted first in order to gain the maximum long-term benefit from the retrofit program. The priority index values for the Interurban overpass were re-calculated by taking the consequence costs corresponding to the 75%, 67%, 60% and 50% of the calculated consequence costs for this structure (Table 8.2). By keeping all other variables uniform, it is seen that the order of retrofit only changes when the considered percentage of consequence costs is taken to be as small as 50% of the estimated consequence costs for the Interurban overpass. 122 Chapter 8 - Bridge retrofit prioritization procedures Table 8.2: Priority index determination for Interurban for different percentages of estimated consequence cost PERCENTAGE OF ESTIMATED CONSEQUENCE COST Yi = Ri/Coi 100 2.18 75 1.29 66 1.01 60 0.77 50 0.49 (< 0.51) 8 . 4 DISCUSSION: The methodology proposed herein is a level-two procedure whereby bridges that have already been screened for retrofit based on certain criteria, or selected for undergoing up gradation as a policy matter due to political, social and economic factors, can be ranked to make the greatest possible reduction in the opportunity loss, or gain the maximum benefit, given a fixed total of construction costs. The proposed scheme is therefore not a rapid screening procedure like other methods discussed in the previous sections. This is a logical way of assigning priority indices to bridges as it first employs decision analysis to figure out the optimal level of retrofit for each bridge thereby eliminating irrationalities in the decision-making process, and then takes the corresponding relative benefit gained for each bridge to decide the order of retrofit of various structures given a scarcity of funds. Other approaches fail to take this aspect into 123 Chapter 8 - Bridge retrofit prioritization procedures account as they only focus on the vulnerability and importance attributes of bridges. The proposed approach thus adds a very important third dimension to the retrofit prioritization process. 124 Chapter 9 - Conclusions and application of proposed methodology C H A P T E R 9 CONCLUSIONS AND APPLICATION OF PROPOSED METHODOLOGY 9.1 CONCLUSIONS: A methodology was developed and illustrated for determining the best retrofit strategy given a set of alternatives for a structure or a number of structures, and for assigning priority indices to candidates being considered for retrofit. Two bridges that are a part of the DRR on the Vancouver Island were selected for demonstration of the proposed procedure. The processes of assessing the nature and extent of site seismicity, subjecting the bridge pier to non-linear analyses, deriving damage states for the pier and other bridge components, relating the damage states to dollar damage indicators and using consequence costs in the decision analysis algorithm were described. The priority index calculation based on cost-benefit ratio analysis was also illustrated. It can be concluded that the damage index approach is a reasonable methodology for determining damage in concrete piers. The residual energy damage index not only takes into account the stiffness and strength degradation of concrete and the confinement effect of the spiral reinforcement, it also considers the reduction in ultimate displacement due to the low cycle fatigue of the longitudinal reinforcement. Damage states so obtained are clearly more accurate than simply deriving them from demand-to-capacity ratio values determined from linear elastic analysis. A considerable scatter of the damage index was found corresponding to each level of seismicity. This is evident from the various damage index values obtained for 125 Chapter 9 - Conclusions and application of proposed methodology different records scaled to the same response spectrum. The scatter is more pronounced for higher seismicity levels as the structure becomes more and more non-linear. It was found that damage is not only dependent on the PGA of a record but more so on the number of large pulses that a seismograph might present. A higher level of damage in such a case is caused due to the reduction in ultimate displacement of the bridge pier due to the low cycle fatigue effects of longitudinal reinforcement. A great deal of difficulty was encountered in determining damage costs due to lack of documented information. The cost of fixing abutment pile pull out can be cited as an example in this regard. Rough estimates had therefore to be made to obtain cost figures for use in decision analysis. There is some fiizziness in damage states for each seismicity level and hence the damage costs corresponding to each state. Fuzzy logic mapping would therefore be the best way of relating damage states to the dollar damage index. This study however employed the deterministic mapping for this purpose due to its simpler nature. The decision analysis showed that taking only the direct costs into account did not change the outcome of the decision for the base and upper bound scenarios. However, accounting for the indirect costs changed the decision outcome to safety retrofit as the optimal course of action. Leaving out the indirect costs can therefore lead the decision maker into taking a course of action that may not be the best strategy. The discount rate was found to have minimal effect on the decision for this study. Also, it was found that the decision outcome only changed for a very short planning period of 25 years, which yielded the no retrofit as the optimal retrofit strategy. For higher values of T such as 50, 75 and 100 years, the decision to retrofit Colquitz to the safety level was found to be the 126 Chapter 9 - Conclusions and application of proposed methodology most preferable course of action considering both direct and indirect costs. Certain importance aspects such as the emergency response, interaction with other lifelines, etc were not given a thorough treatment in this study. Considering these factors in detail would lead to better indirect cost estimates thus leading to consistent and efficient decision-making. The decision analysis techniques not considering probability and risk attributes are not effective in revealing the optimal course of action for a given choice of alternatives. These techniques tend to lead the decision maker into unreal optimism or pessimism and usually lead to the course of action with the minimum consequence cost, which may not be the best strategy for long-term policy making. Finally, there can be some confusion in the definition of various retrofit levels since there may be an overlap of performance objectives from these i f the bridge is not grossly deficient. Colquitz is an example that can be considered as a borderline case for the safety and functional retrofits for the design level earthquake. For such an event, the safety level retrofit only leaves the abutment diaphragm with a potential deficiency as it shows a tendency of failure due to passive pressure from abutment backfill. This minor defect can be repaired very quickly following a design level earthquake and the bridge made functional. However i f the bridge also had major deficiencies in the abutment and/or pier footings and piles corresponding to the design level earthquake, the functional retrofit would ensure a considerably higher performance level as compared to the safety retrofit. In the present case, the performance levels of the bridge for the two retrofit strategies corresponding to the design level earthquake are not too different. The proposed methodology can however be employed regardless of this obscurity to 127 Chapter 9 - Conclusions and application of proposed methodology determine whether the additional expense to retrofit a structure to a higher level is justified or not. 9.2 APPLICATION OF PROPOSED METHODOLOGY: Given the nature of the retrofit program by BC MoTH, this study provides a rational tool for determining the optimal level of retrofit for a given structure or set of structures. This could be applied to any given bridge classified under any given type (whether Lifeline, DRR, ESR or Other). The proposed methodology could therefore provide hindsight into whether what has been done (or is being done) by the B C M o T H was/is the optimal strategy in terms of money spent and levels of safety achieved. It would also help the ministry make future decisions such as; whether or not to upgrade Lifeline, DRR, ESR bridges to the Functional level, to upgrade bridges crossing ESR's to a level higher than the Superstructure retrofit, to retrofit Other bridges to the Superstructure or a higher level or to not retrofit them at all, etc. Sensitivity analyses could be carried out to take into account the subjective nature of information in order to determine the influence of change in values of various parameters on the outcome of the decision. Another facet of this study was to illustrate a cost-benefit ratio based method of assigning priority indices to a set of bridge structures so that they can be retrofitted in a preferable order. This approach can be used to determine the retrofit order of a number of bridges after they have been initially screened and the corresponding optimal retrofit strategies have been determined for these structures. 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Technical and User's Manuals. 134 APPENDIX A STRUCTURAL DRAWINGS OF COLQUITZ RIVER SOUTH BRIDGE AND INTERURBAN OVERPASS 135 4^ Co 4*. 4^ APPENDIX B E X A M P L E S Y N T H F I L E S F O R L O M A P R I E T A -S p L P 3 . d a t 94 0 4 0 8 5 0 0 5 0 8 73 . 1 0 0 9 9 0 10 5 9 9 9 110 1 . 0 0 8 1 1 5 1 . 0 17 . 1 2 0 1 . 0 2 6 12 5 1 . 03 5 13 0 1 . 044 13 5 1 . 0 53 . 1 4 0 1 . 0 6 2 1 4 5 1 . 0 7 1 150 1 . 0 8 0 15 5 1 . 0 8 0 . 1 6 0 1 . 0 8 0 16 5 1 . 0 8 0 17 0 1 . 0 8 0 1 7 5 1 . 0 8 0 . 1 8 0 1 . 0 8 0 18 5 1 . 0 8 0 19 0 1 0 8 0 19 5 1 0 8 0 . 2 0 0 1 0 8 0 2 10 1 0 7 8 2 2 0 1 0 7 5 2 3 0 1 0 7 3 . 2 4 0 1 0 7 0 2 5 0 1 0 6 8 2 6 0 1 0 6 6 2 7 0 1 0 6 3 . 2 8 0 1 0 6 1 2 9 0 1 . 0 5 9 3 0 0 1 . 0 5 6 3 10 1 . 0 5 4 . 3 2 0 1 . 0 5 1 3 3 0 1 . 0 4 9 3 4 0 1 . 0 4 7 3 5 0 1 . 0 4 4 . 3 6 0 1 . 0 4 2 3 7 0 1 . 0 3 9 3 8 0 1 . 0 3 7 3 9 0 1 . 0 3 5 . 4 0 0 1 . 0 3 2 4 10 1 . 0 3 0 4 2 0 1 . 0 2 8 4 3 0 1 . 0 2 5 . 4 4 0 1 . 0 2 3 4 5 0 1 . 0 2 0 4 6 0 1 .0 18 4 7 0 1 . 0 1 6 . 4 8 0 1 .0 13 4 9 0 1 . 0 1 1 . 5 0 0 1 . 0 0 8 . 5 2 0 . 9 9 5 . 5 4 0 . 9 8 1 . 5 6 0 . 9 6 7 . 5 8 0 . 9 5 3 . 6 0 0 . 9 3 9 . 6 2 0 . 9 2 5 . 6 4 0 . 9 1 1 . 6 6 0 . 8 9 7 . 6 8 0 . 8 8 3 . 7 0 0 . 8 7 0 . 7 2 0 . 8 5 6 . 7 4 0 . 8 4 2 . 7 6 0 . 8 2 8 . 7 8 0 .8 14 . 8 0 0 . 8 0 0 . 8 2 0 . 7 8 6 . 8 4 0 . 7 7 2 . 8 6 0 . 7 5 8 . 8 8 0 . 7 4 5 . 9 0 0 . 7 3 1 . 9 2 0 . 7 17 . 9 4 0 . 7 0 3 . 9 6 0 . 6 8 9 . 6 2 8 . 9 8 0 . 6 7 5 1 . 0 0 0 . 6 6 1 1 . 1 0 0 1 . 2 0 0 . 5 95 . 4 9 6 1 . 3 0 0 . 5 6 2 1 . 4 0 0 . 5 2 9 1 . 5 0 0 1 . 6 0 0 . 4 6 3 .3 64 1 . 7 0 0 . 4 3 0 1 . 8 0 0 . 3 9 7 1 . 9 0 0 2 . 0 0 0 . 3 3 1 . 2 6 6 2 . 2 5 0 . 2 7 9 2 . 5 0 0 . 2 7 0 2 . 7 5 0 S p L P 3 . d a t 3 . 0 0 0 . 2 1 6 3 . 5 0 0 . 2 1 9 4 . 0 0 0 . 1 1 7 147 T h r s L P 3 . d a t 94 . 0 4 0 8 5 9 . 0 5 0 • 8 72 . 1 0 0 1 . 0 3 6 . 1 0 5 914 . 1 1 0 1 . 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. 0 2 9 - . 0 2 1 . 0 1 9 - . 0 1 9 - . 0 4 4 . 0 0 8 . 0 0 9 . 0 2 3 . 0 2 4 . 0 0 1 . 0 0 3 . 0 3 8 - . 0 1 1 . 0 3 2 - . 0 0 6 - . 0 0 1 . 0 3 4 . 0 1 6 . 0 2 1 . 0 6 2 - . 0 2 9 - . 0 4 7 - . 0 2 5 - . 0 3 1 - . 0 2 6 . 0 17 - . 0 2 5 - . 0 3 6 . 0 1 1 . 0 13 . 0 1 8 . 0 2 1 - . 0 0 4 . 0 0 8 . 0 3 2 - . 0 1 5 . 0 3 3 - . 0 1 4 . 0 0 7 . 0 3 9 . 0 15 . 0 2 8 . 0 5 3 - . 0 4 0 - . 0 4 1 - . 0 2 5 - . 0 3 0 - . 0 2 9 . 0 16 - . 0 2 7 - . 0 2 8 . 0 0 9 . 0 15 . 0 1 8 . 0 1 5 - . 0 0 2 . 0 14 . 0 2 0 - . 0 1 8 156 S y n t h L P 3 . d a t 0 16 0 0 1 0 1 5 02 6 O i l 0 0 4 0 12 0 14 0 0 0 0 0 5 0 0 5 0 0 1 0 0 5 0 0 5 0 19 0 1 5 . 0 0 7 . 0 2 0 . 0 2 1 . 0 2 1 . 0 0 6 . 0 13 . 0 0 0 . 0 0 8 . 0 0 7 . 0 1 0 . 0 0 9 . 0 1 5 . 0 3 7 . 0 4 2 . 0 2 3 . 0 0 6 . 0 1 0 . 0 1 1 . 0 0 1 . 0 0 5 . 0 0 9 . 0 04 . 0 10 . 0 2 1 . 0 3 3 . 0 2 5 . 0 2 4 . 0 13 . 0 1 0 . 0 1 0 0 0 9 0 0 6 0 2 3 02 8 . 0 0 8 . 0 0 2 . 0 12 . 0 1 5 . 0 0 3 . 0 0 7 . 0 04 . 0 0 1 . 0 0 6 . 0 04 . 0 18 . 0 12 . 0 13 . 0 2 3 . 0 2 2 . 0 17 . 0 0 9 . 0 1 3 . 0 0 5 . 0 0 6 . 0 10 . 0 0 6 . 0 14 . 0 2 1 . 0 4 0 . 0 4 0 . 0 14 . 0 0 0 . 0 12 . 0 1 0 . 0 0 4 . 0 0 6 . 0 0 6 . 0 0 8 - . 0 1 7 • . 0 2 4 - . 0 2 9 - . 0 2 3 - . 0 1 9 - . 0 0 6 . 0 1 1 . 0 10 0 0 8 0 2 6 . 0 0 8 . 0 12 . 0 12 . 0 0 0 . 0 0 6 . 0 0 9 . 0 2 1 . 0 14 . 0 0 9 . 0 0 1 . 0 0 5 . 0 2 7 . 0 3 8 . 0 0 6 . 0 0 7 . 0 0 6 . 0 12 • . 0 2 3 - . 0 2 1 - . 0 0 1 . 0 1 0 . 0 0 4 . 0 2 3 - . 0 1 0 - . 0 0 9 . 0 12 . 0 0 1 . 0 1 0 . 0 0 5 - . 0 1 7 - . 0 1 0 - . 0 0 7 - . 0 0 2 . 0 0 3 - . 0 3 2 - . 0 3 5 . 0 0 9 . 0 0 3 . 0 0 7 . 0 13 - . 0 2 2 - . 0 2 4 . 0 0 1 . 0 13 0 0 4 0 1 9 0 12 0 0 7 .0 10 . 0 0 1 . 0 1 5 . 0 0 2 . 0 16 . 0 0 7 . 0 0 4 . 0 0 2 . 0 0 1 . 0 3 4 . 0 3 2 . 0 11 . 0 0 0 . 0 0 7 . 0 1 0 . 0 2 6 - . 0 2 6 . 0 0 5 . 0 1 7 . 0 0 9 . 0 14 - . 0 1 3 - . 0 0 4 . 0 0 8 . 0 0 3 . 0 1 6 - . 0 0 6 - . 0 2 0 - . 0 0 4 - . 0 0 3 . 0 0 2 - . 0 0 4 - . 0 3 5 - . 0 2 8 . 0 1 0 - . 0 0 3 . 0 0 7 - . 0 0 0 - . 0 3 0 - . 0 2 6 . 0 1 0 . 0 1 9 157 S y n t h L P 3 d a t 0 2 2 0 2 9 03 5 0 4 5 0 4 7 04 9 04 5 0 4 5 0 18 0 10 0 14 0 0 7 0 10 0 12 0 13 . 0 2 4 . 0 5 0 . 0 3 3 . 0 5 7 . 0 5 3 . 0 6 0 . 0 64 . 0 5 0 . 0 3 0 . 0 2 5 . 0 2 2 . 0 2 1 . 0 3 1 . 0 1 2 . 0 1 1 . 0 0 5 . 0 1 9 . 0 0 1 . 0 1 1 . 0 2 5 . 0 2 3 . 0 3 3 . 0 2 1 . 0 0 2 . 0 0 2 . 0 0 2 . 0 0 6 . 0 2 4 . 0 2 9 . 0 2 7 . 0 3 5 . 0 2 5 . 0 3 3 . 0 3 8 . 0 5 1 . 0 4 8 . 0 5 1 . 0 4 6 . 0 4 6 . 0 12 . 0 14 . 0 0 6 . 0 15 . 0 0 9 . 0 0 9 - . 0 2 0 - . 0 2 3 - . 0 4 4 - . 0 2 7 - . 0 5 8 - . 0 3 6 - . 0 6 4 - . 0 6 3 - . 0 3 9 - . 0 2 5 - . 0 2 2 - . 0 1 8 - . 0 2 6 - . 0 3 1 - . 0 1 1 - . 0 1 1 . 0 12 . 0 2 4 . 0 0 5 . 0 13 . 0 2 4 . 0 2 1 . 0 2 9 . 0 14 - . 0 0 1 . 0 0 7 . 0 0 2 . 0 1 6 . 0 2 8 . 0 2 9 . 0 3 0 . 0 3 3 . 0 3 5 . 0 5 5 . 0 5 1 . 0 4 3 . 0 18 . 0 2 5 . 0 0 8 - . 0 1 9 - . 0 2 7 - . 0 2 2 - . 0 6 1 - . 0 2 1 - . 0 1 5 - . 0 2 6 - . 0 1 2 . 0 2 1 . 0 14 . 0 2 2 . 0 10 . 0 0 8 . 0 2 5 . 0 2 5 . 0 3 2 . 0 3 5 . 0 5 6 . 0 4 4 . 0 3 8 . 0 2 1 . 0 2 8 . 0 04 - . 0 2 1 - . 0 3 5 - . 0 2 2 - . 0 6 0 - . 0 2 3 - . 0 1 4 - . 0 1 9 - . 0 1 2 . 0 0 9 . 0 1 6 . 0 2 6 . 0 0 6 . 0 0 8 . 0 2 7 . 0 2 4 . 0 3 1 . 0 3 5 . 0 5 3 . 0 4 4 . 0 3 3 . 0 2 6 . 0 1 9 - . 0 0 2 - . 0 3 0 - . 0 4 4 - . 0 4 0 - . 0 6 1 - . 0 2 5 - . 0 1 3 - . 0 1 4 - . 0 1 0 . 0 0 0 . 0 18 . 0 3 1 . 0 0 3 . 0 0 7 . 0 2 4 . 0 2 3 . 0 3 3 . 0 3 6 . 0 4 9 . 0 4 5 . 0 2 5 . 0 2 5 . 0 12 - . 0 0 5 - . 0 4 5 - . 0 5 1 - . 0 5 6 - . 0 5 7 - . 0 2 5 - . 0 1 6 - . 0 1 2 - . 0 0 3 - . 0 0 3 . 0 2 2 . 0 3 5 - . 0 0 1 . 0 0 4 . 0 2 2 . 0 2 6 . 0 3 5 158 S y n t h L P 3 d a t 0 3 8 0 2 9 03 0 0 2 9 0 0 8 0 0 9 0 05 0 13 0 05 0 12 0 0 2 0 0 3 0 12 O i l 0 15 0 13 0 3 3 03 2 . 0 4 7 . 0 5 0 . 0 5 3 . 0 4 2 . 0 14 . 0 17 . 0 18 . 0 1 1 . 0 0 5 . 0 13 . 0 0 7 . 0 0 9 . 0 0 7 . 0 17 . 0 2 0 . 0 0 6 . 0 3 2 . 0 3 9 . 0 3 7 . 0 3 6 . 0 3 9 . 0 3 8 . 0 4 1 . 0 3 7 . 0 16 . 0 1 1 . 0 0 1 . 0 0 1 . 0 3 4 . 0 2 8 . 0 3 0 . 0 2 8 . 0 07 . 0 0 9 . 0 0 8 . 0 14 . 0 0 9 . 0 14 . 0 0 0 - . 0 0 8 - . 0 1 2 - . 0 1 3 - . 0 1 3 - . 0 1 4 - . 0 3 3 - . 0 3 5 - . 0 4 7 - . 0 5 5 - . 0 4 7 - . 0 3 7 - . 0 1 3 - . 0 2 1 - . 0 1 4 - . 0 1 1 . 0 10 . 0 14 . 0 0 9 . 0 0 4 - . O i l - . 0 2 3 - . 0 1 2 . 0 0 1 . 0 3 5 . 0 4 0 . 0 3 6 . 0 3 8 . 0 3 7 . 0 4 1 . 0 3 8 . 0 3 1 . 0 13 . 0 0 8 . 0 0 0 . 0 0 1 . 0 2 6 . 0 2 4 . 0 0 8 . 0 1 0 . 0 1 3 - . 0 1 2 - . 0 1 5 - . 0 1 8 - . 0 3 8 - . 0 5 9 - . 0 3 4 - . 0 2 4 - . O i l . 0 1 4 . 0 0 1 - . 0 2 8 . 0 0 8 . 0 3 8 . 0 4 2 . 0 4 2 . 0 2 6 . 0 0 3 . 0 0 7 . 0 2 7 . 0 2 1 . 0 0 6 . 0 04 . 0 0 8 - . 0 1 3 - . 0 1 9 - . 0 2 3 - . 0 4 4 - . 0 6 0 - . 0 2 9 - . 0 2 5 - . 0 0 8 . 0 1 1 . 0 0 0 - . 0 3 1 . 0 14 . 0 3 7 . 0 4 5 . 0 4 4 . 0 2 4 - . 0 0 0 . 0 13 . 0 2 8 . 0 1 5 . 0 0 4 . 0 0 1 . 0 0 2 - . 0 1 2 - . 0 2 1 - . 0 3 0 - . 0 4 8 - . 0 5 9 - . 0 2 3 - . 0 2 5 - . 0 0 7 . 0 10 - . 0 0 1 - . 0 3 0 . 0 2 1 . 0 3 6 . 0 4 6 . 0 4 5 . 0 2 2 - . 0 0 1 . 0 15 . 0 2 9 . 0 1 0 . 0 03 . 0 0 3 . 0 0 0 - . O i l - . 0 2 0 - . 0 3 3 - . 0 4 8 - . 0 5 7 - . 0 1 8 - . 0 2 4 - . 0 0 2 . 0 07 - . 0 0 3 - . 0 2 7 . 0 2 7 . 0 3 7 . 0 4 3 . 0 4 4 . 0 1 9 . 0 0 1 . 0 13 159 S y n t h L P 3 . d a t O i l . 0 1 2 0 1 5 . 0 1 6 . 0 1 5 0 1 0 . 0 0 2 0 0 7 - . 0 1 2 - . 0 1 2 0 0 8 - . 0 0 5 0 0 3 - . 0 0 5 - . 0 1 0 0 07 . 0 05 . 0 1 3 . 0 1 3 . 0 1 3 - . 0 1 0 - . 0 0 9 - . 0 09 - . O i l - . 0 0 6 . 0 02 160 APPENDIX C RESPONSE INPUT AND MOMENT-CURVATURE PREDICTION FOR COLQUITZ PIER £91 P9\\ .co i o E E 10 co c £ 1 E m co <£ 5 E E § CD CO • w cu: > c-CO CU > CU Q U. OS o o o o o CN 9191 m co iri II co cu cu Q o 61 ! CD IE io i® lO O'i o! E E, CD < o O CO CO r--f-co CO <-> o . § >> X (-1 E £ X E JE cd\" o f XI ai co . *! o c ' o to Q :o E O > 5 •a Z X I +: > d + .In-T5 a X CN 'ro co O o d o d o d 0) . :8 / CO II If * \" co \"I CN II £ E •in ; APPENDIX D CANNY DATA INPUT AND OUTPUT FILES FOR SAFETY RETROFITTED COLQUITZ PIER FOR EL CENTRO-1 CSFEC1.dat / / a n a l y s i s assumptions and output options t i t l e : s i n g l e column c o l q u i t z south s t r u c t u r e , V i c t o r i a , B . C f o r c e u n i t = KN le n g t h u n i t = m time u n i t = sec g r a v i t y a c c e l e r a t i o n g = 9.81 a n a l y s i s i n y - d i r e c t i o n i n c l u d i n g p - d e l t a e f f e c t output of o v e r a l l response output a l l of beam response output of nodal displacements output a l l of beam, column response output a l l of support response output extreme response //dynamic response c o n t r o l data i n t e g r a t i o n time i n t e r v a l . 0 . 0 2 s t a r t time 0, end time 40.96 Damping constant 0.05 p r o p o r t i o n a l to mass [M] newmark method,Beta-value 0.25 i n c l u d i n g Z - t r a n s l a t i o n a l i n e r t i a f o r c e s s c a l e f a c t o r 9.81 to Y-EQ f i l e = c : \\ s a q t h e s i s \\ s y n t h e c l . d a t master DOFs f o r a n a l y s i s c o n t r o l : Y - t r a n s l a t i o n s , 7-node response l i m i t 0.7 b i n a r y formatted output at every 0-steps //node l o c a t i o n s node 1 t o 6 every 1, (0 0 0), Zi=1.07 node 7 (0 0 9.42) //node degrees of freedom general degrees of freedom : 5-components node 1 e l i m i n a t e a l l components //node weight node 7, w=2450 //element data : column 1 2 BU100 TU100 AU90 CSFEC1.dat 2 3 BU100 TUIOO AU90 3 4 BUIOO TUIOO AU90 4 5 BUIOO TUIOO AU90 5 6 BUIOO TUIOO AU90 6 7 BUIOO TUIOO AU90 r(0 3) / / s t i f f n e s s and h y s t e r e s i s parameters UlOO CA7 3.3e7 0.0346 C(0 0) Y(11500 11500) A ( l 1) B(0.0000001 0.0 000001) P(0 3 0.01 0.01 0 0 0) U90 ELI 2.4647e7 2.22187 / / i n i t i a l l o a d node7, Pz=4160, p o s i t i v e i s compression 168 csfeel.TRF CANNY-E main program Author: Kang-Ning L i Copyright by Canny Consultants Pte L t d (Singapore), 1995-97 Report at Wed Feb 14 11:25:53 2001 s i n g l e column c o l q u i t z south s t r u c t u r e , V i c t o r i a , B.C 3-dimensional dynamic a n a l y s i s U n it system:KN,m,sec,rad. 1. ELEMENT EXTREME RESPONSE (1) Element Forces a) Column (Mj) [x: (Mb)Q(Mt)] [y: (Mb)Q(Mt)]AxialF C l ( l - 2 ) [x: (0.000-0.000) (0.000-0.000)] [y: (11500.000--11425 .831) (10 12 8.033~-10286.299)]4160.000~416 0.000 C2(2-3) [x: (0.000-0.000) (0.000-0.000)] [y: (10286.2 94~-1012 8.03 0) (88 30.228~-8 968.212)]4160.000~4160.000 C3(3-4) [x: (0.000-0.000) (0.000-0.000)] [y: (8968.219--8830.235) (7532 . 441--7650.158)]4160.000-4160.000 C4(4-5) [x: (0.000-0.000) (0.000-0.000)] [y: (7650 . 149--7532 . 455)'(6234 . 635--6332.068)] 4160.000-4160.000 C5(5-6) [x: (0.000-0.000) (0.000-0.000)] [y: (6332.074--6234 . 614) (4936 .83 6--5013.941)]4160.000-4160.000 C6 (6-7) [x: (0.000-0.000) (0.000-0.000)] [y: (5013.946--4936. 711) (3 63 9 .069--3695.846)]4160.000-4160.000 (2) Element D u c t i l i t y a) Column baseR(, ShearD) (, TAxialD) , topR C l ( l - 2 ) bx:0-0.0000-0.0000 by:-0 . 992101. 2947Y, Ae, tx:0-0.0000-0. 0000 ty:-0.8945C-0.8807C C2(2-3) bx:0-0.0000-0.0000 by:-0.8807C-0.8945C, Ae, tx:0-0.0000-0. 0000 ty:-0.7798C-0.7678C C3(3-4) bx:0-0.0000-0.0000 by:-0.7678C-0.7798C, Ae, tx:0 - 0.0000-0. 0000 ty:-0 . 665200 . 6550C C4(4-5) bx:0-0.0000 -6 .0000 by:-0.6550C-0.6652C, Ae, tx:0-0.0000-0. 0000 ty:-0.5506C-0.5421C C5(5-6) bx:0-0.0000-0.0000 by:-0.5421C-0.5506C, Ae, tx:0-0.0000-0. 0000 ty:-0.436000.4293C C6(6-7) bx:0-0.0000-0.0000 by:-0.4293C-0.4360C, Ae, tx:0-0.0000-0. 0000 ty:-0.321400.3164C (3) Extreme responses at c o n t r o l master DOF N7 TY D(0.28298911 - -0.29356885), A(4.9324 - -4.8565), V(1.1842 --1 . 3128) 169 csfecl.TRF 2. COMPUTATION TIME F i n i s h e d computation steps =2048, w i t h 127 steps s t i f f n e s s change T o t a l CPU time =1.00 sec Time of s t i f f n e s s i n i t i a l i z a t i o n =0.00 Time of b i n a r y f i l e output =0.00 Time of member response computation =0.00 Time of matrix LDU decomposition =0.00 Time of matrix s u b s t i t u t i o n =0.00 Time of numerical i n t e g r a t i o n =1.0 0 *** ANALYSIS NORMAL END *** 170 CSFECla.dat / / a n a l y s i s assumptions and output options t i t l e : s i n g l e column c o l q u i t z south s t r u c t u r e , V i c t o r i a , B . C f o r c e u n i t = KN l e n g t h u n i t = m time u n i t = sec g r a v i t y a c c e l e r a t i o n g = 9.81 a n a l y s i s i n y - d i r e c t i o n i n c l u d i n g p - d e l t a e f f e c t output of o v e r a l l response output of nodal displacement, v e l o c i t y and a c c e l e r a t i o n output a l l of column response //dynamic response c o n t r o l data i n t e g r a t i o n time i n t e r v a l 0.02 s t a r t time 0, end time 40.96 Damping constant 0.05 p r o p o r t i o n a l to mass [M] newmark method,Beta-value 0.25 i n c l u d i n g Z - t r a n s l a t i o n a l i n e r t i a forces s c a l e f a c t o r 9.81 t o Y-EQ f i l e = c : \\ s a q t h e s i s \\ s y n t h e c l . d a t master DOFs f o r a n a l y s i s c o n t r o l : Y - t r a n s l a t i o n s , 7-node response l i m i t 0.7 b i n a r y formatted output at every 0-steps //node l o c a t i o n s node 1 t o 6 every 1, (0 0 0), Zi=1.07 node 7 (0 0 9.42) //node degrees of freedom g e n e r a l degrees of freedom : 5-components node 1 e l i m i n a t e a l l components //node weight node 7, w=4050 //element data : column 1 2 BU100 TU100 AU90 2 3 BU100 TU100 AU90 3 4 BU100 TU100 AU90 4 5 BU100 TU100 AU90 CSFECla.dat 5 6 BU100 TUIOO AU90 6 7 BUIOO TUIOO AU90 r ( 0 3) / / s t i f f n e s s and h y s t e r e s i s parameters U100 CA7 3.3e7 0.0346 C(0 0) Y(11500 11500) A ( l 1) B(0.0000001 0.0 000001) P(0 3 0.01 0.01 0 0 0) U90 ELI 2.4647e7 2.22187 / / i n i t i a l l o a d node7, Pz=4160, p o s i t i v e i s compression 172 csfecla.TRF CANNY-E main program Author: Kang-Ning L i Copyright by Canny Consultants Pte L t d (Singapore) , 1995-97 Report at Wed Jan 31 14:09:57 2001 s i n g l e column c o l q u i t z south s t r u c t u r e , V i c t o r i a , B . C 3-dimensional dynamic a n a l y s i s U n i t system:KN,m,sec,rad. 1. ELEMENT EXTREME RESPONSE (1) Element Forces a) Column (Mj ) [x: (Mb)Q(Mt)] [y: (Mb)Q(Mt)]AxialF C l ( l - 2 ) [x: (0.000-0.000) (0.000-0.000)] [y: (11500.001--11500.004) (10 258.143--10348.912)]4160.000-4160.000 C2(2-3) [x: (0.000-0.000) (0.000-0.000)] [y: (10348.919--10258.139) (89 43.654--9022.814)] 4160.000-4160 . 000 C3 (3-4) [x: (0.000-0.000) (0.000-0.000)] [y: (9022.814--8943.669) (7629 .213--7696.72 5)]4160. 000-4160.00 0 C4 (4.-5) [x: (0.000-0.000) (0.000-0.000)] [y: (7696 . 743--762 9 . 209) (6314 . 744--6370.592)] 4160.000-4160.000 C5 (5-6) [x: (0.000-0.000) (0.000-0.000)] [y : (6370.606--6314.718) (5000 .240--5044.4 84)] 4160 . 000-4160.0 00 C6(6-7) [x: (0.000-0.000) (0.000-0.000)] [y: (5044.443--5000.213) (3685 .73 6--3718.380)]4160. 000-4160.000 (2) Element D u c t i l i t y a) Column baseR(, ShearD)(, A x i a l D ) , topR CI (1 -2) bx: 0-0 . 0000-0.0000 by: -4 .5675Y- 1 9973Y, Ae, t x : 0-0 .0000-0 . 0000 t y -0 . 8999C-0.8920C C2 (2 -3) bx: 0-0.0000-0.0000 by: -0 .8920C- 0 .8999C, Ae, t x : 0- 0 .0000-0 . 0000 t y -0 . 7846C-0.7777C C3 (3 -4) bx: 0-0 . 0000-0.0000 by: -0 .7777C- 0 .7846C, Ae, t x : 0-0 .0000- 0 . 0000 t y -0 . 6693C-0.6634C C4 (4 -5) bx: 0-0 . 0000-0.0000 by: -0 .6634C- 0 .6693C, Ae, t x : 0- 0 . 0000-0 . 0000 t y : -0 . 5540C-0.5491C C5 (5 -6) bx: 0-0 . 0000-0.0000 by: -0 .5491C- 0 . 5540C,V Ae, t x : 0-0 . 0000-0 . 0000 t y : -0 . 4387C-0.4348C C6 (6 -7) bx: 0-0.0000-0.0000 by: -0 .4348C-•0 .4386C, Ae, t x : 0-0 . 0000--0 . 0000 ty:-0.3233C-0.3205C (3) Extreme responses at c o n t r o l master DOF N7 TY D(0.34885630 - -0.30588371), A(3.0020 - -2.9756), V(1.0427 --1.1148) 173 c s f e c l a . T R F 2. COMPUTATION TIME F i n i s h e d computation s t e p s =2048, with 73 steps s t i f f n e s s change T o t a l CPU time =1.00 sec Time of s t i f f n e s s i n i t i a l i z a t i o n =0.00 Time of b i n a r y f i l e output =0.00 Time of member response computation =1.00 Time of matrix LDU decomposition =0.00 Time of matrix s u b s t i t u t i o n =0.00 Time of numerical i n t e g r a t i o n =0.00 *** ANALYSIS NORMAL END *** 174 "@en ; edm:hasType "Thesis/Dissertation"@en ; vivo:dateIssued "2001-11"@en ; edm:isShownAt "10.14288/1.0063980"@en ; dcterms:language "eng"@en ; ns0:degreeDiscipline "Civil Engineering"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "University of British Columbia"@en ; dcterms:rights "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en ; ns0:scholarLevel "Graduate"@en ; dcterms:title "Optimal retrofit strategy determination for bridges using decision analysis"@en ; dcterms:type "Text"@en ; ns0:identifierURI "http://hdl.handle.net/2429/11811"@en .