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Ambient modal identification, finite element model updating, and seismic analysis of bridges on Trans-Canada… Khan, Bahram 2017

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AMBIENT MODAL IDENTIFICATION, FINITE ELEMENT MODEL UPDATING, AND SEISMIC ANALYSIS OF BRIDGES ON TRANS-CANADA HIGHWAY by  Bahram Khan  BEng, Cardiff University, 2015  A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Civil Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  December 2017  © Bahram Khan, 2017  ii  Abstract This thesis features finite element model updating of two short-span concrete bridges, namely Gaglardi Way Underpass and Kensington Avenue Underpass. The main objective was to study the effect and determine the importance of finite element model updating by comparing the structural responses for the updated model to the preliminary model. The study was carried out by developing a finite element (FE) model and an operational modal analysis (OMA) model for each bridge. The FE model represented the analytical prototype of the actual structure, while the OMA model was used to extract the modal information for existing structure using the vibration data recorded under normal operating conditions from permanent sensors installed on corners and at mid-span of these bridges. The natural frequencies from OMA were set as a target for the FE model to match. The process of calibrating the analytical FE model to the match the modal information acquired from the experimental model is known as ‘Model Updating’. Having the frequency responses defined, a sensitivity analysis was conducted to determine the parameters that are most sensitive to change, based on which the FE model was automatically updated in an iterative manner. The modal assurance criterion (MAC) and mode shape responses were not used during calibration step since the vibration testing was not dense enough, however, they were solely used as a means of comparing the calibrated FE model to the experimental results. Once the objective of model updating was accomplished, a linear modal time history analysis was carried out using three ground motions having a low, medium range, and a very high peak ground acceleration (PGA), in addition to a fourth very low ambient level ground motion. Comparing the resulting absolute maximum base reactions and the mid-span structural displacements from updated model to the original model, it was concluded that the percentage changes were significantly high, therefore, the chance of original model being uncertain is very high for which model updating is an important and a highly effective technique, where possible, to generate a high confidence FE model that in best possible manner represents the behaviour of an actual structure. iii  Lay Summary In the past Civil and Structural Engineers used to manually design new buildings and study the behaviour of an existing building for modifications using hand calculations. This has greatly changed with innovation in technology that now allows to generate a prototype model for structure of any size and complexity, be it a building, bridge, dam, etc. These models are capable of simulating the exact behaviour of structures, however, for that it is important that the model represents the actual structure in most realistic manner. For the existing structures, the original models developed are calibrated according to the experimental results from testing carried out on an actual structure. This process is called ‘Model Updating’. This thesis features the importance of calibrating a model alongside the whole process itself for two bridges, Gaglardi Way Underpass and Kensington Avenue Underpass, located in Metro Vancouver.   iv  Preface This thesis is original, unpublished, and independent work by the author, Bahram Khan, under the supervision of Dr. Carlos Ventura.   v  Table of Contents Abstract ................................................................................................................................................. ii Lay Summary ....................................................................................................................................... iii Preface.................................................................................................................................................. iv Table of Contents ...................................................................................................................................v List of Tables ..................................................................................................................................... viii List of Figures ........................................................................................................................................x Acknowledgements ..............................................................................................................................xv Dedication .......................................................................................................................................... xvi 1. Introduction .......................................................................................................................................1 1.1. Research Motivation ...............................................................................................................1 1.2. Scope of Work .........................................................................................................................2 1.3. Research Goals ........................................................................................................................3 2. Literature Review ..............................................................................................................................5 2.1. British Columbia Smart Infrastructure Monitoring System (BCSIMS)..................................5 2.2. Finite Element Analysis ..........................................................................................................6 2.2.1. Sources of Error in Finite Element Modelling .................................................................7 2.3. Operational Modal Analysis ...................................................................................................8 2.3.1. Frequency Domain Decomposition .................................................................................9 2.3.2. Stochastic Subspace Identification ................................................................................10 2.4. Finite Element Model Updating ............................................................................................11 vi  2.4.1. Parameters for Model Updating .....................................................................................12 2.4.2. Sensitivity Analysis .......................................................................................................13 2.4.3. Modal Assurance Criterion ............................................................................................14 3. Description of Bridges .....................................................................................................................16 3.1. Gaglardi Way Underpass ......................................................................................................16 3.1.1. Structural Components...................................................................................................17 3.1.2. Instrumentation ..............................................................................................................22 3.2. Kensington Avenue Underpass .............................................................................................24 3.2.1. Structural Components...................................................................................................25 3.2.2. Instrumentation ..............................................................................................................29 4. Modelling ........................................................................................................................................32 4.1. Finite Element Models ..........................................................................................................32 4.1.1. Assumptions in FE Modelling .......................................................................................35 4.2. ARTeMIS Models .................................................................................................................37 5. Experimental and Analytical Results ..............................................................................................39 5.1. Gaglardi Way Underpass ......................................................................................................39 5.1.1. Operational Modal Analysis ..........................................................................................39 5.1.2. Finite Element Analysis .................................................................................................43 5.2. Kensington Avenue Underpass .............................................................................................45 5.2.1. Operational Modal Analysis ..........................................................................................45 5.2.2. Finite Element Analysis .................................................................................................47 vii  6. Finite Element Model Updating ......................................................................................................50 6.1. Gaglardi Way Underpass ......................................................................................................51 6.2. Kensington Avenue Underpass .............................................................................................57 7. Seismic Analysis .............................................................................................................................63 7.1. Gaglardi Way Underpass ......................................................................................................64 7.2. Kensington Avenue Underpass .............................................................................................66 8. Summary and Conclusion ...............................................................................................................70 8.1. Future Work Recommendation .............................................................................................73 References ............................................................................................................................................75 Appendices ...........................................................................................................................................78 Appendix A: Drawings ....................................................................................................................78 Appendix B: Ambient Vibration Data ...........................................................................................101 Appendix C: Modelling Detail.......................................................................................................110 Appendix D: Parameters Used for Model Updating ......................................................................130 Appendix E: Modal Analysis for Updated FE Models ..................................................................131 Appendix F: Selected Ground Motions .........................................................................................135 Appendix G: Seismic Analysis Results .........................................................................................143    viii  List of Tables Table 3.1: Concrete material Properties.............................................................................................. 19 Table 3.2: Steel material properties .................................................................................................... 19 Table 5.1: Modal frequencies for Gaglardi Way Underpass from Operational Modal Analysis ....... 41 Table 5.2: Modal properties of Gaglardi Way Underpass original FE model .................................... 43 Table 5.3: Modal frequencies for Kensington Avenue Underpass from Operational Modal Analysis............................................................................................................................................................. 46 Table 5.4: Modal properties of Kensington Avenue Underpass original FE model ........................... 48 Table 6.1: Modal information before and after FE model updating for Gaglardi Way Underpass .... 54 Table 6.2: Modal information before and after FE model updating for Kensington Avenue Underpass............................................................................................................................................................. 59 Table 7.1: Ground motions selected for seismic analysis ................................................................... 63 Table 7.2: Percentage change in maximum base reactions of Gaglardi Way Underpass updated FE model................................................................................................................................................... 65 Table 7.3: Change in maximum structural displacements for Gaglardi Way Underpass updated FE model................................................................................................................................................... 66 Table 7.4: Percentage change in maximum base reactions of Kensington Avenue Underpass updated FE model ............................................................................................................................................. 67 Table 7.5: Change in maximum structural displacements for Kensington Avenue Underpass updated FE model ............................................................................................................................................. 68 Table C.1: Gaglardi Way Underpass ARTeMIS geometry .............................................................. 123 Table C.2: Gaglardi Way Underpass channel information ............................................................... 125 Table C.3: Kensington Avenue Underpass ARTeMIS geometry ..................................................... 127 Table C.4: Kensington Avenue Underpass channel information ...................................................... 129 ix  Table D.1: Parameters defined for updating Gaglardi Way Underpass FE model ........................... 130 Table D.2: Parameters defined for updating Kensington Avenue Underpass FE model .................. 130 Table E.1: Modal information for updated Gaglardi Way Underpass FE model ............................. 131 Table E.2: Modal information for updated Kensington Avenue Underpass FE model .................... 133 Table F.1: Longitudinal component first mode PSa for two bridges ................................................ 135 Table F.2: Transverse component first mode PSa for two bridges ................................................... 136 Table F.3: Vertical component first mode PSa for two bridges ....................................................... 137 Table F.4: SRSS first mode PSa for two bridges .............................................................................. 138 Table G.1: Maximum and minimum base reactions with percentage difference for Gaglardi Way Underpass before and after finite element model updating .............................................................. 143 Table G.2: Maximum and minimum absolute displacements with percentage difference for north span of Gaglardi Way Underpass before and after finite element model updating .................................. 144 Table G.3: Maximum and minimum absolute displacements with percentage difference for south span of Gaglardi Way Underpass before and after finite element model updating .................................. 145 Table G.4: Maximum and minimum base reactions with percentage difference for Kensington Avenue Underpass before and after finite element model updating .............................................................. 146 Table G.5: Maximum and minimum absolute displacements with percentage difference for south span (A0 to P1) of Kensington Avenue Underpass before and after finite element model updating ....... 147 Table G.6: Maximum and minimum absolute displacements with percentage difference for north span (P1 to A2) of Kensington Avenue Underpass before and after finite element model updating ....... 148    x  List of Figures Figure 2.1: Phases of FEA, adapted from (Pidaparti, 2017, p. 6) ......................................................... 6 Figure 2.2: Sample vibration data (accelerations) in time series .......................................................... 9 Figure 2.3: Singular values of PSD matrix, reproduced from (Structural Vibration Solutions) ........ 10 Figure 2.4: Stabilisation diagram, reproduced from (Structural Vibration Solutions) ....................... 11 Figure 2.5: Sample 3D MAC plot ....................................................................................................... 15 Figure 3.1: Elevation of Gaglardi Way Underpass ............................................................................. 16 Figure 3.2: Location of Gaglardi Way Underpass on satellite map .................................................... 17 Figure 3.3: Gaglardi Way Underpass column elevation ..................................................................... 20 Figure 3.4: Gaglardi Way Underpass abutment bent elevation .......................................................... 21 Figure 3.5: Gaglardi Way Underpass pier bent elevation ................................................................... 21 Figure 3.6: Gaglardi Way Underpass bearing at abutment ................................................................. 22 Figure 3.7: Gaglardi Way Underpass instrument setup ...................................................................... 23 Figure 3.8: Location of Kensington Avenue Underpass on satellite map .......................................... 24 Figure 3.9: Elevation of Kensington Avenue Underpass .................................................................... 25 Figure 3.10: Kensington Avenue Underpass column elevation .......................................................... 26 Figure 3.11: Kensington Avenue Underpass south abutment elevation ............................................. 27 Figure 3.12: Kensington Avenue Underpass north abutment bent elevation ..................................... 27 Figure 3.13: Kensington Avenue Underpass pier bent elevation ....................................................... 28 Figure 3.14: Kensington Avenue Underpass bearing and pedestal at south abutment ....................... 28 Figure 3.15: Kensington Avenue Underpass bearing and pedestal at north abutment ....................... 29 Figure 3.16: Kensington Avenue Underpass instrument setup in plan view ...................................... 30 Figure 3.17: Kensington Avenue Underpass instrument setup in section view ................................. 31 Figure 4.1: Gaglardi Way Underpass FE model in 3D extruded (top) and skeletal (bottom) view ... 33 xi  Figure 4.2: Gaglardi Way Underpass FE model elevation in extruded (top) and skeletal (bottom) views............................................................................................................................................................. 34 Figure 4.3: Kensington Avenue Underpass FE model in 3D extruded (left) and skeletal (right) view............................................................................................................................................................. 35 Figure 4.4: Kensington Avenue Underpass FE model elevation in extruded (top) and skeletal (bottom) views ................................................................................................................................................... 35 Figure 4.5: Gaglardi Way Underpass ARTeMIS Model - west view ................................................. 37 Figure 4.6: Kensington Avenue Underpass ARTeMIS Model - east view ......................................... 38 Figure 5.1: Singular Values of Spectral Densities Matrix for Gaglardi Way Underpass ................... 40 Figure 5.2: OMA mode shapes for Gaglardi Way Underpass. ........................................................... 42 Figure 5.3: Gaglardi Way Underpass preliminary FE mode shapes ................................................... 44 Figure 5.4: Singular Values of Spectral Densities Matrix for Kensington Avenue Underpass .......... 46 Figure 5.5: OMA mode shapes for Kensington Avenue Underpass ................................................... 47 Figure 5.6: Kensington Avenue Underpass preliminary FE mode shapes ......................................... 49 Figure 6.1: Correlation for Gaglardi Way Underpass models ............................................................ 51 Figure 6.2: Sensitivity analysis matrix for Gaglardi Way Underpass ................................................ 52 Figure 6.3: Mode pair graph for Gaglardi Way Underpass ................................................................ 54 Figure 6.4: Modal Assurance Criterion (MAC) for Gaglardi Way Underpass ................................... 55 Figure 6.5: Updated mode shapes correlation for Gaglardi Way Underpass ..................................... 56 Figure 6.6: Correlation for Kensington Avenue Underpass models ................................................... 57 Figure 6.7: Sensitivity analysis matrix for Kensington Avenue Underpass ....................................... 58 Figure 6.8: Mode pair graph for Kensington Avenue Underpass ....................................................... 60 Figure 6.9: Modal Assurance Criterion (MAC) for Kensington Avenue Underpass ......................... 60 Figure 6.10: Updated mode shapes correlation for Kensington Avenue Underpass .......................... 61 xii  Figure A.1: General layout for Gaglardi Way Underpass .................................................................. 78 Figure A.2: Gaglardi Way Underpass elevation ................................................................................. 79 Figure A.3: Gaglardi Way Underpass deck cross-section .................................................................. 80 Figure A.4: Gaglardi Way Underpass column and pipe pile .............................................................. 81 Figure A.5: Gaglardi Way Underpass abutments ............................................................................... 82 Figure A.6: Gaglardi Way Underpass pier ......................................................................................... 83 Figure A.7: I-Girder ............................................................................................................................ 84 Figure A.8: Gaglardi Underpass girder layout .................................................................................... 85 Figure A.9: Gaglardi Way Underpass plate bearing at abutments ...................................................... 86 Figure A.10: Gaglardi Way Underpass neoprene pad bearing at pier ................................................ 87 Figure A.11: PL-2 (Tall) parapet ........................................................................................................ 88 Figure A.12: General layout for Kensington Avenue Underpass ....................................................... 89 Figure A.13: Kensington Avenue Underpass elevation ...................................................................... 90 Figure A.14: Kensington Avenue Underpass deck cross-section ....................................................... 91 Figure A.15: Kensington Avenue Underpass pier column and shaft .................................................. 92 Figure A.16: Kensington Avenue Underpass abutment A2 column and shaft ................................... 93 Figure A.17: Kensington Avenue Underpass south abutment ............................................................ 94 Figure A.18: Kensington Avenue Underpass north abutment ............................................................ 95 Figure A.19: Kensington Avenue Underpass pier .............................................................................. 96 Figure A.20: Kensington Avenue Underpass girder layout ................................................................ 97 Figure A.21: Kensington Avenue Underpass bearing at south abutment (A0) .................................. 98 Figure A.22: Kensington Avenue Underpass bearing at north abutment (A2) ................................... 99 Figure A.23: Kensington Avenue Underpass fabreeka pad bearing at pier ...................................... 100 Figure B.1: Gaglardi Way Underpass channels 370 to 373 .............................................................. 101 xiii  Figure B.2: Gaglardi Way Underpass channels 374-377 .................................................................. 102 Figure B.3: Gaglardi Way Underpass channels 378-381 .................................................................. 103 Figure B.4: Gaglardi Way Underpass channels 382-383 .................................................................. 104 Figure B.5: Kensington Avenue Underpass channels 343-346 ........................................................ 105 Figure B.6: Kensington Avenue Underpass channels 343-350 ........................................................ 106 Figure B.7: Kensington Avenue Underpass channels 351-354 ........................................................ 107 Figure B.8: Kensington Avenue Underpass channels 355-358 ........................................................ 108 Figure B.9: Kensington Avenue Underpass channels 359-360 ........................................................ 109 Figure C.1: Layout for Gaglardi Way Underpass ............................................................................. 111 Figure C.2: Material properties data form ........................................................................................ 112 Figure C.3: Define bent cap section .................................................................................................. 113 Figure C.4: Define column section ................................................................................................... 114 Figure C.5: Define girder section ...................................................................................................... 115 Figure C.6: Define deck section ........................................................................................................ 116 Figure C.7: Define bridge bents ........................................................................................................ 118 Figure C.8: Define bent columns ...................................................................................................... 119 Figure C.9: Define bridge object ...................................................................................................... 120 Figure C.10: Assign north abutment to bridge object ....................................................................... 121 Figure C.11: Assign pier bent to the bridge object ........................................................................... 122 Figure C.12: Gaglardi Way Underpass ARTeMIS model ................................................................ 124 Figure C.13: Gaglardi Way Underpass DOF assignment - east view............................................... 126 Figure C.14: Kensington Avenue Underpass ARTeMIS model ....................................................... 127 Figure C.15: Kensington Avenue Underpass DOF assignment - west view .................................... 128 Figure E.1: Mode shapes for updated FE model of Gaglardi Way Underpass ................................. 132 xiv  Figure E.2: Mode shapes for updated FE model of Kensington Avenue Underpass ....................... 134 Figure F.1: Unscaled spectra for longitudinal components of ground motions ................................ 135 Figure F.2: Unscaled spectra for transverse components of ground motions ................................... 136 Figure F.3: Unscaled spectra for vertical components of ground motions ....................................... 137 Figure F.4: Unscaled spectra for the SRSS of ground motions ........................................................ 138 Figure F.5: Ground motions for Imperial Valley earthquake ........................................................... 139 Figure F.6: Ground motions for Trinidad earthquake ....................................................................... 140 Figure F.7: Ground motions for Kobe earthquake ............................................................................ 141 Figure F.8: Ground motions for Tabas earthquake ........................................................................... 142    xv  Acknowledgements First of all I would like to extend my sincere gratitude to my supervisor Dr. Carlos Ventura who has throughout the program guided me through difficult stages and has been a source of invaluable information, thus leading towards a successful research work. It was his dedication and passion for the field that had me motivated throughout. Secondly, I owe a gratitude to Dr Yavuz Kaya, who also happens to be my second reader, for all his help out of his busy time and for the necessary push required during the beginning of research. I would also like to recognise Ms. Sharlie Huffman (Sr. Seismic & Structural Health Engineer, Huffman Engineering Services) for her help at personal level and in connecting me to engineers and technical staff to acquire any required documentation. Additionally, I would like to thank Eddy Dascotte for his tremendous effort to help resolve technical issues with finite element model updating software, FEMtools. Last but not the least, I owe deepest gratitude to my parents who trusted and invested in me, for all the love and emotional support I got from them, for guiding me through my hard times, and for keeping my morale high.   xvi  Dedication To my family  1  1. Introduction It is of prime importance for structural engineers to understand the behaviour of structures, be it simple short structures or complex skyscrapers. Over the decades, the design process has gradually advanced from hand calculations to computer software that can now automatically predict the responses. The evolution of finite element modelling and analysis has enabled architects to plan and engineers to design on a much higher scale, as a result of which large and eccentric structures can easily be constructed. However, there still lies some discrepancies between the modelled and actual responses due to errors in modelling and the assumptions involved that carry the errors. For already existing structures, this issue is addressed by calibrating the finite element model, by modifying the structural properties, to match the experimental results from ambient vibration testing carried out on structure to determine its modal properties. This technique is known as ‘Model Updating’, based upon which this thesis has been produced. This chapters emphasises the purpose of this research, underlines the scope of work, and states the goals. 1.1. Research Motivation Engineering researchers have been practicing model updating technique for decades to monitor the health of structure and determine how it will respond to a particular event, but the value of calibrating a finite element model is still ambiguous. Every study is based on incomparable scope of work with an exclusive set of objectives that produces a unique set of results and encounters peculiar problems. Although the ultimate aim is to generate a finite element model that best represents an actual structure by calibrating it to the finest detail, yet it is not absolutely known how the structure will behave under an actual scenario due to numerous assumptions involved. A question that may arise is whether updating a finite element model is necessary and how do the two, i.e. calibrated and 2  uncalibrated, models compare. Therefore, a study is necessary to determine how conservative uncalibrated finite element model is. Since neither would give a hundred-percent exact response for structure, would generating a finite element model and analysing it without calibrating be sufficient to determine the structural responses of existing structures, similar to the sort of approach that is used for non-existent structures during the design phase where finite element model updating is not viable. 1.2. Scope of Work The technique of finite element model updating is used in many civil engineering applications ranging from single-storey buildings to multi-storey towers, short single-span bridges to long multi-span bridges, dams, retaining walls, and other land and water infrastructure. Every study poses distinct outcome in which the driving factor also includes the material used for construction, i.e. concrete, steel, wood, or a combination. The scope of work in this project is limited to short two-span concrete bridges supported on an I-girder. Two such bridges, between 55 m to 65 m, instrumented under the British Columbia Smart Infrastructure Monitoring System (BCSIMS) program have been chosen. Simple abutment to abutment finite element models were generated for each bridge. For simplification the approach slabs and mechanically stabilised earth (MSE) wall were not included and rather springs were incorporated in mid-height of columns. The springs were assumed to behave in similar manner the approach slab would have reduced the flexibility of structure. Moreover, the soil conditions on site and the depth of drilled pile shafts were not known, therefore, stiff soil was assumed at ground level and the columns were fixed at base. Operational modal analysis was carried out to determine the ambient modal information of existing structures based on which the preliminary finite element models were calibrated. The unique feature of this study was an attempt to update finite element model using sparsely distributed vibration testing points and no sensors installed on columns, therefore, imposing limitations on matching mode shapes and attaining reasonable MAC values. The aim was to converge maximum number of modes within 10% range and to attain best possible mode shape match 3  and MAC values trying to overcome the limitations. Seismic analysis was carried out on both preliminary and updated finite element models, using ground motions having low, medium range, and high peak ground acceleration (PGA), to determine the impact of finite element model updating on structural responses like base reactions and mid-span displacements. The outcomes from two bridges were compared to reinforce the conclusions drawn. Any inference may not be limited and could be reasonably comparable to finite element model updating approach that uses denser and longer duration ambient vibration testing as well as applicable to steel bridges or longer spans, but for that another study is required to compare the results and eventually conclude. 1.3. Research Goals The ultimate goal was to generate an efficient, robust, and a realistic finite element model by calibrating it to match the test data and study the impact of finite element model updating on structural responses when subjected to a seismic load. For each bridge, the goals were decomposed into five distinct objectives that are listed underneath. 1. Generate a finite element model. 2. Ambient modal identification of existing structure. 3. Correlation between the preliminary finite element model and the test model. 4. Calibrate or update the finite element model to match the test data. 5. Investigate the impact and importance of finite element model updating using linear time-history analysis. For each bridge, the first two steps aim to generate a finite element model and carry out operational modal analysis on test model developed to determine ambient modal information, i.e. natural frequencies and mode shapes, for existing structure using vibration data acquired from permanents sensors installed on bridges. The goal was to calibrate the former using the information 4  obtained from latter. Third step compares the experimental data to the natural frequencies and modes shapes from modal analysis of preliminary finite element model. In step four, the finite element model is eventually updated by adjusting parameters in an iterative manner until it matches the ambient modal information determined in step two. Earthquake ground motions could now be applied, in step five, to the updated and preliminary finite element models. The structural responses for both FE models were compared to study the importance and effect of model updating.   5  2. Literature Review This chapter highlights the concept behind some of the terms that are repeatedly used in this thesis. It additionally provides a literature review of different types of analysis and how the model is calibrated. 2.1. British Columbia Smart Infrastructure Monitoring System (BCSIMS) The Cascadia Subduction Zone in the southwest coast of British Columbia (BC) province, encompassing lower mainland, is considered as most active seismic zone in Canada. It is believed to be capable of producing earthquakes of large magnitudes up to 9.0 on the Richter scale. Such an event was last recorded approximately 300 years ago indicating towards strains being accumulated in the subduction boundary. Although Vancouver has not yet experienced a damaging earthquake, however, the ongoing occurrences of small to medium scale earthquakes with enough potential to damage structures signifies the fact that the southwest coast of BC is still an active seismic zone. To alleviate the risk of damage to structures due to a seismic event, the British Columbia Ministry of Transportation and Infrastructure together with the Earthquake Engineering Research Facility (EERF) at UBC has been instrumenting bridges, tunnels, and buildings all over BC. Lately, the duo launched a program, namely British Columbia Smart Infrastructure Monitoring System (BCSIMS), that integrates the data received from the instrumented structures and the Strong Motion Network (SMN), which is the ground motion vibration data maintained by the Geological Survey of Canada (GSC). This program allows a predefined recipient to immediately receive a notification following an event, incorporating remote Structural Health Monitoring (SHM) system. The main purpose of the BCSIMS program is to determine the seismic capacity of structures, detect any structural damages, and focus on retrofit efforts (Kaya, Ventura, Huffman, & Turek, 2017, pp. 579-581). 6  2.2. Finite Element Analysis Finite element analysis (FEA) is a numerical analysis technique that is capable of solving various engineering problems for which the underlying theory dates back to early 1900s. It serves as a basic foundation that all engineers need to understand to be successful analysts in their respective fields. In the field of Civil Engineering, it is generally employed to predict the response of structure, when subjected to dead and live loads, by discretising the geometry of structure into smaller elements that are interconnected at nodes, without any overlaps. The basic objective of FEA is to determine the unknown degrees of freedom at the nodes and the resulting support reactions (Pidaparti, 2017, p. 3). The evolution in technology, over the decades, has enabled engineers to carry out this analysis in full using a computer software. Model generated with the help of a computer is called finite element model (FEM). As shown in figure 2.1, the analysis is carried out in three basic steps, the pre-processing phase, processing phase, and post-processing phase.  Figure 2.1: Phases of FEA, adapted from (Pidaparti, 2017, p. 6) The first step of pre-processing phase generates a discretised finite element model by defining nodes and their connections, specifies the material properties, and applies loads and boundary 7  conditions. The second processing phase simultaneously develops a set of linear and nonlinear algebraic expressions to obtain the nodal results, such as the displacements and/or forces. The last post-processor phase simply holds the results obtained for nodal stresses, displacements, and support reactions (Pidaparti, 2017, p. 6). 2.2.1. Sources of Error in Finite Element Modelling Mottershead, Link, and Friswell (2010, pp. 2275-2276) have categorised the sources of errors in finite element modelling, some of which can be corrected by model updating while others cannot. The errors listed under category 1 and 2 are generally called model-structure errors since they are related to the mathematical structure of the model. Category 3 errors can normally be fixed by calibrating the model. Category 1: ‘Idealisation errors triggered by assumptions involved in characterising the behaviour of the physical structure.’ The most common sources of such errors are:  Simplification of the structure using erroneous assumptions.  Inaccurately assigned mass properties.  Neglecting particular properties in the finite element formulation.  Imprecise connectivity of the mesh.  Incorrect assignment of boundary conditions.  Error in joint modelling.  Flawed assumptions for the external loads.  Wrong assumptions for the geometrical shape of structure.  Assuming a linear behaviour for a non-linear structure. Category 2: ‘Discretisation errors introduced by numerical methods that are inherent in the finite element method.’ Example for such errors are: 8   Coarse finite element mesh that does allow the modal data to fully converge.  Truncation errors in order reduction techniques.  Higher stiffness as a result of element shape sensitivity. Category 3: ‘Inaccurately assuming the model parameters.’ These include, but are not limited to:  Material properties.  Frame cross-section properties.  Shell or plate thickness.  Spring stiffness.  Non-structural mass. The categories and their sources of error listed in this subsection have been further explained in detail by Friswell and Mottershead (1996, pp. 26-30), in addition to other possible contributing sources of error. 2.3. Operational Modal Analysis Vibration testing is generally conducted in two ways, using either forced vibration or an ambient vibration. The former is carried out by subjecting the system to external vibration using a dynamic shaker or an impulse hammer, whereas, the latter is an output-only measurement carried under natural and operating conditions to determine the modal properties of a structure. In the field of structural engineering ambient vibration testing, also known as Operational Modal Analysis (OMA), is used to determine the natural frequency of a structure and to determine the dynamic responses under various environmental and/or loading conditions. This testing is carried out in a non-destructive manner under normal operating conditions, i.e. without external excitation (forced vibration), by subjecting the structure to ambient vibrations generated by wind and users (Brincker & Ventura, 2015, pp. 3-5). 9  Figure 2.2 shows a sample vibration data acquired from vibration testing of a structure under normal operating condition. Two methods are commonly employed to decipher this kind of vibration data, i.e. frequency domain decomposition and stochastic subspace identification.  Figure 2.2: Sample vibration data (accelerations) in time series 2.3.1. Frequency Domain Decomposition Brincker, Zhang, and Andersen (2001) introduced a new user-friendly method, called frequency domain decomposition (FDD), in extension to the basic frequency domain (BFD) approach. The classical BFD or peak picking technique processes the signal using a discrete Fourier transform, allowing well-separated modes to be estimated directly from the power spectral density (PSD) matrix at the peak, however, downside of this method was that close modes were difficult to detect and the estimation would be heavily biased. The FDD technique, in contrast, decomposes the spectral density function matrix to allow the response spectra to be separated into a set of single degree of freedom systems with each corresponding to an individual mode. This method helps determine close modes with high accuracy even in the case of strong noise contamination of the signals, as well as, the harmonic components in response signals are clearly indicated. As a result of FDD, the average normalised singular values of the PSD matrix are plotted against frequency where the dominating peaks represents different modes. Figure 2.3 illustrates a typical plot for normalised singular values of spectral densities. Both closely spaced modes and well separated modes can be clearly observed. 10   Figure 2.3: Singular values of PSD matrix, reproduced from (Structural Vibration Solutions) 2.3.2. Stochastic Subspace Identification The data driven stochastic subspace identification (SSI) is a highly robust technique among the known modal identification techniques in time domain. Its complex mathematical theory, however, and poorly established connection to the classical correlation driven time domain technique makes it difficult to understand for engineers having a classical knowledge of structural dynamics (Brincker & Andersen, 2006, p. 1). This method identifies the stochastic state space model from output-only measurements by converting the measured time histories to spectra using Discrete Fourier Transform (DFT). The natural frequencies can be identified as the peaks of spectra, while mode shapes can be determined by calculating the transfer functions between all outputs and reference sensor. However, the drawback of this method is that the natural frequencies are selected subjectively, the damping estimation is not quite accurate, and it determines the operational deflection shapes rather than the 11  mode shapes as no modal model is fitted to the data. Nonetheless, the prime advantage of this method is that the identification process is faster as it is done online and it allows to check quality of data acquired from recorders on site (Peeters & Roeck, 2000, p. 48). Figure 2.4 illustrates a typical stabilisation diagram showing the natural frequencies for estimated modes.  Figure 2.4: Stabilisation diagram, reproduced from (Structural Vibration Solutions) 2.4. Finite Element Model Updating Upon comparing the finite element model to the measurements from real structure, it turns out that the frequencies do not match for corresponding modes. The reason for discrepancy is generally due to errors outlined in section 2.2.1. Therefore, the preliminary finite element model has to be updated or calibrated so it can accurately predict the measured results (Marwala, 2010, pp. 1-2). Finite element model updating is a process that strives to correct the finite element model by processing 12  records acquired from ambient vibration testing carried out on structure under normal operating conditions (Mottershead & Friswell, 1993, p. 347). The measured data from vibration testing carried out on site is always assumed to be correct and the finite element model must be calibrated by adjusting the parameters to match the experimental data. A finite element model can be updated using two techniques, i.e. direct and iterative. The former does not take into consideration the changes to the physical parameters which is why the updated finite element model solely represents the measured data without any consideration for the structure being analysed. The resulting mass and stiffness matrices deem to be meaningless and does not represent any physical changes in the finite elements of original model. Moreover, nodal connectivity is not ensured and the matrices are fully populated and not sparse. On the contrary, iterative method updates the physical parameters of finite element model using iterations until the measured data is reproduced to a degree of accuracy specified by user. The advantage of iterative method over direct method is that it ensures accurate nodal connectivity and a rather meaningful mass and stiffness matrices (Marwala, 2010, p. 2).  Mottershead et al. (2010, p. 2276) states that the finite element model should be assessed for its quality after it is updated. A good quality model should typically be able to predict structural responses for types of loading other than those used in vibration testing, it should have the ability to efficiently predict the structural behaviour beyond the frequency range used for updating the finite element model, and should have the capability to predict the effects of structural modifications. The quality requirements shall generally be related to the intended purpose for which the model will be used. 2.4.1. Parameters for Model Updating A finite element model is generated based on the material properties and dimensions of a physical structure. The shape function for the choice of elements will determine the distribution of the mass and stiffness properties so the matrices can be physically understood, therefore, it is crucial to 13  carefully select the parameters for finite element model updating using engineering knowledge. However, certain model updating schemes does not allow the user to select the parameters to be updated. The direct methods, for example, updates the entire stiffness and mass matrices in a single (non-iterative) step. This changes all the terms in the individual matrix, disregarding the element shape functions, and consequently the physical meaning is lost somewhere in-between the updating process. In contrast, the updating schemes that allows the user to select the parameters to be adjusted requires profound engineering knowledge and diligent judgements to make sure that the model being calibrated is not only able to reproduce the experimental results but also have physically meaningful coefficients. Such approach leads to knowledge-based model. (Friswell & Mottershead, 1996, pp. 98-99). It is important to contemplate the number of parameters to be selected and the choice of parameters. To attain high accuracy finite element model in least possible number of iterations or shortest possible calibration time, the best strategy is to keep number of parameters low and use large volume (measurement points and duration) of test data (Friswell & Mottershead, 1996, p. 101). It is necessary to select the parameters that are most sensitive to changes and effectively improves the FE model. 2.4.2. Sensitivity Analysis Sensitivity analysis is a technique that allows the engineers determine how structural behaviour of a finite element model is influenced by modification of parameters like spring stiffness, modulus of elasticity, moment of inertia, etc. This analysis can be carried out either locally or globally. The local sensitivity analysis (LSA) examines the impact of modifying parameters for local elements, while keeping others constants, whereas, the global sensitivity analysis (GSA) assesses the impact over the entire range of interest. As an example, the LSA analyses the results by assigning a unique parameter to each girder, while, the GSA assigns an identical parameter to all girders (Wan & Ren, 2015, p. 2). 14  2.4.3. Modal Assurance Criterion Once the preliminary finite element model is ready and the modal data is acquired for physical structure, the natural frequencies and mode shapes can be compared for two models. One of the most commonly used technique for quantitative comparison of mode shapes is the Modal Assurance Criterion (MAC), which is a 2D or 3D statistical indicator that is most sensitive to large differences and relatively insensitive to small differences in mode shapes. It only yields the degree of consistency between mode shapes, whereas, for natural frequencies a separate means of comparison shall be used. MAC can take a value between 0 and 1 (or 100%), with close to zero representing inconsistent correspondence between the two mode shapes, whereas, value closer to unity indicates a good match. However, it does not validate the model neither is it suitable for orthogonality check as it does not take into consideration the mass and stiffness matrices, which makes it a pre-test mode pairing tool. Moreover, it does not distinguish between systematic errors and local discrepancies (Pastor et al., 2012, pp. 543-545). According to Pastor et al. (2012, p. 545), the MAC value can be closer to zero for the following reasons:  Non-stationary system  Non-linearity in system  Noise in reference mode shape  Invalid parameter extraction technique for the measured data set  Linearly independent mode shapes Moreover, Pastor et al. (2012, p. 545) also states the possible reasons that can lead to a MAC value close to unity:  15   Inadequate number of response degrees of freedom to distinguish between independent mode shapes  Mode shapes resulting from unmeasured forces to the system  Mode shapes primarily being a coherent noise  Mode shapes representing identical motion for distinct frequencies A unit matrix is not an ideal MAC matrix due to the fact that the modal vectors are not directly orthogonal but mass orthogonal. MAC matrix simply identifies two discrete modes from two sets of data that correspond to each other (Pastor et al., 2012, p. 545). Figure 2.5 below illustrates a typical 3D MAC plot  Figure 2.5: Sample 3D MAC plot   16  3. Description of Bridges Two bridges have been studied in this project, namely, Gaglardi Way Underpass and Kensington Avenue Underpass, located in Vancouver, British Columbia, spanning across the Trans-Canada Highway. Both bridges have been reconstructed post 2010, demolishing the old structures, by Kiewit Flatiron General Partnership conceived as a public-private partnership contract. Being a part of the British Columbia Smart Infrastructure Monitoring System (BCSIMS) program, they are instrumented to record the ambient vibrations in real-time, i.e. without any initial excitation. The vibration data collected allows determine the natural frequencies, mode shapes, and damping ratios using operational modal analysis (OMA). The information obtained from this analysis assists in finite element model updating, which has been further explained and discussed in the chapters hereafter. This chapter, in particular, highlights the structural detail of bridges and their instrument setup. Structural drawings have been attached as an appendix, whereas, photos for bridge components, where possible, have been included in the main body for better illustration. 3.1. Gaglardi Way Underpass The Gaglardi Way Underpass, constructed in 2013, is a two lane 56.78 m long and 18.038 m wide concrete bridge across the Trans-Canada Highway. Figures 3.1 and 3.2 shows the elevation view of the bridge and its location on map, respectively. The drawings for general plan layout, the elevation, and deck cross-section can be found in figures A.1, A.2 and A.3 of ‘Appendix A’.  Figure 3.1: Elevation of Gaglardi Way Underpass 17   Figure 3.2: Location of Gaglardi Way Underpass on satellite map 3.1.1. Structural Components The Gaglardi Way Underpass is a 2-span concrete bridge having precast I-girders. As shown in figure A.2 of appendix A, span 1 from north abutment (A0) to the pier (P0) is 27.46 m, while the span 2 from pier (P1) to south abutment (A2) is 29.32 m. Important components for this bridge, i.e. the superstructure and substructure details and material properties, within the scope of this project have been highlighted in this subsection. Tables 3.1 and 3.2 shows the minimum concrete strength for different components of the bridge, the steel material used in reinforcement, and their properties. The modulus of elasticity of concrete was calculated using the formula standardised by American Concrete Institute in ‘Building Code Requirements for Structural Concrete (ACI 318-08)’ for concrete weighing between 90 and 160 lb/ft3 (1442 – 2563 kg/m3). Since the weight or density of concrete used was not 18  provided, therefore, SAP2000 default value of 150 lb/ft3 (2403 kg/m3) was assumed. This density is regarded as normal weight of concrete by most concrete handbooks, except for American Concrete Institutes, where normal concrete weight is 0.145 lb/ft3 (2323 kg/m3). Equation 1 below shows the formula used to compute the modulus of elasticity (E) of concrete based on compressive strength and weight. 𝐸𝑐 = 33𝑤𝑐1.5√𝑓𝑐′   (psi)                    1 Where; 𝑤𝑐 = weight of concrete (lb/ft3) ; 𝑓𝑐′ = compressive strength of concrete at 28 days (psi) As an alternative, shown below is the formula standardised by Canadian Standards Association (CSA) in ‘Design of Concrete Structures (A23.3-14)’ that could have been used. However, the way the formula is structured resulted in a lower modulus of elasticity and, thus, lower frequencies leading to higher discrepancies compared to experimental modal frequencies. 𝐸𝑐 = (3300√𝑓𝑐′ + 6900) ( 𝛾𝑐2300)1.5  (MPa)        2 Where;  γc = weight of concrete (kg/m3) ; 𝑓𝑐′ = compressive strength of concrete at 28 days (MPa) The modulus of elasticity is an estimated value and none of the standardised formulae can be deemed as right or wrong. For this reason, the CSA concrete design handbook permits a leeway between 80 and 120% of the value computed using equation 2. To attain the frequencies with minimum discrepancy, it was decided to use the formula standardised by ACI in equation 1 since the resulting modulus of elasticity for each section was within the range specified by CSA. For example, the modulus of elasticity for deck section using equation 2 was calculated as 28.21 × 103 MPa which is 5.26% lower than 29.78 × 103 MPa, computed using equation 1. 19  Table 3.1: Concrete material Properties Concrete Component Grade (MPa) Modulus of Elasticity (MPa) Column (Above Ground) 35 29.78 × 103 Pile Infill (Drilled Shaft) 30 27.57 × 103 Girder 50 35.60 × 103 Deck 35 29.78 × 103 Bent Cap 35 29.78 × 103  Table 3.2: Steel material properties Steel Component Grade Modulus of Elasticity (MPa) Minimum Yield Stress (MPa) Minimum Tensile Stress (MPa) Effective Yield Stress (MPa) Effective Tensile Stress (MPa) Rebar A955M Grade 520 2 × 105 520 650 572 715 Structural Steel 300W 2 × 105 300 535 330 588  Columns: A total of 13 circular concrete columns of 914 mm diameter are supporting the superstructure. Four of these columns are at each abutment and five are supporting the pier. A steel pipe pile, of same diameter, filled with concrete is driven into the ground that provides foundation support. The exterior columns are 1.7 m from the end of abutment bent cap and the second & third columns are 2.6 m from the centre of the bent cap. In case of pier, they are equally spaced at 3.75 m, while the distance from end 20  to outer column is the same as that for abutments. Figure 3.3 shows the column elevation, for which the drawing can be found in figure A.4 of ‘Appendix A’.  Figure 3.3: Gaglardi Way Underpass column elevation Abutments: A bent abutment, connected to girder bottom only, has been designed at both north and south ends of this bridge. The bent cap is an 18.4 × 1.6 × 1.5 m beam supported by four columns at each end and is skewed at 69° 18’ 19’’. Moreover, the elevation at south abutment is 665 mm higher than the north abutment and 234 mm higher than the pier. Figure 3.4 shows the bent elevation for which the drawing can be found in figure A.5 of ‘Appendix A’. 21   Figure 3.4: Gaglardi Way Underpass abutment bent elevation Pier: A pier with an integral bent, incorporating the girders, has been designed at mid-span. The bent cap is an 18.4 × 2.928 × 1.6 m skewed beam supported by five columns. Figure 3.5 shows the elevation view of pier bent, the drawing for which can be found in figure A.6 of ‘Appendix A’.  Figure 3.5: Gaglardi Way Underpass pier bent elevation Girder: The design uses 1728 mm ‘type 5’ six I-girder, shown in figure A.7 of ‘Appendix A’. The deck is supported on six girders equally spaced at 2.95 m and a constant haunch thickness of 75 mm. A 250 mm thick girder pedestal has been included at the abutments 22  for jacking. The girder can somewhat be seen in figure 3.5. Additionally, figure A.8 in ‘Appendix A’ shows the layout of girders. Bearings: Plate bearings have been used at abutments and a neoprene pad bearing at the pier. Figure 3.6 shows the bearing and girder pedestal at the abutments and figures A.9 & A.10 in ‘Appendix A’ shows the drawings for bearings.  Figure 3.6: Gaglardi Way Underpass bearing at abutment Deck: An 18.038 m and 250 mm thick deck has been designed, for this bridge, with 100 mm thick panels. The cast-in-place concrete finish is a 135 mm thick layer. Parapet: A standard PL-2 (Tall) parapet has been used on both sides of the bridge as a guard. The drawing for this parapet can be found in figure A.11 of ‘Appendix A’. Foundation: The bridge columns at pier and both abutments (bent supports) are supported by 914 mm pipe pile shafts driven into the ground. 3.1.2. Instrumentation Multiple sensors have been installed on the Gaglardi Way Underpass that collects and records vibration data, which is used to monitor the health of the structure. The Ministry of Transportation and Infrastructure uses REF TEK (Trimble brand) seismic recorders for all bridges on Highway 1. A total of 12 sensors have been setup on the deck of span 1, i.e. north abutment (A0) to the pier (P1), and 1 sensor on the column at ground level to receive the testing data. Two uniaxial accelerometers are 23  installed mid-span at the sides of the deck, recording in vertical direction. Two accelerometers on deck level at each end of the pier are recording in three directions, i.e. parallel, vertical, and perpendicular to the span. One tri-axial accelerometer is installed on the middle column of the pier at ground level, recording in all three directions. Two bi-axial accelerometers are setup at each end of the abutment, over the bent cap. Three displacement sensors have also been installed at the abutment, recording the displacement of the bridge as it vibrates. Additionally, one tri-axial free-field sensor placed 13 m away to the east from the abutment, on the Trans-Canada Highway, measures in three orthogonal directions and includes the true north. Temperature and humidity conditions are also being recorded simultaneously. Figure 3.7 shows the instrument setup in detail. One such sensor can be seen, in figure 3.3, attached to the column.  Figure 3.7: Gaglardi Way Underpass instrument setup 24  3.2. Kensington Avenue Underpass The Kensington Avenue Underpass, constructed in 2011, is a five lane (including turn lane) concrete bridge across the Trans-Canada Highway. The length of the bridge is 61.73 m and is 27.3 m wide. The map in figure 3.8 delineates the location for the bridge and figure 3.9 shows the bridge in elevation view. Additionally, figures A.12, A.13, and A.14 in ‘Appendix A’ illustrates the drawings for general layout, the elevation, and deck cross-section.  Figure 3.8: Location of Kensington Avenue Underpass on satellite map 25   Figure 3.9: Elevation of Kensington Avenue Underpass 3.2.1. Structural Components Similar to Gaglardi Bridge, the Kensington Avenue Underpass is a 2-span I-girder precast concrete bridge. As shown in figure A.5 of ‘Appendix A’, south abutment (A0) to the pier (P1) spans 28.545 m, whereas, the span from pier (P1) to north abutment (A2), is 33.185 m. This subsection briefly outlines the essential superstructure and substructure components of the bridge and their properties. For the material properties refer to tables 3.1 and 3.2 since they are consistent according to the standards. Columns: The bridge is supported by 12 columns. Six of these columns are supporting the pier, whereas, the remaining are supporting the north abutment (A2). The diameter of the columns is 914 mm from abutment to the ground below which a 1.22 m pipe pile shaft filled with concrete grout is driven into the ground. For both pier and north abutment (A2), the distance from each end of bent cap to the exterior column is 2.48 m and are equally spaced at 5.25 m. Figure 3.10 shows the columns for which the drawing can be found in figure A.15 and A.16 of ‘Appendix A’. 26   Figure 3.10: Kensington Avenue Underpass column elevation Abutments: The south abutment of this bridge is supported by mechanically stabilized earth (MSE) wall that is supporting a 31.185 × 0.8 × 2.5 m abutment beam. For north abutment (A2) a bent with six columns has been designed. Both north and south abutment are skewed at 55° 20’ 22’’. The bent cap is 31.21 m long prismatic section connected to girder bottom only. For the first 1.5 m from each end, the section size is 1.6 × 1.2 m. The remaining 28.185 m section is 1.6 × 1.5 m. Moreover, the elevation at north abutment station is 467 mm lower than the south abutment station and 805 mm lower than the elevation at pier station. Figures 3.11 and 3.12 shows the south and north abutments for which the drawings are attached in ‘Appendix A’ figures A.17 and A.18. 27   Figure 3.11: Kensington Avenue Underpass south abutment elevation  Figure 3.12: Kensington Avenue Underpass north abutment bent elevation Pier: Similar to north abutment, the pier is a skewed bent designed with six columns but is integrated, i.e. sitting directly under the deck. The bent cap is a 31.21 × 1.6 m prismatic section. The depth of first 1.5 m section, from each end, is 2.628 m deep, while the depth of remaining 28.21 m bent cap section is 2.928 m. Figure 3.13 shows the photo for pier for the which the drawing can be found in figure A.19 of ‘Appendix A’. 28   Figure 3.13: Kensington Avenue Underpass pier bent elevation Girder: The girder designed is similar to what was seen for the bridge in subsection 3.1.1. Nine ‘type 5’ girders of 1728 mm, equally spaced at 2.95 m, are supporting the superstructure. The haunch is constant at 75 mm. A 250 mm thick girder pedestal has been included at the abutments for jacking. The shape and layout of the girders can to some extent be seen in figure 3.13. Additionally, the girder layout is shown in figure A.20, while the girder detail is illustrated in figure A.7 of ‘Appendix A’. Bearings: Plate bearing has been used at the abutments, whereas, fabreeka pad bearings are installed at the pier. Figure 3.14 and 3.15 shows the photos for bearings at the abutments along with girder pedestal. Moreover, the drawings for bearings at abutments and pier are illustrated in figure A.21, A.22 and A.23. Some detail for bearing at the pier can also be found in figure A.19 of ‘Appendix A’.  Figure 3.14: Kensington Avenue Underpass bearing and pedestal at south abutment  29   Figure 3.15: Kensington Avenue Underpass bearing and pedestal at north abutment Deck: The width of the deck is 27.3 m with rest of the details similar to the bridges in subsection 2.1.1. Parapet: A standard PL-2 (Tall) parapet is always used, refer to subsection 2.1.1. Foundation: The columns at north abutment (bent support) and pier are supported by 1.22 m drilled shaft driven into the ground. The south abutment, on the other hand, is supported by mechanically stabilised earth (MSE) wall. 3.2.2. Instrumentation The Kensington Avenue Underpass encompasses 18 sensors (30 channels) for health monitoring of the structure. The sensors have been installed along full length of the bridge. Span 2 have two uni-axial accelerometers installed mid-span at each side, recording the vertical vibration data. The east end of pier (P1) and north abutment (A2) caps have two bi-axial accelerometers measuring in two directions, i.e. vertical and parallel to the span. The west end of the pier (P1) and north abutment (A2) caps have two tri-axial accelerometers installed measure in three directions, i.e. perpendicularly in addition of parallel and vertical. Span 1 have only one uni-axial accelerometer setup at mid-span, measuring vertical vibrations at the western end of the bridge. South abutment (A1) have three uni-axial accelerometers installed. One tri-axial accelerometer is setup at the footing of pier column as well. Two free-field sensors, at 49°14’38.42’’ N, 122°58’7.93’’ W and 49°14’38.51’’ N, 122°58’1.30’’ W, are measuring in three orthogonal directions and includes true north. Three 30  displacement sensors are installed at north abutment (A2) to record the displacements due to vibrations. The onsite conditions are simultaneously recorded by humidity and temperature sensors to take into account its affect, if any. Figures 3.16 and 3.17 shows the detailed setup for these instruments in plan and section view. One such sensor can be seen on third column, from the left, of the pier figure 3.10.  Figure 3.16: Kensington Avenue Underpass instrument setup in plan view 31   Figure 3.17: Kensington Avenue Underpass instrument setup in section view   32  4. Modelling Two engineering software packages, namely, CSI Bridge and ARTeMIS have been used at modelling stage for finite element analysis and operational modal analysis, respectively. The former is a highly sophisticated, intuitive, versatile, and user-friendly interface powered with a highly effective analysis engine and design tools for bridge engineers. It is used to generate a prototype model for a structure, whether existing or in design stages, and mesh into finite elements to carry out structural analysis, determining its expected behaviour. This can range from a simple static analysis to a complex nonlinear dynamic analysis. On the other hand, ARTeMIS, developed by ‘Structural Vibration Solutions A/S’, is an open and user-friendly platform used for ambient modal analysis and damage detection of operational large-scale structures, using raw measured vibration data, in time series, under natural conditions. ARTeMIS comprises two stages for carrying out modal analysis. This chapter features the setup stage only, whereas, the reporting stage has been included in the next chapter. Similarly, for CSI Bridge the pre-processor stage has been included in this chapter and all the post-processor results can be found in chapter 5. This chapter illustrates the final models generated and states the assumptions (if any). For detail on how the structures were modelled, refer to Appendices. 4.1. Finite Element Models Finite element model is a complex and finely detailed discretised prototype of an actual structure with minimal assumptions involved. CSI Bridge smartly produces finite element model for bridges of different categories in several steps. This software is user-friendly compared to other finite element modelling software since it automatically assembles and generates a model using the components defined by user. The first step involves defining the layout line, i.e. the centreline of the bridge. Next it requires different components, namely, properties, substructure, and superstructure, to 33  be defined. The properties component is where material properties and frame sections are defined. Substructure primarily consists of the supporting components (bearings, abutments, bents, columns) of any bridge, whereas, the deck of the bridge is considered as a superstructure. After defining structural loading, the bridge can be assembled by defining the span lengths and the boundary conditions. This section displays the final assembled full-scale bridge models generated based on information in chapter 3. The detail on how each component was defined and the assembly of bridges has been provided in ‘Appendix C’. Figures 4.1 and 4.2 shows the extruded and skeletal views for the finite element models of Gaglardi Bridge produced in two different angles.  Figure 4.1: Gaglardi Way Underpass FE model in 3D extruded (top) and skeletal (bottom) view 34   Figure 4.2: Gaglardi Way Underpass FE model elevation in extruded (top) and skeletal (bottom) views As it can be seen in the figures above, a simple model of bridge was generated from abutment to abutment with a pier bent support in the middle. The model is comprised of bulb I-Girder frame section for girders, a circular concrete section for columns, rectangular concrete beam section for bent caps or abutment, springs acting as bearings, an area shell section was used for deck. To take into account the dead load of parapets and concrete surface layer, line load and area load distributions were used. For parapets, weight per unit cross-section area was calculated and applied across the length of bridge. Similarly, for concrete layer weight per unit area was calculated from concrete density used in material properties and applied along the whole length of bridge. The assumptions and simplifications made during finite element modelling have been stated in subsection 4.1.1. Additionally, figures 4.3 and 4.4 shows the elevation and 3D perspectives of Kensington Bridge finite element model in two different views. This finite element model for this bridge was generated using similar protocol and assumptions. The only major difference was having a wider deck and an abutment instead of bent support at one end. 35   Figure 4.3: Kensington Avenue Underpass FE model in 3D extruded (left) and skeletal (right) view  Figure 4.4: Kensington Avenue Underpass FE model elevation in extruded (top) and skeletal (bottom) views 4.1.1. Assumptions in FE Modelling The following assumptions had to be made during finite element modelling of two underpasses; 36   The bearing stiffness detail was not provided and, therefore, different stiffness values were tested based on trial and error method. Fixing all degrees of freedom resulted in first mode natural frequency that was closest to mode 1 of the experimental model.  The pile shafts driven into the ground were neglected since it would have further increased the number of assumptions in deciding the unknown depth inside ground and in assigning the spring stiffness values at consistent intervals, below ground, to take into consideration the pile bending. Moreover, the soil conditions on site were not known to determine a stiffness coefficient and assign a stiffness value at base level, therefore, stiff soil was assumed and the columns bases were fixed in all degrees of freedom. This coincidentally reduced the disparity between the analytical and experimental frequencies. The primary purpose of this decision was that inclusion of piles and/or detailed foundation caused the natural frequencies to increase due to accumulation of errors resulting from assumptions.  The approach slab and the MSE wall was not incorporated, rather springs were integrated at mid-height of columns to restrict the structural displacement assuming the approach slab to have reduced the flexibility of structure in a similar manner. The spring stiffness was assigned using trial and error method to determine a stiffness value that further improves first mode natural frequency and to attain minimum possible difference in subsequent frequencies, compared to the test model, prior to updating the preliminary finite element model.  The drawing did not specify the length of columns. However, using scaled drawing, 5 m length was chosen for all columns neglecting the ground profile.  Shape function for the undeformed layout line was not known, therefore, small elevation difference of around 50 cm between abutments A0 and A2 was neglected to attain a good correlation, i.e. node-point pairing, between the analytical and test models during the 37  calibration step. As a check, keeping the elevation difference did not significantly affect the mode shapes and/or the modal frequencies. 4.2. ARTeMIS Models The modelling technique used in ARTeMIS is not as complex and detailed as it is in case of finite element modelling. It is as simple as having just nodes, lines and surfaces that roughly defines the geometry of the structure. The setup stage is further subdivided into three steps, i.e. preparing the geometry, data acquisition, and degree of freedom (sensor/channel) information assignment. This section comprises the final models with channels assigned only. The acceleration data collected from sensors and modelling detail have been provided in Appendices B and C, respectively. Figure 4.5 shows the west view of Gaglardi Way Underpass illustrating the sensor map for half of the deck, while figure 4.6 shows the east view of Kensington Avenue Underpass with channels assigned to the corner nodes, at span, and mid-span.  Figure 4.5: Gaglardi Way Underpass ARTeMIS Model - west view N 38   Figure 4.6: Kensington Avenue Underpass ARTeMIS Model - east view As shown in figures above, a sketch representing bridge deck was produced with nodes at corners and mid-span. Data collected from 11 sensors was assigned to the deck of Gaglardi Way Underpass and 15 channels were assigned to the Kensington Avenue Underpass. The program can only read sensors physically connected to the structure to carry out operational modal analysis, therefore, the sensors that were placed away from bridge, such as, the tri-axial free-field sensors placed 13 m away to the east from the abutment of Gaglardi Way Underpass and the sensors recording temperature and humidity conditions, were not included. Moreover, the columns were excluded for both bridges since there were no sensors installed on them to record vibration data, except for one. Including them had no effect on modal properties and mode shapes of the test model neither was it useful in determining the participation of columns or substructure in each mode.  Additionally, the elevation difference of around 50 cm between abutments, i.e. the slope of the bridge, was neglected to attain a good correlation for finite element model updating. The primary reason was that the elevation was only known at abutments and the pier, whereas, the shape function for slope and/or the elevations at mid-span compared to abutment or pier were not known. N 39  5. Experimental and Analytical Results This section demonstrates the modal properties obtained from analytical and experimental models using finite element analysis and operational modal analysis, respectively. A total of 30 minutes of experimental test data was acquired from permanent sensors installed on the bridges that records the ambient vibrations in structure under operating conditions. Among the estimation methods available, Enhanced Frequency Domain Decomposition (EFDD) technique was employed to extract the modal properties of structure since it allows the modes to be manually selected and/or discarded based on engineering judgements. Furthermore, EFDD method also determines the damping in each mode, which is not required for this project but can be used in future study. This was followed by modal analysis of finite element model where 12 mode shapes and frequencies were produced. To generate these modes the dead load of structure was included with target modal participating mass ratio set to 99%. The results of this analysis can be found in the sections and subsections of this chapter. 5.1. Gaglardi Way Underpass The following subsections exhibit the reporting stage of ARTeMIS and the post-processor outcome from CSI Bridge for the two types of analysis carried out on Gaglardi Way Underpass. 5.1.1. Operational Modal Analysis The vibration data acquired from sensors installed on Gaglardi Way Underpass, shown in figures B.1 to B.4 of ‘Appendix B’, was converted from time series to frequency domain using Fourier transformation. Spectral density matrices were estimated, the singular value decomposition of which generated a graph with dominating peaks. The acquired data from recorders was sampled at 200 Hz frequency or 0.005 s interval. To shape the signal in frequency domain the raw data was processed using program default filter type that is 8th order low-pass filter which is a reasonable order to start from. Figure 5.1 shows the graph for singular values of spectral densities generated by program and 40  shown in table 5.1 are the seven best modal frequencies extracted from the power spectral density matrix. Additionally, figure 5.2 shows the mode shapes obtained for these frequencies. Since the sensors are installed at north deck only, the nodes at mid-span nodes of south deck were locally slaved to the corresponding nodes on north deck based on observation of updated FE model. This has further been discussed in the next chapter. On the left are originally obtained mode shapes, while, on the right are mode shapes with slaved nodes.  Figure 5.1: Singular Values of Spectral Densities Matrix for Gaglardi Way Underpass   41  Table 5.1: Modal frequencies for Gaglardi Way Underpass from Operational Modal Analysis Mode Frequency (Hz) Damping (%) Description 1 5.75 4.30 1st Vertical 2 6.72 1.32 1st Torsion 3 7.23 1.86 Longitudinal 4 9.04 0.93 2nd Vertical 5 11.21 0.92 2nd Torsion 6 13.72 0.66 3rd Vertical 7 15.95 0.77 3rd Torsion 42   Figure 5.2: OMA mode shapes for Gaglardi Way Underpass. 43  5.1.2. Finite Element Analysis Table 5.2 shows the modal information for a full-scale FE model of Gaglardi Way Underpass generated based on structural details highlighted in section 3.1, whereas, figure 5.3 illustrates the mode shapes obtained for each of these modes. Table 5.2: Modal properties of Gaglardi Way Underpass original FE model Mode Period (s) Frequency (Hz) Modal Participation Mass (%) Description Sum UX Sum UY Sum UZ 1 0.21 4.75 51.95 37.63 0.06 Substructure 1st Longitudinal 2 0.18 5.71 80.16 95.45 0.23 Substructure Transverse 3 0.15 6.77 86.31 95.99 6.43 Substructure 1st Torsion 4 0.14 6.94 93.66 96.75 6.91 Deck 1st Vertical 5 0.14 7.03 94.55 97.04 6.96 Deck 1st Torsion 6 0.12 8.12 94.87 97.04 33.30 Deck 2nd Vertical 7 0.12 8.18 94.92 97.08 39.13 Deck 2nd Torsion 8 0.12 8.24 94.93 97.09 48.35 Deck 3rd Vertical 9 0.11 9.16 94.94 97.09 49.82 Deck 4th Vertical 10 0.06 17.80 98.24 97.17 49.84 Substructure 2nd Longitudinal & Deck 5th Vertical 11 0.08 13.12 98.24 99.16 49.84 Substructure 2nd Torsion 12 0.03 30.42 98.24 99.16 86.83 Deck 6th Vertical 44   Figure 5.3: Gaglardi Way Underpass preliminary FE mode shapes 45  Observing the modal participation mass ratios, it is implied that in the longitudinal and transverse direction the first two modes are most significant with highest mass contribution. In the vertical direction, the mass contribution is low for most modes. The sixth and twelfth modes have the highest contribution, which are superstructure modes in vertical direction. 5.2. Kensington Avenue Underpass This section presents the results from the experimental and analytical modal analysis carried out for Kensington Avenue Underpass. 5.2.1. Operational Modal Analysis The protocol followed to extract the experimental modal results for this bridge was exactly similar. The Kensington Avenue Underpass comparatively had sensors installed on both spans that did not need slave node equations to be introduced. Figure 5.4 shows the matrix for singular values of spectral densities generated from the vibration data for Kensington Avenue Underpass. The vibration data in time series from sensors can be found in figures B.5 to B.9 of ‘Appendix B’. Expanding on this, table 5.2 shows the five modal frequencies deduced from this graph using simple peak-picking method. The results obtained for this bridge were quite limited since the recorded spectral density matrix had many local modes captured, which is why a huge stretch can be observed in the frequencies for mode four and five. The subsequent chapters will demonstrate the decisions based on engineering knowledge and the changes made to rule out any possible errors triggered by this huge interval. Additionally figure 5.5 shows the mode shapes corresponding to the frequencies recorded in table 5.2. 46   Figure 5.4: Singular Values of Spectral Densities Matrix for Kensington Avenue Underpass Table 5.3: Modal frequencies for Kensington Avenue Underpass from Operational Modal Analysis Mode Frequency (Hz) Damping (%) Description 1 5.23 1.30 1st Torsion 2 6.17 1.35 1st Vertical 3 7.24 1.17 2nd Torsion 4 8.89 0.51 2nd Vertical 5 13.01 0.59 3rd Vertical  47   Figure 5.5: OMA mode shapes for Kensington Avenue Underpass 5.2.2. Finite Element Analysis Table 5.4 shows the modal information obtained from analytical analysis of a full-scale FE model produced for Kensington Avenue Underpass, based on information in section 3.2. Figure 5.6 portrays the mode shapes obtained for each mode number and corresponding frequency.  48  Table 5.4: Modal properties of Kensington Avenue Underpass original FE model Mode Period (s) Frequency (Hz) Modal Participation Mass (%) Description Sum UX Sum UY Sum UZ 1 0.19 5.28 0.02 2.84 12.22 Deck 1st Vertical 2 0.18 5.49 0.02 4.74 15.62 Deck 1st Torsion 3 0.16 6.10 0.03 13.88 16.39 Deck 2nd Vertical 4 0.16 6.39 0.30 62.87 16.99 Deck 3rd Vertical 5 0.14 7.10 0.31 62.92 17.02 Deck 4th Vertical 6 0.13 7.45 0.34 63.12 23.76 Deck 5th Vertical 7 0.12 8.23 0.46 64.12 36.20 Deck 6th Vertical 8 0.12 8.65 0.47 64.26 38.28 Deck 7th Vertical 9 0.11 8.70 0.65 64.69 49.11 Deck 8th Vertical 10 0.08 12.57 80.17 64.73 49.15 Substructure Longitudinal 11 0.08 12.34 80.17 82.50 49.27 Substructure Torsion 12 0.05 22.04 80.17 82.50 73.39 Deck 9th Vertical  The tenth mode has 80% contribution in the longitudinal direction, whereas the first nine and last two modes have almost no contribution in this direction. In the transverse direction, first three modes have a low contribution, fourth and eleventh modes have a high contribution and all other modes have a close to zero contribution. Majority of the modes contribute vertically. 49   Figure 5.6: Kensington Avenue Underpass preliminary FE mode shapes 50  6. Finite Element Model Updating A software, called FEMtools, developed by Dynamic Design Solutions was used to update and optimise the finite element models generated in ‘Chapter 4’. It offers a complete solution to verify and validate the FE models, update the structural properties, and to solve general or structural design optimisation problems. The final outcome of updating and optimisation procedure is a finite element model that is realistic in a best possible manner. This is achieved by assigning the modal results from operational modal analysis as a target that the finite element model has to match. The program then attempts to alter the defined structural properties of FE model in an iterative manner, validates with the experimental data already fed in, and delivers an updated model with its frequencies and mode shapes matching those from the experimental analysis. The model updating procedure is carried out in several steps. After importing the FE and OMA models, the first step is a correlation analysis that makes sure the node-points and degrees of freedom are paired correctly. It additionally pairs the modes for the analytical and test model to compare the non-updated frequencies and generates a MAC matrix defining how good the match is. The next step is a sensitivity analysis to determine the structural parameters that the structure is most sensitive to. The purpose of this step is to have least number of parameters to keep the number of iterations as low as possible. The next and final step is to update the FE model by modifying a set of defined parameters for selected responses until a best possible match is achieved. This chapter encompasses the results accomplished for the bridges being studied, compares them to their respective non-updated counterparts, and highlights the issues faced and decisions made based on engineering knowledge. 51  6.1. Gaglardi Way Underpass This section features the outcomes from finite element model updating of Gaglardi Way Underpass. Figure 6.1 shows the correlation, i.e. node-point pairing, for the experimental model (red) from Operation Modal Analysis plotted on top of analytical model from Finite Element Analysis (blue).  Figure 6.1: Correlation for Gaglardi Way Underpass models To calibrate the finite element model, it was decided to use the first four frequency responses, rather than all seven, to match the experimental modal data. This judgement was backed up by the modal participation mass ratios in table 5.2 suggesting most of the structural mass participates in modes one to four. As a first step towards finite element model updating, a sensitivity analysis was carried out to determine the parameters that would have greatest impact on the modal frequencies of finite element model. For this, only frequency responses were selected, whereas, the MAC and mode shape responses were neglected at this stage since the vibration testing in this project was not dense enough, making the data very limited to achieve reasonable MAC values and to match the mode shapes 52  of preliminary finite element model. However, these responses were still as used as a means of comparing the updated FE model to the test model. Table D.1 in ‘Appendix D’ shows the 7 parameters finalised for updating process. These parameters were selected based on sensitivity analysis results, shown in figure 6.2, with allowable scatter of 20%. A threshold value of 0.01 was chosen, i.e. any parameter with a value less than this was discarded. The x-axis of the sensitivity matrix represents the parameter no in table D.1, whereas, the y-axis represents the mode number (frequency responses) in table 5.1 from OMA.  Figure 6.2: Sensitivity analysis matrix for Gaglardi Way Underpass Levtchitch et al. (2004) states that the modulus of elasticity of concrete increases with age at a rate higher than the rate of increase concrete compressive strength. Even in cases where concrete compressive strength does not increase as it ages, the elasticity always increases. Based on this argument concrete mass density and modulus of elasticity section properties were modified to calibrate the preliminary finite elements model. Deciphering the matrix, both positive and negative results can be observed with positive standing for an increase in frequency response with an increase in respective parameter and vice versa. The bars identify what response is sensitive to which parameter. For 53  example, all four modes are sensitive to parameter two, whereas, parameter four will have greatest effect on frequencies of modes one to four. Moreover, it is implied parameter one will have least impact on the modal frequency of any mode. Once the parameters were finalised, the FE model was ready to be calibrated. Automated model updating was used with program default correlation coefficient of CCABS that is the ‘average value of weighted absolute relative differences between predicted and reference resonance frequencies’. Convergence control variables Eps1 and Eps2 were set to 0.01 and 0.001, respectively. The former is the value of correlation coefficient that must be obtained to stop iterations, whereas, the latter specifies a value that with each iteration is compared against the difference of two consecutive values of the selected correlation coefficient. The program updates the FE model in an iterative manner where the software modifies the parameter, runs modal analysis, compares to the experimental model, and stops if targets are achieved otherwise repeats the cycle with a new value.  Table 6.1 shows the pre-updating and post-updating modal information for the finite element model in comparison to the experimental modal data. The goal to acquire frequencies within 10% was accomplished. Figure 6.3, additionally, is a mode pair graph that should ideally be a diagonal plot which was closely attained. To achieve these outcomes, the elasticity of concrete was increased by a maximum of 20%, whereas, the mass density of concrete was reduced up to 17%. Parameters before and after finite element model updating can also be found in table D.1 of ‘Appendix D’.   54  Table 6.1: Modal information before and after FE model updating for Gaglardi Way Underpass Pre-Updating Information Pair # FEA Mode FEA Frequency (Hz) OMA Mode OMA Frequency (Hz) Δ Frequency (%) MAC (%) 1 1 4.75 1 5.75 -17.35 1.5 2 2 5.71 2 6.72 -15.11 0.1 3 3 6.77 3 7.23 -6.40 16.7 4 4 6.94 4 9.04 -23.24 42.3 Post-Updating Information Pair # FEA Mode FEA Frequency (Hz) OMA Mode OMA Frequency (Hz) Δ Frequency (%) MAC (%) 1 1 5.58 1 5.75 -2.87 2.7 2 2 6.72 2 6.72 -0.05 0.1 3 3 7.91 3 7.23 9.33 4.4 4 4 8.13 4 9.04 -9.98 65.2   Figure 6.3: Mode pair graph for Gaglardi Way Underpass 55  To refine the MAC matrix and better see the mode shapes, the south span was slaved to the corresponding north span. The slave node equations generated were based on the observation of updated finite element model that suggested the shape of non-instrumented span, either in same direction or opposite. Figures 6.4 and 6.5 shows the MAC matrix and the mode shape pairing, respectively, for updated FE model against the experimental model with slaved south span.  Figure 6.4: Modal Assurance Criterion (MAC) for Gaglardi Way Underpass 56   Figure 6.5: Updated mode shapes correlation for Gaglardi Way Underpass It can be observed from table 6.1 that the MAC values for first three modes are very low compared to mode four, which figure 6.5 substantiates. As seen, longitudinal, transverse and torsion modes are involved in the substructure, while the experimental model could only read the modes in the superstructure. Possible reason deduced for this was the absence of sensors on columns to record the vibration data for these major displacement. However, from available sensors the inconsiderable deck movements could be recorded in these modes only since each mode is a combination of three axes (x, y, and z) or degrees of freedom. Other possible reasons for attaining low MACs have been stated in subsection 2.4.3. The subsequent modes, although not used for calibration, can be observed in figure 6.4 to have reasonable MAC values since they are superstructure modes, vertical or torsional, that the sensors installed on deck could easily record. Modes five and six, for example, have a MAC value of 84.9% and 93.5%, therefore, leading to higher confidence in the finite element model. 57  For the parameter values before and after FE model updating, refer to figure D.1 of ‘Appendix D’. Moreover, the modal information and mode shapes for the updated FE model can be found in table E.1 and figure E.1, respectively, of ‘Appendix E’. Compared to the preliminary FE model the mode shapes did not change and the difference in modal mass participation ratios remained small. 6.2. Kensington Avenue Underpass Same steps were followed to update the Kensington Avenue Underpass but with difference in vibration testing setup that did not require any slave node equations and entailed unique issues. Figure 6.6 shows the correlation of analytical and test models after importing them into FEMtools for calibration and plotting them together.  Figure 6.6: Correlation for Kensington Avenue Underpass models A similar process was carried out to choose the parameters for updating, using sensitivity analysis. Table D.2 in ‘Appendix D’ shows the set of 5 mass density and modulus of elasticity parameters defined for which figure 6.7 shows the sensitivity analysis matrix against four frequency responses from OMA in table 5.3. 58   Figure 6.7: Sensitivity analysis matrix for Kensington Avenue Underpass The next step to update the preliminary FE model for this bridge was the most complicated one, having issues that required diligent judgements. A spike in frequency was noticed in subsection 5.2.1 due to local modes in between. The original idea was to sequentially pair the first four modes and determine a fifth pair, using trial and error method, that gives a best mode shape match or MAC value assuming that although the experimental model could not capture any modes between 8.888 Hz and 13.013 Hz, the FE model is expected to have a few modes in between. However, due to technical errors with software, similar to those in the previous section, only first three modes could converge within 10%. Attempting to calibrate higher modes resulted in initial modes being out of acceptable range, therefore, they were discarded and only first three modes were retained.  Levtchitch et al. (2004) argues that 30% increase in modulus of elasticity over 30 years period is a safe assumption. Based on this argument, the Kensington Avenue Underpass is approximately 7-8 years old bridge for which up to 10% increase in elasticity is quite reasonable. Additionally, the mass density of deck and girder concrete material was reduced by 8% to converge FE model frequencies. Modified parameters can be found in table D.2 of ‘Appendix D’. Table 6.2 below shows 59  the comparison of frequencies and MAC values for each mode before and after finite element model updating. Table 6.2: Modal information before and after FE model updating for Kensington Avenue Underpass Pre-Updating Information Pair # FEA Mode FEA Frequency (Hz) OMA Mode OMA Frequency (Hz) Δ Frequency (%) MAC (%) 1 1 5.28 1 5.23 1.01 19.9 2 2 5.49 2 6.17 -11.02 1.9 3 3 6.10 3 7.24 -15.76 2.4 Post-Updating Information Pair # FEA Mode FEA Frequency (Hz) OMA Mode OMA Frequency (Hz) Δ Frequency (%) MAC (%) 1 1 5.69 1 5.23 8.80 19.2 2 2 5.91 2 6.17 -4.23 1.6 3 3 6.55 3 7.24 -9.49 2.4  Likewise, for this bridge a diagonal frequency pair graph was achieved to great extent, shown in figure 6.8, implying a reasonable frequency convergence. Moreover, figure 6.9 shows the MAC correlation matrix for the final updated model, while figure 6.10 collates the modes shapes from the calibrated FE and experimental models. 60   Figure 6.8: Mode pair graph for Kensington Avenue Underpass   Figure 6.9: Modal Assurance Criterion (MAC) for Kensington Avenue Underpass 61   Figure 6.10: Updated mode shapes correlation for Kensington Avenue Underpass Unlike the bridge in the previous section, this bridge did not have mode shapes matched and, therefore, had poor MAC values. To match the mode shapes and attain reasonable MAC values, it is important to calibrate greater number of modes, however, due to technical errors with software, it did not recognise the restricted range of parameter modification and would result in more than double elasticity. Moreover, the limited vibration data with sparsely distributed testing points acted as a hindrance to match the mode shapes. Eventually, only three modes could be converged within 10% acceptable range and were accepted keeping in view the limitations. To match mode shapes and attain 62  higher MACs it is important to carry out a denser vibration testing including columns, therefore, they were not used as an acceptance criteria but to study how well a model can be calibrated based on limited vibration data and using the assumptions stated. The updated finite element model was used to compare the analysis results in next chapter against the Gaglardi Way Underpass, a rather higher confidence model. This will provide a means of comparison to study the degree to which these limitations and mismatched mode shapes affects the structural responses after calibrating the finite element model. Parameters before and after updating the FE model have been listed in table D.2 of ‘Appendix D’. Additionally, the modal frequencies for updated finite element model are given in table E.2 along with mode shapes in figure E.2 of ‘Appendix E’. The modal participations mass ratios were not much different for the updated FE model compared to the preliminary FE model. The only major difference observed was in the fifth mode where calibrated model switched from vertical to deck torsion. The preliminary finite element models generated for two bridges are assumed to represent the physical structures when newly constructed, whereas, the calibrated FE models are presumed to the depict the behaviour of bridges today, 7 to 8 years later, taking into account the increase in elasticity over time. This assumption is supported by Levtchitch et al. (2004) in a conference paper, arguing that the elasticity of concrete increases with age, irrespective of any change in strength. Another study that derives from this study and outcomes in next chapter is to carry out a denser ambient vibration testing, including columns, and compare how well these model converge, how well the mode shapes can be matched, and how the MACs compare. Seismic analysis can then carried out to study how this approach to finite element model updating affects the structural responses. This will help conclude how good is the practice to update a finite element model using limited number of measurements and should this technique be employed in case where availability of resource is a problem or due to time constraints. 63  7. Seismic Analysis This chapter studies the importance of calibrating a finite element model by comparing the preliminary FE model to the updated finite element model. This was done by carrying out a linear modal time history analysis. Three unscaled earthquake ground motions with low, medium range, and a very high PGA were chosen in addition to an ambient level ground motion from the PEER Ground Motion Database developed by the University of California, Berkeley. The ambient level is defined as anything close to zero percent, between 5-20% would be considered as low range, medium would be anything between 20% and 40%, whereas, high range is considered from 40-60%. Anything over that has been considered as very high. Table 7.1 below provides an overview of the earthquake events selected. These ground motions were applied in their respective longitudinal, transverse, and vertical directions for which the spectra have been provided as an ‘Appendix F’ in addition to the Square Root of Sum of Squares (SRSS) spectrum, which is a combination method of two horizontal and a vertical component of the ground motion. Table F.1 to F.3, additionally, in ‘Appendix F’ shows the peak spectral accelerations (PSa) for first mode natural frequency of each bridge. The ground motions for each earthquake event have also been provided in figures F.5 to F.8 in ‘Appendix F’. Table 7.1: Ground motions selected for seismic analysis Name of Event Year Station Magnitude PGA (g) H1 H2 V Imperial Valley 1938 El Centro Array #9 5.0 0.014 0.02 0.014 Trinidad 1980 Rio Dell Overpass - FF 7.2 0.069 0.146 0.027 Kobe 1995 Kakogawa 6.9 0.254 0.339 0.15 Tabas 1978 Tabas 7.35 0.825 0.928 0.698  64  The sections in this chapter provide an insight into the outcomes from this analysis for each bridge. It mainly highlights the differences in base reactions, constituting base shears and moment reactions in directions X, Y and Z, and the mid-span displacements relative to the ground, comprised of deflections and rotations in and about each of the three axes, obtained from the preliminary and updated finite element models. The base reactions are maximum expected lateral and moment forces in response to seismic ground motion at the base of structure and are important since it provides support to the whole structure. Moreover, a dynamic and especially cyclic load can have an effect that is much significant compared to static load of similar magnitude due to the inability of structure to immediately respond to the loading by deflecting or rotating. An estimate of structural displacements is important to determine since higher than allowable value can crack the concrete leading to catastrophic collapse. This chapter only features the differences in absolute maximum responses, whereas, the tables in ‘Appendix G’ includes all the values obtained. These disparities would help conclude the value of finite element modal updating and whether should it be mandatory for finite element analysis, where possible, or can it be overlooked assuming the original model to be sufficient and on safe side. 7.1. Gaglardi Way Underpass This section studies the Gaglardi Way Underpass by conducting a linear modal time history analysis. Table 7.2 shows the difference in base reactions for updated model as a percentage of the original values from non-updated model, for four earthquake ground motions of different intensities. Presented here are only the disparities in the absolute maximum values, whereas, table G.1 of ‘Appendix G’ exhibits both maximum and minimum values with respective percentage change for base reactions. This may result in a slight variation of percentages in cases where the maximum of one model is compared to the absolute minimum of another model, but should not affect the conclusion since the primary objective is to compare the absolute maximum values, irrespective of their direction. 65  Table 7.2: Percentage change in maximum base reactions of Gaglardi Way Underpass updated FE model  FX (%) FY (%) FZ (%) MX (%) MY (%) MZ (%) Imperial Valley -17 17 -6 9 -31 13 Trinidad -19 -8 -13 -3 -18 -9 Kobe 9 -18 -17 -7 -4 -18 Tabas -32 -17 -41 -18 -20 -10  As observed in table 7.2, most of the base reactions reduce after updating the finite element model for Gaglardi Way Underpass, with few exceptions where an increase in response has been observed. Generally, the percentage change varies between -41% (decrease) and 17% (increase). The base shear in the longitudinal direction for Imperial Valley, for example, was 495 kN that reduced to 412 kN after updating the FE model. Small reductions, as low as -3%, were also noted, but since the difference for majority of the responses is over 10%, therefore, it is implied that updating the model has a great effect on base reactions. Table 7.3 below shows the difference in the mid-span structural displacements for an updated model against the original model. Two nodes at the centreline, i.e. the layout line, of the bridge were selected. Each of these nodes represented the mid-span of north and south deck. Tables G.2 and G.3 of ‘Appendix G’ shows both maximum and minimum values along with their respective percentage change for relative displacement of these nodes.    66  Table 7.3: Change in maximum structural displacements for Gaglardi Way Underpass updated FE model  UX (%) UY (%) UZ (%) RX (%) RY (%) RZ (%)  North South North South North South North South North South North South Imperial Valley -31 -31 -6 -3 -27 -41 -41 -21 -25 -27 -30 -23 Trinidad -34 -34 -23 -23 -25 -31 -31 -32 -28 -30 -31 -24 Kobe -8 -8 -27 -26 11 5 -18 -19 -14 -10 -38 -45 Tabas -30 -30 -26 -24 -46 -30 -8 -19 -10 -8 -29 -42  As seen in the table above, updating the FE model has a significant impact on the displacement responses of the finite element model, with an average reduction of around 25%. No increase was observed in displacements other than 11% and 5% change in vertical displacement in response to Kobe ground motion. The minimum and maximum percentage reductions observed were -3% and -46%, respectively. The vertical mid-span displacement of north span, for example, reduced to 7.54 mm from 13.9 mm, with Tabas ground motion. The possible reason for these differences could be the modification of section properties during finite element model updating process that alters the properties like the elasticity of elements and, thus, the responses. Therefore, having a high confidence calibrated model is important for this bridge to rule out any possible uncertainties. 7.2. Kensington Avenue Underpass The seismic analysis conducted in previous section was repeated using same ground motions but using a different bridge structure that was updated according to incomparable testing data and with unique issues and assumptions. This section exhibits the results from linear modal time history analysis of Kensington Avenue Underpass and compares the conclusions deduced for this bridge to those from the previous section. 67  Table 7.4 shows the disparities in the absolute maximum values of base reactions, i.e. base shears and moment reactions, for updated model as a percentage of the non-updated model. Table G.4 in ‘Appendix G’ additionally shows in detail the maximum and minimum base reactions for both original and updated models along with their respective differences. Table 7.4: Percentage change in maximum base reactions of Kensington Avenue Underpass updated FE model  FX (%) FY (%) FZ (%) MX (%) MY (%) MZ (%) Imperial Valley -21 -4 -15 10 -4 21 Trinidad -16 -9 -17 10 -16 -10 Kobe 2 -16 -6 -17 0 -17 Tabas -23 5 -9 -4 2 6  No trend could be observed for the differences with increasing PGA, although Tabas exhibited exceptionally low discrepancies. The differences in base reactions generally range between -23% and 21%, with most of the responses demonstrating a reduction in base reactions after updating the finite element model for Kensington Avenue Underpass. Looking at the responses from Kobe ground motion, for example, the base moment about x-axis reduced by 17% with finite element model updating, from 26.5 MN.m to 22.1 MN.m. Possible reason deduced for low differences could be the nature of Tabas spectrum. Comparing the peak spectral accelerations for the first mode natural frequencies of Kensington Avenue Underpass against Gaglardi Way Underpass in table F.4 of ‘Appendix F, the differences between updated model and the original model are very small. Additionally, the modal participation mass ratios are comparatively a lot lower for the initial modes of Kensington Avenue Underpass, suggesting a small contribution. Overall, majority of the responses demonstrated differences greater than 10%, therefore, a similar conclusion is implied based on an assessment of base reactions that model updating impacts the analysis outcomes. 68  Table 7.5 shows the differences in the mid-span relative displacements of south span (A0 to P1) and the north span (P1 to A2) for updated FE model as a percentage of the displacements from original non-updated model. Only the discrepancies in absolute maximum values are displayed here, whereas, tables G.5 and G.6 in ‘Appendix G, shows both maximum and minimum values with their respective percentage change for both original and updated FE models. Table 7.5: Change in maximum structural displacements for Kensington Avenue Underpass updated FE model  UX (%) UY (%) UZ (%) RX (%) RY (%) RZ (%)  South North South North South North South North South North South North Imperial Valley -18 -26 -6 11 6 28 -22 7 -2 -7 0 -2 Trinidad -8 -23 -16 -16 -26 -21 -33 -9 -16 -23 -13 -18 Kobe -12 -6 -19 -21 -33 -16 -41 -31 -30 -23 -20 -24 Tabas -19 -26 -10 1 -33 -3 -44 2 -27 -23 -7 -9  As observed, the disparity in absolute maximum values for displacements did not seem to be significant for some responses, especially rotations, with Imperial Valley ground motion. This appears to be due to a very low PGA. Overall, the differences in displacements and rotations in and about three different axes indicate towards the non-updated FE model being uncertain since there are a handful of high values, up to 44% lower than the original responses. Majority of the responses reduced with calibration of finite element model, however, increase in structural displacements was also observed for some responses. The vertical displacement in north span, for example, increased by 28% from 0.21 mm to 0.27 mm with an application of ground motion having ambient level PGA, i.e. Imperial Valley, indicating towards the preliminary finite element model as a high-risk model. Overall, no general trend was observed to identify the responses most sensitive to finite element model updating. However, it was observed that the rotations were very minute, up to 8.85×10-69  4 radians of maximum mid-span rotation about y-axis, for example, that reduced to 8.14×10-4 radians with updating the finite element model generated for Gaglardi Way Underpass. The deflections, in comparison, were higher with a maximum of 29.1 mm in vertical direction, for instance, that reduced to 22.1 mm for the same bridge. This implies that base shears and deflections in three axes are more sensitive compared to base moments and rotations about three axes. A handful of responses from this section and the previous one were observed to be higher than 10%, irrespective of PGA, therefore it is deduced that it is highly important to calibrate the finite element model, where possible. Due to a very high chance of uncertainties in the original model, it effectively delivers a rather high confidence finite element model.   70  8. Summary and Conclusion Finite element modelling is a very vast topic that is mainly used to determine the dynamic behaviour of Civil Engineering structures of any size and complexity for a variety of purposes.  Other than design, one important aspect of this modelling is that it helps engineers determine the health of structure and accordingly propose any required structural changes or retrofitting methods. It is important for the finite element model to be a close representation of the actual structure with least possible assumptions involved. One of the methods that make this possible is updating the finite element model based on the outcomes from Ambient Modal Identification, also known as Operation Modal Analysis, of the existing structure. The objective of the project was to study the importance of finite element model updating, in case if it is neglected how valid the results would be and how it impacts the structural responses, i.e. base shears and displacements, under seismic load. Two bridges, namely the Gaglardi Way Underpass and the Kensington Avenue Underpass locating in Metro Vancouver, were studied to reinforce the conclusions drawn. The Gaglardi Way Underpass is a 56.78 m long and 18.038 m wide concrete bridge comprised of six precast I-Girders. Permanent sensors have been installed on the north span of the bridge that records the vibrations induced in the structure under normal operating conditions. The Kensington Avenue Underpass, on the other hand, is a 61.73 m long concrete bridge with 27.3 m wide deck supported on nine precast I-Girders. For this bridge, the sensors are comparatively installed on both spans. Half an hour data was collected from these sensors and processed to determine the actual modal information for two bridges. What makes this project unique is that the vibration testing carried out was not dense enough, i.e. the sensors were installed just on corners and at mid-span, making the data very limited to match mode shapes and attain close to unity (or 100%) MACs. Determination of 71  whether testing carried out on fewer points, either to save time or due to lack of resources, is sufficient for finite element model updating or a denser ambient vibration testing points would be required is corollary to this research. Two models were generated using software packages, namely, ARTeMIS and CSI Bridge, for experimental and analytical modal analysis, respectively. The former is used to carry out ‘Operational Modal Analysis’ (OMA) on existing structure, whereas, the latter is a theoretical procedure that creates a model with finite discrete elements for ‘Finite Element Analysis’ (FEA). ‘Extended Frequency Domain Decomposition’ (EFDD) method was employed to manually extract the experimental modal frequencies and mode shapes, using simple peak-picking technique. Seven experimental modes were identified for Gaglardi Way Underpass, while only five modes could be recognised for the Kensington Avenue Underpass. The recorded data had many local modes captured that were ignored. From the modal analysis of finite element models, twelve modes were acquired for each bridge having dead load of structure included and target modal mass participation factors set to 99%. Looking at the mode shapes, it was observed that the narrow Gaglardi Way Underpass emulated a beam, whereas, the Kensington Avenue Underpass represented general behaviour of a plate element due to its wide deck. The experimental and analytical frequencies had disparities greater than 10%, therefore, both models required to be calibrated. To update the finite element models, a software called FEMtools was used. Since the program does not support the file format from CSI Bridge, the models were imported to SAP2000 that is another finite element analysis software by CSI. After importing and pairing the experimental and analytical models in FEMtools, a sensitivity analysis was carried out to determine the parameters that are most sensitive to the responses of interest. Based on the total range, a threshold value of 0.01 was chosen. Parameters with sensitivity values equal to or higher than this were retained, while others were discarded. For the responses to match, only frequency was selected since the vibration data was not 72  dense enough to match mode shapes and MAC values for the preliminary FE model. Including the MAC and mode shape responses rather hindered in matching frequencies. Nonetheless, they were used as a means of comparison to verify how well the updated finite element model matches the experimental model. Having concrete modulus of elasticity and mass density parameters finalised, the models were calibrated in an iterative manner. As a result, the convergence target to attain frequencies within 10% was greatly accomplished for first four modes of Gaglardi Way Underpass and three modes of Kensington Avenue Underpass. The MAC values for the first three substructure modes of Gaglardi Way Underpass did not match well due to missing sensors on the columns to record the vibration data and determine their participation in each mode. However, the mid-range MAC value of fourth mode and higher than 80% MACs observed for subsequent modes, although not used in calibration, lead to higher confidence in calibrated finite element model. The Kensington Avenue Underpass, on the other hand, couldn’t be updated as per planned course of action due to technical issues with software. Eventually, first three modes could converge only. In this case very low MAC values were acquired and the mode shapes did not match. The results were retained for this bridge concluding this may possibly be due to limited measurement points and not using mode shape and MAC responses during calibration as it hindered in convergence. The preliminary finite elements models were presumed to be representing freshly constructed bridges, whereas, the calibrated FE models represent structures with an increased modulus of elasticity of concrete, assuming 30% increase in 30 years. Once the finite element models were updated, the final objective to determine the importance and impact of model updating on structural responses of two bridges could be studied. Linear modal time history analysis was carried out using four sets of earthquake ground motions. The first one was a very low ambient level ground motion, whereas, the rest were selected based on the peak ground acceleration (low, medium range, and very high). The horizontal, transverse, and vertical components 73  of each ground motion were applied in their respective directions to both preliminary and updated finite element models. The differences in absolute maximums of resulting base reactions and mid-span structural displacements provided a means of comparison between the preliminary and updated FE models.  As a result, the differences were significantly high for most of the responses, therefore, it was concluded that based on the observation of outcomes from two bridges, incorporating both base reactions and displacements, the chance of the original models being uncertain is very high. Hence, model updating is an important and highly effective method towards attaining a model that represents the actual structure in best possible manner.  As a personal opinion, updating a model based on limited vibration data, as in case of Gaglardi Way Underpass, such that it is reliable enough for carrying different types of analysis appears to be highly possible. However, based on observation of outcomes from Kensington Avenue Underpass, some further investigative study will be required to endorse this reasoning. Furthermore, huge displacements were noticed for earthquake ground motion with higher PGA. After a certain limit the responses enters into the non-linear phase which is important to identify and study how the structure behaves nonlinearly. Therefore, this is a good starting point for non-linear analysis to be carried out on existing calibrated model to further investigate the importance and effectiveness of model updating. 8.1. Future Work Recommendation Although the results achieved were quite reasonable, however, there is still room for an additional study to be carried. Some of the areas that can be investigated have been list hereafter;  An ambient vibration testing should be conducted with denser testing points, e.g. 5 to10 m apart, along the whole length of the bridge. It should include the columns as well to record their participation in each mode. Another study can be carried out to determine how accurately was 74  ambient modal information identified and how well the finite element models were calibrated based on limited measurement points and the validity of this approach. Additionally, the impact of finite element model updating using denser measurement points can also be studied using time-history analysis.  The number of mode pairs used to calibrate the bridges were limited due to technical errors with software, the FE model should be updated using maximum number of modes, with all modes shapes matched and close to unity MACs.  The approach slabs and the backfill wall can be incorporated into the existing FE models, taking their interaction into consideration.  The soil conditions were not known in this study, drilled pile shafts that serve as a foundation if incorporated with link elements representing the change in stiffness, i.e. pile bending, with increasing depth, and having the soil conditions determined can help validate the assumptions in this study and conclude whether such assumptions are safe to make in similar future studies.  The finite element models should be updated by modifying the parameters for local elements rather than globally in case if it results in better convergence.   75  References ACI Committee 318. (2008). Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary. Farmington Hills, MI: American Concrete Institute. BCSIMS. (n.d.). Gaglardi Way Underpass Vibration Test Report.  BCSIMS. (n.d.). Preliminary Results of the Ambient Vibration Test for the bridges on the BCSIMS network.  Brincker, R., & Andersen, P. (2006). Understanding Stochastic Subspace Identification. 24th The International Modal Analysis Conference. St. Louis, Missouri: Society for Experimental Mechanics. Brincker, R., & Ventura, C. E. (2015). Introduction to Operational Modal Analysis. Chichester: John Wiley & Sons, Ltd. Brincker, R., Zhang, L., & Andersen, P. (2001). Modal Identification of Output-Only Systems Using Frequency Domain Decomposition. Smart Materials and Structures, 441–445. Canadian Standards Association. (2014). Design of Concrete Structures (A23.3-14). Toronto: CSA Group. Computers and Structures Inc. (2017). Structural Bridge Design Software | CSI Bridge. Retrieved July 7th, 2017, from Structural and Earthquake Engineering Software: https://www.csiamerica.com/products/csibridge Computers and Structures Inc. (2017). Structural Software for Analysis And Design | SAP2000. Retrieved July 7th, 2017, from Structural and Earthquake Engineering Software: https://www.csiamerica.com/products/sap2000 76  Dynamic Design Solutions. (2017). FEMtools. Retrieved July 7th, 2017, from FEMtools: https://www.femtools.com/ Friswell, M. I., & Mottershead, J. E. (1996). Solid Mechanics and Its Applications: Finite Element Model Updating in Structural Dynamics (Vol. 38). (G. GLADWELL, Ed.) Dordrecht: Springer-Science+Business Media. Kaya, Y., Ventura, C. E., Huffman, S., & Turek, M. (2017, May 10). British Columbia Smart Infrastructure Monitoring System. Canadian Journal of Civil Engineering, 44, 579-588. Levtchitch, V., Kvasha, V., Boussalis, H., Chassiakos, A., & Kosmatopoulos, E. (2004). Seismic Performance Capacities of Old Concrete. 13th World Conference on Earthquake Engineering. Vancouver, BC. Marwala, T. (2010). Finite Element Model Updating Using Computational Intelligence Techniques: Applications to Structural Dynamics. Springer London. Mottershead, J. E., & Friswell, M. I. (1993, October 22). Model Updating In Structural Dynamics: A Survey. Journal of Sound and Vibration, 167(2), 347-375. Mottershead, J. E., Link, M., & Friswell, M. I. (2010, October 31). The Sensitivity Method In Finite Element Model Updating: A Tutorial. Mechanical Systems and Signal Processing, 25(7), 2275–2296. Pastor, M., Binda, M., & Harcarik, T. (2012). Modal Assurance Criterion. Procedia Engineering, 48, 543-548. Peeters, B., & Roeck, G. D. (2000, February). Reference Based Stochastic Subspace Identification in Civil Engineering. Inverse Problems in Engineering, 8(1), 47-74. Pidaparti, R. M. (2017). Engineering Finite Element Analysis. Morgan & Claypool Publishers. 77  Structural Vibration Solutions A/S. (2017). Operational Modal Analysis Software Provider. Retrieved July 7th, 2017, from ARTeMIS Modal: http://www.svibs.com/products/ARTeMIS_Modal.aspx Wan, H. P., & Ren, W. X. (2015, June). Parameter Selection in Finite-Element-Model Updating by Global Sensitivity Analysis Using Gaussian Process Metamodel. Journal of Structural Engineering, 141(6).  78  Appendices Appendix A: Drawings  Figure A.1: General layout for Gaglardi Way Underpass 79      Figure A.2: Gaglardi Way Underpass elevation      N 80   Figure A.3: Gaglardi Way Underpass deck cross-section 81   Figure A.4: Gaglardi Way Underpass column and pipe pile 82     Figure A.5: Gaglardi Way Underpass abutments 83   Figure A.6: Gaglardi Way Underpass pier 84   Figure A.7: I-Girder 85       Figure A.8: Gaglardi Underpass girder layout 86   Figure A.9: Gaglardi Way Underpass plate bearing at abutments 87     Figure A.10: Gaglardi Way Underpass neoprene pad bearing at pier 88    Figure A.11: PL-2 (Tall) parapet 89   Figure A.12: General layout for Kensington Avenue Underpass 90         Figure A.13: Kensington Avenue Underpass elevation   N 91       Figure A.14: Kensington Avenue Underpass deck cross-section 92   Figure A.15: Kensington Avenue Underpass pier column and shaft 93   Figure A.16: Kensington Avenue Underpass abutment A2 column and shaft 94      Figure A.17: Kensington Avenue Underpass south abutment 95       Figure A.18: Kensington Avenue Underpass north abutment 96   Figure A.19: Kensington Avenue Underpass pier 97        Figure A.20: Kensington Avenue Underpass girder layout 98    Figure A.21: Kensington Avenue Underpass bearing at south abutment (A0) 99    Figure A.22: Kensington Avenue Underpass bearing at north abutment (A2) 100      Figure A.23: Kensington Avenue Underpass fabreeka pad bearing at pier   101  Appendix B: Ambient Vibration Data  Figure B.1: Gaglardi Way Underpass channels 370 to 373 102   Figure B.2: Gaglardi Way Underpass channels 374-377 103   Figure B.3: Gaglardi Way Underpass channels 378-381 104        Figure B.4: Gaglardi Way Underpass channels 382-383 105   Figure B.5: Kensington Avenue Underpass channels 343-346 106   Figure B.6: Kensington Avenue Underpass channels 343-350 107   Figure B.7: Kensington Avenue Underpass channels 351-354 108   Figure B.8: Kensington Avenue Underpass channels 355-358 109     Figure B.9: Kensington Avenue Underpass channels 359-360 110  Appendix C: Modelling Detail Finite Element Models The finite element modelling process has only been explained for the Gaglardi Way Underpass. Similar steps and assumptions were followed for the Kensington Avenue Underpass, with respective dimensions from subsection 3.2.1. To generate a finite element model in CSI Bridge the following steps are required; 1. Define the bridge layout line. 2. Define the basic properties. 3. Define bridge specific properties. 4. Define the bridge object and make all of its associated assignments. 5. Create an object-based model from the bridge object definition. 6. Define analysis items and parameters including load cases and desired output items. The steps outlined above are explained below to demonstrate how the models were generated including any assumptions involved and/or any decisions made. 1. Layout The first step in creating a bridge object is to define the layout line that are reference lines used for defining the horizontal and vertical alignment of the bridge. They were defined using stations for distance, bearings for horizontal alignment and grades for vertical alignment. Layout lines may be straight, bent or curved both horizontally and vertically. Figure C.1 shows the data form used to define a straight layout line using stations information provided in drawings in ‘Appendix A’. 111   Figure C.1: Layout for Gaglardi Way Underpass 2. Properties This step defines the material properties of the structure and the frame sections. These can be defined when they are needed or can be predefined. The CSI Bridge has a vast range of materials to select from in the library, or they can also be manually defined using calculated parameters. Material properties are used in frame section property definitions and in deck section property definitions in the next step. Similarly, the frame section properties are also used in some of the property definitions included in step 3, such as, the cap beam, columns, girder sections, etc. To define the material properties, the concrete strength values from table 3.1 were used. The modulus of elasticity (E) was calculated using the elasticity formula, from American Concrete Institute, incorporating the weight of concrete and the compressive strength. All other properties were standard concrete values or calculated automatically by the program using equations fed-in. For 112  example, figure C.2 shows the data form used to define bent cap material. All materials in table 3.1 were defined in a similar manner using their respective compressive strengths and modulus of elasticity.  Figure C.2: Material properties data form 113  Additionally, to define steel properties, similar form was used but with material type selected as steel program default weight per unit volume for steel. The modulus of elasticity, maximum yield and tensile stresses, and the effective stresses were used from table 3.2 in third chapter. Four frame sections were defined for this bridge: the bent cap for abutments and the pier, columns, and a girder. The bent caps are rectangular sections, a circular section has been used for columns, and a precast concrete I (Bulb Tee) girder. The software requires dimensions of these sections as an input, which were used from chapter 3 and the drawing in ‘Appendix A’. Figure C.3 to C.5 shows the data forms for defining bent cap section, column, and girder.  Figure C.3: Define bent cap section 114   Figure C.4: Define column section The column section is comprised of 18 reinforcement bars of size 30M with a cover clearance of 70 mm and confinement bars of size 15M. These specifications were included for columns in the ‘Concrete Reinforcement’ information. Standard reinforcement settings were used for other concrete frame sections since the scope of work did not include fibre analysis that takes into account the elasticity of the reinforcement. 115   Figure C.5: Define girder section 3. Bridge Component Properties The bridge component properties and specifications are used to define the superstructure and the substructure of the bridge. The former includes the deck and the diaphragm, whereas, the latter included components like bearing, abutments, and bents. To define the deck, various parametric deck sections are available to select from. They include concrete box girder, concrete flat slab, precast concrete girder and steel girder deck sections. Using a 116  precast concrete I-girder section, the deck was defined according to dimensions in chapter 3 and specifications from drawings in ‘Appendix A’, with a standard haunch thickness of 75 mm. Figure C.6 shows the data table for defining the deck.  Figure C.6: Define deck section 117  Moreover, a diaphragm section was defined for abutments and at the pier that resists lateral forces and transfers load to the supports. The details required to define the diaphragm were not provided in the drawings, therefore, program default thickness of 300 mm was used. In the superstructure properties, the bearing properties specify data for bridge bearings. They are used in abutment and bent assignments to the bridge object in step 4. At abutments, bearings are used in the connection between the girders and the substructure, whereas, at bents they are used in the connection between the girders and the bent cap beam. A bearing property can be specified as a link/support property or it can be user defined. The user defined bearing allows each of the six degrees of freedom to be specified as fixed, free or partially restrained with a specified spring constant. The latter type of bearing has been assigned to the bridges being studied with all six degrees of freedom fixed. The next component defined in the substructure was the abutment properties to specify the support conditions at the ends of the bridge. These abutment properties were to be used in abutment assignments to the bridge object. The specification of the connection between the abutment and the girders either have to be integral or connected to the bottom of the girders only. The Gaglardi Way Underpass had bent abutments at both ends, therefore, this component was not defined. However, the Kensington Avenue Underpass had south end of the bridge supported on an abutment and MSE wall for which a continuous beam, connected to girder bottom, was defined with length as specified in section 3.2. Bent properties section was used to specify the geometry and section properties of the bent cap and the bent columns at ends and at pier. They also specify the base support condition of the bent columns. The bridge bent data requires the user to define the cap beam length, number of columns, type of bent and the girder support condition. Based on the number of columns, the user is also required to enter column data for distance from end to centre of each column and their height. Using information 118  from chapter 3, the bents were defined. Figures C.7 and C.8 shows the data forms for north abutment bent and columns, respectively. At the abutments, the bent cap was connected to the bottom of girder, whereas, the pier had an integral bent, incorporating the girders.  Figure C.7: Define bridge bents 119   Figure C.8: Define bent columns 4. Bridge Object The bridge object definition is the main component of the bridge modeller. This is where the bridge spans are defined, deck section properties are assigned to each span, and abutments and bents, including their skews, are assigned. Figure C.9 shows the bridge object data form to define spans. 120   Figure C.9: Define bridge object The abutment assignment allows to specify the end skew, end diaphragm property, substructure assignment for the abutment which may be none, an abutment property or a bent property, vertical elevation and horizontal location of the substructure, and the bearing property, vertical elevation and rotation angle from the bridge default. Figure C.10 shows the data form to define the north abutment. The south abutment was defined in a similar manner but using specifications from chapter 3 and the drawings in ‘Appendix A’. 121   Figure C.10: Assign north abutment to bridge object The bent assignment, additionally, is similar to the abutment assignment, with only difference that it connects two spans. Figure C.11 shows the bent data form for the pier. 122   Figure C.11: Assign pier bent to the bridge object 5. Create Object-Based Model Once all the properties are defined and components are assigned, the update linked model creates the object-based model from the bridge object definition. It can create a spine model, area object model or a solid object model. In this case, an area object model was created shown in figures 4.1 to 4.4, using maximum submesh size of 1.2. 6. Load Cases and Analysis This step is mainly a processing stage to carry out finite element analysis of interest with load cases (static or dynamic) assigned. To carry out analysis, for example, modal analysis, dead loads of parapet and concrete layer can be incorporated using line load per unit metre and area load per square metre, respectively.  123  ARTeMIS Models Gaglardi Way Underpass  Prepare Geometry Nodes and surfaces have been used to define the geometry of the bridge that was used to extract the modal data from raw data. Using ten nodes, deck of the bridge was modelled only. Four nodes define the corners, two are at the end of span, i.e. pier, and four of these define the mid-span. In ARTeMIS, nodes can only be used at corners or at the points where sensors are installed. Table C.1 shows the coordinates for the nodes in global axis and figure C.12 shows the model created after connecting the nodes using surface feature. Table C.1: Gaglardi Way Underpass ARTeMIS geometry Node Number X Y Z 1 -3.408 9.019 -0.13 2 53.372 9.019 -0.13 3 3.407 -9.019 -0.13 4 60.187 -9.019 -0.13 5 10.322 9.019 -0.13 6 24.052 9.019 -0.13 7 38.712 9.019 -0.13 8 17.137 -9.019 -0.13 9 30.867 -9.019 -0.13 10 45.527 -9.019 -0.13 124    Figure C.12: Gaglardi Way Underpass ARTeMIS model  Data Acquisition and Degrees of Freedom Assignment From a total of fourteen sensors installed on north span of the bridge, 30 minutes of data recorded at a sampling rate of 0.005 was extracted and decoded. The deciphered acceleration data in time series has been attached as an appendix, in figures B.1 to B.4 of ‘Appendix B’. The channel numbers for this bridge are from 370 to 383. Since the columns have been excluded from the geometry, channels 381 to 383 have not been used to determine the mode shapes. Table C.2 defines the channel assignment, the degree of freedom direction for each channel, and other miscellaneous information. Additionally, figure C.13 graphically shows the eastern view of channels assigned to the geometry.   N 125  Table C.2: Gaglardi Way Underpass channel information Name Location (Global Node) X Y Z Type Unit Calibration Factor db Reference Value 370 5 0 0 -1 Acceleration m/s² 1 1 371 8 0 0 -1 Acceleration m/s² 1 1 372 1 0 1 0 Acceleration m/s² 1 1 373 1 1 0 0 Acceleration m/s² 1 1 374 3 0 0 1 Acceleration m/s² 1 1 375 3 -1 0 0 Acceleration m/s² 1 1 376 9 0 0 -1 Acceleration m/s² 1 1 377 9 -1 0 0 Acceleration m/s² 1 1 378 6 0 0 -1 Acceleration m/s² 1 1 379 6 -1 0 0 Acceleration m/s² 1 1 380 6 0 -1 0 Acceleration m/s² 1 1 381 Disconnected 0 0 1 Acceleration m/s² 1 1 382 Disconnected 0 0 1 Acceleration m/s² 1 1 383 Disconnected 0 0 1 Acceleration m/s² 1 1  126   Figure C.13: Gaglardi Way Underpass DOF assignment - east view Kensington Avenue Underpass The basic concept for this bridge remains the same except that the node coordinates and geometry is different only.  Prepare Geometry Again, ten nodes were used to define the corners, span, and mid-span of the bridge. For this bridge, an additional node had to be introduced since the sensor at west end of north span is a few meters inside rather than being at the corner. Table C.3 shows the nodes generated and figure C.14 illustrates the fully defined bridge geometry after connecting the nodes using surface feature.    N 127  Table C.3: Kensington Avenue Underpass ARTeMIS geometry Node Number X Y Z 1 9.265 13.4 -0.15 2 70.995 13.4 -0.15 3 -9.611 -13.9 -0.15 4 52.119 -13.9 -0.15 5 23.538 13.4 -0.15 6 37.81 13.4 -0.15 7 54.403 13.4 -0.15 8 4.662 -13.9 -0.15 9 18.934 -13.9 -0.15 10 35.527 -13.9 -0.15 11 69.889 11.8 -0.15   Figure C.14: Kensington Avenue Underpass ARTeMIS model N 128   Data Acquisition and Degrees of Freedom Assignment Similar to the other bridge, a total of 30 minutes data from nineteen sensors, recorded at a sampling frequency of 200, was deciphered. This data can be found plotted in figures B.5 to B.9 of ‘Appendix B’. The channel numbers assigned to this bridge range from 343 to 361 of which 356, 357, and 358 have not been used towards analysis since columns have been excluded from the model. Figure C.15 shows channels assigned to the model generated in west view for which the node assignment and others detail for each channel are given in table C.4.    Figure C.15: Kensington Avenue Underpass DOF assignment - west view    N 129  Table C.4: Kensington Avenue Underpass channel information Name Location (Global Node) X Y Z Type Unit Calibration Factor db Reference Value 343 1 0 1 0 Acceleration m/s² 1 1 344 1 -1 0 0 Acceleration m/s² 1 1 345 3 1 0 0 Acceleration m/s² 1 1 346 5 0 0 -1 Acceleration m/s² 1 1 347 7 0 0 -1 Acceleration m/s² 1 1 348 10 0 0 -1 Acceleration m/s² 1 1 349 9 0 0 -1 Acceleration m/s² 1 1 350 9 1 0 0 Acceleration m/s² 1 1 351 4 0 0 -1 Acceleration m/s² 1 1 352 4 -1 0 0 Acceleration m/s² 1 1 353 6 0 0 -1 Acceleration m/s² 1 1 354 6 1 0 0 Acceleration m/s² 1 1 355 6 0 1 0 Acceleration m/s² 1 1 356 Disconnected 0 0 1 Acceleration m/s² 1 1 357 Disconnected 0 0 1 Acceleration m/s² 1 1 358 Disconnected 0 0 1 Acceleration m/s² 1 1 359 11 0 0 1 Acceleration m/s² 1 1 360 11 1 0 0 Acceleration m/s² 1 1 361 11 0 -1 0 Acceleration m/s² 1 1    130  Appendix D: Parameters Used for Model Updating Table D.1: Parameters defined for updating Gaglardi Way Underpass FE model Parameter No. Type of Material/Section Property Before Updating After Updating Percent Change 1 Bent Cap Material Modulus of Elasticity (E) 29.78 GPa 35.78 GPa 20% 2 Column Material Modulus of Elasticity (E) 29.78 GPa 35.12 GPa 18% 3 Deck Material Modulus of Elasticity (E) 29.78 GPa 35.78 GPa 20% 4 Girder Material Modulus of Elasticity (E) 35.60 GPa 40.59 GPa 14% 5 Bent Cap Material Mass Density 23.56 kN/m3 20.56 kN/m3 -13% 6 Deck Material Mass Density 23.56 kN/m3 19.56 kN/m3 -17% 7 Girder Material Mass Density 23.56 kN/m3 19.56 kN/m3 -17%  Table D.2: Parameters defined for updating Kensington Avenue Underpass FE model Parameter No. Type of Material/Section Property Before Updating After Updating Percent Change 1 Column Material Modulus of Elasticity (E) 29.78 GPa 31.78 GPa 7 2 Deck Material Modulus of Elasticity (E) 29.78 GPa 32.78 GPa 10 3 Girder Material Modulus of Elasticity (E) 35.60 GPa 37.59 GPa 6 4 Deck Material Mass Density 23.56 kN/m3 21.56 kN/m3 -8 5 Girder Material Mass Density 23.56 kN/m3 21.56 kN/m3 -8    131  Appendix E: Modal Analysis for Updated FE Models Table E.1: Modal information for updated Gaglardi Way Underpass FE model Mode Period (s) Frequency (Hz) Modal Participation Mass (%) Description Sum UX Sum UY Sum UZ 1 0.18 5.58 53.73 36.44 0.05 Substructure 1st Longitudinal 2 0.15 6.72 82.38 95.73 0.19 Substructure Transverse 3 0.13 7.91 85.83 95.98 5.41 Substructure Torsion 4 0.12 8.13 94.38 96.99 6.45 Deck 1st Vertical 5 0.12 8.29 94.54 97.10 6.47 Deck 1st Torsion 6 0.10 9.57 94.82 97.10 37.62 Deck 2nd Vertical 7 0.10 9.66 94.85 97.13 40.44 Deck 2nd Torsion 8 0.10 9.74 94.85 97.14 47.27 Deck 3rd Vertical 9 0.09 10.82 94.85 97.14 48.62 Deck 4th Vertical 10 0.05 21.08 98.22 97.25 48.63 Substructure 2nd Longitudinal & Deck 5th Vertical 11 0.07 15.34 98.22 99.10 48.63 Substructure 2nd Torsion 12 0.03 36.13 98.22 99.10 86.66 Deck 6th Vertical  132   Figure E.1: Mode shapes for updated FE model of Gaglardi Way Underpass   133  Table E.2: Modal information for updated Kensington Avenue Underpass FE model Mode Period (s) Frequency (Hz) Modal Participation Mass (%) Description Sum UX Sum UY Sum UZ 1 0.18 5.69 0.02 3.33 11.87 Deck 1st Vertical 2 0.17 5.91 0.02 5.66 15.01 Deck 1st Torsion 3 0.15 6.55 0.04 19.65 15.50 Deck 2nd Vertical 4 0.15 6.82 0.33 62.85 16.48 Deck 3rd Vertical 5 0.13 7.66 0.33 62.88 16.50 Deck 2nd Torsion 6 0.12 8.05 0.38 63.05 23.20 Deck 4th Vertical 7 0.11 8.87 0.54 63.95 35.55 Deck 5th Vertical 8 0.11 9.36 0.64 64.31 43.03 Deck 6th Vertical 9 0.11 9.39 0.78 64.46 47.86 Deck 7th Vertical 10 0.07 13.44 80.00 64.49 47.93 Substructure Longitudinal 11 0.08 13.13 80.00 82.22 48.05 Substructure Torsion 12 0.04 23.85 80.00 82.22 73.47 Deck 8th Vertical  134   Figure E.2: Mode shapes for updated FE model of Kensington Avenue Underpass 135  Appendix F: Selected Ground Motions  Figure F.1: Unscaled spectra for longitudinal components of ground motions Table F.1: Longitudinal component first mode PSa for two bridges Name of Event Gaglardi Way Underpass PSa (g) Kensington Avenue Underpass PSa (g) Original Updated % Difference Original Updated % Difference Imperial Valley 0.043 0.050 14.149 0.053 0.050 -7.301 Trinidad 0.174 0.200 15.007 0.206 0.200 -3.029 Kobe 0.590 0.802 36.081 0.652 0.802 23.085 Tabas 2.490 2.545 2.202 2.478 2.545 2.692  0.0010.010.11100.01 0.1 1 10PSa (g)Time (s)Longitudinal SpectraImperial Valley Trinidad Kobe Tabas136   Figure F.2: Unscaled spectra for transverse components of ground motions Table F.2: Transverse component first mode PSa for two bridges Name of Event Gaglardi Way Underpass PSa (g) Kensington Avenue Underpass PSa (g) Original Updated % Difference Original Updated % Difference Imperial Valley 0.050 0.033 -34.133 0.037 0.033 -10.668 Trinidad 0.364 0.408 12.213 0.410 0.408 -0.419 Kobe 0.854 0.884 3.429 0.825 0.884 7.040 Tabas 3.531 3.345 -5.263 3.378 3.345 -0.959  0.0010.010.11100.01 0.1 1 10PSa (g)Time (s)Transverse SpectraImperial Valley Trinidad Kobe Tabas137   Figure F.3: Unscaled spectra for vertical components of ground motions Table F.3: Vertical component first mode PSa for two bridges Name of Event Gaglardi Way Underpass PSa (g) Kensington Avenue Underpass PSa (g) Original Updated % Difference Original Updated % Difference Imperial Valley 0.016 0.020 24.691 0.017 0.020 16.092 Trinidad 0.057 0.063 11.583 0.061 0.063 3.954 Kobe 0.275 0.305 10.909 0.314 0.305 -2.866 Tabas 1.515 1.910 26.073 1.770 1.910 7.910  0.0010.010.11100.01 0.1 1 10PSa (g)Time (s)Vertical SpectraImperial Valley Trinidad Kobe Tabas138   Figure F.4: Unscaled spectra for the SRSS of ground motions Table F.4: SRSS first mode PSa for two bridges Name of Event Gaglardi Way Underpass PSa (g) Kensington Avenue Underpass PSa (g) Original Updated % Difference Original Updated % Difference Imperial Valley 0.067 0.059 -11.243 0.065 0.059 -8.360 Trinidad 0.403 0.454 12.646 0.459 0.454 -0.942 Kobe 1.038 1.194 14.985 1.052 1.194 13.473 Tabas 4.323 4.203 -2.764 4.189 4.203 0.334  0.0010.010.11100.01 0.1 1 10PSa (g)Time (s)SRSS SpectraImperial Valley Trinidad Kobe Tabas139   Figure F.5: Ground motions for Imperial Valley earthquake 140   Figure F.6: Ground motions for Trinidad earthquake 141   Figure F.7: Ground motions for Kobe earthquake 142   Figure F.8: Ground motions for Tabas earthquake   143  Appendix G: Seismic Analysis Results Table G.1: Maximum and minimum base reactions with percentage difference for Gaglardi Way Underpass before and after finite element model updating   FX (kN) FY (kN) FZ (kN) MX (kN.m) MY (kN.m) MZ (kN.m)   Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Imperial Valley Original 4.95E+02 -4.67E+02 5.14E+02 -4.90E+02 2.11E+02 -1.88E+02 6.91E+02 -6.75E+02 6.83E+03 -7.60E+03 1.49E+04 -1.48E+04 Updated 4.04E+02 -4.12E+02 5.99E+02 -5.42E+02 1.99E+02 -1.44E+02 7.55E+02 -6.84E+02 5.25E+03 -5.01E+03 1.68E+04 -1.55E+04 Percentage Change -18.41 -11.79 16.53 10.56 -5.73 -23.35 9.25 1.33 -23.16 -34.01 12.62 5.06 Trinidad  Original 2.93E+03 -3.17E+03 5.10E+03 -4.09E+03 5.89E+02 -6.32E+02 6.35E+03 -4.83E+03 3.03E+04 -2.59E+04 1.46E+05 -1.17E+05 Updated 2.57E+03 -2.34E+03 4.70E+03 -4.42E+03 5.20E+02 -5.49E+02 6.19E+03 -5.92E+03 2.20E+04 -2.47E+04 1.33E+05 -1.25E+05 Percentage Change -12.28 -26.11 -7.91 8.01 -11.71 -13.04 -2.56 22.52 -27.26 -4.68 -8.71 6.84 Kobe Original 9.01E+03 -6.88E+03 1.18E+04 -1.04E+04 2.71E+03 -2.63E+03 1.31E+04 -1.26E+04 9.18E+04 -8.01E+04 3.36E+05 -2.83E+05 Updated 8.73E+03 -9.86E+03 9.63E+03 -9.31E+03 1.85E+03 -2.26E+03 1.22E+04 -1.03E+04 8.80E+04 -7.80E+04 2.77E+05 -2.69E+05 Percentage Change -3.13 43.20 -18.12 -10.28 -31.77 -14.28 -7.17 -18.38 -4.05 -2.66 -17.65 -4.69 Tabas Original 3.53E+04 -2.94E+04 3.77E+04 -4.19E+04 1.64E+04 -1.54E+04 4.61E+04 -5.57E+04 4.58E+05 -4.45E+05 1.05E+06 -1.13E+06 Updated 2.07E+04 -2.40E+04 2.88E+04 -3.48E+04 8.36E+03 -9.66E+03 3.66E+04 -4.58E+04 3.68E+05 -3.05E+05 8.49E+05 -1.02E+06 Percentage Change -41.43 -18.30 -23.76 -17.01 -48.95 -37.17 -20.53 -17.67 -19.75 -31.46 -18.80 -10.49  144  Table G.2: Maximum and minimum absolute displacements with percentage difference for north span of Gaglardi Way Underpass before and after finite element model updating   UX (m) North Span UY (m) North Span UZ (m) North Span RX (Radians) North Span RY (Radians) North Span RZ (Radians) North Span   Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Imperial Valley Original 3.46E-04 -3.60E-04 3.34E-04 -3.64E-04 2.25E-04 -2.62E-04 6.68E-06 -5.53E-06 1.10E-05 -1.20E-05 3.78E-06 -3.54E-06 Updated 2.38E-04 -2.49E-04 2.97E-04 -3.41E-04 1.90E-04 -1.87E-04 3.74E-06 -3.97E-06 9.01E-06 -8.82E-06 2.65E-06 -2.62E-06 Percentage Change -31.21 -30.83 -11.08 -6.32 -15.56 -28.63 -44.04 -28.22 -18.08 -26.48 -29.72 -26.07 Trinidad  Original 2.54E-03 -2.07E-03 2.73E-03 -3.57E-03 1.12E-03 -1.17E-03 4.40E-05 -5.10E-05 9.30E-05 -9.80E-05 2.40E-05 -2.90E-05 Updated 1.56E-03 -1.68E-03 2.46E-03 -2.74E-03 7.88E-04 -8.73E-04 2.60E-05 -3.50E-05 7.10E-05 -6.10E-05 1.80E-05 -2.00E-05 Percentage Change -38.42 -18.73 -9.71 -23.18 -29.58 -25.32 -40.91 -31.37 -23.66 -37.76 -25.00 -31.03 Kobe Original 6.32E-03 -7.37E-03 8.14E-03 -8.32E-03 3.16E-03 -2.58E-03 1.28E-04 -1.42E-04 3.07E-04 -2.68E-04 6.50E-05 -7.60E-05 Updated 6.81E-03 -6.25E-03 5.99E-03 -6.12E-03 3.50E-03 -3.41E-03 1.16E-04 -1.08E-04 2.48E-04 -2.65E-04 4.70E-05 -4.30E-05 Percentage Change 7.61 -15.15 -26.42 -26.52 11.06 32.06 -9.38 -23.94 -19.22 -1.12 -27.69 -43.42 Tabas Original 2.10E-02 -2.55E-02 2.76E-02 -2.65E-02 1.39E-02 -1.26E-02 3.58E-04 -3.73E-04 8.39E-04 -6.82E-04 2.55E-04 -2.62E-04 Updated 1.78E-02 -1.42E-02 2.04E-02 -1.62E-02 7.54E-03 -7.30E-03 3.45E-04 -2.68E-04 5.38E-04 -7.56E-04 1.87E-04 -1.69E-04 Percentage Change -15.07 -44.40 -26.04 -38.78 -45.64 -42.22 -3.63 -28.15 -35.88 10.85 -26.67 -35.50  145  Table G.3: Maximum and minimum absolute displacements with percentage difference for south span of Gaglardi Way Underpass before and after finite element model updating   UX (m) South Span UY (m) South Span UZ (m) South Span RX (Radians) South Span RY (Radians) South Span RZ (Radians) South Span   Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Imperial Valley Original 3.46E-04 -3.62E-04 3.49E-04 -3.65E-04 3.12E-04 -3.12E-04 6.68E-06 -7.57E-06 1.30E-05 -1.20E-05 3.08E-06 -3.08E-06 Updated 2.39E-04 -2.49E-04 3.11E-04 -3.53E-04 1.83E-04 -1.71E-04 4.56E-06 -5.95E-06 9.48E-06 -9.16E-06 2.36E-06 -1.93E-06 Percentage Change -30.92 -31.22 -10.89 -3.29 -41.35 -45.19 -31.79 -21.37 -27.06 -23.63 -23.48 -37.40 Trinidad  Original 2.54E-03 -2.07E-03 2.85E-03 -3.72E-03 1.67E-03 -1.46E-03 5.10E-05 -7.20E-05 9.20E-05 -1.05E-04 2.10E-05 -1.80E-05 Updated 1.57E-03 -1.68E-03 2.52E-03 -2.84E-03 1.15E-03 -1.08E-03 3.40E-05 -4.90E-05 7.30E-05 -6.70E-05 1.60E-05 -1.60E-05 Percentage Change -38.48 -18.80 -11.61 -23.47 -31.12 -26.30 -33.33 -31.94 -20.65 -36.19 -23.81 -11.11 Kobe Original 6.35E-03 -7.36E-03 8.09E-03 -8.66E-03 3.86E-03 -3.46E-03 1.66E-04 -1.62E-04 3.01E-04 -3.01E-04 5.60E-05 -5.20E-05 Updated 6.80E-03 -6.26E-03 6.31E-03 -6.40E-03 4.06E-03 -3.67E-03 1.27E-04 -1.34E-04 2.59E-04 -2.72E-04 2.90E-05 -3.10E-05 Percentage Change 7.23 -14.91 -21.99 -26.06 5.32 6.13 -23.49 -17.28 -13.95 -9.63 -48.21 -40.38 Tabas Original 2.11E-02 -2.55E-02 2.91E-02 -2.64E-02 1.63E-02 -1.46E-02 4.40E-04 -4.76E-04 8.85E-04 -7.96E-04 2.62E-04 -2.66E-04 Updated 1.79E-02 -1.42E-02 2.21E-02 -1.79E-02 1.14E-02 -1.06E-02 3.87E-04 -3.23E-04 5.86E-04 -8.14E-04 1.54E-04 -1.31E-04 Percentage Change -15.32 -44.39 -23.85 -32.36 -30.29 -27.37 -12.05 -32.14 -33.79 2.26 -41.22 -50.75  146  Table G.4: Maximum and minimum base reactions with percentage difference for Kensington Avenue Underpass before and after finite element model updating   FX (kN) FY (kN) FZ (kN) MX (kN.m) MY (kN.m) MZ (kN.m)   Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Imperial Valley Original 5.86E+02 -6.68E+02 6.62E+02 -7.41E+02 4.14E+02 -3.59E+02 1.07E+03 -1.04E+03 9.80E+03 -1.19E+04 2.55E+04 -2.43E+04 Updated 4.85E+02 -5.31E+02 6.97E+02 -7.11E+02 3.52E+02 -2.66E+02 1.18E+03 -1.00E+03 7.90E+03 -1.14E+04 3.07E+04 -2.91E+04 Percentage Change -17.21 -20.51 5.29 -4.04 -14.93 -25.92 10.10 -3.48 -19.33 -4.18 20.58 19.69 Trinidad  Original 2.54E+03 -2.25E+03 6.56E+03 -5.85E+03 9.57E+02 -1.33E+03 7.52E+03 -7.44E+03 5.21E+04 -4.44E+04 2.83E+05 -2.37E+05 Updated 2.14E+03 -1.78E+03 5.98E+03 -5.51E+03 1.08E+03 -1.10E+03 7.99E+03 -8.26E+03 4.39E+04 -3.97E+04 2.53E+05 -2.17E+05 Percentage Change -15.73 -20.78 -8.92 -5.87 12.38 -16.86 6.27 10.97 -15.81 -10.63 -10.44 -8.76 Kobe Original 8.52E+03 -6.83E+03 1.60E+04 -1.71E+04 5.04E+03 -4.62E+03 2.65E+04 -2.35E+04 1.56E+05 -1.72E+05 6.47E+05 -7.04E+05 Updated 8.72E+03 -6.21E+03 1.45E+04 -1.42E+04 4.75E+03 -4.58E+03 2.21E+04 -2.14E+04 1.72E+05 -1.65E+05 5.85E+05 -5.66E+05 Percentage Change 2.27 -9.15 -9.49 -16.83 -5.91 -0.84 -16.64 -9.17 9.63 -4.05 -9.61 -19.68 Tabas Original 2.71E+04 -3.31E+04 3.34E+04 -4.29E+04 1.33E+04 -1.59E+04 7.94E+04 -8.07E+04 5.15E+05 -4.44E+05 1.49E+06 -1.64E+06 Updated 2.31E+04 -2.55E+04 3.39E+04 -4.49E+04 1.29E+04 -1.45E+04 7.78E+04 -6.67E+04 5.25E+05 -4.53E+05 1.32E+06 -1.75E+06 Percentage Change -14.55 -23.03 1.61 4.68 -2.60 -8.79 -2.01 -17.37 2.03 1.94 -10.89 6.24  147  Table G.5: Maximum and minimum absolute displacements with percentage difference for south span (A0 to P1) of Kensington Avenue Underpass before and after finite element model updating   UX (m) South Span UY (m) South Span UZ (m) South Span RX (Radians) South Span RY (Radians) South Span RZ (Radians) South Span   Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Imperial Valley Original 2.20E-05 -2.00E-05 6.90E-05 -6.10E-05 1.61E-04 -1.70E-04 2.83E-06 -3.10E-06 3.03E-06 -3.11E-06 4.72E-06 -5.04E-06 Updated 1.70E-05 -1.80E-05 6.50E-05 -6.40E-05 1.46E-04 -1.80E-04 2.32E-06 -2.42E-06 2.93E-06 -3.06E-06 4.60E-06 -5.02E-06 Percentage Change -22.73 -10.00 -5.80 4.92 -9.32 5.88 -18.03 -21.78 -3.36 -1.70 -2.59 -0.42 Trinidad  Original 9.20E-05 -1.05E-04 5.54E-04 -6.40E-04 8.93E-04 -9.94E-04 1.80E-05 -1.50E-05 2.50E-05 -2.40E-05 4.60E-05 -5.20E-05 Updated 8.90E-05 -9.70E-05 4.79E-04 -5.38E-04 7.18E-04 -7.38E-04 1.00E-05 -1.20E-05 2.10E-05 -2.00E-05 4.00E-05 -4.50E-05 Percentage Change -3.26 -7.62 -13.54 -15.94 -19.60 -25.75 -44.44 -20.00 -16.00 -16.67 -13.04 -13.46 Kobe Original 3.05E-04 -3.71E-04 1.65E-03 -1.56E-03 3.08E-03 -3.01E-03 6.30E-05 -6.60E-05 7.70E-05 -6.80E-05 1.22E-04 -1.18E-04 Updated 2.21E-04 -3.26E-04 1.27E-03 -1.33E-03 2.08E-03 -1.85E-03 3.30E-05 -3.90E-05 5.40E-05 -5.10E-05 9.50E-05 -9.80E-05 Percentage Change -27.54 -12.13 -23.13 -14.65 -32.68 -38.64 -47.62 -40.91 -29.87 -25.00 -22.13 -16.95 Tabas Original 1.26E-03 -9.00E-04 4.27E-03 -3.27E-03 1.19E-02 -1.23E-02 2.08E-04 -2.39E-04 1.91E-04 -1.43E-04 3.62E-04 -3.24E-04 Updated 1.03E-03 -8.50E-04 3.83E-03 -2.90E-03 8.30E-03 -6.74E-03 1.35E-04 -1.27E-04 1.39E-04 -1.34E-04 3.37E-04 -2.56E-04 Percentage Change -18.75 -5.56 -10.33 -11.09 -30.42 -45.39 -35.10 -46.86 -27.23 -6.29 -6.91 -20.99 148  Table G.6: Maximum and minimum absolute displacements with percentage difference for north span (P1 to A2) of Kensington Avenue Underpass before and after finite element model updating   UX (m) North Span UY (m) North Span UZ (m) North Span RX (Radians) North Span RY (Radians) North Span RZ (Radians) North Span   Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Imperial Valley Original 5.00E-05 -4.40E-05 2.43E-04 -2.55E-04 2.09E-04 -1.94E-04 1.30E-05 -1.40E-05 5.76E-06 -6.29E-06 6.07E-06 -7.26E-06 Updated 3.70E-05 -3.40E-05 2.67E-04 -2.83E-04 2.60E-04 -2.67E-04 1.30E-05 -1.50E-05 5.45E-06 -5.85E-06 6.90E-06 -7.13E-06 Percentage Change -26.00 -22.73 9.88 10.98 24.40 37.63 0.00 7.14 -5.37 -7.04 13.68 -1.72 Trinidad  Original 1.65E-04 -1.86E-04 2.34E-03 -2.83E-03 1.95E-03 -2.07E-03 1.16E-04 -1.12E-04 5.20E-05 -6.60E-05 5.00E-05 -6.00E-05 Updated 1.38E-04 -1.44E-04 2.00E-03 -2.37E-03 1.46E-03 -1.63E-03 1.00E-04 -1.05E-04 4.10E-05 -5.10E-05 4.00E-05 -4.90E-05 Percentage Change -16.36 -22.58 -14.56 -16.34 -25.19 -21.29 -13.79 -6.25 -21.15 -22.73 -20.00 -18.33 Kobe Original 5.07E-04 -6.66E-04 6.83E-03 -6.37E-03 5.68E-03 -5.47E-03 4.01E-04 -4.08E-04 1.42E-04 -1.59E-04 1.61E-04 -1.44E-04 Updated 4.39E-04 -6.23E-04 5.10E-03 -5.41E-03 4.74E-03 -4.25E-03 2.73E-04 -2.80E-04 1.02E-04 -1.23E-04 1.22E-04 -1.18E-04 Percentage Change -13.41 -6.46 -25.36 -15.13 -16.49 -22.20 -31.92 -31.37 -28.17 -22.64 -24.22 -18.06 Tabas Original 2.53E-03 -2.08E-03 1.60E-02 -1.45E-02 1.39E-02 -1.38E-02 7.14E-04 -7.48E-04 4.24E-04 -3.09E-04 3.64E-04 -3.41E-04 Updated 1.86E-03 -1.67E-03 1.61E-02 -1.25E-02 1.28E-02 -1.35E-02 6.93E-04 -7.66E-04 3.25E-04 -2.89E-04 3.14E-04 -3.30E-04 Percentage Change -26.50 -19.83 0.96 -13.77 -8.12 -1.58 -2.94 2.41 -23.35 -6.47 -13.74 -3.23  

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