UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Risk-based retofit decision model for bridges Nishimura, Kim S. 1997

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_1997-0454.pdf [ 8.03MB ]
Metadata
JSON: 831-1.0050299.json
JSON-LD: 831-1.0050299-ld.json
RDF/XML (Pretty): 831-1.0050299-rdf.xml
RDF/JSON: 831-1.0050299-rdf.json
Turtle: 831-1.0050299-turtle.txt
N-Triples: 831-1.0050299-rdf-ntriples.txt
Original Record: 831-1.0050299-source.json
Full Text
831-1.0050299-fulltext.txt
Citation
831-1.0050299.ris

Full Text

RISK-BASED RETROFIT DECISION MODEL FOR BRIDGES by KIM S. NISffiMURA B.Eng., McGill University, 1995 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CIVIL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August 1997 ©Kim S. Nishimura, 1997 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of C^VI'L- E-AlC^ (\\€£-&.\r4 The University of British Columbia Vancouver, Canada Date A U G U S T 2.2. \^°[rf DE-6 (2/88) ABSTRACT A risk-based methodology for making bridge retrofit decisions is demonstrated through a case study of two reinforced concrete highway bridges which were damaged in the Northridge earthquake. An expected value decision model is constructed in order to select the optimal retrofit option for each bridge. The decision alternative which minimizes the total cost of the structure over its life is sought. The total cost includes the initial retrofit cost and the probabilistically predicted future damage cost. Seismic assessments of the Fairfax-Washington and La Cienega-Venice bridges were performed. The seismic hazard at the bridge sites, estimated in terms of intensity and annual probability, was established. The probability of damage was linked to the probability of occurrence of different levels of strong ground motion for a specific site. Inelastic dynamic analyses of the vulnerable bridge components produced estimates of the seismic structural damage for different earthquake intensity levels. These estimates were in the form of damage indices. The damage estimates were then interpreted in terms of dollar losses. Using the hazard information and the damage costs, an expected annual cost of future damages was calculated. Adding the estimated cost of retrofit and the present value of future damages, the total expected cost for each decision alternative was determined. Finally, the sensitivity of the decision model to the input values was investigated. The methodology presented demonstrates rational decision making in the face of inexact or approximate information. ii TABLE OF CONTENTS ABSTRACT TABLE OF CONTENTS LIST OF FIGURES LIST OF TABLES ACKNOWLEDGMENTS CHAPTER 1: Introduction 1.1 Background 1.1.1 History of the Caltrans Seismic Retrofit Program 1.1.2 The Northridge Earthquake 1.1.3 Seismic Retrofitting Process 1.1.4 Expected Value Decision Analysis 1.2 Objectives of Study 1.3 Scope of Study CHAPTER 2 : Bridges Damaged in the Northridge Earthquake 2.1 Overview of the Seismic Performance of Caltrans Highway Bridges 2.2 Case Study 2.2.1 Fairfax-Washington Undercrossing 2.2.1.1 Bridge Description 2.2.1.2 Damage Summary 2.2.2 La Cienega-Venice Undercrossing 2.2.2.1 Bridge Description 2.2.2.2 Damage Summary 2.2.3 Influence of Local Soil Conditions on Damage 2.2.4 Damage Cost Analysis 2.2.5 Retrofit Option 2.2.5.1 Retrofit Cost CHAPTER 3 : Preliminary Screening 3.1 Review of Existing Screening Methods 3.1.1 A T C Screening Method 3.1.2 WSDOT Screening Method 3.1.3 IDOT Screening Method 3.1.4 Caltrans Screening Method 3.2 A New Risk-Based Screening Method 30 3.2.1 Vulnerability Assessment 30 3.2.1.1 Seismic Hazard Analysis at the Bridge Site 30 3.2.1.2 Classification of Bridges based on Structural Characteristics 33 3.2.1.3 Fragility Analysis 33 3.2.2 Importance Assessment 36 3.2.3 Synthesis of Vulnerability and Importance 37 3.2.4 Discussion •-• 38 C H A P T E R 4: Expected Value Decision Analysis 39 4.1 Bayesian Decision Theory 39 4.2 Bridge Seismic Retrofit Decisions 40 4.2.1 The Decision Process 40 4.2.2 Case Study Decision Model 42 C H A P T E R 5: Seismicity 44 5.1 Seismic Hazard 44 5.1.1 Source Zones 45 5.1.2 Annual Occurrence Rates 48 i '5.1.3 Earthquake Probabilities 51 5.2 Earthquake Records 54 5.2.1 Surface Records 54 5.2.2 Selecting and Scaling Natural Earthquake Records 55 5.2.3 Simplified Selection and Scaling Procedure 56 5.2.4 Earthquake Records Used in Case Study 57 C H A P T E R 6: Damage Analysis 63 6.1 Damage Indices 63 6.1.1 Damage Index Calibration 65 6.2 Computer Program RUAUMOKO 67 6.2.1 Description of Program Features 67 6.3 General Aspects of the Bridge Bent Modeling 69 6.3.1 Standard Caltrans Single-Column Bent 71 6.3.2 Fairfax-Washington Bent 73 6.3.3 La Cienega-VeniceBent 74 6.4 Pushover Analyses 75 6.5 Inelastic Dynamic Analyses 76 6.6 Analysis Results 76 6.7 Discussion 81 iv CHAPTER 7: Loss Estimate 83 7.1 Damage Estimate 83 7.1.1 Damage Categorization 83 7.1.2 Expected Reduction in Damage (ERD) 84 7.1.3 Summary of Damage Estimate 85 7.2 Damage Cost Estimate 87 7.2.1 Direct Costs 88 7.2.1.1 Relating Direct Costs to Damage Indices 89 7.2.1.2 Calculation of Direct Damage Costs 92 7.2.2 Indirect Costs 95 7.2.2.1 Calculation of Indirect Damage Costs 97 7.2.3 Summary of Damage Cost Estimate 99 CHAPTER 8: Decision and Sensitivity 101 8.1 Initial Investment of Retrofit Options 101 8.2 Net Present Cost (NPC) 102 8.2.1 Planning Period. 102 8.2.2 Discount Rate 102 8.2.3. N P C Calculation 103 8.3 Cost Comparison 104 8.4 Benefit/Cost Analysis 106 8.5 Sensitivity Analysis 107 8.5.1 Seismicity 107 8.5.2 Damage Costs I l l 8.5.3 Discount Rate 112 8.6 Discussion 113 CHAPTER 9: Conclusions 115 REFERENCES 119 APPENDIX A: Structural drawings of Fairfax-Washington and La Cienega-Venice bridges A l APPENDIX B : Caltrans seismic work cost information B l APPENDIX C: PCACOL files for moment-axial load interaction of bridge columns CI APPENDIX D: RESPONSE files for moment-curvature predictions for bridge columns D I APPENDIX E: RUAUMOKO files for inelastic damage analysis E l v LIST OF FIGURES CHAPTER 1 Figure 1.1: Epicentre of the Northridge Earthquake (from NIST, 1994) 4 CHAPTER 2 Figure 2.1: Map of Main Bridge Damage Sites (from NIST, 1994) 10 Figure 2.2: Column Damage on the Fairfax-Washington Bridge (from Caltrans, 1994a) 13 Figure 2.3: Column Damage on the La Cienega-Venice Bridge (from Caltrans, 1994a) 16 CHAPTER 3 Figure 3.1: Basics Steps of Probabilistic Seismic Hazard Analysis (from Reiter, 1990) 32 Figure 3.2: Hierarchy of Structural Properties (from Basoz and Kiremidjian, 1995) 33 Figure 3.3: Fragility curves (from Basoz and Kiremidjian, 1995) 35 CHAPTER 4 Figure 4.1: Decision tree 43 CHAPTER 5 Figure 5.1: Source zones for coastal California (from Hanson et al., 1995) 47 Figure 5.2: Design spectrum (from NCHRP 12-33, 1993) 56 Figure 5.3: Northridge earthquake excitation (a) acceleration time history and (b) acceleration response spectrum 59 Figure 5.4: Whittier earthquake excitation (a) acceleration time history and (b) acceleration response spectrum 60 CHAPTER 6 Figure 6.1: Bilinear hysteresis model in RUAUMOKO (from Carr, 1996) 70 Figure 6.2: Nonlinear model of FW bent 3 74 Figure 6.3: Nonlinear model of CV bent 4 75 Figure 6.4: Analysis results for FW (a) displacement time history, (b) acceleration time history and (c) damage index time history 78 Figure 6.5: Analysis results for CV (a) displacement time history, (b) acceleration time history and (c) damage index time history 79 Figure 6.6: Variation of the global damage index with the PGA for (a) FW and (b) CV 80 CHAPTER 7 Figure 7.1: Deterministic Mapping (from Gunturi and Shah, 1993) 90 Figure 7.2: Relationship between DDI and RDI 91 vi LIST OF TABLES CHAPTER 2 Table 2.1: Replacement Costs in 1994 US dollars (from Caltrans, 1994b) 19 Table 2.2: Seismic Work Costs in 1992 US dollars (from Caltrans, 1992) 22 Table 2.3: Estimated Retrofit Costs in 1992 US dollars 23 CHAPTER 5 Table 5.1: Modified Mercalli Intensity Scale (from EERI, 1994a) 49 Table 5.2: Conversion from MMI to Richter Magnitude 50 Table 5.3: Annual Occurrence Rates for Zone 23 (from Hanson et al., 1995) 51 Table 5.4: Probabilities of Earthquakes of Intensity Ij 52 Table 5.5: Annual Earthquake Probabilities 54 Table 5.6: Relationship between MMI and PGA 61 CHAPTER 6 Table 6.1: Damage Classification suggested by Park, Ang and Wen 66 Table 6.2: Damage classification suggested by Stone and Taylor 66 Table 6.3: Characteristics of the standard Caltrans column (from Stone and Taylor, 1993) 72 CHAPTER 7 Table 7.1: Damage categories used in loss estimate 84 Table 7.2: Summary of global damage indices 85 Table 7.3: Average replacement costs for different bridge types in 1995 US dollars (from Caltrans, 1995) 90 Table 7.4: Estimated removal and replacement costs in millions, 1989 US dollars 92 Table 7.5: Estimated vs. actual replacement costs in millions, 1989 US dollars 93 Table 7.6: Estimated direct costs for FW in millions, 1989 US dollars 94 Table 7.7: Estimated direct costs for CV in millions, 1989 US dollars 94 Table 7.8: Indirect cost per vehicle in 1994 US dollars 97 Table 7.9: Estimated Indirect Costs for FW in millions, 1989 US dollars 98 Table 7.10: Estimated Indirect Costs for CV in millions, 1989 US dollars 98 Table 7.11: Estimated total costs for FW in millions, 1989 US dollars 99 Table 7.12: Estimated total costs for CV in millions, 1989 US dollars 99 CHAPTER 8 Table 8.1: Cost estimate for retrofit option in 1989 US dollars 102 Table 8.2: NPCs (direct costs only) for the two options in millions, 1989 US dollars 105 vii Table 8.3: NPCs (direct plus indirect costs) for the two options in millions, 1989 US dollars 105 Table 8.4: First four data sets used in sensitivity analysis for earthquake probability data 108 Table 8.5: NPCs obtained by varying the earthquake probability data (in millions, 1989 US dollars) : 109 Table 8.6: Percentage change in NPCs due to the variation of the earthquake probability data 110 Table 8.7: NPCs obtained by varying the direct costs (in millions, 1989 US dollars) I l l Table 8.8: NPCs obtained by varying the indirect costs (in millions, 1989 US dollars) 112 Table 8.9: NPCs obtained by varying the discount rate (in millions, 1989 US dollars) 113 A C K N O W L E D G E M E N T S Many thanks to my supervisor, Dr. Robert Sexsmith, who provided guidance and advice throughout this research project. I would like to thank Mark Yashinsky and Rachel Falsetti of Caltrans. Their help in locating references and in obtaining various Caltrans data was greatly appreciated. The financial support of the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. IX CHAPTER 1 Introduction One very important lesson learned from earthquakes which have occurred in the past is that bridge structures are quite vulnerable when subjected to seismic loading. Many bridges were designed before the advent of seismic provisions in building codes. For this reason, it has been a priority for highway and transportation departments over the past few years to repair or retrofit such structures in order to achieve an acceptable level of seismic performance. The high costs associated with retrofitting bridges, however, make it infeasible to retrofit all structures in need of upgrading. Rational decisions must be made about which bridges should be retrofitted and about the order in which they should be retrofitted. A variety of priority schemes have been proposed and are currently in use in transportation departments across North America. Factors involved in the decision-making process include the importance of the structure, the cost of retrofit, and the level of seismic risk. This last criterion is the most difficult to determine since it requires knowledge of the likely level of damage that a bridge will sustain in an earthquake. If the performance of a bridge in an earthquake could be predicted with reasonable accuracy along with the damage to the structure and the cost of repair or replacement, then retrofit decisions and disaster planning would be made much easier. The majority of the research on the seismic response of bridges has been driven by the poor performance of existing bridges in actual earthquakes. The major earthquakes which 1 Chapter 1 - Introduction have occurred in California over the past 25 years have contributed and continue to contribute to advances in research about the seismic behaviour of bridges. Not only have they revealed information about actual bridge behaviour, but they have also unveiled direct and indirect consequences of bridge damage. This information will be particularly valuable in trying to predict the economic consequences of bridge damage in future earthquakes. 1.1 Background 1.1.1 History of the Caltrans Seismic Retrofit Program The 1971 San Fernando earthquake was a key event in making people recognize the vulnerability of California's bridges to strong ground motion. Until then, bridges had been designed to resist only minor seismic forces. At that point in time, most of the state's transportation system was already in place, and the cost of damage to California highway bridges due to earthquakes had totaled approximately $100 000. In the San Fernando earthquake alone the cost of damage was $15 million (NIST, 1994). With the serious bridge damage caused by the earthquake as an admonition, Caltrans launched Phase 1 of their seismic retrofit program, which focused on preventing superstructures from falling off their supports. This entailed retrofitting bridges with cable and rod restrainers, shear keys, bearing replacements and catcher blocks. At a cost of 55 million dollars, 1400 of the state's 12 000 bridges were retrofitted. When the Whittier Narrows earthquake hit California in 1987, the need to provide existing bridge columns with additional shear strength and ductility was made evident. The 1989 Loma Prieta earthquake occurred two years later, creating enough political pressure for 2 Chapter 1 - Introduction Caltrans to launch Phase 2 of their seismic retrofit program. Phase 2 targeted 1039 bridges for seismic retrofit at a total cost of 750 million dollars. Finally, the Northridge earthquake shook southern California in 1994. The earthquake caused the collapse of 6 major highway bridges and the damage of 157 others; the cost of repair and replacement was roughly $1.5 billion. As a result, 1364 more bridges were added to the retrofit list at an estimated cost of 1050 million dollars (Yashinsky et al., 1995). Clearly, the lessons learned from large earthquakes have been a driving force in the implementation and orientation of Caltrans' bridge seismic retrofit program. These historical earthquakes also raise public awareness and stimulate research. It is important to make use of the available data if hazard mitigation is to become a priority. 1.1.2 The Northridge Earthquake The Northridge earthquake occurred at 4:31am local time on January 17, 1994. Its epicentre lay below the city of Northridge in California's San Fernando Valley, 30 km northwest of Los Angeles. Its focal depth was 19 km. With a surface wave magnitude of 6.8, this earthquake shook the heavily populated Los Angeles area (see Figure 1.1). Since there was no evidence of surface rupture, the Northridge earthquake was described as a blind thrust of a previously unmapped fault beneath the San Fernando Valley (NIST, 1994). 3 Chapter 1 - Introduction Figure 1.1: Epicentre of the Northridge Earthquake (from NIST, 1994) 4 Chapter 1 - Introduction According to the California Strong Motion Instrumentation Program, the peak horizontal and vertical ground accelerations were 1.82g and 1.18g respectively at the Tarzana site approximately 7 km south of the epicentre. The closest free-field sensor to the 5/14 interchange recorded a peak horizontal acceleration of 0.9lg and a peak vertical acceleration of 0.6g approximately 15 km from the epicentre and 6 km from the interchange. The free-field sensors near the damaged Santa Monica structures did not function, but based on the free-field acceleration peaks at surrounding sites, the peak horizontal and vertical accelerations were estimated to be approximately 0.5g and 0.2g respectively (Caltrans, 1994a). Relative to traditional attenuation curves, the peak ground accelerations recorded during the Northridge earthquake were approximately one standard deviation larger. At an average distance of 27 km north of the source, the average peak horizontal acceleration was 0.70 g, the average peak vertical acceleration was 0.47 g and the average duration of ground shaking was 8 seconds (Astaneh-Asl et al., 1994). 1.1.3 Seismic Retrofitting Process It is not economically feasible to retrofit all the seismically deficient bridges of a transportation network over a very short period of time. The bridges which are in more critical need of retrofitting should be considered first. Bridges must therefore be ranked according to the order in which they should be retrofitted. The prioritization of bridges must consider economic and social issues as well as the structure's seismic deficiencies. After the bridges in a network have been prioritized, a more detailed seismic assessment of the more critical ones will determine whether they should be retrofitted or whether the risk of seismic Chapter 1 - Introduction damage should be accepted. According to Buckle et al. (1991) the seismic retrofitting process can be summarized in three steps: 1. Preliminary screening 2. Detailed evaluation 3. Design of retrofit measures The chapters of this thesis describe some of the existing preliminary screening methods and then focus on a detailed evaluation process; results from the latter are used in an expected value retrofit decision model. 1.1.4 Expected Value Decision Analysis Bayesian decision theory suggests that expected values can be used to rank the alternatives in a decision problem which involves uncertainty. The expected value for each alternative is the sum of the products of the costs of the possible outcomes and their corresponding probabilities. In the case of bridge seismic retrofitting, the decision which minimizes the total cost of the structure over its life is sought. The total cost includes the initial retrofit cost and the probabilistically predicted future damage cost. A decision analysis can be thought of as a very thorough screening procedure. If unlimited funds were available for screening bridges, a complete decision analysis could be performed for all the bridges in a given network. In this ideal situation, the bridges could then be prioritized based on the results of a benefit/cost analysis. The benefit is the expected cost savings to be gained from the retrofit and the cost is the initial cost of the rehabilitation. Clearly, retrofit projects with higher benefit/cost ratios are more economically justifiable. The rules and principles followed in making rational decisions should therefore apply to screening 6 Chapter 1 - Introduction procedures as well. A screening method is simply a quicker and less costly way of ranking bridges. 1.2 Objectives of Study The primary objectives of this thesis are to develop and demonstrate a risk-based retrofit decision model for bridges. This involves identifying what information is needed, how it can be obtained and, finally, how it can be organized in a decision analysis. Where the required information is unavailable, reasonable estimates are made. Ultimately, the goal is to provide a rational tool which will facilitate retrofit decision-making and disaster planning. A secondary objective is to examine how current screening procedures are dealing with the key issues involved in retrofit decision analysis. Since screening and decision making have the same goal of establishing seismic retrofit priorities, it is logical to expect screening rules and decision rules to be based on the same principles. 1.3 Scope of Study The expected value decision process is demonstrated through a case study involving two Caltrans-owned reinforced concrete box girder bridges which were damaged in the 1994 Northridge earthquake. These two bridges were screened by Caltrans, but had not yet been retrofitted in Phase 2 of their seismic retrofit program. The hypothetical retrofit decision that could have been made in 1989, after the Loma Prieta earthquake, is examined. This hindsight study is a valuable exercise since actual damage costs are known; other relevant aspects of the decision process can therefore be explored. Although the decision process discussed in this thesis enables the comparison of several retrofit schemes, only the two options of either no retrofit, or a fully effective retrofit are considered here. 7 Chapter 1 - Introduction Seismic assessments of the Fairfax-Washington and La Cienega-Venice bridges located on the Santa Monica freeway were performed. As a first step in the expected value decision process, the seismic hazard at the bridge sites was established. The annual probabilities were determined for specific earthquake intensity levels. In this way, the probabilities of occurrence of all possible future earthquakes could be accounted for in the decision process. Using engineering judgment, vulnerable elements in the bridges were identified. Models of these elements were subjected to inelastic dynamic analyses under earthquake motions corresponding to each intensity level specified previously. The nonlinear analyses yielded quantitative estimates of the seismic structural damage in the form of damage indices. The damage estimates were subsequently interpreted in terms of dollar losses. Using the hazard information and the damage costs, an expected annual cost of future damages was calculated. Applying a time conversion factor to the expected annual cost, the present value of future damages was obtained. Adding the estimated cost of retrofit and the present value of future damages, the total expected cost for each decision alternative was determined. Finally, the sensitivity of the decision model to the input values was investigated. The methodology presented demonstrates rational decision making in the face of inexact or approximate information. 8 CHAPTER 2 Bridges Damaged in the Northridge Earthquake 2.1 Overview of the Seismic Performance of Caltrans Highway Bridges Most bridges in the Los Angeles area performed very well in the Northridge earthquake. In particular, the adequate seismic performance of bridges designed after the late 70's attested to the importance of revisions to bridge codes which occurred at about that time. These revisions seemed to have succeeded in more accurately accounting for earthquake loads in the design of bridge structures. According to strong ground motion records, approximately 1600 Caltrans bridges were subjected to accelerations greater or equal to 0.25g during the Northridge earthquake. Of these, 132 had been retrofitted during Phase 1 of the Caltrans program, and 79 had been retrofitted during Phase 2. None of the bridges with Phase 2 retrofits experienced serious damage, but some with Phase 1 retrofits failed (Yashinsky et al., 1995). Nonetheless, certain highway bridges were severely damaged as a consequence of the earthquake. This damage resulted in considerable cost to the State of California in the form of repair and replacement of bridges as well as transportation delays and disruptions. In some cases, bridge damage hindered emergency response. Several of the collapsed bridges were located less than 12 km north of the epicentre. Other severely damaged structures were located in an area approximately 25 km south of Northridge on a section of the Santa Monica Freeway (see Figure 2.1). 9 Chapter 2 - Bridges Damaged in the Northridge Earthquake Chapter 2 - Bridges Damaged in the Northridge Earthquake Steel bridges fared well in the Northridge earthquake with the exception of 4 bridges which displayed damage to their concrete substructures, steel diaphragms, and/or connections of their reinforced concrete substructures to their steel superstructures. Despite these signs of distress, damage was considered minor and all of the steel bridges remained serviceable after the earthquake (Astaneh-Asl et al., 1994). The majority of bridges which were damaged were concrete box girder systems. The preliminary report issued by the Canadian Association for Earthquake Engineering (CAEE, 1994) discusses the seismic performance of the extensively damaged highway structures. It states that displacements at expansion joints and at the abutments of several bridges caused noticeable damage. Pounding damage was also observed in some instances. The report stresses that inadequate shear capacity in short columns, inadequate hinge restrainers and insufficient seat widths were largely to blame for the observed damage. The Earthquake Engineering Research Institute's reconnaissance report (EERI, 1994b) points out that architectural flares on columns made the shear problem worse since they failed to spall off during the strong shaking. This had the effect of reducing the effective length of many columns. The EERI report also brings forth the observation that several column shear failures occurred in multi-column bents. Bridge designs of this nature had been ranked low on the retrofit priority list prior to the Northridge earthquake. Other observations include damage due to skewed superstructure hinges and the apparent success of steel jacket and foundation retrofits. In addition, an internal report by the National Institute of Standards and Technology (NIST, 1994) highlighted the poor seismic performance of steel rocker bearings. Detailed 11 Chapter 2 - Bridges Damaged in the Northridge Earthquake discussions of the structural damage to specific bridges can be found in all of the aforementioned reports. 2.2 Case Study The proposed decision process will be demonstrated through a case study of two Caltrans highway bridges which were damaged in the Northridge earthquake. The two structures are described in the following sections. Bridge descriptions and damage summaries are based on the Post Earthquake Investigation Report issued by the Caltrans Division of Structures (Caltrans, 1994a). 2.2.1 Fairfax-Washington Undercrossing 2.2.1.1 Bridge Description The Fairfax-Washington Undercrossing is a Caltrans highway bridge located on Interstate 10, also known as the Santa Monica Freeway. The structural drawings are found in Appendix A. The bridge consists of two structures joined by a floating slab connection. Each structure consists of two frames with a total length of 577 feet. The right bridge (eastbound structure) is a seven span structure with a width varying from 72 feet to 74 feet, while the left bridge (westbound structure) is an eight span structure with a width varying from 72 feet to 110 feet. The superstructure is a reinforced concrete box girder with a depth varying from 4'-9" to 5'-6". The hinge between the two frames of each side of the bridge has a seat width of 6". The overall skew of the structure varies from 5 degrees to 45 degrees. The superstructure rests on bearings which are anchored to concrete blocks at the abutments. The latter are founded on spread footings. 12 Chapter 2 - Bridges Damaged in the Northridge Earthquake The substructure consists of pier walls for the bents adjacent to the abutments, and either three or four column bents at all other locations. All columns are round and prismatic with a diameter of 4'; some are pinned at the base while others are designed to be fixed. Designed in 1962 and constructed in 1964, the Fairfax-Washington Undercrossing is a pre-1971 structure which was retrofitted with cable restrainers at the hinge in 1974. 2.2.1.2 Damage Summary The bridge suffered what was classified by Caltrans as major damage without collapse. All columns in bent 3 lost their confinement steel and experienced a complete disintegration of their concrete cores. In addition, the longitudinal steel buckled, forming a mushroom shape (see Figure 2.2). Figure 2.2: Column Damage on the Fairfax-Washington Bridge (from Caltrans, 1994a) 13 Chapter 2 - Bridges Damaged in the Northridge Earthquake Due to the partial collapse of the bent 3 columns, the superstructure sagged at that location and came to rest on pier 2 and on the hinge in span 3. This caused the superstructure to lift off the rocker bearing at the west abutment. The columns in bent 4 were also damaged, exhibiting large shear cracks at mid-height. Some other columns showed signs of minor spalling. It is possible that the west abutment underwent some longitudinal movement during the earthquake since a one foot gap was observed between the soil and the abutment face during the post earthquake investigation. It should also be noted that the excavation of two of the footings at bent 3 revealed that no apparent damage had occurred below ground level. According to the members of the Northridge Earthquake Post Earthquake Investigation Team dispatched by the Caltrans Division of Structures, an analysis of the damage development and collapse mechanism can be summarised as follows: Eastbound Structure: The transverse displacement of the first frame was largely resisted by the columns of bent 3. Following the development of plastic hinges at the tops of the columns, the compression concrete crushed and the longitudinal steel buckled. At this point, the shear demand in the top portion of the columns caused them to collapse. The second frame showed signs of minor damage due to plastic hinging at the tops of the columns. It was speculated that the lesser damage could be attributed to the frame's greater redundancy and to the columns' greater ductility. The redundancy comes from the frame's additional bent, while the increased column ductility stems from the fact that they were pinned at the base and contained less longitudinal steel. 14 Chapter 2 - Bridges Damaged in the Northridge Earthquake Westbound Structure: Most aspects of the seismic response of the westbound structure are very similar to those described for the eastbound structure. However, in the left bridge, the columns of bent 4 had major shear cracks at the columns' mid-height. The pinned connections at the base of the columns as well as the proportionately greater amount of longitudinal column reinforcement were noted in order to explain the observed shear failures. 2.2.2 La Cienega-Venice Undercrossing 2.2.2.1 Bridge Description The La Cienega-Venice Undercrossing is another Caltrans bridge located on the Santa Monica freeway a few kilometres east of Fairfax-Washington. The structural drawings are found in Appendix A. The eastbound and westbound portions of the structure are connected by a longitudinal joint at the median. The bridges consist of 3 frames with seven spans for a total length of 871 feet. The left bridge has a constant width of 70 feet while the right bridge has a width which varies from 70 feet to 85 feet. The superstructure is again a reinforced concrete box girder with a constant depth of 6'-3". The hinge seat width is approximately 6", and the skew varies from 5 degrees to 41 degrees. The substructure consists of pier walls for the bents adjacent to the abutments, and either three of four column bents at all other locations. All columns are round and prismatic with a diameter of 4'; some are pinned at the base while others are designed to be fixed. Like the Fairfax-Washington Undercrossing, this structure was designed in 1962 and built in 1964. The hinges were retrofitted with 1 1/4" diameter H.S. rods in 1978. 15 Chapter 2 - Bridges Damaged in the Northridge Earthquake 2.2.2.2 Damage Summary La Cienega-Venice was classified as having suffered major damage (collapsed structure). Global damage included the collapse of bents 3 to 7 which caused the superstructure to come to rest on masonry storage units under the bridge. The confinement steel in many of the columns from these bents was lost, concrete cores disintegrated, and longitudinal steel buckled. In addition, span 6 of the westbound structure dropped when the restrainers at the hinge failed either by shearing or by pulling out. As in the case of Fairfax-Washington, there was no sign of damage below ground level. Figure 2.3 shows some of the column damage. Figure 2.3: Column Damage on the La Cienega-Venice Bridge (from Caltrans, 1994a) 16 Chapter 2 - Bridges Damaged in the Northridge Earthquake The collapse mechanism proposed by Caltrans' Post Earthquake Investigation Team is similar to that proposed for the Fairfax-Washington Undercrossing. In the case of columns with damage to their upper portion, the same hypothesis of plastic hinging followed by crushing of the concrete core, buckling of the longitudinal steel and an increase in the shear demand was suggested. The fact that some columns experienced this type of failure near the base of the column may be attributable to the differences in stiffness of the column footings due to asphalt, compacted fill or other surrounding materials. Finally, the restrainer rods at the hinge in span 6 of the westbound freeway failed, causing the collapse of this span. It is thought that the vertical displacement associated with the collapse of bent 7 columns contributed to the unseating of the span. 2.2.3 Influence of Local Soil Conditions on Damage The EERI reconnaissance report (EERI, 1994b) revealed that the damage observed in the area of the Santa Monica Freeway overpasses was localised. Several bridges with similar structural characteristics located closer to the epicentre displayed much less damage. The report suggests that local soil conditions may have been responsible for the poor seismic performance of the FW and CV bridges. A study of the subsurface conditions carried out after the earthquake revealed that the area consisted of low-lying ground with scattered swamps. Soft peats and organic clays were found up to depths of 20 feet. According to the observations of the EERI team, there was a great deal of variability in the soil conditions in the vicinity, from very soft soils to more adequate granular materials. The soil log of test borings included with the structural drawings were examined for the two bridges (see Appendix A). In both cases, loose sands were reported near the surface 17 Chapter 2 - Bridges Damaged in the Northridge Earthquake with a transition to dense sands and sandstone at greater depths. Although this shows that the bridges were founded on competent subsurface materials, it is still possible that surrounding areas of softer soil amplified the ground motions. 2.2.4 Damage Cost Analysis The principal value of performing a hindsight decision analysis lies in the fact that actual damage costs are known. While future decisions necessarily include subjective estimates of future damage costs, the known damage costs in a hindsight study provide the ability to focus on other aspects of the decision problem. Bridge damage can result in several costly consequences. The most obvious of these is the need to repair the damaged structure. In certain cases, the extent of the damage is such that the bridge must be removed and replaced with a completely new structure. Another serious consequence of seismic damage relates to deaths and injuries to people using the bridge. Perhaps less obvious are the financial repercussions caused by the loss of use of the bridge. Bridges often constitute vital links in a transportation network; disruptions to the flow of traffic can affect a large portion of an urban population. Also, the response of emergency vehicles after an earthquake can be delayed if certain critical bridges are out of service. In the case of the FW and CV bridges, damage was deemed irreparable and they were demolished and replaced by new structures. Since no cost data exists relating to the bridge's loss of use and since no casualties or injuries were reported, actual damage costs only include those associated with the replacement of the structures. It should be noted that actual removal costs were not available for the individual bridges. The amounts of the bids for the 18 Chapter 2 - Bridges Damaged in the Northridge Earthquake replacement of the FW and CV bridges were obtained from Caltrans and are listed in table 2.1. Table 2.1: Replacement Costs in 1994 US dollars (from Caltrans, 1994b) Bridge Replacement Cost FW $5.54 million + incentive CV $9.86 million + incentive The incentive in Table 2.1 refers to incentive contracts written by Caltrans to encourage early completion of the projects. These are discussed in more detail in Chapter 7. Taking advantage of hindsight in this particular case, the actual removal/replacement costs will be compared to the damage costs predicted in Chapter 6. This gives an indication of the accuracy of the loss estimate. 2.2.5 Retrofit Option Prior to the Northridge earthquake, the FW and CV bridges had figured relatively low on Caltrans' retrofit priority list. According to the EERI reconnaissance report (EERI, 1994b), this was mainly due to the fact that they were both multi-column bent structures and were expected to perform better than the less redundant single-column bent systems. Caltrans had generally established that single column bent retrofits were a priority over multiple column bent retrofits. While Caltrans essentially made the decision to not retrofit the structure prior to the Northridge earthquake, the objective of this study is to examine the hypothetical retrofit 19 Chapter 2 - Bridges Damaged in the Northridge Earthquake decision that could have been made in 1989. In this study, only the two options of either no retrofit, or a fully effective retrofit, were considered. A retrofit scenario for each bridge was proposed based on observed structural deficiencies. The suggested retrofit scheme was based on a review of seismic retrofitting techniques by Mitchell et al. (1994). These authors highlight some of the most common deficiencies in various bridge components and describe techniques to mitigate the problems. In light of the very poor detailing in the columns of these bridges, column retrofits were considered a plausible retrofit option. Extra confinement for the concrete core would be needed to ensure a more ductile seismic response. Added lateral support for the longitudinal bars would also be required to prevent buckling. A full-height, grouted steel jacket would be effective in fulfilling these requirements. The jacket would also increase the shear capacity of the columns. The column footings were also deemed inadequate based on the guidelines provided by Mitchell et al. (1994). Due to the absence of top steel and due to their poor flexural and shear strengths, complete foundation retrofits were recommended. This would involve adding top steel and increasing the footing size. Finally, anchoring the abutments to the surrounding soil could reduce seismic damage by limiting movement of the superstructure. For the sake of this hindsight study, it was therefore assumed that following the Loma Prieta earthquake in 1989, the decision-maker was presented with two options: 1) retrofitting the footings, jacketing all of the bridge columns and providing abutment tiebacks and 2) doing nothing and accepting the risk of future seismic damage. Since the purpose of this study is to make bridge retrofit decisions based on risk and cost, it is essential that the decision-maker have access to all pertinent cost information. In 20 Chapter 2 - Bridges Damaged in the Northridge Earthquake deciding whether or not to retrofit a particular bridge, the decision-maker will need to know the present cost of the various retrofit options. 2.2.5.1 Retrofit Cost General cost estimates based on past seismic work were obtained from Caltrans (Caltrans, 1992). These values reflect averages of previous bridge retrofit contracts. The cost of the proposed retrofit scheme in 1992 US dollars was estimated by adding up the costs associated with the foundation retrofits, the column jacketing and the abutment tiebacks. Table 2.2 shows the costs of specific seismic work for Caltrans. The data used to obtain these cost estimates are found in Appendix B. 21 Chapter 2 - Bridges Damaged in the Northridge Earthquake Table 2.2: Seismic Work Costs in 1992 US dollars (from Caltrans, 1992) Description Unit Total Cost Replace bearings ea $2 550 5' diam. CIDH piles If $450 Catcher Blocks ea $2 300 Abutment Tiebacks ea $5 000 Rebuild Abutment If $3 600 Hinge Seat Extender ea $5 800 Column retrofit (F type) column $111 000* Column retrofit (P type) column $17 000* Replace Bridge (Remove) sf $20 (Replace) sf $68 Restrainers '(Restrainer cable type) lb $5.30 (Restrainer rod type) lb $3.50 * Cost revised to reflect average of contract totals Note that an F type column retrofit consists of a full-height grouted steel shell and a complete footing retrofit. The letter F refers to the fixity at the base of the column. This type of retrofit prevents the lap splice at the base of the column from slipping and hence ensures the formation of a plastic hinge. A P type retrofit is a partial-height steel shell in which the gap between the casing and the concrete column is filled with polystyrene. This allows the lap splice to slip, causing a hinge to form at the base of the column in the event of seismic loading (Caltrans, 1986). 22 Chapter 2 - Bridges Damaged in the Northridge Earthquake One can simply add up the costs for the seismic work involved in a contemplated retrofit scenario to get an estimated retrofit cost. Of course, the cost obtained in this way will be approximate and will vary according to the particularities of each individual bridge. Knowing that the column damage was either directly or indirectly responsible for the sustained seismic damage during the Northridge earthquake, it seemed fair to assume that the retrofit would completely eliminate the damage under the imposed loads. The investment of the retrofit option for each bridge is tabulated below (see Table 2.3). Table 2.3: Estimated Retrofit Costs in 1992 US dollars Bridge Estimated Retrofit Cost FW $3.38 million CV $4.29 million These estimated retrofit costs are used in the decision process described in Chapter 4. The total expected cost, comprising the retrofit costs and the expected future damage costs, is the criterion by which the options are ranked in this case study. Seismic assessments of the two bridges are carried out in order to obtain estimates of the future damage costs. Prior to this exercise, a review and discussion of current bridge screening methods put retrofit decision analysis into perspective. Since establishing seismic retrofit priorities is a common goal of the screening and decision processes, it is important to determine which approaches achieve this goal rationally. Chapter 3 deals with the topic of screening methods and how they relate to sound decision making. 23 CHAPTER 3 Preliminary Screening Method The purpose of a preliminary screening method is to identify and prioritize the bridges in a transportation network which are in most critical need of seismic retrofitting. Ideally, decision analysis would determine which structures are the best retrofit candidates by identifying the potential cost savings expected from a seismic upgrade. Due to limitations in time and in funding, it is infeasible to perform a full analysis for every existing bridge in a transportation system. Nonetheless, bridges must somehow be ranked according to a systematic procedure; high priority structures can then be subjected to a detailed decision analysis which will determine if a given retrofit scenario is cost effective. In recent years, several screening methods have been proposed by different groups and researchers. Prioritizing structures based on their total expected lifetime cost is the objective of an expected value decision analysis. A sound preliminary screening method is one that strives to meet this same objective. Evidently, some approximations and simplifications are required in order to accelerate the process. This chapter reviews some of the existing screening methods and discusses the advantages and shortcomings of each one. 3.1 Review of Existing Screening Methods Presently, the prioritization methods developed by Caltrans (Sheng and Gilbert, 1991) and by the Applied Technology Council (ATC-6-2, 1983) are commonly used in the United States. New approaches are being developed and some are now in use. The Washington 24 Chapter 3 - Preliminary Screening Method State Department of Transportation (Babaei and Hawkins, 1991) and the Illinois Department of Transportation (Cherng and Wen, 1992) have adopted different methodologies. Researchers at Stanford University have recently proposed another screening method which they believe deals with the element of seismic risk in a more logical way (Basoz and Kiremidjian, 1995). In Canada, a group of researchers at Ecole Polytechnique have proposed a rapid screening procedure for existing Canadian bridges (Filiatrault et al., 1994). The proposed procedure was inspired by several of the U.S. screening methods which are discussed in the following sections. 3.1.1 A T C Screening Method The ATC approach (ATC-6-2, 1983) consists of giving a vulnerability rating, a seismicity rating and an importance rating for each bridge. The vulnerability rating depends on structural characteristics which make a bridge particularly susceptible to earthquake damage. Bearings, columns, piers, footings, abutments and foundations all fit into this category. The seismicity rating is dependent upon the expected peak ground acceleration at the bridge site. The importance rating depends on the length and width of the bridge and the potential impact on the transportation network. These three ratings are then weighted and combined to produce an overall seismic rating. One of the major drawbacks of this approach is the fact that it only applies to conventional girder and box girder structures with spans under 500 ft. In addition, the vulnerability and seismicity ratings are treated separately in the ATC approach; however, a bridge's vulnerability is naturally related to ground motion. Finally, the weighting factors used for the three key variables are determined in such a way that the interdependence of various 25 Chapter 3 - Preliminary Screening Method bridge attributes is neglected. In general, this simple approach was satisfactory at the time it was developed, but a new method which takes advantage of the wealth of earthquake knowledge acquired over recent years is needed. 3.1.2 WSDOT Screening Method The Washington State Department of Transportation (WSDOT) (Babaei and Hawkins, 1991) considers several characteristics affecting the importance and vulnerability of the bridge to failure. The importance factor accounts for transportation concerns as well as the worth of the structure expressed as a ratio of the retrofit cost to the replacement cost of the structure. The vulnerability factor includes the peak ground acceleration in addition to all the same structural components that are considered in the ATC vulnerability rating. The WSDOT approach has limitations similar to those identified in the ATC approach. Moreover, it completely excludes single span bridges from the screening process; although single span bridges may be less likely to collapse, they can still represent important links in a transportation network. 3.1.3 BOOT Screening Method The prioritization method adopted by the Illinois Department of Transportation (Cherng and Wen, 1992) differs from the previous two by the fact that it is a risk-based method. Risk is defined as the product of the probability of failure and the consequences of failure. The probability of failure is determined based on the local seismicity, on the probability of structural failure and on the probability of ground failure. The consequences of failure form the second component in the risk calculation. This component uses a value function to measure various consequences on a common scale. Closure of an emergency 26 Chapter 3 - Preliminary Screening Method route and disruption to traffic are two examples of the attributes that could be used in the value function. Each attribute is assigned a value between 0 and 1 (with higher numbers corresponding to more severe consequences). This value is then multiplied by a scaling constant (between 0 and 1) which indicates the importance of an attribute with respect to all other attributes. The value function, expressed below, is obtained by adding up the results for all of the attributes: n v[*,,x 2,...,xj = £* ,v , (x 1 . ) (3-1) ;=i where Vj is the attribute value function (between 0 and 1), k; is the scaling constant (between 0 and 1) and x; is attribute i. Of the screening methods discussed so far, the EDOT approach is unique in its consideration of the relationship between bridge vulnerability and seismicity. It does this by calculating a probability of failure. By using risk in the ranking process, this procedure gets closer to approximating a true decision analysis. This method also takes into account the fact that certain bridge attributes are related; it does so by introducing scaling constants and value functions. One of the main problems with the IDOT approach, as with the others, is that it does not consider the effect of material and structural type on the seismic behaviour of the bridge. 3.1.4 Caltrans Screening Method The Caltrans philosophy is to retrofit the bridges which are at the greatest risk and which are the most vital to the transportation system (Sheng and Gilbert, 1991). Ultimately, their goal is to identify the structures which are the most susceptible to collapse during a large earthquake. Bridges are classified as high risk if structural characteristics make them more 27 Chapter 3 - Preliminary Screening Method vulnerable to collapse, or if transportation characteristics are expected to make the cost of loss very high. The risk analysis involves the calculation of a risk number between 0 and 1. A number close to 0 implies very low risk, while values closer to 1 imply very high risk. A weight and preweight are assigned to each attribute considered in the risk analysis. The attributes are as follows: • bedrock acceleration • soil conditions • number and type of hinges • column design (single of multiple bents) • height • skew • length of the bridge • abutment type • year of construction (relates to confinement details of column) • traffic exposure (average daily traffic) • facilities crossed • route type (major and minor) • detour length The risk number is defined as the summation of the product of the assigned weight and preweight score of each attribute: 28 Chapter 3 - Preliminary Screening Method RiskNumber = ^  [{we/g/jf,.) * (preweightj)] (3-2) i=l The weight and preweight are determined using engineering judgment. The weighting factor for attribute i is indicative of the importance of the attribute relative to all others. For example, if it is believed that the column design is much more consequential than the soil conditions or abutment type, then the weight for the column design attribute will be higher than the weight for the other two. The preweight score for each attribute is developed using a combination of engineering judgment and available data. For example, the preweight for the skew attribute is calculated as follows: preweight,skew) = x2 (3-3) where x is the skew in degrees (i.e., the angle between the main axis of the bent and the transverse axis of the bridge). Caltrans is also considering a long term risk algorithm which is currently in a conceptual form. In this algorithm, the risk number is obtained by multiplying the weighted factors for seismicity, importance and vulnerability. The Caltrans approach to screening bridges has many of the same shortcomings as the ATC and WSDOT approaches. It does not take into consideration the material and structural type, it disregards the dependence of a bridge's vulnerability on the local seismicity and it does not incorporate risk into the screening process. The method may have been state of the art at the time it was developed, but it falls short of achieving current goals. 29 Chapter 3 - Preliminary Screening Method 3.2 A New Risk-Based Screening Method Most recently, Basoz and Kiremidjian (1995) proposed a more comprehensive risk-based screening method for prioritizing bridges for seismic retrofitting. This method involves the assessment of two criteria, vulnerability and importance, and the subsequent synthesis of the criteria to obtain the priority score for each bridge. The vulnerability of a bridge is defined by the authors as "the damage potential of existing bridges subjected to future earthquakes" while the importance of a bridge is defined as "the socio-economic impact of the failure to a community". The overall ranking of a bridge is a function of its vulnerability and of its importance. 3.2.1 Vulnerability Assessment As mentioned above, the vulnerability of a bridge represents its potential to sustain significant damage or collapse. Unlike many other approaches, that of Basoz and Kiremidjian considers that vulnerability is a function of seismicity. Logically, a bridge which is subjected to high levels of ground motion is more vulnerable than one which is not. A vulnerability assessment involves the following three steps: • seismic hazard analysis at the bridge site • classification of bridges based on their structural characteristics • fragility analysis 3.2.1.1 Seismic Hazard Analysis at the Bridge Site The method developed by Cornell (1968) and McGuire (1976) form the basis for the seismic risk analysis. Determining the seismic hazard at a site is done probabilistically in such a way that all possible earthquakes from all possible sources are incorporated into the analysis. 30 Chapter 3 - Preliminary Screening Method Once all of the sources have been identified, a recurrence relationship is established for each source: LogN = A- BM (3-4) where M is the Richter magnitude, N is the number of earthquakes with magnitude greater or equal to M and A and B are constants. From historical data, one can then estimate the relationship between a ground motion parameter (acceleration, for example) and the distance from the source. This attenuation relationship can be defined for different magnitudes and involves some degree of uncertainty. Finally, a seismic hazard curve is obtained for each bridge; this curve shows the probability of exceedance as a function of a specified ground motion parameter. These basic steps are summarized in Figure 3.1. 31 Chapter 3 - Preliminary Screening Method Step 1 SOURCES Magnitude M Step 2 RECURRENCE <D O o < 03 0) CL Uncertainty i Attenuation Distance Step 3 GROUND MOTION o c to " a <D a> o x LU XI ra o Acceleration Step 4 PROBABILITY OF EXCEED ANCE Figure 3.1: Basics Steps of Probabilistic Seismic Hazard Analysis (from Reiter, 1990) The probabilistic approach considers other hazards such as liquefaction or landslide along with ground shaking. Computer programs are available to perform this type of seismic hazard analysis. 32 Chapter 3 - Preliminary Screening Method 3.2.1.2 Classification of Bridges Based on Structural Characteristics The structural properties of a bridge inevitably affect its vulnerability to seismic loading. Only two bridge classifications exist at the present time. Since both classifications are not sufficiently detailed to be used as part of a bridge prioritization method, Basoz and Kiremidjian have themselves developed a series of bridge classes which will categorize bridges according to their expected seismic behaviour. The properties considered in the classification are material type, structural type as well as properties such as continuity, number of columns or bents, number of spans, etc. These predefined bridge classes will facilitate the vulnerability assessment of existing bridges, (see Figure 3.2) Figure 3.2: Hierarchy of Structural Properties (from Basoz and Kiremidjian, 1995) 3.2.1.3 Fragility Analysis The fragility analysis involves developing a ground motion-damage relationship for the bridge class that the bridge falls under. The probability of exceeding certain levels of damage under a certain ground motion is then presented in the form of a fragility curve. The fragility 33 Chapter 3 - Preliminary Screening Method curve can also be used to determine the probability of the bridge being in a certain damage category under a certain level of ground motion. It is therefore necessary to develop fragility curves for all the new bridge classes. Vulnerability can be assessed for different damage levels. For the purposes of bridge prioritization, two damage levels should be considered: collapse and serviceability. The fragility curve for the collapse damage level will differ from the curve for the serviceability damage level. Logically, the probability of a bridge being at the serviceability damage level after a given ground motion can be considerably higher than the probability of it being at the collapse damage level. Normally, one would consider the fragility curves for collapse in ranking bridges for seismic retrofit. However, for bridges which have been identified as playing an important role in post-disaster operations, the fragility curves for serviceability should be used. The sample curves shown in Figure 3.3 demonstrate how the probability of a particular bridge type being in a given damage state, dr, (serviceability or collapse damage state) can be determined for a specific level of ground acceleration, A, i.e., P[D=dr| A] where D is the damage random variable. 3 4 Chapter 3 - Preliminary Screening Method P[D=dR|A] Figure 3.3: Fragility curves (from Basoz and Kiremidjian, 1995) Since the newly developed bridge classes only include primary structural characteristics, the fragility curves must be altered to account for secondary characteristics such as skew, age or previous retrofitting. The curves are therefore scaled using a modifier, P-The vulnerability assessment for any given bridge can be summarized as follows: 1. obtain structural information from an inventory 2. assign the bridge to one or more of the predefined bridge classes, 3. obtain information on the location of the bridge and soil condition at the bridge site, 4. perform seismic hazard analysis to compute the seismicity hazard curve, 5. select the corresponding ground motion-damage relationship for the bridge class that the bridge is assigned to and find the expected value of being in a certain damage state given the seismic hazard at the site, 35 Chapter 3 - Preliminary Screening Method 6. evaluate the vulnerability parameter V. 3.2.2 Importance Assessment The importance assessment considers the consequences of a bridge failure for the surrounding community. The factors which are considered in this assessment are the following: • public safety • emergency response • long term economic impacts • defense route • interaction with other lifelines, and • historical significance In reviewing the six factors listed above, several attributes must be investigated. Some of these attributes include the average daily traffic, the detour length, the type of route carried by the bridge, the type of facility crossed and other lifeline systems carried. Ideally, the effect of each of the attributes would be measured on a common scale. However, it is impossible to associate each attribute with a dollar loss or a time loss. A method to measure the impact of all the attributes on a common scale is needed. A value model is therefore developed to evaluate the importance of the bridge based on a long list of attributes. The model is formed by quantifying the values of decision makers which will determine trade-offs between the various attributes. In the value model, utility functions are required to assess the effects of various attributes in a consistent manner and on a common scale. Utility functions simply assign a numerical value to each possible 36 Chapter 3 - Preliminary Screening Method consequence of a given attribute. The importance criterion is determined by combining all the utility functions using relative weights assigned in the value model. The steps for importance assessment of any given bridge are summarized as follows: 1. obtain a decision maker's values for all importance attributes 2. develop utility functions and scaling factors for all importance attributes 3. for a given bridge obtain attributes for lifeline network analysis 4. perform network analysis: • connectivity analysis for emergency response • serviceability analysis for long term economic recovery 5. obtain total utility value for importance assessment 3.2.3 Synthesis of Vulnerability and Importance The final ranking of a bridge is given as a function of vulnerability and importance and can be expressed as follows: U^kyUn+kjUj, (3-5) where Ui is the utility value for bridge i to be used in obtaining the rank, R, Uvi and Uu are the utility values for vulnerability and importance respectively, and k v and ki are the scaling factors for vulnerability and importance respectively. This equation can be used to rank the bridges based on the expected dollar loss. In order to accomplish this, relations between damage and dollar loss must be included in the utility functions for both vulnerability and importance criteria. 37 Chapter 3 - Preliminary Screening Method 3.2.4 Discussion The screening procedure proposed by Basoz and Kiremidjian is believed to be the most complete and the most rational in its approach. It makes effective use of the extensive collection of bridge information which is currently available. By integrating expert systems and geographical information systems into their methodology, they have developed a flexible procedure which truly takes advantage of the resources at hand. In the vulnerability assessment, the suggested bridge classes and fragility curves account for the fact that different structural types will respond differently to a given ground motion. In the importance assessment, the attributes considered are weighted and combined in a logical manner which accounts for the relationship between them. While this method is the most comprehensive among the existing screening procedures, it nonetheless involves classifying a particular bridge and determining the probability of damage for that class. This is clearly not as accurate as a decision analysis which consists of a detailed damage analysis of the bridge itself. However, by probabilistically estimating damage and by accounting for the consequences of the damage, this prioritization method parallels the approach of decision analysis. With its objective of ranking bridges according to the expected dollar loss, this risk-based screening procedure is a sensible alternative to detailed decision analysis when time and funds are restricted. 38 CHAPTER 4 Expected Value Decision Analysis 4.1 Bayesian Decision Theory Bayesian decision theory provides a mathematical model for making decisions in the face of uncertainty. It makes use of probabilistic methods along with subjective and objective elements of a problem to determine the optimal course of action. It accounts for the various consequences of each possible course of action and considers the likelihood with which each consequence will occur. A decision problem involves the following elements (Benjamin and Cornell, 1970): 1. available actions 2. possible events or states of nature with their assigned probabilities 3. utilities associated with action-state pairs (i.e. measurements of a decision maker's preferences) Statistical validity requires that the events considered in the decision problem be mutually exclusive. Events should also be collectively exhaustive; this means that together the events should completely fill the sample space. The sum of the probabilities of all events will always be equal to one in the case of collectively exhaustive events. The competing alternatives in a decision problem can be ranked according to expected values. The expected value for each alternative is the sum of the products of the possible outcomes and their corresponding probabilities. It has been shown that expected monetary value is a valid criterion for choosing among alternative actions in the case of large 39 Chapter 4 - Expected Value Decision Analysis government agencies dealing with budgets of a significant size (Benjamin and Cornell, 1970). Under such circumstances, the decision maker can represent preferences in terms of dollars. 4.2 Bridge Seismic Retrofit Decisions In the case of bridge seismic retrofitting, the decision maker may prefer the alternative with the lowest overall cost. For each alternative, this involves summing all costs incurred over the life of the structure (i.e. the initial retrofit cost and the probabilistically predicted future damage cost) and discounting them to the present. Hence, the parameter which will govern the decision is the Net Present Cost (NPC). Comparing the NPC of the retrofit options with the NPC due to seismic damage to the unstrengthened bridge will reveal whether a seismic retrofit is advisable and, if so, which retrofit option is the most cost efficient. Expected value decision analysis is a rational and systematic way of selecting a seismic retrofit scheme for a bridge. It ensures that all possible events, all probabilities of occurrence of the events and all potential consequences of the events are incorporated into the decision. Given the uncertainty in a problem, it looks at all of the available information and yields a decision based on risk. Simply stated, it tells you the expected value of an outcome if a certain course of action is chosen. Until the future can be predicted, this is the best that one can hope for. 4.2.1 The Decision Process At the outset of any bridge retrofit decision, one needs to decide which retrofit schemes will be considered. Among the specified retrofit scenarios, the alternative of doing nothing should always be included. Taking no action at all may be the most cost effective decision. Moreover, the no retrofit option will provide the reference needed to calculate the 40 Chapter 4 - Expected Value Decision Analysis expected cost savings for the option with the lowest TMPC. The decision maker would then compare the expected savings for several bridges in a network and logically choose to retrofit the bridges for which the benefit is greatest. In this way, prospective bridge rehabilitation projects can be compared and prioritized. The bulk of the work in any decision analysis consists of obtaining all the required data and providing reasonable estimates and approximations wherever necessary. The methodology proposed here for making bridge retrofit decisions consists of the following steps: 1. seismic hazard analysis 2. damage analysis 3. loss estimate 4. decision calculations 5. sensitivity The seismic hazard analysis consists of defining the seismicity at the bridge site and determining the probabilities of occurrence of earthquakes of various intensities. Specific ground motion records must then be selected and scaled for use in the damage analysis. The purpose of the damage analysis is to obtain an estimate of the damage expected for a particular bridge for different levels of ground motion. Inelastic dynamic analyses and damage indices are used to estimate the structural damage. The next step in the decision process is the loss estimate. This consists of interpreting the analytical results and categorizing the damage. Damage states are then associated with direct and indirect damage costs. Once all pertinent data have been collected, they are organized in a decision model and the expected values for 41 Chapter 4 - Expected Value Decision Analysis the different retrofit scenarios are calculated. This allows the decision maker to select the optimal course of action. Finally, the sensitivity of the decision model to various input parameters is investigated. 4.2.2 Case Study Decision Model An expected value decision model can be diagrammed as a decision tree with many options. In the current case study of two Caltrans bridges, only the two options of either no retrofit or a fully effective retrofit are considered. The decision tree depicted in Figure 4.1 clearly shows the various elements involved in the decision process. The available actions, retrofit and no retrofit, make up the two main branches of the tree. For the no retrofit option, there are various earthquake intensity levels which represent the possible states of nature, and their corresponding probabilities are simply the annual probabilities of occurrence. These seismic events are mutually exclusive since there is no overlap between them. They are also collectively exhaustive and, accordingly, the sum of the probabilities is equal to one. Each MMI level is associated with a damage cost . These damage costs represent the utilities associated with each option. Utilities can be viewed as numerical assessments of the outcome of an event. In this case, the estimated dollar loss is used as a measure of the consequence of a seismic event within a specified MMI range. 42 Chapter 4 - Expected Value Decision Analysis j Intensity Probability Cost Cj y 1 0-IV P(0 - IV) c, 2 V — P(V) / X ^ S - 3 — VI — P(VI) c 3 ^ 4 VI — P(VII) c 4 / No Retrofit \ ^ 5 VII — P(VIII) — — c 5 / Option IX — P(IX) c 6 — x — P(X) c 7 / \ XI — P(XI) c 8 Expected Annual Cost g \ Retrofit Option Figure 4.1: Decision tree 43 CHAPTER 5 Seismicity A key element in a bridge retrofit decision analysis is the determination of the earthquake risk. Future seismic events cannot be predicted with certainty, but can be estimated based on currently available seismological information. The purpose of the seismic hazard analysis is to determine the probabilities of occurrence of earthquakes of various intensities based on the seismicity at the bridge site. Earthquake records can then be selected and scaled for use in the damage analysis. 5.1 Seismic Hazard Information about the seismicity of the area in which a particular bridge is located must be obtained before any attempts are made to perform a structural analysis. The available seismic data should be compiled in order to reveal what range of ground motions can be expected at the bridge site. A thorough seismological study involves several steps (Reiter, 1990): 1. locating all potential faults around the site 2. determining the frequency and magnitude of earthquakes along each fault 3. determining the distance of each fault from the site 4. determining the attenuation of intensity with distance for each fault 5. developing a site-specific curve which gives the probability of exceedance of different levels of ground motion 44 Chapter 5 - Seismicity This data compilation requires rigorous computations and is consequently quite time consuming. In addition, seismological information will not always be readily available for each bridge site investigated. For these reasons, a less extensive way of obtaining the required information should be adopted for the purposes of the detailed evaluation. The seismic data used by the United States Geological Survey to produce the 1990 seismic hazard maps will be used in the present methodology (Hanson et al., 1995). These data include a series of earthquake source zones. For each of these sources, annual occurrence rates as well as earthquake probabilities can be calculated. 5.1.1 Source Zones The seismicity of an area can be defined by earthquake source zones. Such zones are defined as regions which have similar geological and tectonic characteristics and which have the same earthquake potential. These can be modeled either by area sources or line sources. Area sources are normally used to model earthquakes which can be approximated by point ruptures. Earthquakes which fall into this category are low-magnitude earthquakes with a limited rupture length. Some higher magnitude earthquakes are also modeled with area sources, on the condition that their recurrence rate is long relative to the periodicity of the ground motion considered. High magnitude earthquakes with relatively short recurrence rates are modeled as linear ruptures. These line sources are capable of representing regions of higher ground motion near a fault. If the actual location of the expected faulting is unknown (despite the knowledge that the area is susceptible to frequent strong ground motion), then a field of parallel lines is used to model the seismicity. 45 Chapter 5 - Seismicity Coastal California is divided into 41 finite seismic source zones. For each zone, historic data have been used to determine the seismicity and, subsequently, the annual occurrence rate for different levels of earthquake magnitude. A map showing these zones is depicted in Figure 5.1. 46 Chapter 5 - Seismicity 5.1.2 Annual Occurrence Rates Since uniform seismicity is assumed to exist within each source zone, annual occurrence rates are also uniform throughout each. Among the most common recurrence models is the Gutenberg-Richter relationship which is based on comprehensive studies of worldwide seismicity. The recurrence relationship is of the following form: where M c is the central magnitude within a range which covers 0.6 units of magnitude (M-0.3 to Mc+0.3), N c is the average number of earthquakes per year with magnitude in this range, and a and b are constants determined from a regression analysis of data from the seismological studies of the area over a period of time. For several historical earthquakes, the magnitude is either unavailable or unreliable. For these earthquakes, the following regression equation was used in order to estimate the magnitude from the epicentral intensity: where I„ is the epicentral intensity on the Modified Mercalli scale. This intensity scale is used to categorize the severity of an earthquake at a site by assigning to it a roman numeral between I and XII. Each of the twelve categories is associated with either a description of the reaction of people, of the effect on inanimate objects (from common household items to entire structures), of the ground behaviour, or any combination of the above (see Table 5.1). Clearly, the Modified Mercalli Intensity Scale is very subjective. It is therefore imperative that damage descriptions accompany the intensity values obtained using this scale. \ogNc =a-bMc (5-1) M c = 1.3 + 0.6/, (5-2) 48 Chapter 5 - Seismicity Table 5.1: Modified Mercalli Intensity Scale (from EERI, 1994a) MMI Level Description I Not felt except by a very few under favorable circumstances. II Felt only by a few persons at rest, especially on the upper floors of buildings. Suspended objects may swing. III Felt quite noticeably indoors, especially on upper floors of office buildings, but not necessarily recognized as an earthquake. Standing cars may rock slightly. Vibration similar to that of a passing truck. IV If during the day, felt indoors by many; outdoors by few. If at night, few awakened. Dishes, windows and doors rattle, walls creak. A sensation such as a heavy truck striking the building. Standing cars rock noticeably. V Felt by nearly everyone, many awakened. Some dishes and windows broken, some plaster cracked, unstable objects overturned. Disturbance of trees, poles and other tall objects. Pendulum clocks may stop. VI Felt by all; many people run outdoors. Fallen plaster, minor chimney damage. Movement of moderately heavy furniture. VII Everybody runs outdoors. Damage negligible buildings of good design and construction; slight to moderate in well-built ordinary structures; considerable in poorly built or badly designed structures. Some chimneys broken. Noticed by persons driving cars. VIII Damage slight in specially designed structure; considerable in ordinary substantial buildings. Panel walls thrown out of frame structures. Chimneys, factory stacks, monuments, walls, and columns fall. Heavy furniture overturned and damaged. Changes in well water. Sand and mud ejected in small amounts. Persons driving in cars are disturbed. IX Damage considerable in specially designed structures; well-designed frame structures thrown out of plumb; great damage in substantial buildings, which suffer partial collapse. Buildings shifted off foundations, ground noticeably cracked, underground pipes broken. X Some well-built wooden structures destroyed, most masonry structures destroyed, foundations ruined, ground badly cracked. Rails bent. Considerable landslides from steep slopes and river banks. Water splashed over banks. Shifted sand and mud. XI Few, if any, masonry structures remain standing. Bridges destroyed. Broad fissures in ground. Underground pipes out of service. Earth slumps and land slips in soft ground. Rails bent greatly. XII Total damage. Waves are seen on ground surface. Lines of sight and level are distorted. Objects thrown into the air. 49 Chapter 5 - Seismicity In dealing with seismic data, it is convenient to use equation 5-2 to convert intensities on the M M I scale to epicentral magnitudes. The conversion is shown in Table 5.2. Table 5.2: Conversion from MMI to Richter Magnitude Intensity, I Magnitude, M Magnitude Range V 4.3 4.0-4.6 VI 4.9 4.6-5.2 VII 5.5 5.2 - 5.8 VIII 6.1 5.8 - 6.4 IX 6.7 6.4-7.0 X 7.3 7.0-7.6 XI 7.9 7.6-8.2 XII 8.5 8.2 - 8.8 When evaluating the seismic hazard at a specific bridge site, the first thing to do is to determine the seismic source zone based on the location of the bridge. Once the source zone is identified, the annual occurrence rates for various ranges of earthquake magnitude can be obtained directly from a table. For example, both Caltrans bridges described in Chapter 2 are located in zone 23. The data for zone 23 is listed in Table 5.3: 50 Chapter 5 - Seismicity Table 5.3: Annual Occurrence Rates for Zone 23 (from Hanson et al., 1995) Intensity, I Magnitude, M Magnitude Range Annual Occurrence Rate, N 0-IV 2.0 0.0-4.0 -V 4.3 4.0-4.6 0.117 VI 4.9 4.6-5.2 0.04950 VII 5.5 5.2-5.8 0.02101 VIII 6.1 5.8-6.4 0.00893. IX 6.7 6.4-7.0 0.00379 X 7.3 7.0-7.6 0.00161 XI 7.9 7.6-8.2 0.00069 5.1.3 Earthquake Probabilities Deriving the probabilities of encountering certain levels of ground motion will enable the introduction of the element of risk into the decision process. As seen in Table 5.3, the USGS data include annual occurrence rates for ground motions with intensities reaching or exceeding V on the MMI scale, or, equivalently, 4.0 on the Richter magnitude scale. To derive annual earthquake probabilities from these data, conditional probabilities must first be calculated. The conditional probability, P(Ij|l>V), is defined as the probability of experiencing an earthquake of intensity Ii given that an earthquake of intensity greater or equal to V occurs. P(L I I>V) is the ratio of the annual occurrence rate, N, for magnitude L, and the total number of events with magnitude V or greater per year: 51 Chapter 5 - Seismicity P(I,\l>V)=-^- (5-3) The conditional probabilities for zone 23 are listed in Table 5.4: Table 5.4: Probabilities of Earthquakes of Intensity Ij j Intensity, Ij Annual Occurrence Rate, Nj Probability, P(Ij / I>V) 1 0 - V - -2 V 0.117 0.578 3 VI 0.04950 0.244 4 VII 0.02101 0.104 5 VIII 0.00893 0.0441 6 IX 0.00379 0.0187 7 X 0.00161 0.00795 8 XI 0.00069 0.00341 I - 0.20253 1= 1.0 Since the annual occurrence rates for earthquakes with intensities lower than V are not known, these events are not included in the sample space. In damage loss estimation, it is common to work with annual damage costs. It is therefore essential to convert the conditional probabilities of Table 5.4 to annual probabilities of occurrence of at least one earthquake with intensity Ij or greater. The theorem of total probabilities states that P(A)^P(A\Bi)P(Bi) 52 Chapter 5 - Seismicity where B; are mutually exclusive and collectively exhaustive events (Benjamin and Cornell, 1970). It can therefore be said that as the event L is a subset of the event I>V. P(I>V) can easily be determined if we make the assumption that the occurrence of earthquakes follows a Poisson process such that the probability of occurrence per unit time is independent of time. The probability of at least one earthquake with intensity L or greater within time t is expressed as follows: To determine the probability of one or more earthquakes of intensity V or greater occurring in one year in zone 23, the following calculation was performed: P (I>V) = \-e-°20253 = 0.1833 This translates to an 18% chance that one or more earthquakes with epicentral intensity between V and XI will occur in one year. This value was used to calculate the annual earthquake probabilities which are listed in Table 5.5. As previously mentioned, any earthquake magnitude which falls in the range Mj-0.3 and Mj+0.3 is assigned to the category Mj. Each magnitude range and hence each intensity level constitutes a statistical event. It can be immediately observed that the sample space now includes all intensity levels, from 0 to XI. These events are mutually exclusive, i.e. there is no overlap between the categories, and the sum of the probabilities of occurrence of these events is equal to one. p(iJ) = PUJ\i*v)P(izv) (5-4) P(I>Ij) = \-e (5-5) 53 Chapter 5 - Seismicity Table 5.5: Annual Earthquake Probabilities j Intensity, Ij Annual Probability, P(Ij) 1 0 - V 0.817 2 V 0.106 3 VI 0.0448 4 VII 0.0190 5 VIII 0.00808 6 IX 0.00343 7 X 0.00146 8 XI 0.000624 E= 1.0 5.2 Earthquake Records In anticipation of the next step in the decision analysis, specific earthquake records are needed to drive the seismic analyses. Ground motion records can be obtained and scaled in a number of ways. This section discusses some of the options and proposes a simple approach to selecting earthquake records. 5.2.1 Surface Records The proposed method involves obtaining ground surface acceleration-time records. Surface records are preferable since they can be used without alteration. They inherently account for the local site conditions (soil type, local geology, etc..) Moreover, filtering bedrock motions up through the soil layers introduces an element of uncertainty and hence was avoided. Since a great number of surface records currently exist and have been made 54 Chapter 5 - Seismicity publicly accessible by agencies such as the USGS and the CSMLP, availability was not considered to be a problem. 5.2.2 Selecting and Scaling Natural Earthquake Records In selecting a seismic forcing function, two options may be considered: the use of synthetic records and the use of natural records. The latter alternative was chosen since it is possible that natural records reflect aspects of ground motion which are not accounted for in the generation of synthetic records. When using natural earthquake records as the input for a dynamic analysis, one option is to establish a design or target spectrum in order to make the ground motion site-specific. This is the approach taken by Stone and Taylor (1993). In their work, the target spectrum was generated based on statistical data from the area of interest. Clearly, this method is only appropriate when there exists sufficient historic earthquake data for the site in question. Subsequently, existing attenuation relationships were used to account for the earthquake's magnitude and the distance of the site from the source. Once the target spectrum was obtained, response spectra from historical records were matched to it by applying a scale factor. Stone and Taylor selected suites of 3 to 5 earthquakes which best matched the target spectrum and which together spanned the spectrum. This, they argued, was more realistic than generating a single synthetic record which would be forced to match the entire spectrum. Ideally, several categories of earthquake ground motions each with a specific magnitude and distance from the source would be used as the input motions for the analyses. However, finding a sufficient number of such earthquakes would be difficult and time consuming. Since the Stone and Taylor method depends on the availability of historic data for 55 Chapter 5 - Seismicity a region and since collecting enough earthquakes to fill all categories of magnitude-source distance combinations is infeasible, it was decided that a simpler, more practical procedure would be adopted. 5.2.3 Simplified Selection and Scaling Procedure The suggested procedure consists of using available natural earthquake surface records and scaling their response spectra with respect to the design spectrum for a specific site. The design spectrum can readily be obtained from the draft of the NCHRP Bridge Design Specifications (TSfCHRP 12-33, 1993) and is shown in Figure 5.2. c <u <J £ 2 <v o O c E .2> o * T3 0) N wO E A , ra \/ v v —A—Soil Profile Type S1 —0—Soil Profile Type S2 —O—Soil Profile Type S3 —K— Soil Profile Type S4 • 0.5 1 1.5 2 Period (seconds) 2.5 Figure 5.2: Design spectrum (from NCHRP 12-33, 1993) In Figure 5.2, the seismic response coefficient, C s m , has been normalized with respect to the PGA. NCHRP 12-33 contains maps showing the estimated PGA for different geographical regions in the United States. The NBCC supplies this information for Canadian cities. The soil profile types indicated on the design spectrum range from rock and stiff soils (Si) to soft 56 Chapter 5 - Seismicity clays and silts (S4). Complete descriptions of the soil profile types are found in NCHRP 12-33. As an example of how Figure 4.2 can be used to generate a site-specific spectrum, a soft clay site with a P G A of 0.2g would have a design spectrum which follows the curve for the S4 soil profile type with a plateau at 0.5g (2.5 times 0.2g). Scaling earthquake records to the design spectrum will ensure that the ground motions used in the analyses are site-specific, i.e., that they accurately reflect the types of earthquakes which are expected at a site. Finally, the time-history of each fitted record can be scaled to different levels of peak ground acceleration. Since it is not possible to cover all combinations of magnitude and source distance, the variation of the P G A will control the intensity of the earthquake. In this way, a low intensity earthquake will represent a large magnitude earthquake far away as well as a small magnitude earthquake very close by. As emphasized by Stone and Taylor (1993), it is important to select several records which together cover the spectral range. 5.2.4 Earthquake Records Used in Case Study For the present case study, two different earthquake records were used to drive the analyses. Ground surface records from the Northridge and Whittier earthquakes were chosen as input motions since they historically represent two major seismic events in the Los Angeles Basin. Generally, one would not have the foresight to predict future strong ground motion at a specific site. Thus, the evaluation of an existing bridge to determine its potential for seismic damage would involve applying the methodology described in the previous section. 57 Chapter 5 - Seismicity The Northridge surface record selected for use in the analysis of the FW and C V bents was recorded 19 km from the epicentre of the earthquake at the Wadsworth V A hospital in Los Angeles. This accelerograph station is located approximately 3.5 km from the FW and C V bridges. The soil conditions at this site were similar to those observed at the site of the two Santa Monica structure, namely loose sands at the surface with a transition to dense sands and then to sandstone. The digitized array of the time-history was obtained from the internet where the USGS National Strong-Motion Program has placed the acceleration data recorded at various accelerograph stations across the United States. The peak ground acceleration from this particular record was 0.39g horizontally (325° orientation, i.e., North-West) and 0.17g vertically. Figure 5.3 shows the time history and response spectrum of the earthquake excitation. A second ground motion was selected for use in the time-history analyses for the sake of comparison. The Whittier surface record used in the seismic analyses was recorded approximately 25 km from the epicentre of the earthquake at an accelerograph station at a Hollywood storage building. The peak ground acceleration from this particular record was 0.1 lg horizontally (90° orientation, i.e., East). Figure 5.4 shows the time history and response spectrum of the earthquake excitation. 58 Chapter 5 - Seismicity 3 0.15 0.10 I 0.05 g 0.00 o < -0.05 0.10 •D C 3 o -0.15 -I 0 I l,ll 1 11 M 1 r in p II 10 15 Time (s) 20 25 30 ( a ) 0.4 Ui c 0.3 o +^ TO k_ 0.2 CD V O O 0.1 < 0 4 J 0.5 1 Period, T 1.5 (b) Figure 5.4: Whittier earthquake excitation (a) acceleration time history and (b) acceleration response spectrum Given the conditional probabilities for seismic events ranging in intensity between V and XI, one would also like to know the expected loss for each intensity. This would enable the application of an expected value decision model. By scaling the time history of the earthquake record accordingly, a ground motion corresponding to each intensity was 60 Chapter 5 - Seismicity produced. The following equation was used to convert the intensity on the M M I scale to a peak ground acceleration in units of cm/s2 (Finn, 1995): loga= 0.3087- 0.041 (5-6) where a is the peak ground acceleration in cm/s2 and I is the intensity on the M M I scale. In using equation 5-5 it was assumed that each intensity level corresponded to an intensity range, i.e. a M M I of V could have any value between 4.5 and 5.5. In this way, a peak ground acceleration range corresponding to each intensity level was defined. The values are given in Table 5.6: Table 5.6: Relationship between MMI and PGA Intensity, I Intensity Range PGA range (cm/s2) PGA range (g) 0 - I V 0.0-4.5 0 -22 0.000 - 0.022 V 4.5 - 5.5 22-45 0.022 - 0.046 VI 5.5-6.5 45-91 0.046 - 0.093 VII 6.5-7.5 91 - 186 0.093 -0.190 VIII 7.5 - 8.5 186- 378 0.190-0.385 IX 8.5-9.5 378 - 767 0.385 - 0.782 X 9.5-10.5 767 - 1560 0.782 - 1.590 XI 10.5 - 11.5 1560 -3170 1.590 - 3.230 From Table 5.6 it is apparent that a ground motion with a peak ground acceleration of 0.2g would be the equivalent of an earthquake of intensity VIII. In order to simulate earthquake excitations for each intensity level, the original records were each scaled in turn to 0.05g, O.lg, 0.2g, 0.9g and 1.6g. Scaling the time-histories to different P G A levels not only enables 61 Chapter 5 - Seismicity a comparison of the structural damage under different intensities of ground motion, but also makes possible the calculation of an expected loss value. As shown in the decision tree of Figure 4.1, estimating expected damage costs for all intensity levels is critical to the integrity of the decision analysis. 62 CHAPTER 6 Damage Analysis This chapter presents a systematic procedure to quantify the damage which can be expected for a particular bridge under varying intensities of earthquake loading. The damage analysis involves performing seismic analyses of the bridges under investigation. A nonlinear analysis program was used to model specific structural components of the bridges and subject them to a sampling of earthquake excitations. Certain bents of the Fairfax-Washington and La Cienega-Venice bridges, which were damaged in the Northridge earthquake, were modeled. If the degree of damage in each bent could be analytically predicted, the information could be extrapolated to give an indication of the damage to the entire bridge. This seems reasonable since most of the damage encountered was located in the columns of the bents. In addition, the mode of failure for these columns was similar in all cases. One exception to this trend was the dropping of spans due to hinge restrainer failure in certain cases. No attempts were made to model this failure mode. The analysis procedure is more clearly demonstrated by its application to the Caltrans bridges. 6.1 Damage Indices Damage indices are nondimensional parameters used to quantify the seismic damage in individual structural elements, storeys or complete structures. They are convenient to work with because they measure structural damage without relying on the subjectivity of the 63 Chapter 6 - Damage Analysis evaluator. Damage indices may be obtained from non-linear dynamic analysis, from the measured response of a structure during an earthquake or from a comparison of a structure's physical properties before and after an earthquake. There exist several different damage index definitions, each proposed by a different group of researchers. Most of these definitions use deformation and/or energy absorption as measures of the level of damage. A review of damage indices is given in Williams and Sexsmith (1994). One such definition is the Park and Ang damage index. This definition was used for the current project because it is relatively simple and because it has been extensively calibrated against observed damage. It is defined as the following: The first term is referred to as the deformation damage and it is based solely on displacement. u.m and u.u are the maximum and ultimate ductilities. In the case of frame members, they represent curvature ductilities. The second term, known as the strength damage, accounts for cumulative damage due to load cycling. The parameter p in this term, which can take any value between 0.0 and 0.5, represents the strength deterioration of the element after yielding occurs. Low values of B are used for well reinforced and confined concrete members whereas higher values are required in the case of poorly detailed structural sections. As the latter was the case in the bridge bents investigated, the parameter P was assigned a value of 0.3. Eh and F y are the absorbed hysteretic energy and the yield force (yield moment in the case of frame members) respectively. 64 Chapter 6 - Damage Analysis Local damage indices are used to measure the damage in individual structural elements, while global indices represent the overall damage state of the structure. To obtain the global index, a weighted average of the local indices is calculated. Naturally, the more severely damaged elements absorb more energy. Therefore, using the local energy absorption as a weighting factor ensures that the global index will be representative of the most extreme damage state. Dgiobai = ^ r (6-2) 2 A where Di is the local damage index at location I and Ej is the energy absorbed at location i. Since the seismic analysis will yield local damage index values for the members of the bridge bent, equation 6-2 will enable the conversion to a global damage index for the structure. 6.1.1 Damage Index Calibration Recently, attempts have been made to correlate observed damage with damage indices. As mentioned previously, one of the main reasons for selecting the Park and Ang damage index for the present study is that several independent researchers have calibrated this index using experimental test results. Hence, they have proposed damage classifications which qualitatively describe the expected damage for specific ranges of damage index values. For example, Park, Ang and Wen (1985) suggested the classification shown in Table 6.1. It is assumed that a damage index of 0.4 is the limit of repairable damage and a damage index of 1.0 represents collapse. 65 Chapter 6 - Damage Analysis Table 6.1: Damage Classification suggested by Park, Ang and Wen D<0.1 No damage or localized minor cracking 0.1<D<0.25 Minor damage - light cracking throughout 0.25<D<0.4 Moderate damage - severe cracking, localized spalling 0.4<D<1.0 Severe damage - crushing of concrete, reinforcement exposed D>1.0 Collapsed Stone and Taylor (1993) also defined damage categories for the Park and Ang damage index. Their classification was based on experimental results from tests on 82 Caltrans-design circular bridge columns. They determined threshold values of the damage index to distinguish between repairable and irreparable structural damage. These values are shown in Table 6.2. Table 6.2: Damage classification suggested by Stone and Taylor D<0.11 No damage or localized minor cracking 0.11<D<0.4 Repairable - extensive spalling but inherent stiffness remains 0.4<D<0.77 Irreparable - still standing but failure imminent D>0.77 Collapsed Apart from the values of the damage index at collapse, the two damage classifications are in very close agreement. One must also remember that the definition of structural collapse is somewhat ambiguous and can be defined in different ways. Luckily, the difference in the cost consequences between severe or irreparable damage and collapse is not likely to be big. In other words, whether a structure is irreparable or collapsed is almost irrelevant in terms of damage cost since both will probably be demolished and replaced. However, collapse may 66 Chapter 6 - Damage Analysis imply larger indirect costs associated with life loss and with the loss of the bridge's post-earthquake availability. The assessment of seismic risk involves determining the probability of occurrence of earthquakes of various magnitudes, estimating the structural damage and obtaining the consequences associated with this damage. Structural damage must be clearly defined in order to make this a practical process. If damage estimates rely too heavily on the judgment of the evaluator, the results of the decision analysis will not be meaningful. The damage index is a valuable tool because its measure of damage is much less subjective. Using the numerical value of the damage index to estimate the damage state of a bridge after an earthquake is believed to be a simple and systematic way of predicting losses associated with earthquakes. 6.2 Computer Program R U A U M O K O The program RUAUMOKO was developed at the University of Canterbury, New Zealand by Athol J. Carr (1996). The program produces a time-history response of a non-linear two-dimensional framed structure to ground acceleration or time varying force excitation. R U A U M O K O was deemed to be particularly useful in the case of damage prediction, since damage indices as well as dissipated energy are computed at the end of each non-linear analysis. 6.2.1 Description of Program Features The program has the capability of performing static, modal and dynamic time-history analyses. It is possible to apply loads to a structure in a load pattern; the load pattern is multiplied by a time-history which is specified in the input file. This constitutes a dynamic 67 Chapter 6 - Damage Analysis force excitation. Using this feature with a slow ramp loading function enables the user to perform a pushover analysis. As in all inelastic dynamic analysis programs, several different member types are available for the modeling of the structure. However, the program distinguishes itself among others by offering thirty different built-in hysteresis models for inelastic frame and spring members. This gives the user a great deal of flexibility. Another very important aspect of the program is the computation of seven different damage indices as well as the absorbed energy for the nonlinear members. When the main goal of the analysis is to estimate structural damage, it is very convenient to have the damage indices as part of the output file. A distinctive feature of R U A U M O K O is the incorporation of on-screen graphics if the program is run in the interactive mode. The deformed shape of the structure and the plastic hinges are displayed and updated on the screen. The various mode shapes are also shown along with the corresponding periods. The graphics are helpful in assuring that the model geometry is correct; they are also useful in assessing the locations and the sequence of plastic hinging. At the end of the analysis, a summary of the results along with the damage information is printed as output. The post-processor DYNAPLOT is used to produce time-history responses of various forces, displacements, deformations, and combinations of the above. It can also produce hysteresis loops for the various members and nodes. 68 Chapter 6 - Damage Analysis 6.3 General Aspects of the Bridge Bent Modeling All the analysis models were constructed in a similar fashion. Values of weight per unit length were specified to represent the weight of the superstructure as well as the column weights. The program converts these values to units of mass with which it creates a mass matrix. The diagonal mass matrix was used in all cases. Another similarity is the use of the Rayleigh or Proportional damping model with a fraction of critical damping of 5%. This is a typical value for a reinforced concrete frame (Dowrick, 1987). The stiffness matrix was based on the member models used. Although R U A U M O K O has seven different member models, only two of these were used in the modeling of the bridge bents: frame members (beam and beam-column members) and spring members. R U A U M O K O incorporates thirty different hysteresis rules to account for stiffness degradation of frame and spring members during a nonlinear analysis. To get an accurate model of the hysteretic behaviour of the members, hysteresis parameters would ideally be calibrated using experimental data. In the absence of such data, assumptions need to be made based on the structural type and the material properties. Since the material properties and structural details were simply obtained from the structural drawings, the more sophisticated hysteresis rules were dismissed; the simple bilinear model depicted in figure 6.1 was deemed appropriate under the circumstances. 69 Chapter 6 - Damage Analysis t k F F + . : *" /" A A A / d / rlc _ / ^ — -Figure 6.1: Bilinear hysteresis model in R U A U M O K O (from Carr, 1996) The very light transverse reinforcement in the tied columns suggested that the concrete was very poorly confined and hence it was assumed that strength degradation would be significant. As mentioned in section 6.1, the Park and Aug damage index definition incorporates a parameter, B, which accounts for this effect. Hence, it was assumed that a B value of 0.03 would adequately reflect the consequences of strength deterioration in the concrete members. The static loads on the bent were applied as nodal loads evenly spaced across the top of the bent. These loads represented the dead load of the superstructure. . When using R U A U M O K O to run a nonlinear analysis, the user must define the yield surface of the inelastic members. One must therefore compute the moment-axial load interaction diagram for these members. The computer program PCACOL (Portland Cement 70 Chapter 6 - Damage Analysis Association, 1993) was used to produce the interaction diagrams for the various column elements prior to the nonlinear analysis (see Appendix C). The moment-curvature relationship for column members was also needed in order to provide the ultimate curvature ductilities required by the program R U A U M O K O to calculate damage indices. The computer program RESPONSE (Collins and Mitchell, 1990) was used to obtain this relationship for the specific axial loads present on the columns. Based on the curves obtained from RESPONSE, ultimate ductilities were determined for the column members (see Appendix D). An elastic analysis was performed in order to get a general idea about the distribution of member forces and to identify possible zones of failure. The elastic behaviour of the bents was investigated using the computer program P C A F R A M E (Portland Cement Association, 1993). An initial estimate for the natural frequency of the bent was obtained by applying an arbitrary lateral load at the level of the superstructure. The analysis provided information about the distribution of bending moments, axial forces and shear forces in the bent. The bent was analyzed under the vertical load of the superstructure and an increasing lateral load, P, at the level of the superstructure. This provided some insight into the bent's overall behaviour. The models are individually described in the sections that follow. 6.3.1 Standard Caltrans Single-Column Bent Prior to the analysis of the FW and CV bridge bents, a preliminary analysis was performed on a standard Caltrans single column bent. The characteristics of the column are listed in Table 6.3: 71 Chapter 6 - Damage Analysis Table 6.3: Characteristics of the standard Caltrans column (from Stone and Taylor, 1993) Column Characteristic Values Investigated Diameter, D 122 cm Length/Diameter ratio, L/D 6 Concrete strength, fc' 27.6 MPa Axial reinforcement yield, ultimate stress 414 Mpa, 724 MPa Spiral reinforcement yield, ultimate stress 414 Mpa, 724 MPa Axial load level = Pe/(fc'*Ag) 0.10 Clear cover to spiral bars 5.1 cm Diameter of spiral reinforcing bar 1.59 cm Soil overburden 37 m sand Distance from causative fault 20 km This column is but one in a series of columns studied by Stone and Taylor (1993). Their research focused on a sampling of columns with different aspect ratios, axial load levels, and subsurface conditions. Several analyses were performed in which the earthquake magnitude and the epicentral distance were varied. They then developed curves which expressed the damage index as a function of the magnitude and epicentral distance. The purpose of their work was to study the seismic performance of bridge columns designed according to current Caltrans specifications in the interest of developing a more rational seismic design procedure. The purpose of analyzing this particular column was to see if the damage index obtained agreed with the analytical predictions of Stone and Taylor (1993). A nonlinear analysis using R U A U M O K O yielded a damage index which was in close accord with the 72 Chapter 6 - Damage Analysis graphical predictions. The analytical models used by Stone and Taylor were calibrated against an impressive amount of test data; therefore, a correlation with their results was encouraging. The modeling therefore proceeded for the FW and CV bents. 5.3.2 Fairfax-Washington Bent Bent 3 of the Fairfax-Washington bridge sustained major damage during the Northridge earthquake. The details of this damage have been outlined in section 2.2.1.2. If the degree of damage in this bent could be analytically predicted, the information could probably be extrapolated to give an indication of the damage to the entire bridge. This seems reasonable since most of the damage encountered was located in the columns of the bents. In addition, the mode of failure for these columns was similar in all cases. Information about the geometry of the bent as well as reinforcement details are given in the structural drawings in Appendix A. The columns of bent 3L are more heavily reinforced longitudinally than are the columns of bent 3R. However, the transverse reinforcement is the same in both cases. The base of all the columns were designed to be fixed. The elastic analysis of the bent suggested that the columns would yield in flexure before their shear capacity was exceeded. This correlated with the observed damage. Figure 6.2 shows the analytical model of bent 3 of the Fairfax-Washington bridge. Since the box girder is very stiff relative to the columns and since no damage was detected in the superstructure during the post earthquake investigation, the beam elements in the model were assumed to remain elastic. Small, stiff elements were included at both top and bottom of the columns, accounting for the depth of the foundation and of the superstructure. Since the 73 Chapter 6 - Damage Analysis superstructure is essentially a uniformly distributed load, a sufficient number of nodes were required along the horizontal portion of the model to accurately represent this load. LA. 1 1 1 1 1 1 1 LT] LLJ 5537 5^30 2440 8310 8310 8310 6450 8310 8310 2440 mm Figure 6.2: Nonlinear model of FW bent 3 5.3.3 L a Cienega-Venice Bent Bent 4 of the La Cienega-Venice bridge was also modeled and analyzed. As described in section 2.2.2.2, many of the columns in this bent failed during the strong ground motion. The structural drawings found in Appendix A show the geometry of the bent and the reinforcement details. Most aspects of the modeling and analysis of the bent were similar to those described for the Fairfax-Washington bent and hence will not be repeated. As in the latter case, an elastic analysis preceded the development and analysis of the nonlinear model. The elastic analysis confirmed, once again, that the columns would fail in flexure. The nonlinear model used in RUAUMOKO is depicted in Figure 6.3. The first fundamental difference between the previous and the current model is the embankment of the superstructure. The difference in the deck elevation between the north end of bent 4 of the westbound structure and the south end of bent 4 of the eastbound structure is almost 2 74 Chapter 6 - Damage Analysis metres. A second fundamental difference between the two models is the fixity at the base of the FW columns vs. the pinned connection at the base of the CV columns. The detail for the connection between the column and the footing for the bent 4 columns of CV is such that it may be considered a hinged connection. It should be noted that the 3 columns belonging to the westbound structure contained more longitudinal reinforcing steel than the columns supporting the eastbound structure. The transverse reinforcement, # 4 lapped hoops at 12" spacing, was identical for all the columns. 2440 7684 7684 6464 7753 7753 2440 mm Figure 6.3: Nonlinear model of CV bent 4 6.4 Pushover Analyses Pushover analyses were performed for both nonlinear models in order to verify whether their response to lateral load would be as expected. This type of analysis is also useful in determining failure mechanisms and the sequence of hinging. In R U A U M O K O , a pushover analysis is achieved by using the dynamic loading option with a slow ramp loading function. In this manner, a monotonic lateral load is applied to the bent at the level of the superstructure; this load increases slowly up to the ultimate load. 75 Chapter 6 - Damage Analysis For the bent of the FW bridge, the pushover analysis showed that the correct mode of failure was not achieved using the proposed model. In order to cause plastic hinging in the tops of the columns only, a stiff rotational spring was introduced at the base of the column. Since the column footings were supported on multiple pile foundations, it was deemed reasonable to allow a very small amount of rotational freedom. The pushover analysis of the CV bent revealed that hinges would form sequentially in the upper portion of the columns. Since this was in agreement with the actual damage sustained by the columns, it was considered appropriate to move on to a nonlinear analysis of the model. 6.5 Inelastic Dynamic Analyses Dynamic time history analyses were done on the aforementioned bents using the original and scaled ground surface records identified in section 5.2.4. Each bridge studied was therefore analyzed under two different earthquake loads, each scaled to seven different values of peak ground acceleration. The main purpose of this exercise was to determine and quantify the damage associated with each level of excitation. In addition to varying the PGA, several analysis runs were done in which the bents were subjected to an increasing length of the earthquake. This made it possible to observe the progress of the damage in the various members. The durations considered were 5s, 10s, 15s, 20s and 28s. The actual duration of the ground motion was 28s. 6.6 Analysis Results The main objective of the analyses was to extract damage indices for the various structural elements under different levels of earthquake loading. As the beam elements were 76 Chapter 6 - Damage Analysis assumed to remain elastic throughout the earthquake, local damage indices were only generated for the columns. Equation 6-2 was used to calculate a global damage index for each bent for each load case. Since the only available data about the seismic behaviour of the prototype bents were in the form of damage summaries and postulated collapse mechanisms, this was the basis for comparison with the analysis results. Some typical time-histories of the structural response of each bent for the unsealed Northridge earthquake excitation are presented. Figure 6.4 shows time histories of the relative acceleration and displacement at the level of the superstructure as well as the time history of the global damage index for the FW bent. The peak displacement, acceleration and damage index for this bent are 50mm, 0.43g and 0.414 respectively. The large displacement peak which occurs just after 10s caused yielding in most of the columns. The strong shaking between 10s and 15s resulted in a permanent deformation in the bent and in a final damage index of 0.414. Clearly, failure occurred suddenly for this model. Figure 6.5 shows time histories of the acceleration, displacement, and global damage index for the CV bent. The peak displacement, acceleration and damage index for the La Cienega-Venice bent are 30mm, 0.20g and 0.365 respectively. Once again, significant yielding and permanent displacements are observable around the 10s mark. However, the failure of the bent appears to be much more ductile in nature with the damage steadily increasing between 5s and 20s. 77 Chapter 6 - Damage Analysis Figure 6.4: Analysis results for FW (a) displacement time history, (b) acceleration time history and (c) damage index time history 78 Chapter 6 - Damage Analysis Figure 6.5: Analysis results for C V (a) displacement time history, (b) acceleration time history and (c) damage index time history 7 9 Chapter 6 - Damage Analysis Figure 6.6 shows the global damage indices calculated for the FW and C V bents for the different levels of peak ground acceleration. Results are shown for analyses using the Northridge earthquake input motion and for analyses using the Whittier earthquake excitation. The upper limit of 1.0 on these graphs represents collapse. Since no physical meaning is associated with a damage index greater than 1.0, all values greater than this were simply assigned the collapse threshold damage index of 1.0. Figure 6.6: Variation of the global damage index with the P G A for (a) FW and (b) C V 80 Chapter 6 - Damage Analysis The P G A required to cause collapse and the PGA required to cause irreparable damage both vary for the two different earthquake records. However, the damage indices increase in a similar fashion for both earthquakes when the PGA is increased. Sensitivity analyses which will be discussed in Chapter 8 will ascertain the impact of the discrepancy on the final decision. 6.7 Discussion The proposed evaluation method is an attempt to outline a damage prediction procedure which is at once rational and probabilistic in nature. The overall simplicity of the method was also an important consideration. The determination of earthquake probabilities from the seismic data and the selection of earthquake records involve uncertainty; however, it is felt that a good compromise was reached between accuracy and simplicity. Moreover, the results of the seismic analysis should be viewed as approximations of the expected structural damage only. More complex analyses would be more time consuming and may not be any more accurate. Inevitably, certain obstacles were encountered in the modeling and analysis stages. The estimation of the hysteresis behaviour was notably difficult. Typically, it is not easy to model the hysteresis of older structures because of the poor seismic detailing and the minimal concrete confinement. Since the bridges investigated were constructed in the early 1960's, they exhibited both of these deficiencies. The hysteresis model used was the best estimate under the given circumstances. The modeling of the bents also involved making assumptions with respect to the actual concrete and reinforcing steel properties since information from samples of these materials was not available. The modeling of the fixity at the base of the 81 Chapter 6 - Damage Analysis columns was another problem which required a trial and error process. Finally, the possibility of a shear failure following the initial hinging of the columns presented another challenge. It is widely accepted that shear resistance varies with the ductility demand. The damage reports for the F-W and C-V bridges described yielding of the columns followed by an increase in shear flow. However, a constant effective shear area was specified in the analyses thereby neglecting the decrease in the shear capacity. Despite the assumptions, uncertainties and analytical simplifications, the results of the inelastic damage analysis will provide the decision-maker with a damage estimate which is measurable. The interpretation of the damage indices obtained from the seismic analysis will be discussed in the following chapter. 82 CHAPTER 7 Loss Estimate The results of the seismic analyses have provided the decision maker with numerical indicators of the seismic damage. However, the important task of interpreting these results and giving them physical meaning remains. The loss estimate entails interpreting the quantitative damage information and establishing relationships between the damage and the consequences. First, the damage indices will be used to generate descriptive damage estimates. This will be achieved by associating different ranges of the damage index with a specific damage state. Each damage state will in turn be associated with a damage cost. This chapter explains the above process and demonstrates its application for the bridges used in the case study. 7.1 Damage Estimate The damage estimate for an individual bridge will require an interpretation of the analytical results. This will be achieved by relating the global damage index obtained from the analysis to a damage category. 7.1.1 Damage Categorization Characterizing damage involves a certain degree of subjectivity. The two damage classifications presented in Chapter 6 showed that despite the subjectivity associated with characterizing damage, relatively consistent categories can be obtained. These classifications were used to define three broad categories of damage which are shown in Table 7.1. 83 Chapter 7 - Loss Estimate Table 7.1: Damage categories used in loss estimate D<0.1 No damage 0.1<D<0.4 Repairable damage 0.4<D Irreparable damage Although the categories may seem too broad to be of any use as a damage estimating tool, they are particularly revealing in terms of cost. It is not as important to know exactly how much cracking and spalling has occurred as it is to know if it can be repaired. Since the ultimate goal is to make a decision based on expected cost, this classification will be a very good starting point. 7.1.2 Expected Reduction in Damage (ERD) Before estimating the damage cost corresponding to each of the damage states for a particular type of bridge, the effectiveness of a seismic retrofit should be considered. It would be valuable to quantify the reduction in damage which can be expected if a retrofitted bridge were subjected to the same earthquake as the unretrofitted structure. In the case of buildings, tables exist which list the expected reduction in damage (ERD) factors for various types of structural systems (VSP Associates, Inc., 1992a). These values were determined using engineering judgment. Since no such tables exist for bridges, it is recommended that the ERD factors be determined analytically. By modifying the bridge models in the analysis to account for retrofitted structural elements, it is possible to obtain damage indices for the case when the bridge has been strengthened. The ratio of the damage indices for the two cases could then be used as an approximation of the expected reduction in damage (ERD) factor. 84 Chapter 7 - Loss Estimate ERD = \- ™<t**&**> (7-1) DI (unretrofitted) It is clear from equation 7-1 that a retrofit scheme that reduces the damage index to zero will yield an ERD value of 1. With the exception of infrequent, very large earthquakes (M>8), it is reasonable to assume that the retrofitting procedure will often succeed in reducing the expected damage to negligible levels. This is particularly true in the case of older, very poorly detailed structures. Since the FW and C V bridges fall into this category of bridges, it was assumed that the ERD would be close to 1. 7.1.3 Summary of Damage Estimate Based on the analysis results presented in Chapter 6, damage estimates were obtained for the bents of the FW and C V bridges. The global damage index values shown in Figure 6.6 and summarized below in Table 7.2 were used to infer the structure's overall damage state. Table 7.2: Summary of global damage indices M M I PGA Range Damage Index Northridge Whittier FW C V FW C V V 0.023 - 0.046 0.0 0.0 0.0 0.0 VI 0.046 - 0.093 0.0 0.0 0.0 0.0 VII 0.093 -0.190 0.0 0.0 0.0 0.0 VIII 0.190 - 0.385 0.308 0.182 0.279 0.362 IX 0.385 - 0.782 0.414 0.365 >1.0 >1.0 X 0.782 - 1.59 >1.0 >1.0 >1.0 >1.0 XI 1.59-3.23 >1.0 >1.0 >1.0 >1.0 85 Chapter 7 - Loss Estimate Referring to the damage classification given in Table 7.1, it was predicted that bent 3 of the FW bridge would suffer irreparable damage as a result of the unsealed Northridge ground motion (PGA of 0.39g) while bent 4 of the CV bridge would be on the verge of severe, irreparable damage. When the Whittier earthquake was scaled to a P G A similar to that of the Northridge earthquake and then used to drive the seismic analyses, complete collapse was predicted for both bents. The damage descriptions given in Chapter 2 were consulted in order to compare the analytically predicted damage and the actual damage that the bridges exhibited after the Northridge earthquake. Recalling the damage to the columns of bent 3 of the FW bridge, it was observed that all confinement steel was lost, the concrete cores disintegrated and the longitudinal steel buckled, forming a mushroom shape. According to this description and to the photograph of Figure 2.2, it is safe to say that the columns failed. In this case, the analysis results underestimated the damage to these columns. The columns of bent 4 of the CV bridge experienced a very similar failure mechanism. The reconnaissance reports describe damage resembling that of the FW columns. The only reason that this bridge was classified as a collapsed structure was because of the hinge restrainer failure which caused span 6 to drop. Otherwise, the CV bridge and the FW bridge responded to the earthquake in almost the same way. It should be restated that a significant difference between these two bents is the fact that the FW columns were all fixed at the base, while the CV columns were hinged. The analytical damage prediction for the CV bent indicated moderate to severe damage including major cracking and localized spalling. Again, this constitutes an underestimation of the seismic damage. 86 Chapter 7 - Loss Estimate There are several possible ways to explain why the damage estimates seem to fall short of reflecting the actual observed damage. The first and most obvious explanation is that the ground motion at the site was underestimated. Since free-field sensors in proximity of the FW and CV bridges malfunctioned, the ground motion was approximated by that recorded at an accelerograph station nearly 4 km away. Seismologists would attest that the ground motion can vary significantly within this distance. Although the soil conditions at the station and at the bridge sites were similar, soil effects may nonetheless be responsible for variability in the ground motion. The accuracy or inaccuracy of the model could also account for the discrepancy between observed and predicted damage. It is quite possible that in the development of the analysis model certain assumptions regarding material properties or member fixity were inexact. A thorough discussion on this subject was presented in section 6.7. 7.2 Damage Cost Estimate The next step in the evaluation process is to estimate the dollar loss associated with the predicted damage. Estimates will be based on a review of cost information for several bridges. It will be shown how, in the absence of such information, the judgment of experts in the field of seismic damage can be incorporated into the estimate. Before all this is done, however, it is important to determine which costs will be included in the cost model. This may vary from one bridge owner to another and from one bridge to another. The following sections list the costs which could be incurred following a damaging earthquake. In general, damage costs can be divided into two categories: direct costs and indirect costs. 87 Chapter 7 - Loss Estimate 7.2.1 Direct Costs The direct costs are subdivided into the following two categories (Building Systems Development et al., 1989): 1. Facilities repair/replacement • related to the physical damage to the structure (and its contents). • usually estimated by joint effort of engineering firms and construction companies 2. Deaths and injuries • depends on the function of the structure and on the value of life Among the direct costs, only those associated with the repair or replacement of the structure will be considered herein. Since occupancy is typically small for bridge structures and can be expected to be proportional to the repair and replacement costs, costs associated with life loss and injury are not included in the study. In the preliminary screening methods described in Chapter 3, it was stated that earthquake damage was related to the structural characteristics of a bridge. The bridge classes defined in section 3.2.1.2 were developed in order to group bridges which are expected to exhibit a similar seismic behaviour. Ideally, estimated repair and replacement costs for each of these bridge classes would be compiled in a database such that the direct costs would depend on several attributes such as the bridge type, span length and traffic volume. Since no such database exists at the present time, rough approximations were made for the direct costs. 88 Chapter 7 - Loss Estimate 7.2.1.1 Relating Direct Costs to Damage Indices In assigning direct damage costs to damage states, a relationship between the response damage index (RDI) and the dollar damage index (DDI) must be established. In this case, the RDI corresponds to the Park and Ang damage index as defined in section 6.1. In this project, the DDI is defined as the ratio between the cost of repair and the total cost of removal and replacement; it can therefore take any value between 0 and 1. A great deal of cost data would have to be collected before average damage costs could be assigned to each damage state for a specific type of bridge. Since a sufficiently large damage cost database is not presently available, the judgment of experts in the field of seismic structural damage is required. Researchers have proposed several strategies for mapping structural damage to monetary damage. A summary of the mapping methods are found in the paper by Gunturi and Shah (1993). The method proposed here is deterministic mapping, the simplest of all approaches. Deterministic mapping consists of establishing a relationship between the DDI and RDI values based on the experience and judgment of experts (see Figure 7.1). For the purpose of the bridge study and in the absence of expert judgment, statistical data provided by the Division of Structures at Caltrans were used to perform the deterministic mapping. Information about the bridge repair contracts which followed the Northridge earthquake (Caltrans, 1994b) and additional published cost data pertaining to seismic work and construction statistics (Engineering News-Record, 1994-97) were used to develop a relationship between the RDI and DDI. It should be noted that all values calculated in this way are only approximate. Here, emphasis is placed on the procedure by which damage costs are determined and not the accuracy of the cost estimates themselves. 89 Chapter 7 - Loss Estimate 1.6 1.4 1.2 1 0.8 0.6 re 0.4 o 0.2 0 •D c 0) O) re E re a 0 Expert 1 — B — Expert 2 A Average 0 0.2 0 4 0 6 0 8 1 Response Damage Index Figure 7.1: Deterministic Mapping (from Gunturi and Shah, 1993) To calculate the DDI, the repair cost and the replacement cost are needed. Table 7.3 shows average replacement costs for various types of bridges as reported by Caltrans (Caltrans, 1995). These values are given in units of cost per square foot of bridge deck. Table 7.3: Average replacement costs for different bridge types in 1995 US dollars (from Caltrans, 1995) Type of Bridge Total # of Bridges Amount SqFt. of Deck Wt. Avg. Cost/SqFt. RC Slab 17 $6 466 177 80 407 $80.42 RC Box Gdr 10 14 774 702 173 560 85.13 CIP/PS Slab 5 5 260 219 48 281 108.95 CIP/PS Box Gdr 70 211 691 470 2 315 672 91.42 PC/PS "I" Gdr 2 1 862 557 14 474 128.68 PC/PS Slab 2 750 502 6 973 107.63 Steel Gdr 6 74 064 563 448 965 164.97 Totals 112 $314 870 190 3 088 332 $101.95 90 Chapter 7 - Loss Estimate The range of the repair costs were derived based on the repair contract bids which followed the Northridge earthquake. Along with the cost information, the damage classification proposed by Park et al. which was presented in section 6.1.1 were used to associate the RDI values with a damage cost. Using the threshold values presented in table 7.1, relationships between the RDI and the DDI were determined (see Figure 7.2). 0 0.1 0.2 0.3 0.4 0.5 Damage Index (DI) Figure 7.2: Relationship between DDI and RDI Figure 7.2 shows the DDI increasing along a second order curve between a RDI of 0.1 and a RDI of 0.4. The proposed curve simply reflects a trend observed in a study of the available cost data. In Figure 7.2, the DDI is equal to the ratio of the repair cost to the total cost of removal and replacement of the bridge. For this reason, the maximum value of the DDI is 1.0. In keeping with the threshold damage indices defined in Table 7.1, damage is negligible below a RDI of 0.1 and beyond a RDI of 0.4, the damage is considered irreparable. 91 Chapter 7 - Loss Estimate 7.2.1.2 Calculation of Direct Damage Costs Prior to calculating the direct damage costs for the bents of the FW and C V bridges, the removal and replacement costs per square foot of bridge deck area were needed. According to the Division of Structures at Caltrans (Caltrans, 1992), the average bridge costs approximately $20 per square foot to remove (in 1992 US dollars). As both the FW and C V bridges are reinforced concrete box girder systems, the replacement cost was estimated using the Table 7.3 figure of $85.13 per square foot (in 1995 US dollars). Of course, the calculations assume that each bridge would be replaced with exactly the same structure. All costs were then converted to 1989 US dollars using equation 7-2: P = F 1 (7-2) where P is the present worth, F is the future worth, i is the discount rate and n is the number of interest periods (years). Discrete compounding and a discount rate of 4% were assumed in the dollar conversions. The total estimated removal and replacement costs for the two bridges are summarized in Table 7.4. Table 7.4: Estimated removal and replacement costs in millions, 1989 US dollars Bridge Deck Area (SqFt.) Removal Cost Repl. Cost Total Cost FW 94 628 1.69 6.40 8.09 CV 128 473 2.31 8.61 10.92 92 Chapter 7 - Loss Estimate In reality, the aforementioned bridges were replaced by cast-in-place prestressed box girder structures with smaller bridge deck dimensions. Although deck widths did not vary significantly, the bridge which replaced the FW was 86 feet shorter in length and the replacement for the C V was 94 feet shorter than the original structure. Table 7.5 compares the estimated replacement costs with the actual replacement costs (not including incentives). Table 7.5: Estimated vs. actual replacement costs in millions, 1989 US dollars Bridge Estimated Replacement Cost Actual Replacement Cost FW 6.40 4.55 C V 8.61 8.10 Clearly, the estimated replacement costs are very approximate. Assuming that the analytical results are accurate, one should expect that actual replacement costs may exceed or fall short of the estimates by a few million dollars on the average highway bridge. Tables 7.6 and 7.7 show the estimated direct damage costs for the two bridges for the different scenario earthquakes. 93 Chapter 7 - Loss Estimate Table 7.6: Estimated direct costs for FW in millions, 1989 US dollars M M I Northridge Whittier DI DDI DC DI DDI DC V 0.0 0.0 0.0 0.0 0.0 0.0 VI 0.0 0.0 0.0 0.0 0.0 0.0 VII 0.0 0.0 0.0 0.0 0.0 0.0 VIII 0.308 0.475 3.84 0.279 0.35 2.8 IX 0.414 1.0 8.09 >1.0 1.0 8.09 X >1.0 1.0 8.09 >1.0 1.0 8.09 XI >1.0 1.0 8.09 >1.0 1.0 8.09 Table 7.7: Estimated direct costs for C V in millions, 1989 US dollars M M I Northridge Whittier DI DDI DC DI DDI DC V 0.0 0.0 0.0 0.0 0.0 0.0 VI 0.0 0.0 0.0 0.0 0.0 0.0 VII 0.0 0.0 0.0 0.0 0.0 0.0 VIII 0.182 0.075 0.82 0.362 0.775 8.47 IX 0.365 0.775 8.47 >1.0 1.0 10.93 X >1.0 1.0 10.93 >1.0 1.0 10.93 XI >1.0 1.0 10.93 >1.0 1.0 10.93 94 Chapter 7 - Loss Estimate 7 .2.2 Indirect Costs The indirect costs are subdivided as follows (Building Systems Development, Inc. et al., 1989): 1. Economic impacts • business interruption • unemployment • tax impact 2. Social impacts • individual pain and loss • disruption to the community The estimation of direct costs can be performed quite accurately since information and statistics about structural repair are readily available. The indirect costs, however, are more difficult to quantify in terms of dollar losses. There has been very little information published on the subject. Since the estimation of indirect costs associated with seismic bridge damage is a complex topic in itself, some major simplifications will be required if indirect costs are to be accounted for in decision-making for the seismic retrofit of bridges. The monetary value associated with social impacts is a particularly ambiguous and controversial issue. Costs associated with individual pain and loss could be quite significant. For example, a motorist whose daily commute is increased by an hour or more due to a collapsed viaduct would experience financial losses due to increased transportation costs and due to valuable time lost during the commute. Attempts to quantify the losses associated with the disruption to the community, however, would be highly subjective. If the post-disaster serviceability of a specific bridge were imperative for reasons of community welfare, it would 95 Chapter 7 - Loss Estimate have been identified in the preliminary screening process. It is improbable that a bridge in this category would have a retrofit deferred on the basis of a detailed evaluation. Based on these observations, it was decided that indirect cost estimates would account for the losses associated with the decrease in economic activity and for individual losses caused by a bridge's unserviceability. A reasonable and convenient way to estimate the economic loss associated with an unserviceable bridge is to consider typical incentive/disincentive clauses in bridge construction or bridge repair contracts. If a bridge owner wishes to encourage early completion of construction, he/she will provide a bonus for every day that the contractor is ahead of the specified schedule. Similarly, a penalty would be applied for late completion. Caltrans used this strategy in order to hasten the repair and replacement of bridges which had been damaged in the Northridge earthquake. For example, if Caltrans specified 150 days as the allowable time in which to complete a project, then the bid of a contractor who thought that the work could be done in 140 days could be reduced by 10 times the per day incentive. The amount of the incentive/disincentive appears to be a good way of attributing a dollar value to the indirect cost due to a bridge's unserviceability. Indirect costs obtained in this manner were verified by considering what each bridge user would be willing to pay in order to use a particular bridge every day. It is reasonable to assume that a motorist would attribute a certain value to time saved commuting. Values of the average daily traffic (ADT) were obtained from Caltrans for the two Santa Monica Freeway bridges. Table 7.8 shows the cost per day for each bridge user if the contract incentive value of 100 000 dollars per day for a major highway bridge is used: 96 Chapter 7 - Loss Estimate Table 7.8: Indirect cost per vehicle in 1994 US dollars Bridge ADT (vehicles/day) Indirect Cost ($/day) Indirect Cost ($/vehicle) FW 246 000 100 000 $0.41 CV 233 000 100 000 $0.43 As it is safe to assume that each motorist crossing the bridge would agree to a one-way toll of about 45 cents, the assumed indirect costs were deemed to be fair estimates. In fact, motorists would presumably pay much more for the convenience of using the bridge. For major highway bridges, it was assumed that it would take 90 days to remove and replace an irreparable bridge and that it would take 45 days to repair and reopen a repairable bridge. These estimates are based on actual repair and replacement times as reported by Caltrans (Caltrans, 1994b). It should be noted that in this model, indirect costs are only incurred if the seismic damage is serious enough to warrant a closure of the bridge. This can be determined by looking at the displacements, the permanent deformations and the damage indices obtained from the nonlinear analyses. In general, damage indices between 0.1 and 0.4 indicate that the bridge will require repair and damage indices greater or equal to 0.4 suggest that the bridge will be removed and replaced. 7.2.2.1 Calculation of Indirect Damage Costs Tables 7.9 and 7.10 show the estimated indirect damage costs for the two bridges for the different scenario earthquakes. 97 Chapter 7 - Loss Estimate Table 7.9: Estimated Indirect Costs for FW in millions, 1989 US dollars M M I Northridge Whittier DI IC DI IC V 0.0 0.0 0.0 0.0 VI 0.0 0.0 0.0 0.0 VII 0.0 0.0 0.0 0.0 VIII 0.308 4.5 0.279 4.5 IX 0.414 9.0 >1.0 9.0 X >1.0 9.0 >1.0 9.0 XI >1.0 9.0 >1.0 9.0 Table 7.10: Estimated Indirect Costs for C V in millions, 1989 US dollars MMI Northridge Whittier DI IC DI IC V 0.0 0.0 0.0 0.0 VI 0.0 0.0 0.0 0.0 VII 0.0 0.0 0.0 0.0 VIII 0.182 4.5 0.362 4.5 IX 0.365 4.5 >1.0 9.0 X >1.0 9.0 >1.0 9.0 XI >1.0 9.0 >1.0 9.0 98 Chapter 7 - Loss Estimate 7.2.3 Summary of Damage Cost Estimate The direct, indirect and total damage costs for the two bridges are summarized in Tables 7.11 and 7.12. Table 7.11: Estimated total costs for FW in millions, 1989 US dollars M M I Northridge Whittier DC IC TC DC IC TC V 0.0 0.0 0.0 0.0 0.0 0.0 VI 0.0 0.0 0.0 0.0 0.0 0.0 VII 0.0 0.0 0.0 0.0 0.0 0.0 VIII 3.84 4.5 8.34 2.83 4.5 7.33 IX 8.09 9.0 17.09 8.09 9.0 17.09 X 8.09 9.0 17.09 8.09 9.0 17.09 XI 8.09 9.0 17.09 8.09 9.0 17.09 Table 7.12: Estimated total costs for C V in millions, 1989 US dollars MMI Northridge Whittier DC IC TC DC IC TC V 0.0 0.0 0.0 0.0 0.0 0.0 VI 0.0 0.0 0.0 0.0 0.0 0.0 VII 0.0 0.0 0.0 0.0 0.0 0.0 VIII 0.82 4.5 5.32 8.47 4.5 12.97 IX 8.47 4.5 12.97 10.93 9.0 19.93 X 10.93 9.0 19.93 10.93 9.0 19.93 XI 10.93 9.0 19.93 10.93 9.0 19.93 99 Chapter 7 - Loss Estimate Despite the roughness of the cost estimates, they are considered satisfactory for use in a decision analysis. Sensitivity analyses in which the estimated direct and indirect costs are varied within certain limits will be discussed in Chapter 8. 100 CHAPTER 8 Decision and Sensitivity In previous chapters, earthquake probabilities have been determined, damage indices have been obtained and relationships between damage and its consequences have been established. This chapter organizes the data into an expected value decision model. This type of decision analysis and its application to bridge retrofitting were discussed in Chapter 4. The use of Bayesian Decision Theory will ensure that consequences of the decision, risk preferences of the decision maker as well as likelihood judgments in the form of probabilities are appropriately accounted for in the analysis. The expected value of the NPC will be used to rank the retrofit options. A sensitivity study will then reveal how the various input parameters affect the decision and hence, whether more accurate or precise information should be sought. 8.1 Initial Investment of Retrofit Options A feasible retrofit option for the bridges studied along with a cost estimate for the option were presented in Chapter 2. The cost estimates for the retrofit option were previously given in 1992 US dollars. These costs must be converted to 1989 US dollars since 1989 is the year in which the hypothetical decision is being made. Equation 7-2 was used to make the conversion. The retrofit costs are summarized in the Table 8.1: 101 Chapter 8 - Decision and Sensitivity Table 8.1: Cost estimate for retrofit option in 1989 US dollars Bridge Estimated Retrofit Cost FW $3.0 million CV $3.81 million 8.2 Net Present Cost (NPC) The net present cost (NPC) of damage due to seismically induced ground shaking is the sum of the initial cost of the rehabilitation and the present value of the annual damage costs expected to accrue each year over the planning period. Since present values are considered in the analysis, it is first necessary to define the planning period and the discount rate. 8.2.1 Planning Period The planning period, T is the length of time under consideration in the undertaken project. In the case of bridge retrofitting, T is considered the effective life span of the structure. If it is assumed that damaged bridges will always be replaced, then the planning period can be considered infinite. However, when future values are discounted to the present, NPCs will converge to the same value beyond a certain number of years. Preliminary calculations showed that beyond about 100 years, the time span considered had very little effect. This value was therefore used throughout the decision analyses. 8.2.2 Discount Rate The discount rate is the interest rate which will be used to bring future costs to the present. The discount rate should be the actual interest rate minus the inflation rate. The 102 Chapter 8 - Decision and Sensitivity inclusion of inflation in the discount rate would imply inflated future costs; this would cause the effect of inflation to be canceled out in the calculation of present values. Where investments and costs are high as in the case of structural rehabilitation of bridge structures, it is important to choose a discount rate which best reflects the projected economy over the planning period. This is not a simple task and many researchers disagree on which discount rate to use. In general, discount rates around 3% or 4% are considered acceptable for the public sector and rates around 4% to 6% are considered acceptable for the private sector. In the current decision analysis a discount rate of 4% was assumed. 8.2.3 N P C Calculation The expected net present cost is defined as NPC =Cr+ + — ^ + + — E - ± - F (8-1) (1+0 (1 + / ) 2 (l + / ) r where C r is the initial cost of the rehabilitation, Ej is the expected annual damage cost for year j , i is the discount rate, and T is the length of the planning horizon which should reflect the effective life of the structure. If it assumed that the annual expected damage cost is constant each year during the life of the structure, then the following simplification can be made: " l - ( l + / ) - r ' NPC = C+E (8-2) where E is the expected annual damage cost which is constant over the planning period. The assumption that the expected annual damage cost is constant implies that the annual probabilities of earthquakes of various intensities are also constant. Moreover, it implies that the effectiveness of the retrofit in reducing damage is constant as well. Historic 103 Chapter 8 - Decision and Sensitivity seismicity has shown that the annual probabilities of earthquakes are not constant and are in fact noticeably lower after an earthquake of significant intensity. However, since any bridge retrofit program is a relatively long term project which considers effects over the entire life span of the structure, the short term variations in earthquake probabilities may be considered negligible. Finally, it is assumed that a properly executed rehabilitation will maintain its ability to reduce seismic damage through passing years. Logically, the retrofit process is expected to improve the seismic performance of the bridge. Therefore, expected damage costs will be reduced by a certain amount. The ERD factors defined in Chapter 6 are used to adjust the expected damage cost to account for the structural rehabilitation. The expected damage cost, E, is calculated in the following manner: E=fjP(I})x(l-ERDj)xC}. (8-3) 7=1 where P(L) is the annual probability of occurrence of an earthquake of intensity Ij, ERDj is the expected reduction in damage due to the retrofit for an earthquake of intensity Ij (note that E is zero in the case of a retrofit for which ERD is equal to one) and Q is the estimated damage cost for an earthquake of intensity Ij. With the annual earthquake probabilities given in Chapter 5 and the damage cost estimates presented in Chapter 7, the NPC of the no retrofit option can be calculated using equation 8-2. In this case, C r is zero. For the retrofit option, E is zero. 8.3 Cost Comparison The NPC for the retrofit option presented in section 8.2 and the NPC for the no retrofit alternative were compared for the FW and CV bridges. Clearly, the course of action 104 Chapter 8 - Decision and Sensitivity which leads to the lowest expected cost is the most desirable. Table 8.2 shows the NPC of each option when only direct costs are considered. Table 8.2: NPCs (direct costs only) for the two options in millions, 1989 US dollars Option NPC Northridge Whittier FW CV FW C V Retrofit 3.0 3.81 3.0 3.81 No Retrofit 1.84 1.43 1.65 3.15 The results show that when only direct costs are considered in the decision model, the optimal alternative is to do nothing in all cases. Table 8.3 shows the NPC of each option if in addition to the direct costs, the indirect costs are considered. Table 8.3: NPCs (direct plus indirect costs) for the two options in millions, 1989 US dollars Option NPC Northridge Whittier FW C V FW C V Retrofit 3.0 3.81 3.0 3.81 No Retrofit 3.58 2.85 3.38 4.89 Including indirect costs in the decision analysis considerably increased the NPC for the no retrofit option. The average costs of the no retrofit option for the FW and C V bridges are 105 Chapter 8 - Decision and Sensitivity $3.48 million and $3.87 respectively. The results now show that on average, the optimal decision is to retrofit the structure. In this decision analysis, the indirect costs are large enough to change the decision outcome. 8.4 Benefit/Cost Analysis Benefit/cost ratios simplify the comparison and ranking of prospective retrofit projects. Typically, the numerator is the expected present value of future benefits and the denominator is the initial investment. When dealing with bridge seismic retrofit projects, the benefit can be viewed as the difference between the present value of future earthquake damage costs for the unretrofitted structure and the rehabilitation cost, i.e. the dollar amount that will be saved if the project is undertaken. Evidently, if future damage costs are greater than the retrofit cost, the project is not justified. To demonstrate how bridges in a network can be prioritized based on the benefit/cost ratio, calculations were done for the two bridges in the case study. Retrofitting the Fairfax-Washington bridge is expected to save an average of $480 000 in future damage costs, while retrofitting the La Cienega-Venice bridge is expected to save only $60 000 in damage costs. These cost savings must now be compared to the initial investment cost. The benefit/cost ratio is 0.160 for the Fairfax-Washington bridge and 0.016 for the La Cienega-Venice bridge, indicating that the former bridge should be the first to be retrofitted. When time or money is restricted, projects with higher benefit/cost ratios should be given priority. 106 Chapter 8 - Decision and Sensitivity 8.5 Sensitivity Analysis Since many of the input values used in the decision model were approximated or assumed, it is important to investigate the sensitivity of the decision to these values. The main input data involving uncertainty are the following: 1. seismic data 2. damage costs 3. discount rate 4. planning period The purpose of the sensitivity analysis is to examine how the outcome of the decision will change if the aforementioned values are varied within reasonable ranges. 8.5.1 Seismicity A key component of the seismic data which influences the decision process is the selection of the ground motion which drives the inelastic analysis of the bridge bents. Since all natural earthquake records are very different in terms of frequency content, simple scaling procedures will not render equivalent earthquake excitations. Even if site-specific design spectra are used future ground motions can never be predicted with a great deal of accuracy. For these reasons, the inelastic analyses of the bridge bents were performed using two different earthquake records: the Northridge and the Whittier earthquakes. The original records were scaled to various levels of PGA. The results of the decision analysis using direct and indirect costs clearly show that the decision model is sensitive to the input motion used in the seismic analyses (see Table 8.3). Although the decision to retrofit remains unchanged for the FW bridge, the expected NPCs for the CV bridge are very different for the two input 107 Chapter 8 - Decision and Sensitivity motions. Analyses performed using the Northridge earthquake yield results which suggest that the bridge should not be retrofitted. In contrast, using the Whittier earthquake as input caused the retrofit option to be favoured for this same bridge. The annual occurrence rates specified by the USGS and used as the principal indicator of risk in the decision analysis are also associated with a certain degree of uncertainty. Since the frequency of ground motions is very difficult to predict with great accuracy, it was assumed that values were accurate to ±25%. New values of the NPC were calculated using in one case a lower bound (-25%) and, in the other, an upper bound (+25%) to the earthquake probabilities for each MMI level. Since two cases are considered for each M M I level and since there are seven M M I levels, this results in fourteen different sets of earthquake probability data. To illustrate how the data were varied, Table 8.4 shows the first four out of the fourteen sets of data. Table 8.5 shows the NPC values calculated for each of the fourteen data sets. Table 8.4: First four data sets used in sensitivity analysis for earthquake probability data M M I Original Set 1 Set 2 Set 3 Set 4 V 0.117 0.088 0.146 0.117 0.117 VI 0.04950 0.04950 0.04950 0.0370 0.0620 VII 0.02101 0.02101 0.02101 0.02101 0.02101 VIII 0.00893 0.00893 0.00893 0.00893 0.00893 IX 0.00379 0.00379 0.00379 0.00379 0.00379 X 0.00161 0.00161 0.00161 0.00161 0.00161 XI 0.00069 0.00069 0.00069 0.00069 0.00069 108 Chapter 8 - Decision and Sensitivity Table 8.5: NPCs obtained by varying the earthquake probability data (in millions, 1989 US dollars) Data Set NPC Northridge Whittier FW C V FW C V Original 3.58 2.85 3.38 4.89 1 3.63 2.89 3.43 4.96 2 3.53 2.81 3.33 4.82 3 3.60 2.87 3.40 4.92 4 3.56 2.84 3.36 4.86 5 . 3.59 2.86 3.39 4.90 6 3.57 2.85 3.37 4.87 7 3.21 2.63 3.06 4.29 8 3.95 3.07 3.70 5.48 9 3.25 2.60 3.05 4.50 10 3.90 3.11 3.70 5.27 11 3.44 2.69 3.24 4.72 12 3.71 3.02 3.51 5.05 13 3.52 2.78 3.32 4.82 14 3.64 2.92 3.44 4.96 The outcome of the decision remains unchanged due to variations in the annual occurrence rates. Table 8.6 shows the percentage change in the NPCs for the fourteen data sets. 109 Chapter 8 - Decision and Sensitivity Table 8.6: Percentage change in NPCs due to the variation of the earthquake probability data Data Set % Change from Original NPCs Northridge Whittier FW CV FW C V 1 1.43 1.43 1.43 1.43 2 -1.40 -1.40 -1.40 -1.40 3 0.60 0.60 0.60 0.60 4 -0.60 -0.60 -0.60 -0.60 5 0.25 0.25 0.25 0.25 6 -0.25 -0.25 -0.25 -0.25 7 -10.32 -7.74 -9.46 -12.24 8 10.30 7.73 9.44 12.21 9 -9.04 -8.92 -9.57 -7.84 10 9.03 8.91 9.56 7.83 11 -3.84 -5.72 -4.06 -3.33 12 3.84 5.71 4.06 3.33 13 -1.64 -2.45 -1.74 -1.43 14 1.64 2.45 1.74 1.43 The highest percentage changes in the NPCs were observed for data sets 7, 8, 9 and 10. These data sets correspond to variations of -25% and +25% in the occurrence rates for M M I levels VIII and IX. The annual occurrence rates for these M M I levels therefore have a greater influence on the NPCs. In general, however, the percentage changes are quite small and indicate that the NPCs and the decision outcome are not sensitive to these changes in the annual occurrence rates. 110 Chapter 8 - Decision and Sensitivity 8.5.2 Damage Costs The direct and indirect damage costs were each varied in order to investigate the sensitivity of the decision model to these values. The direct costs, which include the costs of repair or replacement of the structure, can be estimated with reasonable accuracy. Using engineering judgment and experience as well as available statistical data should ensure that the anticipated direct costs are within an accuracy range of about ±20%. The effect of placing upper and lower bounds on the costs resulted in two additional data sets. The NPC for each data set is shown in Table 8.7. Table 8.7: NPCs obtained by varying the direct costs (in millions, 1989 US dollars) Data Set NPC Northridge Whittier FW CV FW C V Original 3.58 2.85 3.38 4.89 1 (-20%) 3.21 2.57 3.05 4.26 2 (+20%) 3.95 3.14 3.71 5.52 Recalling that the NPCs of retrofit for the FW and CV bridges are 3.0 and 3.81 million respectively, Table 8.7 shows that the changes in the direct costs do not affect the decision. A similar analysis can be performed for indirect costs. Since indirect costs are by nature difficult to define, they were varied within broader ranges. In data sets 1 and 2, values were decreased by 50% and increased by 50% respectively. The changes in the NPC are listed in Table 8.8. I l l Chapter 8 - Decision and Sensitivity Table 8.8: NPCs obtained by varying the indirect costs (in millions, 1989 US dollars) Data Set NPC Northridge Whittier FW C V FW C V Original 3.58 2.85 3.38 4.89 1 (-50%) 2.71 2.14 2.51 4.02 2 (+50%) 4.44 3.56 4.24 5.75 Although a 50% increase in the indirect costs did not affect the final decision, a 50% decrease makes the do nothing option the more attractive of the two alternatives in all cases. These results indicate that the indirect costs dominate the decision process in this case. It is expected that if indirect costs are omitted from a bridge retrofit decision, the optimal course of action will often be to do nothing. Since there are no set rules in assigning indirect costs, this leaves bridge owners and decision makers with the difficult task of quantifying these losses. 8.5.3 Discount Rate The decision analysis was repeated using the following values for the discount rate: 3%, 5% and 6%. The results when all costs are considered are shown in Table 8.9. High discount rates lower the NPCs. When future costs are heavily discounted as they are brought back to the present, the potential financial consequences of a future earthquake are lessened. Decision makers will therefore be more willing to accept the risk of structural damage. Table 8.9 indicates that when the discount rate is reduced from 4% to 3%, the optimal decision is to retrofit the bridge in all cases. When the discount rate is increased to 5% and 6%, however, 112 Chapter 8 - Decision and Sensitivity the lower NPCs suggest that the do nothing option is favorable. Clearly, the decision model is very sensitive to the discount rate chosen. Table 8.9: NPCs obtained by varying the discount rate (in millions, 1989 US dollars) Data Set NPC Northridge Whittier FW CV FW C V Original 3.58 2.85 3.38 4.89 1 (i=3%) 4.85 3.87 4.58 6.63 2 (i=5%) 2.76 2.20 2.60 3.76 3 (i=6%) 2.20 1.75 2.08 3.00 8.6 Discussion The decision analysis showed that when all costs were considered, it was preferable to retrofit the Fairfax-Washington bridge. NPCs calculated for the La Cienega-Venice bridge produced conflicting results for the two different ground motions. This immediately reinforces the notion that the choice of the earthquake record can have a considerable effect on the decision outcome. Ideally, a suite of earthquakes should be used in the seismic analyses such that average values can be obtained and used in the decision model. Although the model appears to be relatively insensitive to changes in the annual earthquake occurrence rates, the NPCs are more affected by changes in the rates for M M I levels VIII and IX. If one wished to improve the accuracy of the decision model, the occurrence rate estimates for these two intensity levels could be looked at more closely. The 113 Chapter 8 - Decision and Sensitivity data for moderate (MMI V-VI) and great (MMI X-XTI) earthquakes do not seem to be as influential. Variations of ±20% in the direct damage costs did not affect the final decision in any way. However, varying the indirect costs significantly changed the expected NPCs for the do nothing option. A 50% decrease in the indirect costs rendered a decision which was opposite to the original decision. Since these costs clearly play an important role in the decision model, it would be to the decision maker's benefit to research the indirect costs more carefully. Finally, the discount rate significantly affects the decision analysis. Different options are favoured when the rate is lowered from 4% to 3% or when it is increased to 5%. Lower discount rates result in higher NPCs and the decision to retrofit the structure. Higher discount rates imply lower NPCs and favour the no retrofit option. 114 CHAPTER 9 Conclusions The purpose of this study was to demonstrate an expected value decision model for the seismic retrofit of bridges. The net present cost (NPC) was used to rank the retrofit options. A case study of two Caltrans highway bridges was introduced in order to demonstrate the various steps involved in the decision procedure. The hypothetical retrofit decision that could have been made following the 1989 Loma Prieta earthquake was investigated. The two options considered for each of the bridges were 1) not retrofitting the structure or 2) performing a fully effective retrofit. The process of gathering all information essential to the decision analysis and obtaining reasonable estimates when necessary was described. The earthquake hazard at the bridge sites was determined through studies of available seismicity data. Earthquakes believed to be representative of the expected ground motions were then selected and scaled for use in the non-linear dynamic analyses. The goal of these analyses was to predict future earthquake damage by means of structural damage indices. The damage indices were then related to predefined damage categories which, in turn, were associated with damage costs. Direct and indirect costs, based on seismic damage cost information from previous earthquakes, were projected for a given damage category. An expected value of the future earthquake damage costs was then calculated and discounted to the present (or to the year 1989 in this case). The 115 Chapter 9 - Conclusions NPC, which includes the initial retrofit cost and the expected future damage costs, was calculated for the two retrofit options. The decision analysis indicated that if all costs (direct and indirect) were considered, the optimal course of action would be to carry out complete seismic retrofits of the two bridges. The Fairfax-Washington bridge was predicted to cost $3.0 million to retrofit and average damage costs were expected to be $3.55 million. The retrofit cost and average damage costs for the La Cienega-Venice bridge were $3.81 million and $3.95 million respectively. However, when indirect costs are ignored, the no retrofit decision is favoured. In fact, the indirect costs are approximately equal to the direct costs. Hence it is logical that they should strongly influence the decision. Sensitivity analyses concluded that changes in the seismic hazard data did not affect the decision outcome. The decision was also relatively insensitive to variations in the direct damage costs. The earthquake record selection, however, was shown to have an impact on the end result of the study. For this reason, it is recommended that five or six earthquake records be used in the seismic analyses; damage indices can then be averaged and the resulting costs will be more meaningful. The decision was also sensitive to variations in the indirect costs. When indirect costs are high, as in the case of severely damaged bridges, they will inevitably play a pivotal role in the decision process. More research pertaining to the indirect economic consequences of earthquakes on transportation networks is needed. Finally, the discount rate used to determine present values of future costs can significantly affect the outcome of the decision analysis. One can only use the best guess for the discount rate since it is impossible to predict the value of future dollars with certainty. 116 Chapter 9 - Conclusions If decision makers are consistent and methodical in performing expected value decision analyses, then bridges analysed in this way can be prioritised for seismic retrofitting. Simple benefit/cost analysis will reveal which retrofit projects have the potential for greater cost savings. In the case study, it was shown that retrofitting the Fairfax-Washington bridge was more cost efficient than retrofitting the La Cienega-Venice bridge. The type of decision analysis demonstrated in the case study encompasses the fields of seismology, structural engineering and economics. Knowledge in each of these domains is essential to sound decision making. Currently available seismic hazard information in the United States and in Canada is sufficient for use in a decision problem such as this one. The role of the structural engineer, however, needs to be clarified. A variety of powerful analytical tools are now available for use in seismic damage prediction; however, many aspects of the problem require judgment and little precedent is available. How sophisticated should the analysis models be? What approximations are acceptable? In the area of economics, work needs to be done setting up seismic damage cost data banks. The cost information currently exists, but it has not been compiled and stored such that it is readily accessible. Moreover, the indirect economic and social impacts of earthquakes need to be researched. The indirect damage costs are expected to be significant in large earthquakes; an effort must be made to quantify these losses. Despite the gaps in knowledge and the simplifications, it is still possible to make consistent and rational decisions using the available information. The use of decision analysis in the seismic retrofitting process is a topic worthy of more research. Bridge rehabilitation 117 Chapter 9 - Conclusions projects can often cost millions of dollars. Is the expense justified? The decision model proposed in this thesis sheds light on the answer to this question. 118 REFERENCES 1. Ang, A . H . - S . , K i m , W.J . and K i m , S.B. 1993. Damage Estimation of Existing Bridge Structures. Structural Engineering in Natural Hazards Mitigation: Proceedings, A S C E Structures Congress 1993, Irvine, C A . V o l . 2, pp. 1137-1142. 2. Astaneh-Asl, A . , Bolt, B . , McMul l in , K , Donikian, R., Modjtahedi, D . and Cho, S. 1994. Seismic Performance of Steel Bridges During the 1994 Northridge Earthquake. Report to the California Department of Transportation. Department of Civi l Engineering, College of Engineering, University of California at Berkeley. Apri l , 1994. 3. A T C - 6 - 2 1983. Seismic Retrofitting Guidelines for Highway Bridges. Report A T C - 6 - 2 , Applied Technology Council, Redwood City, C A . 4. Babaei, K . and Hawkins, N . 1991. Bridge Seismic Retrofit Prioritization. Proceedings, Third U . S . National Conference on Lifeline Earthquake Engineering, Los Angeles, C A . pp. 149-155. 5. Basoz, N . and Kiremidjian, A . S . 1995. Prioritization of Bridges for Seismic Retrofitting. Report N o . 114. The John A . Blume Earthquake Engineering Center, Department of Civi l Engineering, Stanford University, Stanford, C A . 6. Benjamin, J.R. and Cornell, C A . 1970. Probability, Statistics, and Decision for Civil Engineers. McGraw-Hi l l Book Company, New York, N Y . 684 pp. 7. Buckle, I. G. and Friedland, I . M . 1995. Improved Screening Procedure for Seismic Retrofitting of Highway Bridges. Proceedings, Fourth International Bridge Engineering Conference. San Francisco, C A . pp. 59-70. 8. Building Systems Development, Inc., Integrated Design Services and Claire B . Rubin, Consultant. 1989. Establishing Programs and Priorities for the Seismic Rehabilitation of Buildings: A Handbook. F E M A - 1 7 4 . Federal Emergency Management Agency, Washington, D . C . 9. C A E E 1994. Preliminary Report on the Northridge, California, Earthquake of January 17, 1994. Canadian Association for Earthquake Engineering. Vancouver, B C . 10. Caltrans. 1986. Bridge Memo to Designers Manual. Internal literature. Caltrans Division of Structures, Sacramento, C A . 119 References 11. Caltrans. 1992. Summary of Seismic Work Costs. Internal literature. Caltrans Division of Structures, Sacramento, CA. 12. Caltrans. 1994a. Post Earthquake Investigation Report. Internal Report. Caltrans Division of Structures, Sacramento, CA. 13. Caltrans. 1994b. Northridge Informal Bids Contracts. Internal literature. Caltrans Divison of Structures, Sacramento, CA. 14. Caltrans. 1995. Construction Statistics 1995. Internal literature. Caltrans Division of Structures, Sacramento, CA. 15. Carr, A.J. 1996. R U A U M O K O user's guide. Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. 16. Cherng, R. and Wen, Y K . 1992. Reliability Based Cost-Effective Retrofit ofHighway Transportation Systems Against Seismic Hazard. Civil Engineering, University of Illinois, Urbana, EL. 17. Collins, M.P. and Mitchell, D. 1990. RESPONSE Version 1.0 for Prestressed Concrete Structures. © Andreas J. Felber 1990. Department of Civil Engineering, University of Toronto, Toronto, ON. 18. Cornell, C. A. 1968. Engineering Seismic Risk Analysis. Bulletin of the Seismological Society of America, Vol. 58, pp. 1583-1606. 19. De la Colina, J., Eberhard, M.O., Ryter, S.W. and Wood, S.L. 1996. Sensitivity of Seismic Assessment of a Double-Deck, Reinforced Concrete Bridge. Earthquake Spectra, Vol. 12, No. 2, May, 1996, pp. 217-244. 20. DiPasquale, E. and Cakmak, A.S. 1987. Detection and Assessment of Seismic Structural Damage. Report No. NCEER-87-0015. National Center for Earthquake Engineering Research, Buffalo, NY. 21. Dowrick, D.J. 1987. Earthquake Resistant Design. Second Edition. John Wiley & Sons, Chichester, Britain. 519 pp. 22. EERI 1994a. Expected Seismic Performance of Buildings. Earthquake Engineering Research Institute Ad Hoc Committee on Seismic Performance. February, 1994. 23. EERI 1994b. Northridge Earthquake, January 17, 1994, Preliminary Reconnaissance Report. Report 94-01, Earthquake Engineering Research Institute, March, 1994. 120 References 24. EERI Committee on Seismic Risk. 1989. The Basics of Seismic Risk Analysis. Earthquake Spectra, Vol. 5, No. 4. pp. 675-702. 25. Engineering News-Record. 1997. Rising from the Rubble, Jan. 20, pp. 40-47. Engineering News-Record. 1996. Link Built to Outlast Liquefying, Nov. 11, p. 14. Canada Project Speeding Along, Aug. 26, p. 13. Unique Retrofit in New Zealand, Aug. 12, pp. 21-22. Engineering News-Record. 1995. Caltrans Now Permits Composite Wraps, Dec. 25, pp. 15-16. Panels SpeedRedecking, Oct. 23, p. 25. Engineering Brains Challenged in Wake of Kobe's Seismic Brawn, Jan. 30, pp. 10-16. Engineering News-Record. 1994. Caltrans Hastens Retrofits, March 21, p. 14. 26. Filiatrault, A., Tremblay, S. and Tinawi, R. 1994. A rapid seismic screening procedure for existing bridges in Canada. Canadian Journal of Civil Engineering, Vol. 21. pp. 626-642. 27. Finn, L. 1995. Lecture notes. Department of Civil Engineering, University of British Columbia, Vancouver, BC. 28. Grant, E.L. , Ireson, W.G. and Leavenworth, R.S. 1990. Principles of Engineering Economy. 8th edition. John Wiley & Sons, U.S.A. 591pp. 29. Gunturi, S.K.V. and Shah, H.C. 1993. Mapping Structural Damage to Monetary Damage, Structural Engineering in Natural Hazards Mitigation: Proceedings, A S C E Structures Congress 1993, Irvine, CA. Vol. 2, pp. 1331-1336. 30. Hanson, S.L. and Perkins, D . M . 1995. Seismic Sources and Recurrence Rates as Adopted by USGS Staff for the Production of the 1982 and 1990 Probabilistic Ground Motion Maps for Alaska and the Conterminous United States, USGS Open-File Report 95-257 Preliminary. United States Geological Survey, Golden, CO. 31. Kwan, J. 1993. Application of Decision Analysis to Seismic Rehabilitation of Historic Buildings: A Case Study of Rehabilitation of Stanford University Memorial Church. M . A . Sc. Thesis, Department of Civil Engineering, University of British Columbia, Vancouver, BC. 32. McGuire, R.K. 1976. FORTRAN Computer Program for Seismic Risk Analysis. USGS Open-File Report 76-67. United States Geological Survey, Golden, CO. 121 References 33. Mitchell, D.M., Sexsmith, R.G. and Tinawi, R. 1994. Seismic retrofitting techniques for bridges - a state of the art report, Canadian Journal of Civil Engineering, Vol. 21, pp. 823-835. 3 4. NCHRP 12-33 1993. Draft LRFD Bridge Design Specifications and Commentary. National Cooperative Highway Research Program. 35. NIST 1994. 1994 Northridge Earthquake Performance of Structures Life and Fire Protection Systems, Internal Report, National Institute of Standards and Technology, Gaithersburg, MD. 36. Park, Y.J., Ang, A.H.-S. and Wen, Y.K. 1985. Seismic damage analysis of reinforced concrete buildings. Journal of Structural Engineering, ASCE, Vol. I l l , no. ST$, pp. 740-757. 37. Portland Cement Association 1993. PCACOL-Version 2.30. Design and Investigation of Reinforced Concrete Column Sections. Portland Cement Association, Skokie, E L . 38. Portland Cement Association 1993. PCA-Frame-Version 1.0. Three Dimensional Static Analysis of Structures. Portland Cement Association, Skokie, E L . 39. Reiter, L., 1990. Earthquake Hazard Analysis: Issues and Insights. Columbia University Press, New York, NY. 254 pp. 40. Rodriguez-Gomez, S. and Cakmak, A.S. 1990. Evaluation of Seismic Damage Indices for Reinforced Concrete Structures. Report No. NCEER-90-0022. National Center for Earthquake Engineering Research, Buffalo, NY. 41. Sheng, L.H. and Gilbert, A. 1991. California Department of Transportation Seismic Retrofit Program The Prioritization and Screening Process. Proceedings, Third U.S. National Conference on Lifeline Earthquake Engineering, Los Angeles, CA. pp. 1110-1119. 42. Snyder, R., Caltrans Public Affairs. Private Communication on May 8, 1997. 43. Stone, W.C. and Taylor, A W . 1993. Seismic Performance of Circular Bridge Columns Designed in Accordance with AASHTO/CALTRANS Standards. NIST Building Science Series 170, National Institute of Standards and Technology, Gaithersburg, MD. 44. VSP Associates, Inc. 1992a. A Benefit Cost Model for the Seismic Rehabilitation of Hazardous Buildings, Volume 1: A User's Manual. FEMA-227. Federal Emergency Management Agency, Washington, DC. 122 References 45. VSP Associates, Inc. 1992b. A Benefit Cost Model for the Seismic Rehabilitation of Hazardous Buildings, Volume 2: Supporting Documentation. FEMA-228. Federal Emergency Management Agency, Washington, DC. 46. Williams, M.S. and Sexsmith, R.G. 1994. Review of Methods of Assessing Seismic Damage in Concrete Structures. Technical Report 94-02. Earthquake Engineering Research Facility, University of British Columbia, Vancouver, BC. 47. Williams, M.S. and Sexsmith, R.G. 1997. Seismic Assessment of Concrete Bridges Using Inelastic Damage Analysis. Engineering Structures, Vol. 19, No. 3, pp. 208-216. 48. Yashinsky, M., Hipley, P. and Nguyen, Q. 1995. The Performance of Bridge Seismic Retrofits During the Northridge Earthquake. Internal Report. Caltrans Office of Earthquake Engineering. June, 1995. 123 A p p e n d i x A Structural drawings o f Fa i r fax-Washing ton and L a Cienega-Venice bridges I Z-4 t. STATE 7 CAUF. £-i-Co/umn rafzfance. Una 1 SanTti tColUrW) TOP REINFORCEMENT • iG^>f• ^^ZQM=M£lU£^^£ME^Z-ba.nl cofi ^r-r&rt/IS ~fypa-,SM AS BUILT PLANS ^ate Completed [Document N a j ^ £ ~ - ~ LAYOUT D//I<SP»4M Nor&-~. N'umbost a-f-erair o-f bars //id/cafe. ctisfa/>ca. in fee.-/ Avnt £ca/a/nt? rifferenca. liha torborrom rain forca-ma/ir. /)/} co/umns si/ni/ar. DBIbCX DCPAttTWCHT tmj DESIGN SECTION / *"r-- '— rr^~r- - * ^ t , ' V * t g * t ^ y STATE OF CALIFORNIA ocrARmofT OF r u s u c waaies omnon o r H C K N A T S FAIRFAX -WASH i NGTON UNDERCROSSING DUION I *JL.i 9/gj BENT 3L BUAMltliCS SCMXOS n$*df\ SKKx^"j"-tf2fc> 43* I KEREBT C E R T I F Y W A T T H I S IS A T R V S AKO A C C C S A T E COFT OF THE ABOVE DOCOHBKf TAIEW CBIIEa KT DIRECTIOH ABB COCTROt 'OB W I S DAT2 ~Jt S A C H A f T i l T O , C A U F f B 3 I . ' . FUElSUAST T O 1UTH OKI RATIOS ST THE DIRECTOR O F .PUTSHIC JJORKSH.-"" . PATE 3.'' S I G N A T U R E — J F I L E '-. . ' / ' / y , CO Q_ a H 4 0) f J Q o o | T O O 9T*Tt 7 e u i r . Pr&ttway— cOack drain "tin/co '.•tie.: t f ?ltfr*)*l • 71?/° REINFORCEMENT « =* , i-- a 11 Al \ 11 4 C 1", \i BOTTOM RE/NFORCEWENT PLANS OF CAP • - ^ i . T UH Stirrup, spacihq ground •' i h II 2 | - Por dra/h fiipa ovt-lej daja/fs S<t& ' OnotAaga Pa Ar/'/s "sneer1. -A L /4Q~ 1 T «<1 - H I " --^ t-— - .. ,! Jag , g«g "//{.attend 9-6 mfs coo. 1 1—1—» > - J a etch and OT bent cop-i d * ELE i/A TION y- Tepo-f Fooling io'-r Z7-? LAYOUT DIAGRAM Ylt LA . f ! Li. 3^ ~ -"5 <*•••'• / = 1 "7 4* l-<'/Ofi tvi/A /'-6' lap at 3p/ices. f»/SS s ^**»*ii > S'ui/a-l fi"'pa SECTION &-B Seals: '/i --/-0' fr/ohc-: Numbicr! al anetj of bars incfi'ccte. e/istaace //) fee/ r^ram £. Co/vmn sa^<zs-a/>c:&. Ana r"af rai'/j-foAOfnafi/ and i. bz/ivzsn ca/unns re-fese/tca /ina- bo^/of reihF co/e/rMS S/rr-i/af. indict les handle bars -./i-I-** .. , ansa »i»BTMtKT HB D E S I G N S E C T I O N / t m ^ - „ . . A*. CU»/-T>T)B» *j>y£»U.~f Wet STATE OF C A U F O m u O W l m t E H I OF RIOUC W M l U atVWOW Of MOIWAYf FAIRFAX -WASHINGTON UNDERCROSSING BENT 3R s^^tff rtoratf BWBCEJ3-IJ00 | rti lunx C-SSliO O-li . aumm HO. r-smto-1? ^ j, |^|^,PSii | \ |^|\r 1 HEREBY W F T I F ' T1IJ5 IS A .THUi W D ACCtlHME COPT CP Til E AR07E D0CUKL':n TAKEN iVHDEa MY DIRECTIOS AWB CQSTROL^ Oa THJS DATE IK 6ACRAMEHT0, CAUrflKTA PURS'JAHT TO 'AOTHOIIZATIOK BT W E DIBECTOR op,Krainc DATE ^-3 ~ arcattm .^-A^y/^ yf-<7^TITLE , • i •s"« 7 C * L . IV'orS'-' -p^s-' 3 2 ft 5-5 AS BUILT PLANS Contract N o . i ^ z ^ ^ — Date Completed Document Najflaazag'-— -J 3-7 A* •<9 .1- J1" .•* "*:*i.vv 1 ?! - > s V r I f i 3-) B i 52 .X2 If' : .1^ I'M*' ' ' " " " I .. H 2 C l A 3 S I F I C A T - C H 0 F . M A T C P . t A L B A S E D QM S T A M D A B D GRMHI.StZE. L l M 1 T 5 DlAfiRAM OMOWUta TMt &A3U TOO. CATIMATU a r c**se v s t e t r n m r r i o M w w i n o c r e n -i ( MlUVNCM OF CLAS1 KA.MC5. M <1 I F GftWU IS PteSCvT IN APPRECIABLE £ A - Q U m S THK TKfcM " G R A V E L L Y * WIAV ^ , flS AODCO TO T H E C t A i S UAMC, V t Z . I ,V** *&«Avet-uv M U O " TK« T E R M S " c o A f t i f i * ' M E D I U M * AMO a n K e " « wWtM UAC&-IO D E S C R I B E 3AMO, KILT AMD C A A V t L REFER. TO STAUOAJLb C f A P C atZK L I M I T S . _ .OS- ." do 70 60 40 JO >0 L E G E N D O F E A R T H M A T E R I A L S &1 G R A V E L I SILTY CLAV CM 0^  J S A M D E I SILT I I C L A Y \ ! 3 A H B Y CLAV O R | C L A Y E Y SAMD [ | SAUDY SILT O R I 1 S l t Y Y SAUO I I ORGANIC MATTER I FILL M A T E R I A L I l a w o u s ROCK I S E D I M S M T A W ROCK I M E .TAMOR w i ic R O C K G E N O • £ PLAM OF AWV B 4 U M Q P l t tCTBOMETEU ® 2 i i * C 0 N Q PfKCTOOMCTER JH ^ A M P L E R AOttiHA (ORVj E3 ROTARY B O A I N G ( W E T ) 0 AUGER BOUIHfl (DRY.) I ? | £ j J C T ^ORtHO ^ COM BOttlMO r — i | j T E S T P I T B O R I N G Q P 6 R A T I C M a r*p na/c et. \ " 5QIL TUBE Bf**j per font' (Oflng j MO Ih A i m e r *4fft a JO*! OB-tffl Cr-*3 noftxf) T>fir>nD&J* materia/ ctV$* Ab co«/i/-- '-F*S Air \vr>/r*tr f;/ip^ P E N E T R A T I O N SoRiHa N O T E S CViulQtrcfbn of forth n o l w U at A«oni on ihii ihevl i i boicJ vpaa fiald b^Mctiaii wid ti n«* l« b« w w d n f d to fapty wchowkal ttftotyrb. E r * FAIRFAX-WASH INGTDN UNDERCROSSING L O G O F T E S T B O R I N G S Btuci t S3-'Seo | n t £ i H E « F M -airin in*- nil!'- is « reus A B O J K O H A T S C O P V O P T M A W E aorirairt T » I E » S « ? M ST B I S S C T ' O ™ « » n C O K T B C C on T I I : S O A T E IK S » : « « - . ! J T » O . c i i . i r . u s u PinscAirr ?o Air»om2«?io« »r T H E D i » 3 ; T f i i cr r u j L i r costs. rjcsAtimr^ 8 AS BUILT PLANS Conlract N o . ^ z m ^ — Date Comple t ed «5 5 5 5 5 o . i H W Q " 3 : i 2 9 3 . i - •; O 3 rt <j» — i rf o B n ^ n M O ^ 5 J ? r ^ n • 5 « no O 2 So »> -Of-8 IS • » o 9 •II » a e o a ^ hi S : c> o « " o n r . r i o S o o D O . . * * * " * s " * * " a S * S * g g g * 5 S ^ 2 5 5 5 S B £ - i S f l s i p i n n o g o n f l i - f l n n J n p i » v > o « M 0 0 6 6 1 " E 5 ! r ™ n M 5 5 5 3 5 5 3 3 " " r> n - 5 is N I -Pint-2 • » — I Typt I fyll rV -1= 'T: N I 4 04 o J HEKEBT tniTJFT THA* Tinn IS ft I S O S AKD ACCVHATE COPY OF THK AftorK DOCUKEBT TAKE* / >-» | IfTIDEB ftt DIRECTION AKD COSTBOL Ort «MB DATE 3" S A C R A M V U T O , SALIlfilStA Pl/HSUAtlT tt) I -D'S AUTHOHJiUTlOH BT T H E BISECTOR OF TOU-TC - J O / " - - -A p p e n d i x B Caltrans seismic w o r k cost informat ion August 1992 FROM: Structures Estimating SUBJECT: Summary of seismic work costs ITEM DESCRIPTION 1. REPLACE BEARINGS 2. 5' DIAM. CIDH PILES (for 40' length) 3. CATCHER BLOCKS 4. ABUTMENT TIEBACKS 5. REBUILD ABUTMENT 6. HINGE SEAT EXTENDER 7. COLUMN RETROFIT (F TYPE) 8. COLUMN RETROFIT (P TYPE) 9. REPLACE BRIDGE (REMOVE) (REPLACE) 10. RESTRAINERS (RESTRAINER CABLE TYPE) (RESTRAINER ROD TYPE) UNIT TOTAL COST EA LF EA EA EA LF EA COLUMN COLUMN SF SF LB LB $2,550 $450 $18,000 $2,300 $5,000 $3,600 $5,800 $170,000 $18,500 $20 $68 $5.30 $3.50 SUMMA OF SEISMIC WORK COSTS AUGUST 1992 REPLACE BEARINGS EA ITEM 10-422204 REPLACE BEARING PADS 03-327404 REPLACE BEARING PADS 03-350104 REPLACE BEARING PADS 12-108244 REPLACE BEARING PADS 06-355404 REPLACE BEARING 05-322104 REPLACE BEARING UNIT QUANTITY CONTRACT $ 7 15 14 14 16 10 1400 2000 1100 2493 1800 4000 UNIT AVE BID $ 3804 3838 WTD. MEAN $2531 •ADJUSTED FOR COST INDEX: x 208/206 SAY $2550/EA 5' DIAMETER CIDH PILES EA ITEM UNIT UNIT QUANTITY CONTRACT $ AVE BID $ 07- 110404 08- 325804 60" CIDH PILES (LF) 60" CIDH PILES (LF) 480 300 450 437.5 612.54 332.19 SAY $450/LF OR $18,000 for 40'length Drill 4 »G — ~ O 12. i*o| •— §0 t-/0 4 —. mil •mat • Airmail* mmndbtmtt i t? *--g-S E C T I O N A - A btr •nl/. T»l. * A B U T M E N T S E C T I O N EA 04-127041 ITEM Concrete (CY) Steel (LB) Excavation(CY) Backfill(CY) Drill&Bond(LF) QUANTITY CONTRACT $ AVE BID $ 41 18649 56 37 415 $1,700.00 $0.80 $170.00 $350.00 $15.00 $1,156.00 $0.86 $211.88 $226.25 $20.25 TOTAL/49 EA CONTRACT AVE BID TOTALS TOTALS $69,700.00 $14,919.20 $9,520.00 $12,950.00 $6,225.00 $2,313 SAY $2300/EA $47,396.00 $16,038.14 $11,865.28 $8,371.25 $8,403.75 $1,879 ABUTMENT TIEBACKS 'L», Based on 1991 averages for Tieback Anchor item: weighted mean 4995 range = 1580--5100-8000 SAY $5000/EA R E B U I L D A B U T M E N T e x a m p l e s i z e : 12' 3" • 4 7.5' U St ruc tu re E x c a v a t i o n 5 4 S F / L F x $ 1 . 1 2 / c f $61 S t ruc tu re B a c k f i l l 5 4 S F / L F x $ 2 . 2 2 / c f $ 1 2 0 Furn i sh P i les 6 0 L F x $ 1 0 / L F $ 6 0 0 Drive Pi les 0 . 6 5 p i l e / L F x $ 1 0 0 0 / E A $ 6 5 0 S t ruc tu r a l C o n c r e t e 2 . 1 7 C Y / L F x $ 4 5 0 / C Y $ 9 8 0 Bar Re inf S t e e l 7 0 0 # / L F x $ 0 . 5 0 $ 3 5 0 R e m o v e C o n c r e t e 2 . 1 7 C Y / L F x $ 3 0 0 / C Y $ 6 5 0 T e m p o r a r y S h o r i n g $ 2 0 0 / L F $ 2 0 0 T O T A L $ 3 , 6 1 1 S A Y $ 3 6 0 0 / L F H I N G E S E A T E X T E N D E R E A 0 4 - 1 2 7 0 4 1 LP I T E M A c c e s s o p e n i n g ( E A ) 9 " c o r e d ho le (LF) D i a p h r a g m b o l s t e r ( E A ) pipe res t ra iner (LB) Q U A N T I T Y C O N T R A C T $ A V E BID $ 1 4 2 5 8 7 . 2 6 1 0 0 0 1 0 8 3 . 7 5 1 4 0 1 1 6 1 0 0 0 1 3 6 9 . 3 2 . 2 2 . 5 T O T A L / E A C O N T R A C T T O T A L S $ 1 , 0 0 0 . 0 0 $ 5 6 0 . 0 0 $ 2 , 0 0 0 . 0 0 $ 1 , 2 9 1 . 9 7 $ 4 , 8 5 2 A V E BID T O T A L S $ 1 , 0 8 3 . 7 5 $ 4 6 4 . 0 0 $ 2 , 7 3 8 . 6 0 $ 1 , 4 6 8 . 1 5 $ 5 , 7 5 5 S A Y $ 5 8 0 0 / E A C O L U M N (F) RETROFIT EA 04-131011 ITEM Column casing(LBS) Excavation(CY) Backfill(CY) Drill&Bond(LF) Remove Conc(CF) Piles(furn&drive-EA) Rebar(LB) Concrete(CY) (/col) QUANTITY CONTRACT $ AVE BID $ 7681 391 219 392 43.6 30 23227 1.8 1.84 30 90.38 25 39.47 25 14.06 100 97.22 3468 3445 0.79 0.65 TOTAL/COL (w/ftg) CONTRACT TOTALS $13,825.80 $11,730.00 $5,475.00 $9,800.00 $4,360.00 $104,040.00 $18,349.33 $167,580 AVE BID TOTALS $14,133.04 $35,338.58 $8,643.93 $5,511.52 $4,238.79 $103,350.00 $15,097.55 $186,313 155341 Column casing(LBS) 9913 1.11 1.79 $11,003.43 $17,744.27 Excavation(CY) 142.5 50 154.64 $7,125.00 $22,036.20 Backfill(CY) * * $0.00 $0.00 Drill&Bond(LF) 256 12 16.16 $3,072.00 $4,136.96 Remove Conc(LS) 1 6000 11288.86 $6,000.00 $11,288.86 Tiedown Anchor(EA) 4 5150 4944.06 $20,600.00 $19,776.24 Rebar(LB) 9500 0.54 0.65 $5,130.00 $6,175.00 Concrete(CY) 90 160 174.96 $14,400.00 $15,746.40 TOTAL/COL $67,330 $96,904 (w/ftg) 07-110401 LP' Column casing(LBS) Excavation(CY) Backfill(CY) Drill&Bond(LF) Remove Conc(LS) Piles(furn&drive-EA) Rebar (LB) Concrete(CY)-ftg. 11300 100 50 264 1 24 12000 60 1.45 100 50 12 750 3943 0.6 200 H = 20'-30' 2.3 59.86 48.21 12.04 1421 3740 0.67 551 TOTAL/COL (w/ftg) $16,385.00 $10,000.00 $2,500.00 $3,168.00 $750.00 $94,632.00 $7,200.00 $12,000.00 $146,635 $25,990.00 $5,986.00 $2,410.50 $3,178.56 $1,421.00 $89,760.00 $8,040.00 $33,060.00 $169,846 COLUMi ) RETROFIT (CONT.) EA ITEM (/col) QUANTITY CONTRACT $ AVE BID $ CONTRACT TOTALS AVE BID TOTALS 04-130981 Column casing(LBS) (#35-113,135) Excavation(CY) Backfill(CY) Drill&Bond(LF) Remove Conc(LS) Piles(furn&drive-EA) Rebar (LB) Concrete(CY)-ftg. 4811.667 72.5 30 10 1 4 6283.333 48.5 2 2.4 40 65.97 70 61.25 12 14.14 2667 1900 7468 8405 0.5 0.64 250 254 TOTAL/COL (w/ftg) $9,623.33 $2,900.00 $2,100.00 $120.00 $2,666.67 $29,872.00 $3,141.67 $12,125.00 $62,549 $11,548.00 $4,782.83 $1,837.50 $141.40 $1,900.17 $33,620.00 $4,021.33 $12,319.00 $70,170 SAY $170.000/COL COLUMN (P) RETROFIT (/col) 04-130981 Column casing(LBS) 1525 2 2.4 $3,050.00 $3,660.00 (#37-241 k) Excavation(CY) 25 40 67.97 $1,000.00 $1,699.25 Backfill(CY) 25 70 61.25 $1,750.00 $1,531.25 (#37-242k) Column casing(LBS) 1635.5 2 2.4 $3,271.00 $3,925.20 Excavation(CY) 56.5 40 67.97 $2,260.00 $3,840.31 Backfill(CY) 56.5 70 61.25 $3,955.00 $3,460.63 H = 30 ,-40' TOTAL/COL $15,286 $18,117 ; casing = 5'-3" COLUMi. /) RETROFIT (CON'T.) (/col) 07-114854 ( 6 6 ^ 8 2,3,5,8,9,11,13—2/15/90) (#53-1854) Column casing(LBS) 8341 1.88 $15,681.08 Excavation(CY) 14 73 $1,022.00 Backfill(CY) 14 40 $560.00 Clean&Paint Casing 8341 0.1538 $1,282.85 H = 25'-55' TOTAL/COL $18,546 casing = 16' SAY $18.500/COL REPLACE BRIDGE Based on Bridge (/SF) Cost Summary, 1991 Div. of Structures, Construction Statistics For an average bridge of dimensions 400' x 50' = 20,000 SF : Remove - 20000 x $20/SF = $400,000 Replace - 20000 x $68/SF = $1,360,000 USE SAY $1,760,000/bridge $20/SF to remove $68/SF to replace Appendix C P C A C O L files for moment-axia l load interaction o f bridge columns I 40 Results file: Moment-axial load interaction diagram for side columns of FW bent 3 PCACOL-Version 2.30 Computer program for the Strength Design of Reinforced Concrete Sections General Information: File Name: D:\PCACOL\FWCOL3L.COL Project: fwcol31 Code: ACI 318-83 Column: Units: SI Metric Engineer: kirn Date: 01/14/97 Time: 10:56:07 Run Option: Investigation Run Axis: X-axis Material Properties: Short (nonslender) column Column Type: Structural fc =20 MPa fy = 345 MPa Ec =22610 MPa Es = 199955 MPa fc =17 MPa erup = 0 mm/mm eu = 0.003 mm/mm Stress Profile: Parabolic Geometry: Circular: Diameter = 1220 mm Gross section area, Ag = 1.16899e+006 mmA2 Ix = 1.08745e+011 mmA4 Xo = 0 mm Iy = 1.08745e+011 mmA4 Yo = 0 mm Reinforcement: Rebar Database: A S T M Size Diam Area Size Diam Area Size Diam Area 10 11 100 15 16 200 20 20 300 25 25 500 30 30 700 35 36 1000 45 44 1500 55 56 2500 Confinement: User-defined; phi(c) = 1, phi(b) = 1, a = 1 N-10 ties with N-30 bars, N-10 with larger bars. Pattern: Irregular Total steel area, As = 36000 mmA2 at 3.08% Area X-Loc Y-Loc Area X-Loc Y-Loc Area X-Loc Y-Loc (mmA2) (mm) (mm) (mmA2) (mm) (mm) (mmA2) (mm) (mm) 1000 0 530 1000 110 518 1000 216 484 1000 311 429 1000 394 355 1000 459 265 1000 504 164 1000 527 55 1000 527 -55 1000 504 -164 1000 459 -265 1000 394 -355 1000 311 -429 1000 216 -484 1000 110 -518 1000 -0 -530 1000 -110 -518 1000 -216 -484 1000 -311 -429 1000 -394 -355 1000 -459 -265 1000 -504 -164 1000 -527 -55 1000 -527 55 1000 -504 164 1000 -459 265 1000 -394 355 1000 -311 429 1000 -216 484 1000 -110 518 1000 -421 229 1000 -421 -229 1000 0 -494 1000 421 -229 1000 0 494 1000 421 229 Bending Load, P X-Mom. Y-Mom N.A. depth about (kN) (kN-m) (kN-•m) (mm) XPureComp. 31681 -0 0 2682.82 Balanced 11577 5836 -0 723.65 Pure Bend. 0 5096 -0 375.08 Program completed as requested! PCAC0LV2.30 / 0 O '.. / o o \ / o 0 y j o o \ X o o 1 \ o o / \ 0 o / \ o o / xs 0 0 / 31681 -1220 mm diam. 0 P fs=0 f c = 20 MPa n k / fs=0.5fy j fy = 345 MPa N J Confinement: Other c l r cover = 62 mm spacing = 0 mm 36 N-35 at 3.08% As = 36000 mm~2 I I I I I I I I ^ 1] 6082 0vlnx (kN-m) Ix = 1.087e+011 mmA Iy = 1.087e+011 mm" 4 4 -12420-X<~> = 0 mm Q 1993 PCA Y n = fl mm Licensed To: Licensee name not yet s p e c i f i e d . F i l e name: D:\PCAC0L\FWC0L3L. COL Pro jec t : Thesis Mater ia l Propert ies : Column Id: fwcol31 Ec = 22610 MPa eu = 0.003 mm/mm Engineer: kim fc = 17.00 MPa Es = 199955 MPa Date: 01/14/97 Time: 10:56:07 Stress P r o f i l e : Parabol ic Code: ACI 318-83 phi(c) = 1.00, phi (b) = 1.00 X-ax is slenderness i s not considered. 143 Results file: Moment-axial load interaction diagram for right side columns of FW bent 3 PCACOL-Version 2.30 Computer program for the Strength Design of Reinforced Concrete Sections General Information: File Name: D:\PCACOL\FWCOL3R.COL Project: fwcol31 Code: ACI 318-83 Column: Units: SI Metric Engineer: kirn Date: 01/14/97 Time: 10:56:07 Run Option: Investigation Run Axis: X-axis Short (nonslender) column Column Type: Structural Material Properties: fc =20 MPa Ec =22610 MPa fc =17 MPa eu = 0.003 mm/mm Stress Profile: Parabolic fy =345 MPa Es = 199955 MPa erup = 0 mm/mm Geometry: Circular: Diameter = 1220 mm Gross section area, Ag = 1.16899e+006 mmA2 Ix= 1.08745e+011 mmA4 Xo = 0 mm Iy = 1.08745e+011 mmA4 Yo = 0 mm Reinforcement: Rebar Database: A S T M Size Diam Area Size Diam Area Size Diam Area 10 11 100 15 25 25 500 30 45 44 1500 55 16 200 20 30 700 35 56 2500 20 300 36 1000 Confinement: User-defined; phi(c) = 1, phi(b) = 1, N-10 ties with N-35 bars, N-10 with larger bars. 144 Layout: Circular Pattern: All Sides Equal [Cover to transverse reinforcement (ties)] Total steel area, As = 28000 mmA2 at 2.40% 28N-35 Cover =51 mm Bending Load, P X-Mom. Y-Mom. N.A. depth about (kN) (kN-m) (kN-m) (mm) X Pure Comp. 29057 -0 -0 2682.82 Balanced 11130 5162 -0 723.65 Pure Bend. -0 4162 -0 340.99 Program completed as requested! 1220 mm diam. f c = 20 MPa f y = 345 MPa Confinement: Other c l r cover = 62 mm spacing = 83 mm 28 N-35 at 2.40% As = 28000 mrtf-2 Ix = 1.087e+011 mm'M I Iy = 1.087e+011 mm"4 n = 0 mm 1993 PCA o = 0 mm P n k N 29057 -9660 PCACOL V2.30 5345 tfMnx (kN-m) L i c e n s e d To: Licensee name not yet s p e c i f i e d . F i l e name: D:\PCAC0L\FWC0L3R.C0L P r o j e c t : Thesis Column I d : fwcol3r Engineer: kirn Date: 01/14/97 Time: 10:56:07 Code: ACI 318-83 X-axis slenderness i s not considered. M a t e r i a l P r o p e r t i e s : Ec = 22610 MPa eu = 0.003 mm/mm fc = 17.00 MPa Es = 199955 MPa St r e s s P r o f i l e : P a r a b o l i c phi ( c ) = 1.00, phi(b) = 1.00 14k Results file: Moment-axial load interaction diagram for type M columns of CV bent 4 PCACOL-Version 2.30 Computer program for the Strength Design of Reinforced Concrete Sections General Information: File Name: D:\PCACOL\CVCOLM.COL Project: fwcoBl Code: ACI 318-83 Column: Units: SI Metric Engineer: kirn Date: 01/14/97 Time: 10:56:07 Run Option: Investigation Run Axis: X-axis Material Properties: fc =20 MPa Ec =22610 MPa fc =17 MPa eu = 0.003 mm/mm Stress Profile: Parabolic Short (nonslender) column Column Type: Structural fy = 345 MPa Es = 199955 MPa erup = 0 mm/mm Geometry: Circular: Diameter = 1220 mm Gross section area, Ag = 1.16899e+006 mmA2 Ix= 1.08745e+011 mmA4 Xo = 0 mm Iy = 1.08745e+011 mmA4 Yo = 0 mm Reinforcement: Rebar Database: A S T M Size Diam Area Size Diam Area Size Diam Area 10 25 45 11 25 44 100 15 500 30 1500 55 16 200 20 30 700 35 56 2500 20 300 36 1000 Confinement: User-defined; phi(c) = 1, phi(b) =1, a = 1 N-10 ties with N-35 bars, N-10 with larger bars. 1 4 7 Pattern: Irregular Total steel area, As = 48000 mmA2 at 4.11% Area X-Loc Y-Loc Area X-Loc Y-Loc Area X-Loc Y-Loc (mmA2) (mm) (mm) (mmA2) (mm) (mm) (mmA2) (mm) (mm) 1000 0 530 1000 103 520 1000 203 490 1000 294 441 1000 375 375 1000 441 294 1000 490 203 1000 520 103 1000 530 -0 1000 520 -103 1000 490 -203 1000 441 -294 1000 375 -375 1000 294 -441 1000 203 -490 1000 103 -520 1000 -0 -530 1000 -103 -520 1000 -203 -490 1000 -294 -441 1000 -375 -375 1000 -441 -294 1000 -490 -203 1000 -520 -103 1000 -530 0 1000 -520 103 1000 -490 203 1000 -441 294 1000 -375 375 1000 -294 441 1000 -203 490 1000 -103 520 1000 184 445 1000 0 481 1000 340 340 1000 445 184 1000 481 -2 1000 445 -184 1000 340 -340 1000 184 -445 1000 0 -481 1000 -184 -445 1000 -340 -340 1000 -445 -184 1000 -481 0 1000 -445 184 1000 -340 340 1000 -184 445 Bending Load, P X-Mom. Y-Mom. N.A. depth about (kN) (kN-m) (kN-m) (mm) X Pure Comp. 35617 1 0 2682.82 Balanced 12257 6843 1 723.65 Pure Bend. 0 6479 1 413.01 Program completed as requested! f c = 20 MPa f y = 345 MPa Confinement: Other c l r cover = 62 mm spacing = 13 mm 48 N-35 at 4.11% As = 48000 mm" 2 Ix = 1.087e+011 mmA4 Iy = 1.087e+011 mm/v4 o = 0 mm 1993 PCA o = 0 mm— -1G560 7248 0v|nx (kN-m) Licensed To: Licensee name not yet s p e c i f i e d . F i l e name: D:\PCAC0L\CVC0LM.C0L P r o j e c t : Thesis Column Id: cvcolm Engineer: kirn Date: 01/14/97 Time: 10:56:07 Code: ACI,318-83 X-axis slenderness i s not considered. M a t e r i a l P r o p e r t i e s : Ec = 22610 MPa eu = 0.003 mm/mm f c = 17.00 MPa Es = 199955 MPa Str e s s P r o f i l e : P a r a b o l i c p h i ( c ) = 1.00, phi(b) = 1.00 i;44 Results file: Moment-axial load interaction diagram for type J columns of CV bent 4 PCACOL-Version 2.30 Computer program for the Strength Design of Reinforced Concrete Sections General Information: File Name: D:\PCACOL\CVCOLJ.COL Project: fwcol31 Code: ACI 318-83 Column: Units: SI Metric Engineer: kirn Date: 01/14/97 Time: 10:56:07 Run Option: Investigation Run Axis: X-axis Material Properties: Short (nonslender) column Column Type: Structural fc =20 MPa fy = 345 MPa Ec =22610 MPa Es = 199955 MPa fc =17 MPa erup = 0 mm/mm eu = 0.003 mm/mm Stress Profile: Parabolic Geometry: Circular: Diameter = 1220 mm Gross section area, Ag = 1.16899e+006 mmA2 Ix= 1.08745e+011 mmA4 Xo = 0 mm Iy= 1.08745e+011 mmA4 Yo = 0 mm Reinforcement: Rebar Database: A S T M Size Diam Area Size Diam Area Size Diam Area 10 11 100 15 16 200 20 20 300 25 25 500 30 30 700 35 36 1000 45 44 1500 55 56 2500 Confinement: User-defined; phi(c) = 1, phi(b) = 1, a = l N-10 ties with N-35 bars, N-10 with larger bars. I S O Layout: Circular Pattern: All Sides Equal [Cover to transverse reinforcement (ties)] Total steel area, As = 24000 mmA2 at 2.05% 24N-35 Cover = 51 mm Bending Load, P X-Mom. Y-Mom. N.A. depth about (kN) (kN-m) (kN-m) (mm) XPureComp. 27745 -0 -0 2682.82 Balanced 10936 4781 -0 723.65 Pure Bend. 0 3640 -0 321.82 Program completed as requested! f c = 20 MPa f y = 345 MPa Confinement: Other c l r cover = 62 mm spacing = 103 mm 24 N-35 at 2.05% As = 24000 mmA2 Ix = 1.087e+011 mm"'4 Iy = 1.087e+011 mm" 4 o = 0 mm 1993 PCA b = 0 mm tfMnx (kN-m) Licensed To: Licensee name not yet s p e c i f i e d . F i l e name: D:\PCAC0L\CVC0LJ.C0L P r o j e c t : Thesis Column Id: c v c o l j Engineer: kirn Date: 01/14/97 Time: 10:56:07 Code: ACI 318-83 X-axis slenderness i s not considered. M a t e r i a l P r o p e r t i e s : Ec = 22610 MPa eu = 0.003 mm/mm f c = 17.00 MPa Es = 199955 MPa S t r e s s P r o f i l e : P a r a b o l i c p h i ( c ) = 1.00, phi(b) = 1.00 L52. A p p e n d i x D R E S P O N S E files for moment-curvature predict ions for bridge columns RESPONSE Input File for left side columns on FW bent 3 Response Version 1 Data-File Copyright 1990 A. Felber Name of Section: fwcol31 Units M/U'Metric/U.S. Customary': M Number of Concrete Types (1-5): 1 Type f c ec' fcr Tension Stiffening Number [Mpa] [Milli-Strain] [Mpa] Factor 1 20.00 -2.000 2.00 0.00 Number of Rebar Types (1-5): 1 Type Elastic Modulus fy esh esrupt fu Number [Mpa] [Mpa] [—Milli-Strain--] [Mpa] 1 200000 345 20.000 150.000 552 Number of Tendon Types (1-5): 0 Height of Section: 1220 mm Distance to Moment Axis: 610 mm Shear Y/N 'Yes/No': N Number of Concrete Layers (1-20): 11 Layer y bottom width top width height Type Number [mm] [mm] [mm] [mm] Number 1 0 0 550 65 1 2 65 550 664 33 1 3 98 664 890 94 1 4 192 890 1092 145 1 5 337 1092 1213 178 1 6 515 1213 1213 189 1 7 704 1213 1092 178 1 8 882 1092 890 145 1 9 1027 890 664 94 1 10 1121 664 550 33 1 11 1154 550 0 65 1 Number of Rebar Layers (0-10): 9 Layer y Area Type Number [mm] [mraA2] Number 1 76 4000 1 2 168 6000 1 3 337 4000 1 4 497 2000 1 5 610 4000 1 6 723 2000 1 7 883 4000 1 8 1052 6000 1 9 1144 4000 1 Consider displaced Concrete Y/N: N Thermal & Shrinkage Strains Y/N : N Initial Strains Y/N: N Moment vs. Curvature for FWC0L3L f 5 5 RESPONSE Input File for right side columns on FW bent 3 Response Version 1 Data-File Copyright 1990 A. Felber Name of Section: fvvcoDr Units M/U 'Metric/U. S. Customary': M Number of Concrete Types (1-5): 1 Type f c ec' fcr Tension Stiffening Number [Mpa] [Milli-Strain] [Mpa] Factor 1 20.00 -2.000 2.00 0.00 Number of Rebar Types (1-5): 1 Type Elastic Modulus fy esh esrupt fu Number [Mpa] [Mpa] [—Milli-Strain--] [Mpa] 1 200000 345 20.000 150.000 552 Number of Tendon Types (1-5): 0 Height of Section: 1220 mm Distance to Moment Axis: 610 mm Shear Y/N'Yes/No': N Number of Concrete Layers (1-20): 11 Layer y bottom width top width height Type Number [mm] [mm] [mm] [mm] 1 0 0 550 65 1 2 65 550 664 33 1 3 98 664 890 94 1 4 192 890 1092 145 1 5 337 1092 1213 178 1 6 515 1213 1213 189 1 7 704 1213 1092 178 1 8 882 1092 890 145 1 9 1027 890 664 94 1 10 1121 664 550 33 1 11 1154 550 0 65 1 Number of Rebar Layers (0-10) 9 Layer y Area Type Number [mm] [mmA2] Number 1 67 3000 1 2 148 4000 1 3 320 4000 1 4 489 2000 1 5 610 2000 1 6 731 2000 1 7 900 4000 1 8 1072 4000 1 9 1153 3000 1 Consider displaced Concrete Y/N: N Thermal & Shrinkage Strains Y/N : N Initial Strains Y/N: N }5Q> Moment vs. Curvature for FWC0L3R 157 RESPONSE Input File for type M columns on C V bent 4 Response Version 1 Data-File Copyright 1990 A. Felber Name of Section: cvcolm Units M/U 'Metric/U. S. Customary1: M Number of Concrete Types (1 -5): 1 Type f c ec' fcr Tension Stiffening Number [Mpa] [Milli-Strain] [Mpa] Factor 1 20.00 -2.000 2.00 0.00 Number of Rebar Types (1-5): 1 Type Elastic Modulus fy esh esrupt fu Number [Mpa] [Mpa] [—Milli-Strain--] [Mpa] 1 200000 345 20.000 150.000 552 Number of Tendon Types (1-5): 0 Height of Section: 1220 mm Distance to Moment Axis: 610 mm Shear Y/N 'Yes/No': N Number of Concrete Layers (1-20): 11 Layer y bottom width top width height Type Number [mm] [mm] [mm] [mm] 1 0 0 550 65 1 2 65 550 664 33 1 3 98 664 890 94 1 4 192 890 1092 145 1 5 337 1092 1213 178 1 6 515 1213 1213 189 1 7 704 1213 1092 178 1 8 882 1092 890 145 1 9 1027 890 664 94 1 10 1121 664 550 33 1 11 1154 550 0 65 1 Number of Rebar Layers (0-10) 9 Layer y Area Type Number [mm] [mmA2] Number 1 85 4000 1 2 145 6000 1 3 276 6000 1 4 457 6000 1 5 610 4000 1 6 763 6000 1 7 944 6000 1 8 1075 6000 1 9 1135 4000 1 Consider displaced Concrete Y/N: N Thermal & Shrinkage Strains Y/N : N Initial Strains Y/N: N /58 Moment vs. Curvature for CVCOLM 157 RESPONSE Input File for type J columns on CV bent 4 Response Version 1 Data-File Copyright 1990 A. Felber Name of Section: cvcolj Units M/U 'Metric/U. S. Customary': M Number of Concrete Types (1-5): 1 Type f c ec' fcr Tension Stiffening Number [Mpa] [Milli-Strain] [Mpa] Factor 1 20.00 -2.000 2.00 0.00 Number of Rebar Types (1-5): 1 Type Elastic Modulus fy esh esrupt fu Number [Mpa] [Mpa] [—Milli-Strain--] [Mpa] 1 200000 345 20.000 150.000 552 Number of Tendon Types (1-5): 0 Height of Section: 1220 mm Distance to Moment Axis: 610 mm Shear Y/N'Yes/No': N Number of Concrete Layers (1-20): 11 Layer y bottom width top width height Type Number [mm] [mm] [mm] [mm] Number 1 0 0 550 65 1 2 65 550 664 33 1 3 98 664 890 94 1 4 192 890 1092 145 1 5 337 1092 1213 178 1 6 515 1213 1213 189 1 7 704 1213 1092 178 1 8 882 1092 890 145 1 9 1027 890 664 94 1 10 1121 664 550 33 1 11 1154 550 0 65 1 Number of Rebar Layers (0-10): 9 Layer y Area Type Number [mm] [mmA2] Number 1 89 3000 1 2 193 4000 1 3 345 2000 1 4 473 2000 1 5 610 2000 1 6 474 2000 1 7 875 2000 1 8 1027 4000 1 9 1131 3000 1 Consider displaced Concrete Y/N: N Thermal & Shrinkage Strains Y/N : N Initial Strains Y/N: N ItoO Moment vs. Curvature for CVCOLJ 3000 1 2500 •g- 2000 z •£ 1500 a> E o 2 1000 500 0 J 1 1 I- 1 1 1—: 1 0 10 20 30 40 50 60 70 Curvature (x 1000 rad/m) A p p e n d i x E R U A U M O K O files for inelastic damage analysis l(oZ Sample Input File for FW bent 3 - unsealed ground motion Fairfax-Washington bridge: bent3 201100000 0 37 36 5 4 1 4 9.81 5.0 5.0 0.1 28.0 1.0 0 5 10 0 1 10 0.7 0.1 00 NODES 1 2.44 0.0 1 1 0 0 0 0 2 2.44 0.53 000 000 3 2.44 6.07 000 000 4 2.44 6.91 00 0 0 00 5 10.75 0.0 1 1 0 0 0 0 6 10.75 0.53 000 000 7 10.75 6.07 0 0 0 0 0 0 8 10.75 6.91 000 000 9 19.05 0.0 1 1 0 000 10 19.05 0.53 000 00 0 11 19.05 6.07 000 000 12 19.05 6.91 0 00 000 13 27.36 0.0 1 1 0 000 14 27.36 0.53 0 00 000 15 27.36 6.07 0 00 000 16 27.36 6.91 000 000 17 33.81 0.0 1 1 0 000 18 33.81 0.53 0 00 000 19 33.81 6.07 000 000 20 33.81 6.91 00 0 000 21 42.12 0.0 1 1 0 0 00 22 42.12 0.53 000 00 0 23 42.12 6.07 000 00 0 24 42.12 6.91 000 000 25 50.42 0.0 1 1 0 0 0 0 ! Control Parameters ! Frame and Time-history ! Output and Plotting Options ! Iteration Control 26 50.42 0.53 0 00 000 27 50.42 6.07 0 00 000 28 50.42 6.91 0 00 000 29 0.0 6.91 000 000 30 52.86 6.91 00 0 000 31 3.44 0.0 111 000 32 11.75 0.0 111 000 33 20.05 0.0 111 000 34 28.36 0.0 111 000 35 34.81 0.0 111 000 36 43.12 0.0 111 000 37 51.42 0.0 111 000 ELEMENTS 1 3 12 2 1 2 3 3 3 3 4 IG3 4 3 5 6 5 1 6 7 6 3 7 8 7 3 9 10 8 1 10 11 9 3 11 12 10 3 13 14 11 1 14 15 12 3 15 16 13 3 17 18 14 2 18 19 15 3 19 20 16 3 21 22 17 2 22 23 18 3 23 24 19 3 25 26 20 2 26 27 21 3 27 28 22 4 4 29 23 4 4 8 24 4 8 12 25 4 12 16 26 4 16 20 27 4 20 24 28 4 24 28 29 4 28 30 30 5 1 31 31 5 5 32 32 5 9 33 33 5 13 34 34 5 17 35 35 5 21 36 36 5 25 37 PROPS 1 FRAME 2 0 110 1 ! Parameters 2.9103e7 1.1193e7 1.167 0.982 5.423e-2 0.0 ! Elastic properties 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0-3421 0.0 -31681 -11577 5836 6082 5700 5100 12420 008 8 8 80.1 0.1 2 FRAME 2 0 110 1 ! Parameters 2.9103e7 1.1193e7 1.167 0.982 5.423e-2 0.0 ! Elastic properties 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -3421 0.0 -29057 -11130 5162 5345 5000 4150 9660 0 0 10 10 10 10 0.1 0.1 3 FRAME 20 1000 2.9103e7 1.1193e7 1.167 0 5.423e2 0.0 0.0 0.0 0.0 0.0 -3421 0.0 4 FRAME 10 1 000 2.9103e7 1.1193e7 1.167 0 2.17e-l 0.0 -3798 -3798 -2742 2742 0.0 0.0 5 SPRING 1 0 0 0 0 0 25e4 0 WEIGHTS 4 2107 2107 0.0 8 3421 3421 0.0 12 3421 3421 0.0 16 3421 3421 0.0 20 3421 3421 0.0 24 3421 3421 0.0 28 2107 2107 0.0 29 561 561 0.0 30 752 752 0.0 37 0.0 0.0 0.0 LOADS 4 0.0-2107 0.0 8 0.0-3421 0.0 12 0.0 -3421 0.0 16 0.0 -3421 0.0 20 0.0 -3421 0.0 24 0.0 -3421 0.0 28 0.0 -3421 0.0 29 0.0 -561 0.0 30 0.0-752 0.0 37 0.0 0.0 0.0 ! Parameters ! Elastic Properties EQUAKE 3 1 0.02 1.0 Sample Input File for C V bent 4 - unsealed ground motion La Cienega-Venice bridge: bent4 2011000000 18 17 4 4 1 4 9.81 5.0 5.0 0.01 28.0 1.0 0 5 10 0 1 10 0.7 0.1 00 ! Control Parameters ! Frame and Time-history ! Output and Plotting Options ! Iteration Control NODES 1 0.0 0.0 1 1 0 0 0 0 2 0.0 7.57 000 000 3 0.0 8.52 0 00 000 4 7.68 0.00 1 1 0 0 0 0 5 7.68 7.19 000 000 6 7.68 8.14 000 000 7 15.37 0.0 1 1 0 000 8 15.37 6.80 000 000 9 15.37 7.75 000 000 10 21.83 0.0 1 1 0 000 11 21.83 6.48 00 0 000 12 21.83 7.43 00 0 000 13 29.59 0.0 1 1 0 000 14 29.59 6.09 00 0 0 00 15 29.59 7.04 000 000 16 37.34 0.0 1 1 0 000 17 37.34 5.70 0 0 0 0 0 0 18 37.34 6.65 000 000 ELEMENTS 1 1 1 2 2 3 2 3 3 1 4 5 4 3 5 6 5 1 7 8 6 3 8 9 7 2 10 11 8 3 11 12 9 2 13 14 10 3 14 15 11 2 16 17 12 3 17 18 13 4 3 6 14 4 6 9 15 4 9 12 16 4 12 15 17 4 15 18 PROPS 1 FRAME 2 0 110 1 ! Parameters 2.4597e7 0.9460e7 1.167 0.982 5.423e-2 0.0 ! Elastic properties 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -3260 0.0 -35617 -12257 6843 7248 7050 6400 16560 00 888 80.1 0.1 2 FRAME 2 0 110 1 ! Parameters 2.4597e7 0.9460e7 1.167 0.982 5.423e-2 0.0 ! Elastic properties 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -3260 0.0 -27745 -10936 4781 4930 4550 3650 8280 0 0 10 10 10 10 0.1 0.1 3 FRAME 20 1000 2.4597e7 0.9460e7 1.167 0 5.423e2 0.0 0.0 0.0 0.0 0.0 -3260 0.0 4 FRAME 10 1 000 2.4597e7 0.9460e7 1.167 0 2.17e-l 0.0 -2971 -2971 -2297 2297 0.0 0.0 WEIGHTS 3 3375 3375 0.0 6 3260 3260 0.0 9 3260 3260 0.0 12 3260 3260 0.0 15 3260 3260 0.0 18 3375 3375 0.0 LOADS 3 0.0 -3375 0.0 6 0.0 -3260 0.0 9 0.0-3260 0.0 12 0.0 -3260 0.0 15 0.0 -3260 0.0 18 0.0 -3375 0.0 ! Parameters ! Elastic Properties EQUAKE 3 1 0.02 1.0 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0050299/manifest

Comment

Related Items