Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Mohammad Noh, Nurbaiah
Doctor of Philosophy - PhD
University of British Columbia
The seismic vulnerability of reinforced concrete (RC) frames with unreinforced masonry (URM) infill walls has been a concern in areas with high seismic activity. The seismic response of this structural system is usually modelled in the form of global building analysis using simplified procedures without considering the aspects resulting from the response between the infill walls and the frame. Another factor usually ignored is the soil-structure interactions (SSI), which can considerably impact the actual structure's behaviour. Current design standards do not provide adequate instructions or transparent methodologies for assessing the risk of the infilled RC building systems with consideration of the SSI effect. This research aims to provide a conceptual framework and benchmark data for assessing building risk, particularly for code-conforming RC frames with URM infill walls incorporating SSI in Vancouver, British Columbia. The study starts by selecting a simple and reliable analytical model for the infill wall response. A systematic guideline was developed to evaluate various parameters to define the monotonic and hysteretic response of infill walls modelled by equivalent struts. Different strut formulations and hysteretic models have been analyzed in detail and used to reproduce several experimental tests available in the literature. The numerical analyses are performed using the OpenSees computer program. Subsequently, this study assesses the seismic risk of the three- and six-storey regular RC moment-resisting frame (MRF) building systems, with and without URM infill walls, representing low- to mid-rise structures through incremental dynamic analyses (IDA). These structures are designed per the National Building Code of Canada 2010 and detailed based on the 2014 Canadian Standards Association A23.3 standard provision for seismically active regions. Two different ductility classes of seismic building design, namely ductile and moderately ductile, are considered to identify the capability, equality, and/or difference in the seismic performance of these designed buildings. Finally, a parametric study was conducted to determine the performance of the building with the consideration of the SSI. The goal was pursued through a parametric study in which the structure type and shallow foundation embedment depth were varied. Overall, the study's findings suggest that bare RC frame buildings are prone to collapse during earthquakes as the number of stories increases. The presence of URM infill walls greatly affects the collapse behaviour of the frame structure. Ductile RC MRF buildings outperform moderately ductile RC MRF buildings in terms of collapse performance, with the capacity of the building system being a significant factor. Additionally, the results indicate that the SSI effect significantly impacts the structural performance and vulnerability, particularly for low-rise buildings with surface foundations. It was discovered that implementing a realistic model with a wide range of parameters in the analysis is evident and now practicable.
SEISMIC RISK ASSESSMENT OF CODE-CONFORMING REINFORCED CONCRETE MOMENT RESISTING FRAME BUILDINGS: CONSIDERATION OF UNREINFORCED MASONRY INFILL WALL AND SOIL-STRUCTURE INTERACTIONS by Nurbaiah Mohammad Noh B.Eng., Universiti Teknologi MARA, 2007 M.Sc., Universiti Teknologi MARA, 2008 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE COLLEGE OF GRADUATE STUDIES (Civil Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan) August 2023 © Nurbaiah Mohammad Noh, 2023 ii The following individuals certify that they have read, and recommend to the College of Graduate Studies for acceptance, a dissertation entitle: SEISMIC RISK ASSESSMENT OF CODE-CONFORMING REINFORCED CONCRETE MOMENT RESISTING FRAME BUILDINGS: CONSIDERATION OF UNREINFORCED MASONRY INFILL WALL AND SOIL-STRUCTURE INTERACTIONS submitted by NURBAIAH MOHAMMAD NOH in partial fulfilment of the requirements of the degree of Doctor of Philosophy. Dr. Solomon Tesfamariam, School of Engineering Supervisor Dr. Ahmad Rteil, School of Engineering Supervisor Committee Member Dr. Kasun Hewage, School of Engineering Supervisor Committee Member Dr. Sina Kheirkhah, School of Engineering University Examiner Dr. Khaled Galal, Concordia University External Examiner iii Abstract The seismic vulnerability of reinforced concrete (RC) frames with unreinforced masonry (URM) infill walls has been a concern in areas with high seismic activity. The seismic response of this structural system is usually modelled in the form of global building analysis using simplified procedures without considering the aspects resulting from the response between the infill walls and the frame. Another factor usually ignored is the soil-structure interactions (SSI), which can considerably impact the actual structure's behaviour. Current design standards do not provide adequate instructions or transparent methodologies for assessing the risk of the infilled RC building systems with consideration of the SSI effect. This research aims to provide a conceptual framework and benchmark data for assessing building risk, particularly for code-conforming RC frames with URM infill walls incorporating SSI in Vancouver, British Columbia. The study starts by selecting a simple and reliable analytical model for the infill wall response. A systematic guideline was developed to evaluate various parameters to define the monotonic and hysteretic response of infill walls modelled by equivalent struts. Different strut formulations and hysteretic models have been analyzed in detail and used to reproduce several experimental tests available in the literature. The numerical analyses are performed using the OpenSees computer program. Subsequently, this study assesses the seismic risk of the three- and six-storey regular RC moment-resisting frame (MRF) building systems, with and without URM infill walls, representing low- to mid-rise structures through incremental dynamic analyses (IDA). These structures are designed per the National Building Code of Canada 2010 and detailed based on the 2014 Canadian Standards Association A23.3 standard provision for seismically active regions. Two different ductility classes of seismic building design, namely ductile and moderately ductile, are considered to identify the capability, equality, and/or difference in the seismic performance of these designed buildings. Finally, a parametric study was conducted to determine the performance of the building with the consideration of the SSI. The goal was pursued through a parametric study in which the structure type and shallow foundation embedment depth were iv varied. Overall, the study's findings suggest that bare RC frame buildings are prone to collapse during earthquakes as the number of stories increases. The presence of URM infill walls greatly affects the collapse behaviour of the frame structure. Ductile RC MRF buildings outperform moderately ductile RC MRF buildings in terms of collapse performance, with the capacity of the building system being a significant factor. Additionally, the results indicate that the SSI effect significantly impacts the structural performance and vulnerability, particularly for low-rise buildings with surface foundations. It was discovered that implementing a realistic model with a wide range of parameters in the analysis is evident and now practicable. v Lay Summary The world has experienced and continues to experience severe earthquakes. Since the frequency and intensity of earthquakes cannot yet be predicted, many highly populated regions around the world, including Canada, must incorporate earthquake engineering more frequently to reduce the seismic risk of buildings. Reinforced concrete (RC) frame buildings are the most common form of modern construction worldwide. Studies show that seismic activities greatly influence the level of structural damage and building collapse in RC frame buildings. However, there is limited information addressing seismic design practice with consideration of the unreinforced masonry infill (URM) walls and soil-structure interaction (SSI) effects on RC frame structures, and the validity of the nonlinear behaviour of the structures remains to be determined. Therefore, this study focuses on the effect of URM infill walls and SSI on the performance of RC buildings constructed in Vancouver, Canada. Based on the performance-based approach, a guideline has been developed to evaluate the performance of the building in the case of a collapse, taking into account the two aforementioned aspects. Overall, this study provided information essential to industry and researchers for enhancing the performance of buildings, improving the seismic design of infilled RC frame buildings, and demonstrating the possibility of achieving sustainable, economical, and better-performing buildings through this assessment. vi Preface I, Nurbaiah Mohammad Noh, prepared this thesis's contents, including the literature review, numerical models of the studied-infilled RC frame, data collection and analyses, interpretation of the result, and writing the chapters (manuscripts) under the supervision of Dr. Solomon Tesfamariam. This dissertation is prepared based on a compilation of two published peer-reviewed journal papers (Chapters 3 and 4) and one paper under preparation (Chapter 5). Dr. Solomon Tesfamariam facilitated the partial funding for this research. Published Paper Noh, N. M., Liberatore, L., Mollaioli, F., & Tesfamariam, S. (2017). Modelling of masonry-infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. This paper includes a version of Chapter 3 and some sections in Chapter 2. Dr. Solomon Tesfamariam of the University of British Columbia, Okanagan, Dr. Laura Liberatore and Dr. Fabrizio Mollaioli of the Sapienza University of Rome, Italy, offered technical assistance and reviewed and provided critical feedback in improving the manuscript and thesis. Noh, N. M. & Tesfamariam, S (2018). Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. doi: 10.3389/fbuil.2018.00053 This paper includes a version of Chapter 4. I conducted all the numerical analyses and wrote the first draft of the manuscript. Dr. Solomon Tesfamariam guided the evolution of the project and manuscript edits. Moreover, the preliminary findings reported in Chapter 4 are presented at the 1st China-Canada Symposium on Structural and Earthquake Engineering. vii Papers under preparation Noh, N. M. and Tesfamariam, S (2023). Seismic vulnerability of RC frame buildings considering soil-structure interaction (SSI) effects. A version of Chapter 5 of this dissertation is under preparation to submit to the Journal of Earthquake Engineering. viii Table of Contents Abstract...................................................................................................................................... iii Lay Summary .............................................................................................................................. v Preface ...................................................................................................................................... vi Table of Contents ..................................................................................................................... viii List of Tables ............................................................................................................................ xii List of Figures .......................................................................................................................... xiv List of Abbreviation ............................................................................................................... xxviii List of Symbols........................................................................................................................ xxx Acknowledgements ............................................................................................................... xxxiii Dedication ............................................................................................................................. xxxv CHAPTER 1: Introduction .......................................................................................................... 1 1.1 Background and Motivation ........................................................................................ 1 1.2 Research Questions ................................................................................................... 9 1.3 Research Objectives and Scope ................................................................................. 9 1.4 Thesis Organization ...................................................................................................11 CHAPTER 2: Literature review .................................................................................................14 2.1 Introduction ................................................................................................................14 2.2 Seismic performance of RC frame buildings with URM infill wall: Lessons from earthquakes ..........................................................................................................................17 2.3 In-plane behaviour of URM infill walls ........................................................................24 2.3.1 Experimental studies of infilled RC Frames subjected to in-plane lateral load ........24 ix 2.3.2 Failure modes of infilled frames due to in-plane loads ...........................................31 2.4 Numerical Modelling of URM infill walls subjected to in-plane failure .........................34 2.4.1 Local Method: Micro-modelling ..............................................................................35 2.4.2 Simplified method: Macro-modelling .....................................................................42 2.5 Behaviour of masonry infill panels in RC frames subjected to pure out-of-plane effect and combination between in- and out-of-plane effect .............................................................45 2.6 Effects of soil-structure interaction on the seismic response of buildings ...................51 2.6.1 A computational method for modelling SSI system under seismic loading .............58 2.6.2 Soil domain modelling techniques based on the substructure approach ................62 CHAPTER 3: Development of a computational model of masonry-infilled RC frames subjected to cyclic loading ..........................................................................................................................67 3.1 Background ...............................................................................................................67 3.2 Modelling approaches for masonry infilled RC frame .................................................70 3.2.1 Micro-modelling and meso-modelling .....................................................................72 3.2.2 Macro-modelling ....................................................................................................73 3.2.3 Single strut modelling.............................................................................................78 3.3 Structural and non-structural modelling with OpenSees .............................................94 3.3.1 RC Frame modelling ..............................................................................................94 3.3.2 Infill wall panel modelling .......................................................................................98 3.4 Numerical simulation with OpenSees: Selection and calibration .............................. 101 3.4.1 Experimental data ................................................................................................ 101 3.4.2 Numerical Model .................................................................................................. 104 x 3.5 Verification of selected model .................................................................................. 120 3.6 Summary ................................................................................................................. 126 CHAPTER 4: Seismic collapse performance of code-conforming RC MRF buildings ............. 129 4.1 Background ............................................................................................................. 129 4.2 Code-Conforming RC Frame Structures and Ground Motion Selection ................... 133 4.2.1 Selection of Buildings: Characteristics and Configuration .................................... 133 4.2.2 Seismic Design Procedure ................................................................................... 135 4.2.3 Nonlinear Simulation Models: RC Frames and URM Infill Walls ........................... 137 4.2.4 Ground Motion Selection ..................................................................................... 143 4.3 Incremental Dynamic Analysis (IDA) ........................................................................ 146 4.4 Collapse Fragility Assessment ................................................................................. 148 4.5 Mean Annual Frequency .......................................................................................... 151 4.6 Summary ................................................................................................................. 156 CHAPTER 5: Seismic vulnerability of RC frame buildings considering soil-structure interaction (SSI) effects ........................................................................................................................... 159 5.1 Background ............................................................................................................. 160 5.2 Description of the methodological framework .......................................................... 165 5.2.1 Structural and Geotechnical Details ..................................................................... 167 5.2.2 Nonlinear Modelling of Infilled RC frame buildings with SSI ................................. 171 5.2.3 Soil-foundation Modelling: The BNWF model ....................................................... 172 5.2.4 Nonlinear Dynamic Analysis ................................................................................ 176 5.3 Influence of SSI on Period of Buildings Supported by Shallow foundations ............. 182 xi 5.4 Comparison of SSI effects on the seismic performance of RC MRF frame buildings 184 5.5 Summary ................................................................................................................. 190 CHAPTER 6: Conclusions and Recommendations ................................................................. 193 6.1 Summary and Conclusions ...................................................................................... 193 6.2 Originality and Contribution...................................................................................... 199 6.3 Limitations ............................................................................................................... 201 6.4 Recommendations for Future Research .................................................................. 201 Bibliography ............................................................................................................................ 203 Appendices ............................................................................................................................. 238 Appendix A – Incremental dynamic analysis output ............................................................. 238 xii List of Tables Table 2.1: Capacity model referring to the arching mechanism (All expression is derived based on deformation sensitivity). .......................................................................................................48 Table 3.1: Coefficient value to calculate the properties of the strut (Decanini & Fantin, 1987). ..81 Table 3.2: Failure modes of masonry infill. ................................................................................90 Table 3.3: The equivalent width equations. ...............................................................................93 Table 3.4: Model plastic hinge parameters. ...............................................................................97 Table 3.5: Geometric characteristic (Stylianidis, 2012; Pires, 1990). ....................................... 103 Table 3.6: Mechanical Properties of the material (Stylianidis, 2012; Pires, 1990). ................... 103 Table 3.7: Parameters for the material behaviour. ................................................................... 105 Table 3.8: Mechanical properties of the infill assigned to the equivalent strut. ......................... 112 Table 3.9: Concrete01 material parameters for the equivalent strut. ....................................... 113 Table 3.10: Cyclic deterioration parameters for the Pinching4 Material hysteretic model. ....... 117 Table 3.11: Geometry of the investigated specimens. ............................................................. 121 Table 3.12: Infill Frame properties from Experimental Test. .................................................... 121 Table 3.13: Comparing Infill frame strength from model prediction to experimental result. ...... 122 Table 3.14: Strut model parameters for Concrete01 material. ................................................. 122 Table 3.15: Strut model parameters for Pinching4 material. .................................................... 125 Table 4.1: Summary of design characteristics of Ductile and Moderately Ductile RC frames. . 136 Table 4.2: First three fundamental periods of 3- and 6- storey RC MRF buildings. .................. 142 Table 4.3: Result of seismic collapse assessment for ductile and moderately ductile RC MRF with and without URM infill walls. .................................................................................................... 153 Table 5.1: Foundation characteristics. ..................................................................................... 169 Table 5.2: Details of soil parameters. ...................................................................................... 170 Table 5.3: Fixed- and flexible-based structure periods – 1st mode. .......................................... 182 xiii Table 5.4: Period lengthening caused by SSI. ......................................................................... 184 Table 5.5: The fragility function parameters for fixed-based and flexible-based models. ......... 186 xiv List of Figures Figure 1.1: Reinforced concrete frame with masonry infills under construction: (a) in Tangier, Morocco, (b) in Kathmandu, Nepal (https://taxonomy.openquake.org/terms/infilled-frame. By permission from GEM foundation). ............................................................................................. 2 Figure 1.2: RC frame with infill walls buildings collapse; (a)The Van, Turkey Earthquake on 23 October 2011(From © Bekdaş, Sayin, Çelik Sola, & Güner, 2016. Assessment of the material quality of damaged structures after earthquake in Van, Turkey. Journal of Materials in Civil Engineering, 1-13. Page 3. By permission from American Society of Civil Engineers), (b) The Gorkha, Nepal, Earthquake on 25 April 2015 (From © Syakya & Kawan, 2016. Reconnaissance based damage survey of buildings in Kathmandu valley: An aftermath of 7.8 Mw, 25 April 2015 Gorkha (Nepal) earthquake. Engineering Failure Analysis, 59, 161-184. Page 171. By permission from Elsevier), (c) The Mexico Earthquake on 19 September 2017 (From © Galvis, Miranda, Heresi, Dávalos, & Ruiz-García, 2020. Overview of collapsed buildings in Mexico City after the 19 September 2017 (Mw7.1) earthquake. Earthquake Spectra, 36(2), 83–109. By permission from SAGE Publications), and (d) L’Aquila, Italy, Earthquake on 6 April 2009 (From © Augenti & Parisi, 2010. Learning from Construction Failures due to the 2009 L’Aquila, Italy, Earthquake, Journal of Performance of Constructed Facilities, 24(6), 536–555. Page 541. By permission from American Society of Civil Engineers). ........................................................................................................ 5 Figure 2.1: The effect of masonry infill on the modification of the lateral load transfer mechanism, (a) bare frame- predominant frame action, and (b) fully infill frame- predominant truss action (Based on work from Kaushik, Rai, & Jain, 2006). ....................................................................16 Figure 2.2: Damaged or collapsed during the 2001 Bhuj earthquake, (a) The damage and hinge regions of the columns in the open first storey of this building, (b) infilled low-rise RC frame with uniform strength and stiffness experienced nearly uniform damage along its height. (From © xv Murty, Goel, Goyal et al., 2002. Reinforced Concrete Structures. Earthquake Spectra, 8(1_suppl), 149-185. Page 167. By permission from SAGE Publications). ..................................................18 Figure 2.3: Observed damage cases of infill walls on RC frame structures during the 2003 Bingöl earthquake; (a) Failure ground stories and damaged buildings due to soft storey, (b) Diagonal cracks and separation of infill walls, (c) Failure columns due to short column effect, and (d) Captive column developed by partial height masonry wall (From © Doǧangün, 2004. Performance of reinforced concrete buildings during the May 1, 2003 Bingöl Earthquake in Turkey, Engineering Structures, 26(6), 841-856. Page 846,849,851. By permission from Elsevier). ..........................19 Figure 2.4: Six-storey RC MRF that is exhibiting a soft-storey failure mechanism at the ground storey (detail of ground floor columns, right) subjected to Wenchuan Earthquake (Free et al., 2008, Image reproduced under fair dealing for research purposes). .........................................20 Figure 2.5: Damage pattern infill walls and RC frames; (a) out-of-plane failure, L’Aquila earthquake, 2009 (From © Augenti & Parisi, 2010. Learning from Construction Failures due to the 2009 L’Aquila, Italy, Earthquake, Journal of Performance of Constructed Facilities, 24(6), 536–555. Page 541. By permission from American Society of Civil Engineers), (b) and (c) beam shear and infill wall diagonal cracking failure, Nepal Earthquake, 2015 (From © Syakya & Kawan, 2016. Reconnaissance based damage survey of buildings in Kathmandu valley: An aftermath of 7.8 Mw, 25 April 2015 Gorkha (Nepal) earthquake. Engineering Failure Analysis, 59, 161-184. Page 171. By permission from Elsevier), (d) infill shear failure, Pidie Jaya earthquake, 2016 (From © Idris et al., 2022. Post-earthquake damage assessment after the 6.5 Mw earthquake on December, 7th 2016 in Pidie Jaya, Indonesia. Journal of Earthquake Engineering, 26(1), 409–426. Page 421. By permission from Taylor & Francis), (e) diagonal failure and partial collapse (OOP failure), Kefalonia earthquake, 2014 (From © Bournas, 2018. Concurrent seismic and energy retrofitting of RC and masonry building envelopes using inorganic textile-based composites combined with insulation materials: A new concept. Composites Part B: Engineering, 148, 166–179. Page 168. Creative Commons Attribution License (CC-BY 4.0) xvi (https://creativecommons.org/licenses/by-nc/4.0/)), and (f) tension strut failure, Van earthquake, 2011. (From © Yön, Onat, & Öncü, 2019. Earthquake damage to nonstructural elements of reinforced concrete buildings during 2011 Van Seismic sequence. Journal of Performance of Constructed Facilities, 33(6). Page 6. By permission from American Society of Civil Engineers). .................................................................................................................................................22 Figure 2.6: Infill Failure Modes; (a) Corner Crushing and Diagonal Compression, and (b) Shear Sliding, Diagonal Cracking, and Frame Failure. (From © Asteris et al., 2011. Mathematical macromodeling of infilled frames: state of the art. Journal of Structural Engineering, 137(12), 1508–1517. Page 1509. By permission from American Society of Civil Engineers). ..................33 Figure 2.7: Finite element modelling strategies for masonry; (a) masonry sample, (b) detailed micro-modelling, (c) simplified micro-modelling, and (d) macro (meso)-modelling (Lourenco, 1996, Image reproduced under fair dealing for research purposes). .........................................41 Figure 2.8: Macro model of equivalent diagonal strut and its related parameters (From © Panthi, Dahal, Shrestha, & Thapa, 2021. Fundamental period of RC buildings with infill walls in Nepal. Asian Journal of Civil Engineering, 22, 983-993. Page 987. Adapted with permission from Springer Nature). ......................................................................................................................42 Figure 2.9: Macro model techniques: (a) Single-, (b) double-, and (c) triple-strut model (From © Furtado et al., 2015. Modelling of masonry infill walls participation in the seismic behaviour of RC buildings using OpenSees. International Journal of Advanced Structural Engineering (IJASE), 7(2), 117–127. Page 119. Creative Commons Attribution License (CC-BY 4.0)(https://creativecommons.org/licenses/by-nc/4.0/)). ............................................................43 Figure 2.10: Infill seismic response conditions; (a) Arching behaviour with three hinges mechanism and (b) Rigid-body mechanism with the hinge at the bottom of the panel (From © Braga et al., 2011. Performance of non-structural elements in RC buildings during the L’Aquila, 2009 earthquake. Bulletin of Earthquake Engineering, 9(1), 307–324. Page 319. By permission from Springer Nature). ..............................................................................................................46 xvii Figure 2.11: Three-dimensional masonry infill wall model; (a) model proposed by Kadysiewski and Mosalam (2009) (From © Mosalam, & Günay, 2015. Progressive collapse analysis of reinforced concrete frames with unreinforced masonry infill walls considering in-plane/out-of-plane interaction. Earthquake Spectra, 31(2), 921–943. Page 927. Image reproduced under fair dealing for research purposes), and (b) Simplified model proposed by Furtado et al. (2015) (From © Furtado et al., 2015. Influence of the in plane and out-of-plane masonry infill walls’ interaction in the structural response of RC buildings. Procedia Engineering, 114, 722–729. Page 724. Creative Commons Attribution License (CC-BY-NC-ND 4.0) (https://creativecommons.org/licenses/by-nc-nd/4.0/)). .............................................................50 Figure 2.12: Schematic illustration of the numerical model of the SSI;(a) Direct analysis approach using continuum modelling, and (b) Substructure approach using rigid foundation or flexible foundation assumptions (From © Li et al., 2014. Influence of soil–structure interaction on seismic collapse resistance of super-tall buildings. Journal of Rock Mechanics and Geotechnical Engineering, 6(5), 477–485. Page 478. Creative Commons Attribution License (CC-BY-NC-ND 3.0) (https://creativecommons.org/licenses/by-nc-nd/3.0/)). ......................................................59 Figure 2.13: Schematic illustration of a substructure approach steps to analysis of the soil–structure interaction problem; (a) Structure response problem, (b) Evaluation of FIM, (c) Estimation of impedance function, and (d) Analysis of structure on compliant base subjected to FIM (Kramer & Stewart, 2004, Image reproduced under fair dealing for research purposes). ...61 Figure 3.1: Schematic diagram of the equivalent strut model for infilled frames (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). .....................................................................................75 Figure 3.2: Multiple strut model proposed by: (a) Crisafulli (1997); Crisafulli & Carr (2007), (b) El-Dakhakhni et al. (2004), and (c) Sattar & Liel (2016a). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of xviii the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). .........................................................................................................76 Figure 3.3: Schematic diagram of typical infill frame model proposed by Burton & Deierlein, (2013). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). ....................77 Figure 3.4: In-plane lateral force-displacement envelope of the model proposed by: (a) Liberatore (2001) and Liberatore & Decanini (2011), and (b) Panagiotakos & Fardis (1996). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). .....................................................................................80 Figure 3.5: Hysteretic law proposed for the equivalent struts: (a) Klingner & Bertero (1978), and (b) Cavaleri & Di Trapani (2014); Cavaleri et al. (2005). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). .........................................................................................................87 Figure 3.6: Hysteretic law for equivalent strut proposed by Panagiotakos & Fardis (1996). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). ...........................................................87 Figure 3.7: Hysteretic law for equivalent strut proposed by Liberatore (2001). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). .....................................................................................89 Figure 3.8: Geometrical parameters used in the model proposed by Saneinejad & Hobbs (1995). (From © Noh, Liberatore, Mollaioli, & Tesfamariam (2017). Modelling of masonry infilled RC xix frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). ....................92 Figure 3.9: RC frame modelling using distributed plasticity elements. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). .........................................................................................................95 Figure 3.10: RC frame modelling using concentrated/lumped plasticity elements. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). .....................................................................................96 Figure 3.11: Monotonic behaviour of component model developed by Ibarra & Krawinkler (2005). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). ...........................................................97 Figure 3.12: Concrete01 Material model in OpenSees (Mazzoni et al., 2006). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). .....................................................................................99 Figure 3.13: Hysteretic Material model in OpenSees (Mazzoni et al., 2006). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). ................................................................................... 100 Figure 3.14: Piching4 Material model in OpenSees (Mazzoni et al., 2006). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). ................................................................................... 101 xx Figure 3.15: Bare frame, Model 1. Numerical and experimental results: (a) Experiment 1, and (b) Experiment 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). .................. 106 Figure 3.16: Bare frame, Model 2. Numerical and experimental results: (a) Experiment 1, and (b) Experiment 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). .................. 107 Figure 3.17: Cumulative displacement dissipated energy: Experiment 1. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). ....................................................................................................... 108 Figure 3.18: Contribution of the frame and the infill in the experimental tests: (a) Experiment 1 and (b) Experiment 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). .................. 109 Figure 3.19: Comparison of the equivalent strut backbone curves proposed by Panagiotakos & Fardis (1996), Dolšek & Fajfar (2008), and Liberatore (2001); Liberatore et al. (2016): (a) Experiment 1, and (b) Experiment 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). ............................................................................................................................................... 111 Figure 3.20: Force-displacement curves of masonry infilled RC frames obtained using various strength models: (a) Experiment 1, and (b) Experiment 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of xxi the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). ....................................................................................................... 111 Figure 3.21: Force-displacement comparison of Experiment 1 using Concrete01 Material for masonry infill with: a) Model 1 of RC frame, and b) Model 2 of RC frame. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). ....................................................................................................... 114 Figure 3.22: Force-displacement comparison of Experiment 2 using Concrete01 Material for masonry infill with: a) Model 1 of RC frame, and b) Model 2 of RC frame. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). ....................................................................................................... 114 Figure 3.23: Force-displacement comparison of Experiment 1 using Hysteretic Material for masonry infill with: a) RC frame Model 1 and b) RC frame Model 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). ....................................................................................................... 116 Figure 3.24: Force-displacement comparison of Experiment 2 using Hysteretic Material for masonry infill with: a) RC frame Model 1 and b) RC frame Model 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). ....................................................................................................... 116 Figure 3.25: Force-displacement comparison of Experiment 1 using Pinching4 Material for masonry infill with: a) RC frame Model 1, and b) RC frame Model 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: xxii State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). ....................................................................................................... 118 Figure 3.26: Force-displacement comparison of Experiment 2 using Pinching4 Material for masonry infill with: a) RC frame Model 1, and b) RC frame Model 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). ....................................................................................................... 118 Figure 3.27: Cumulative displacement dissipated energy, Comparison for Experiment 1: a) Model 1, and b) Model 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). .................. 120 Figure 3.28: Comparison between experimental and numerical results, specimen SU1 (Kyriakides, 2011). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). .................. 123 Figure 3.29: Comparison between experimental and numerical results, experimental data by Kakaletsis & Karayannis (2008): (a) specimen S, and (b) specimen IS. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). ....................................................................................................... 124 Figure 3.30: Comparison between experimental and numerical results, experimental data by Mehrabi et al. (1996): (a) specimen #4, and (b) specimen #5. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). ....................................................................................................... 124 xxiii Figure 4.1: Collapse risk assessment of RC frame framework. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/))................................................................................................................................... 133 Figure 4.2: Code-conforming RC frame buildings; (a) Frame plan, (b) Frame elevations and types, and (c) typical columns and beams detailing. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). ............................................................................................................................................... 134 Figure 4.3: Schematic of RC frame modelling using lumped plasticity elements; (a) overview of the overall model, (b) detail model for infilled—RC frame, (c) monotonic curve for RC frame member developed by Ibarra et al. (2005), (d) in-plane lateral force-displacement envelope model proposed by Decanini et al. (2014), and (e) hysteretic curve (cyclic behaviour). (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). ................................................................ 140 Figure 4.4: Spring model for column shear failure. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). ............................................................................................................................................... 141 Figure 4.5: Example of selected ground motion records for 3S_D&MD_NI (T1 = 1.5 s). Selected ground motion records for; a) 3S_D&MD_NI, b) 3S_D&MD_I, c) 6S_D_NI, d) 6S_MD_NI and e) xxiv 6S_D&MD-I. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). ............................................ 145 Figure 4.6: Incremental dynamic analysis curves for 3-storey buildings; (a) 3S_D_NI, (b) 3S_MD_NI, (c) 3S_D_I, and (d) 3S_MD_I. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). ............................................................................................................................................... 147 Figure 4.7: Incremental dynamic analysis curves for 6-storey buildings; (a) 6S_D_NI, (b) 6S_MD_NI, (c) 6S_D_I, and (d) 6S_MD_I. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). ............................................................................................................................................... 148 Figure 4.8: Fragility curves of (a) 3-storey and (b) 6-storey MRF RC frame with and without URM infill walls. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). ............................................ 150 Figure 4.9: Ground motion hazard curve for Vancouver for different periods on soil Class C. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). ................................................................ 152 xxv Figure 4.10: Mean annual frequency of collapse for ductile and moderately ductile RC MRF buildings with and without URM infill walls comparison with other building design codes. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). ................................................................ 154 Figure 5.1: Buildings Collapsed during;(a) the Mexico City earthquake of 1985 (From © Abdel Raheem et al., 2015. Evaluation of soil–foundation–structure interaction effects on seismic response demands of multi-story MRF buildings on raft foundations, Int J Adv Struct Eng, 7, Creative Commons Attribution License (CC-BY 4.0)), (b) the Kobe earthquake of 1995 (From © Badry & Satyam, 2016. An efficient approach for assessing the seismic soil structure interaction effect for the asymmetrical pile group. Innov. Infrastruct. Solut. 1, Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)), and (c) the Bhuj earthquake of 2001 (From © Murty, Goel, Goyal et al., 2002. Reinforced Concrete Structures. Earthquake Spectra, 8(1_suppl), 149-185. Page 167. By permission from Sage Publication). ............................................................................................................................ 162 Figure 5.2: Methodological framework for the vulnerability analysis of the infilled RC MRF buildings with SSI. ................................................................................................................... 166 Figure 5.3: Ductile and moderately ductile RC MRF models used for the seismic vulnerability assessment considering SSI; (a) 3-storey (Low-rise) building, (b) 6-storey (Mid-rise) building. ............................................................................................................................................... 168 Figure 5.4: Schematic diagram of the isolated shallow footing (a) Elevation, and (b) Plan view. ............................................................................................................................................... 170 Figure 5.5: Numerical model in OpenSees; (a) overview of the overall model, (b) Infilled RC frame model with lumped plasticity and strut model, and (c) BNWF schematic model proposed by Raychowdhury & Hutchinson (2009) (From © Raychowdhury & Hutchinson, 2009. Performance xxvi evaluation of a nonlinear Winkler-based shallow foundation model using centrifuge test results, Earthquake Engng Struct.Dyn, 38, 679–698. Page 682. Adapted with permission from John Wiley and Sons). .............................................................................................................................. 172 Figure 5.6: The schematic diagram of; (a) Graphical representation BNWF model, and (b) Example series of Winkler springs below a rigid foundation represented by one-dimensional finite element (zero length element) (From © Raychowdhury & Hutchinson, 2009. Performance evaluation of a nonlinear Winkler-based shallow foundation model using centrifuge test results, Earthquake Engng Struct.Dyn, 38, 679–698. Page 682. Adapted with permission from John Wiley and Sons). .............................................................................................................................. 173 Figure 5.7: Hysteretic behaviour of BNWF model springs; (a) q-z spring (axial and rotational), (b) p-x springs (passive resistance), and (c) t-x springs (sliding resistance) (From © Raychowdhury & Hutchinson, 2009. Performance evaluation of a nonlinear Winkler-based shallow foundation model using centrifuge test results, Earthquake Engng Struct.Dyn, 38, 679–698. Page 683. Adapted with permission from John Wiley and Sons). ............................................................. 174 Figure 5.8: IDA curves of the 3-storey bare RC MRF; (a) 3S_D_NI without SSI, (b) 3S_MD_NI without SSI, (c) 3S_D_NI with SSI, and (d) 3S_MD_NI with SSI. ............................................ 178 Figure 5.9: IDA curves of the 6-storey bare RC MRF; (a) 6S_D_NI without SSI, (b) 6S_MD_NI without SSI, (c) 6S_D_NI with SSI, and (d) 6S_MD_NI with SSI. ............................................ 179 Figure 5.10: Median IDA curves of the 3-storey RC MRF with SSI (Df=0.0 m and 1.0 m); (a) 3S_D_NI, (b) 3S_D_I, (c) 3S_MD_NI, and (d) 3S_MD_I. ........................................................ 180 Figure 5.11: Median IDA curves of the 6-storey RC MRF with SSI (Df=0.0 m and 1.0 m); (a) 6S_D_NI, (b) 6S_D_I, (c) 6S_MD_NI, and (d) 6S_MD_I. ........................................................ 181 Figure 5.12: Base flexibility effect on period; (a) moderately ductile RC frame, and (b) ductile RC frame. ..................................................................................................................................... 183 Figure 5.13: Base flexibility effect on the period-elongation ratio. ............................................ 184 xxvii Figure 5.14: Seismic fragility curves of the 3-storey RC MRF considering different building configurations with and without SSI; (a) 3S_D_NI, (b) 3S_D_I, (c) 3S_MD_NI, and (d) 3S_MD_I. ............................................................................................................................................... 188 Figure 5.15: Seismic fragility curves of the 6-storey RC MRF considering different building configurations with and without SSI; (a) 6S_D_NI, (b) 6S_D_I, (c) 6S_MD_NI, and (d) 6S_MD_I. ............................................................................................................................................... 189 xxviii List of Abbreviation 𝐵𝑁𝑊𝐹 Beam on Nonlinear Winkler Foundation 𝐶𝑆𝐴 Canadian Standard Association 𝐶𝐶 Corner crushing 𝐶𝑀𝑅 Collapse Margin Ratio 𝐶𝑃 Collapse Prevention 𝐷𝐶 Diagonal compression 𝐷𝐾 Diagonal crack 𝐸𝑆𝐹𝑃 Equivalent Static Force Procedure 𝐹𝐸𝑀 Finite Element Model 𝐹𝐸𝑀𝐴 Federal Emergency Management Agency 𝐹𝐹 Frame failure 𝐼𝐷𝐴 Incremental Dynamic Analysis 𝐼𝑀 Intensity Measure 𝐼𝑃 In-plane 𝐼𝑆𝑃𝐴 Inelastic Static Pushover Analysis 𝐿𝑆 Limit State 𝑀𝑅𝐹 Moment-Resisting Frame 𝑀𝐶𝐸 Maximum considered Earthquake 𝑁𝐵𝐶𝐶 National Building Code of Canada 𝑁𝐿𝑇𝐻𝐴 Non-Linear Time History Analysis 𝑁𝑅𝐻𝐴 Nonlinear Response History Analysis 𝑂𝑂𝑃 Out-of-plane 𝑃𝐸𝐸𝑅 Pacific Earthquake Engineering Research Center xxix 𝑃𝐺𝐴 Peak Ground Acceleration 𝑃𝐺𝑉 Peak Ground Velocity 𝑃𝑆𝐷 Pseudo-dynamic Test 𝑃𝑆𝐷𝑀 Probabilistic Seismic Demand Model 𝑅𝐶 Reinforced Concrete 𝑅𝐷𝑅 Roof drift ratio 𝑆𝐼 Spectral Intensity 𝑆𝑆 Sliding shear 𝑆𝑆𝐼 Soil-structure interaction 𝑈𝐵𝐶 The University of British Columbia 𝑈𝐻𝑆 Uniform Hazard Spectrum 𝑈𝑅𝑀 Unreinforced Masonry Wall xxx List of Symbols 𝐴 Area 𝑏 Width of wall 𝐵 Width footing 𝐶 Cohesion coefficient ℎ𝑚 Height of the Masonry Panel ℎ Storey Height 𝐷𝑓 Embedment depth 𝐸 Modulus of Elasticity 𝐺 Shear Modulus 𝐻 Height of footing 𝐼 Moment of Inertia of the Columns 𝐼𝐸 Importance Factor 𝐾1𝐾2 Coefficients that change according to 𝜆ℎ 𝐾𝑐𝑟 Cracked Stiffness 𝐿 Length of footing 𝑚 Effective Mass 𝑀𝑣 Higher moment constant 𝑅 Response Modification Factor 𝑅𝑑 Ductility Response Modification Factor 𝑅𝑜 Over-strength Response Modification Factor 𝑆(𝑇) Spectral Acceleration for a Certain Period, T 𝑡𝑚 Thickness of the Masonry Panel 𝑇𝑎 Fundamental Period of Structure 𝑉𝑠 Shear wave velocity xxxi 𝑉𝑠,30 Average Shear Wave Velocity in the Top 30 meters of Soil 𝑤𝑗 Seismic Weight of Level j 𝑊 Total Seismic Weight 𝛽𝐷𝑅 Uncertainty due to quality rating of design requirement 𝛽𝑖 Ratio of storey shear at storey i over that at roof 𝛽𝑀𝐷𝐿 Uncertainty due to quality rating of numerical model 𝛽𝑅𝑇𝑅 Uncertainty due to record-to-record variability in ground motions 𝛽𝑇𝑂𝑇 Total system collapse uncertainty 𝛽𝐸𝐷𝑃ǀ𝐼𝑀 Dispersion of the Demand 𝜀𝑐 Concrete Strain 𝜀𝑐𝑐50 50% of Confined Concrete Strain 𝜀𝑐𝑢 Crushing Strain of Concrete 𝜀𝑠𝑡 Steel Strain 𝜀𝑠𝑐𝑟 Buckling Strain of Longitudinal Rebar 𝜀𝑠𝑚 Steel Strain at Maximum Tensile Stress 𝜀𝑠𝑢 Fracture Strain of Steel 𝜀𝑦 Yielding Strain of Steel Eh Cyclic Dissipated Energy 𝑓𝑐′ Compressive Strength of Concrete 𝑓𝑐𝑟 Cracking Stress of Concrete 𝑓𝑠𝑦 Yield Stress of Steel 𝑓𝑦ℎ Yield Strength of Transverse Steel 𝜎𝑐 Compressive Stress in Concrete 𝜎𝑠 Longitudinal Steel Strain 𝜌𝑠 Volumetric Ratio of Transverse Reinforcement xxxii l Cyclic deterioration parameter 𝜆ℎ Non-dimensional parameters depending on the geometric and mechanical characteristics of the frame-infill system 𝜆𝑐 The expected value of the collapse  Poisson ratio 𝜃𝑝 Plastic rotation 𝜔 Natural Vibration Frequency g Specific weight  Internal friction ∆𝑢 Ultimate Roof Drift Ratio ∆𝑦 Yielding Roof Drift Ratio xxxiii Acknowledgements All praise to Allah SWT, the almighty and the most merciful. Without his blessing, this research would not have been accomplished. I would like to express my sincere gratitude to my PhD supervisor, Dr. Solomon Tesfamariam, for their invaluable guidance and support throughout my research journey. His extensive knowledge, expertise, and unwavering commitment to excellence have shaped my academic and professional growth. I am deeply grateful for their mentorship, patience, and encouragement, which have enabled me to overcome numerous challenges and achieve my research goals. I am fortunate to have had such a dedicated and inspiring supervisor, and I will always cherish the lessons and skills I have learned under his guidance. Thank you for your unwavering support and for being an exceptional mentor. I would also like to express my appreciation to Dr. Kasun Hewage and Dr. Ahmad Rteil for their dedication and constant commitment to serving on my research committee and for providing invaluable constructive criticism and ideas. I would also like to extend my thanks Dr. Fabrizio Mollaioli and Dr. Laura Liberatore (Sapienza University of Rome) for their assistance and direction regarding the URM infill wall assessment. I must take this opportunity to sincerely acknowledge the support of the faculty and staff at the School of Engineering for providing research spaces and assistance. I would also like to thank the University Teknologi Mara and the Malaysia Ministry of Higher Education for financial support during my Ph.D. study. xxxiv My sincere thanks also go to my overall graduate school career and my best research colleagues at The University of British Columbia, especially Dr. Gizachew Demisse, Jayanthan Madheswaran, Dr. Ngandu Balekelay Celestin Balek, Dr. Yekenalem Abebe, Dr. Matiyas Ayalew Bezabeh, Selamawit Dege Dires and Dr. Konstantinos Skandalos for their support and encouragement during the difficult phases of my research. I would like to express my deepest gratitude to my loving husband Muhamad Shafizan Jaafar, and our wonderful kids, Nursyakirah Dayana, Muhammad Syahid, and Nursyaza Azzahara, who have been my constant source of inspiration and support throughout my PhD journey. Your unwavering encouragement, patience, and understanding have been instrumental in helping me achieve my goals and fulfil my dreams. Thank you for always believing in me, making countless sacrifices, and being there for me every step of the way. Your love and support have been the foundation of my success, and I could not have done it without you. I am blessed to have such an amazing family, and I look forward to sharing many more achievements and milestones with you in the coming years. Finally, I thank my parents, Fatimah Alang and Mohammad Noh Abdullah, for their love and support throughout my PhD program. Their encouragement and belief in me have been a great source of strength during my challenging moments. xxxv Dedication I dedicate this thesis to my family, who always supported, encouraged, cared for, and understood me throughout my academic endeavour, especially this one. Completing this thesis would not have been possible without their support, understanding, patience, and love. Last but not least, dedicated to the strongest person I know; Nurbaiah Mohammad Noh (me). . 1 CHAPTER 1: Introduction Reinforced concrete moment-resisting frames (RC MRF) with unreinforced masonry (URM) infill walls are used to construct most low- and medium-rise residential, educational, and commercial buildings. This building type can be found worldwide, including regions prone to high seismic activity levels. This chapter provides an overview of the current challenges in assessing the seismic performance of RC frame buildings, which helps to support the motivation for this study. In conjunction with the problem statement, this chapter provided research questions, the research objectives, and the scope of the study. This chapter ends with a list of activities to accomplish the chapter-specific study objectives. 1.1 Background and Motivation RC frame buildings with URM infill walls, henceforth denoted as masonry-infilled RC frame structures, are widely adopted for multi-storey building construction, particularly for low to medium-rise buildings (Mossalam & Günay, 2015; Khan, 2019; Bhaskar, Bhunia, Karthik, & Samadhiya, 2022). The standard construction process for this type of building begins with constructing the RC frame, followed by installing the URM infill wall. The URM infill walls are considered a non-structural component but significantly contribute to increased lateral strength and stiffness of RC frames (Wararuksajja, Srechai, & Leelataviwat, 2020). URM infill walls are widely used for interior and exterior walls due to their functionality (Figure 1.1). The good performances of infills concerning temperature, noise, moisture, fire, and durability make them a popular form of construction in seismic regions (Mazumder, 2015; Longo, Wiebe, da Porto, & Modena, 2018). 2 (a) (b) Figure 1.1: Reinforced concrete frame with masonry infills under construction: (a) in Tangier, Morocco, (b) in Kathmandu, Nepal (https://taxonomy.openquake.org/terms/infilled-frame. By permission from GEM foundation). In many cases, the URM infill walls are considered as the non-structural element and leads to the oversight of the significant influence exerted by infill walls on the entire structural system behaviour during design and analysis processes. The rationale behind neglecting infill walls in the design and analysis process can be attributed to several factors, including a lack of sufficient knowledge regarding the behaviour of URM infills, the complex interaction between the RC frame and infills (Asteris, Chrysostomou, Giannopoulos, & Ricci, 2013) and suggested by various 3 building design codes (Kauffman & Memari, 2014). Furthermore, several standards recommend separating URM infill walls from RC frames (SNIP-II-7-81 1996; NZS1170.5:2004). The infills change the behaviour and failure pattern of the infilled frames under lateral loading significantly (Fiorato, Sozen, & Gamble, 1970; Klingner & Bertero, 1978; Bertero & Brokken, 1983; Paulay & Priestley, 1992; Saneinejad & Hobbs, 1995; Panagiotakos & Fardis, 1996; Asteris, 2003; Asteris, Cotsovos, Chrysostomou, Mohebkhah, & Al-Chaar, 2013; Liberatore & Mollaioli, 2015; Sattar & Liel, 2016b). The response of masonry infill walls to seismic excitation can be either positive or negative depending on several occurrences, such as detailing aspects, infill configurations, and mechanical properties. These factors can influence the relative stiffness and strength between the frames and the masonry walls, and the type of connection between masonry and frames (Catherin Jeselia, Jayalekshmi, & Venkataramana, 2013; Mondal & Tesfamariam, 2014; Tarque, Candido, Camata, & Spacone, 2015; Tesfamariam, Goda, & Mondal, 2015; Noh, Liberatore, Mollaioli, & Tesfamariam, 2017; Noh & Tesfamariam, 2018; Maidiawati & Tanjung, 2021). The infills are known to have a complicated failure mode, in which the infills fail in a brittle manner, while the RC frame can sustain lateral load over large post-yield deformation. In general, the infill walls contribute significantly to the overall in-plane lateral stiffness, strength, and energy dissipation of a building. However, the presence of infill walls on a bare frame can increase the risk of damage or collapse during earthquake due to undesired forces distribution under cyclic loads, and due to failure of URM infills (Wararuksajja et al., 2020; Medriosa, Maidiawati, Tanjung, & Zaidir, 2022). Failure of URM infills in one part of the building could potentially lead to a reduction in the overall structure ductility and stability. Furthermore, the failure of URM infill can lead to the progressive collapse of adjacent structural elements, especially in older or poorly designed buildings. 4 Damage observation from recent earthquakes in China, Indonesia, Italy, Mexico, Pakistan, Turkey, Taiwan, and India revealed that many RC buildings suffered severe structural damage or collapse (Vicente, Rodrigues, Varum, Costa, & da Silva, 2012; Piroglu & Ozakgul, 2013; Mosalam & Günay, 2015; Aguiar & Mieles, 2016; Chen, Xie, Dai, Zhang, & Chen, 2016; Chen et al., 2017; Roeslin, Ma, & García, 2018; Rafi, Ahmed, Lodi, Varum, & Arshad, 2022; Idris et al., 2022). The observed deficiencies in RC buildings that led to severe damages includes mansonry infill wall failures, beam-column joint failure due to inadequate design or detailing of shear capacity, structural irregularities, short-column mechanism, soft-storey mechanism, foundation failures due to settlemen, titiling, or sliding, and the secondary element and and surrounding failures (Dias-Oliveira, Rodrigues, Asteris, & Varum, 2022). However, these observations from past earthquakes underscore the critical role played by the unreinforced masonry (URM) infill walls and reinforcement detailing in the overall seismic performance of RC frame buildings. As shown in Figure 1.2, URM infill walls caused numerous RC structures to collapse during these seismic events. The collapse of infilled RC-framed buildings incurs vast losses in life and property during earthquakes, demonstrating how vulnerable these buildings are. Therefore, it emphasize the importance of understanding and highlights the critical need to address the vulnerabilities and risks associated with these structural systems, in order to develop an appropriate mitigation strategies. 5 (a) (b) (c) (d) Figure 1.2: RC frame with infill walls buildings collapse; (a)The Van, Turkey Earthquake on 23 October 2011(From © Bekdaş, Sayin, Çelik Sola, & Güner, 2016. Assessment of the material quality of damaged structures after earthquake in Van, Turkey. Journal of Materials in Civil Engineering, 1-13. Page 3. By permission from American Society of Civil Engineers), (b) The Gorkha, Nepal, Earthquake on 25 April 2015 (From © Syakya & Kawan, 2016. Reconnaissance based damage survey of buildings in Kathmandu valley: An aftermath of 7.8 Mw, 25 April 2015 Gorkha (Nepal) earthquake. Engineering Failure Analysis, 59, 161-184. Page 171. By permission from Elsevier), (c) The Mexico Earthquake on 19 September 2017 (From © Galvis, Miranda, Heresi, Dávalos, & Ruiz-García, 2020. Overview of collapsed buildings in Mexico City after the 19 September 2017 (Mw7.1) earthquake. Earthquake Spectra, 36(2), 83–109. By permission from SAGE Publications), and (d) L’Aquila, Italy, Earthquake on 6 April 2009 (From © Augenti & Parisi, 2010. Learning from Construction Failures due to the 2009 L’Aquila, Italy, Earthquake, Journal of Performance of Constructed Facilities, 24(6), 536–555. Page 541. By permission from American Society of Civil Engineers). Despite numerous experiments and assessments of infilled RC frame behaviour over the years, there is currently insufficient clear evidence to support a valid design approach and no reliable procedure for developing an analysis model for this type of structure. Furthermore, assessments of the structure's global response are currently limited because most previous 6 studies focused on the interaction between infill and frame. Past studies have shown that the infill-frame interaction around the structural joint substantially influences the global structural response (Sattar & Liel, 2016b; Butenweg, Marinkovic, Fehling, Pfetzing, & Kubalski, 2018; Saengyuan & Latcharote, 2022). Besides, the global response evaluation study of RC frame buildings only focused on non-ductile buildings that did not include seismic design (Shing, Stavridis, Koutromanos, Willam, Blackard, Kyriakides, Billington, & Arnold, 2010; Koutromanos, Stavridis, Shing, & Willam, 2011; Baradaran Shoraka, 2013; Burton & Deierlein, 2013; Jeon, Park, & DesRoches, 2015; Sattar & Liel, 2016a, 2016b; Sanada, 2017; Gao, Stavridis, Bolis, & Preti, 2018; Rosman et al., 2019; Fikri & Ingham, 2022 ). This has resulted in the lack of literature on RC frame structures with acceptable seismic performance, representing modern building designs in most seismic cities or regions. According to Basha and Kaushik (2015), the infills remain to have a negative impact even on the ductile RC frame, where the shear failure in columns could not be prevented. Based on lessons learned from past earthquakes and studies, it has become evident that assessing the seismic risk of RC frame buildings with URM infill walls should be performed to understand the level of safety and seismic vulnerability of this structure for future earthquakes appropriately (Rajeev & Tesfamariam, 2012b; Siamak, 2013; Tesfamariam et al., 2015; Noh & Tesfamariam, 2018; Lu, Ji, & Yan, 2022). Several methods have been proposed based on the probability approach to assess the seismic collapse risk of infilled RC frame buildings. However, most seismic assessment methodologies, which follow the conventional structural design process, currently used for various buildings focused primarily on which structures are modelled as fixed-based conditions without considering the possibility and potential impact of the interaction between superstructure and soil (Villaverde, 2007; Zafarkhah & Dehkordi, 2017; Mohamadi & Tahghighi, 2019; Oz, Senel, Palanci, & Kalkan, 2020; Requena-Garcia-Cruz, Bento, Durand-Neyra, & Morales-Esteban, 2022; Sriwastav, 2022). During severe seismic events, the dynamic response of the structure is 7 influenced not only by the behaviour of the superstructure but also by the type and behaviour of the soil present in and around the substructure. Neglecting the flexibility effect based on the interaction between structure and soil in the model cannot predict the proper behaviour of the buildings. The structural response to the ground motion is affected by the interaction between the structure and the soil flexibility, soil-structure interaction (SSI). There is no explicit agreement on whether SSI is beneficial or detrimental to structural seismic response (Rajeev & Tesfamariam, 2012a; Wani, Vemuri, Rajaram, & Babu, 2022). Incorporating SSI effects into structural design and analysis positively impacts structural seismic behaviour, increasing the structure's damping and fundamental period and reducing base shear. Studies also have observed that the flexible-base condition modifies the response of the building in comparison to the fixed-base condition and results in increasing inter-storey and overall deformations and therefore decreases the stiffness of the structure (Chandra, 2014; Abdel Raheem, Ahmed, & Alazrak, 2015; Rosman et al., 2019; Forcellini, 2021; Wani et al., 2022). However, the increased deformations of the system led to undesirable effects on the whole structure's second-order (P-△) response, experiencing instability. As a result, the structure is vulnerable to long-period wave vibrations. Overall, investigations on the effect of the SSI on building capacity evaluation discovered that it does not have a beneficial or detrimental impact on all types of buildings in all types of soil. Structures constructed on soft soil exhibit significantly different seismic responses than those constructed on medium or hard soil (FEMA-440, 2005; ASCE/SEI, 2007; Jayalekshmi & Chinmayi, 2014; Abdel Raheem et al., 2015; Sairam et al., 2018; Oz et al., 2020). The findings presented above indicate a requirement for comprehensive research on RC structures, representing the vast majority of designed and constructed structures. The results of the post-earthquake damage evaluation show that a thorough understanding of all vulnerability 8 characteristics connected to the seismic behaviour of infilled RC framed structure, which includes the interaction between structural and non-structural elements and between superstructure and foundation, is essential. Although the effects on buildings are somewhat predictable, the consequences for recovery are considered unpredictable, and such structures' life safety risks are unknown. Therefore, to facilitate practising engineers in mitigating risk or evaluating seismic performance for a new structure, it is necessary to develop a reliable risk assessment framework, as existing seismic building codes are insufficient to prevent future damage and losses. Three important issues were raised in this study.  Firstly, the reliable analytical method needs to be investigated to select the most appropriate model to properly assess the infilled framed structures, particularly due to the in-plane effect.  The second issue that needs to be clarified is the beneficial and detrimental effects of a code-conforming building when subjected to severe earthquakes.  Lastly, the lack of studies considering the SSI effect in the seismic analysis of buildings needs to be counted when evaluating the maximum response of buildings. These three issues will be further investigated by implementing the probabilistic methodology to develop the seismic risk assessment framework, thus overcoming the above limitations. 9 1.2 Research Questions The following research questions were selected based on the problem statement. 1. Which predictive equations reliably estimate the main parameters of infill wall response? 2. How effectively can moderately ductile and ductile RC frame buildings with URM infill walls respond to the effects of an earthquake? 3. How is the dynamic response of a structure affected by the interaction between soil and structure? When the SSI effect is considered, is the depth of the foundation's embedment in the soil important for the seismic performance of the building? 1.3 Research Objectives and Scope This research aims to develop an improved conceptual framework and provide benchmark data for assessing the risk of code-conforming RC frames with unreinforced masonry infill walls due to severe seismic effects. Several supporting objectives are identified to achieve the proposed objectives. Each can contribute to the body of knowledge related to the seismic performance of code-conforming RC buildings. The supporting goals in this research are summarized as follows: 1. Develop general guidelines for evaluating the parameters to define the monotonic and hysteretic response of the masonry infill walls. This requires a detailed understanding of computational analysis as a research tool and a comprehensive study of the advantages and disadvantages of the approach chosen. This study validates the computational model of the RC frame members, and the URM infill wall developed using OpenSees software, based on the proposed framework, with past experimental 10 works. These guidelines will offer an adequate model for the in-plane analyses of URM-infilled RC frames. 2. Demonstrate the proposed guidelines to assess the seismic risk of the code-conforming RC frame buildings with and without URM infill walls under in-plane effect to evaluate the buildings' seismic safety and fragility collapse. This can be carried out using a parametric study, which includes different ductility levels, heights, and infill wall configurations that are representatives of a modern buildings, through nonlinear response history analysis (NRHA). 3. Investigate the seismic vulnerability of RC frame buildings with and without URM infill walls by considering the effect of SSI with various parameters. To this aim, varying shallow foundation depths of embedment at the same soil site location are investigated. The research focused on analyzing modern reinforced concrete (RC) frame buildings with regular floor plans, specifically low- to mid-rise structures without basements. In the analysis, the contribution of infill walls without openings is considered non-integral with the RC frames. The design of RC frame members aimed for ductility and moderate ductility in RC moment resisting frames (MRFs). Additionally, the analysis considered the effects of soil-structure interaction (SSI). However, it is important to note that the research did not aim to assess the risk level of individual structures in Vancouver. Instead, the primary goal was to develop frameworks that local governments in Vancouver and other parts of Canada could use to promote and implement measures for mitigating the seismic risk associated with infilled RC frames. 11 1.4 Thesis Organization This dissertation is organised per the objectives of the study, which is written based on manuscripts submitted and published in various journals. Each chapter includes a summary of the preceding chapter, an overview of the chapter, and a summary of the findings. The contents of each chapter of the dissertation are described below. Chapter 1 provides a brief introduction that clarifies the background of the problem, research questions, objectives, and the scope of the dissertation are also clarified. Chapter 2 presents a detailed literature review of the performance of RC frames with URM infill walls during past major earthquakes to motivate the study of the seismic performance of RC frame buildings. Then, a summary of the failure modes of the masonry-infilled frames is presented. Next, the previous and current study of assessing the infilled RC frames is systematically reviewed, and its limitations are highlighted. Subsequently, the masonry modelling proposed by several past researchers is investigated to provide a basis for this study. Then, the available empirical equations of the strength and stiffness of the masonry infill wall model for in-plane are studied. Following this, this study critically reviews the SSI effects on the seismic performance of RC frame systems. Overall, the review focuses on the studies conducted on the collapse response of structures under severe earthquake loads. Chapter 3 presents the development of a general guideline for evaluating the parameters to define the monotonic and hysteretic response of the masonry infill walls modelled by equivalent struts, specifically for the in-plane lateral cyclic response. To select a simple and reliable analytical model that suitable for representing the infill wall response, different strut formulations and hysteretic models have been analyzed in detail and used to reproduce several experimental tests 12 available in the literature. The numerical analyses are performed using the OpenSees computer program. Three uniaxial material models available in OpenSees are used to assess their capability in reproducing the experimental hysteretic response. Finally, from the comparison among different models and numerical and experimental results, suggestions are made to properly model the in-plane non-linear response of infills. Chapter 4 presents a collapse risk assessment of code-conforming reinforced concrete moment resisting frame (RC MRF) buildings in Vancouver, Canada. This assessment investigates the three- and six-storey regular RC MRF building systems, with and without unreinforced masonry infill walls, representing low- to mid-rise structures. These buildings are designed according to the National Building Code of Canada 2010 (NBCC 2010) and detailed based on the 2014 Canadian Standards Association A23.3 standard provision for high seismic regions. Two different ductility classes of seismic building design, namely ductile and moderately ductile, are considered to identify the capability, equality, and/or difference in the seismic performance of these designed buildings. Nonlinear dynamic analysis is applied in the performance-based seismic assessment procedures to assess the collapse response of structural for the set of 50-pair ground motion records. Next, the seismic fragility curves are developed through incremental dynamic analysis (IDA). Finally, the mean annual frequency of collapse is calculated through a combination of the fragility curve and hazard curve. Chapter 5 investigates whether the seismic performance and vulnerability of reinforced concrete (RC) structures were affected by soil–structure interaction (SSI). A set of RC frames were modelled with and without considering the SSI effect using the OpenSees program. A nonlinear Winkler-based method was applied to model the soil–foundation interaction. Nonlinear incremental dynamic analyses were performed to assess the seismic behaviour and fragility of RC buildings regarding the rigid and flexible-base assumptions. This chapter investigates the 13 seismic vulnerability of buildings with various indicators of collapse to assess the impact of each deficiency on building performance and define building safety. Chapter 6 comprises key results/summary, major conclusions, contributions, and limitations of this research. Suggestions/recommendations for future research are also provided. 14 CHAPTER 2: Literature review The previous chapter explicitly outlined the research questions and objectives of the thesis and the summaries for all chapters. This chapter focuses on literature studies that summarize the seismic performance of the RC frame buildings with and without the masonry infill walls subjected to past major earthquakes. Next, the previous experimental and numerical research on infilled-frame buildings is reviewed to identify the behaviour of infilled RC frames, focusing on local and global effects and the in-plane failure modes of URM infill walls. The theoretical model based on the failure mechanism of the infill wall proposed in previous research is then presented. Next, the analytical model techniques for the infill URM walls are discussed. This section further discusses only the macro model technique. The influence of the interaction between the soil and the structure considered an important factor in the performance of RC buildings, is the topic of the final section. 2.1 Introduction Earthquakes are well-known natural hazards that can risk any structure, yet infilled reinforced concrete (RC) frames are one of the structures most vulnerable to earthquake action due to the presence of infill walls (De Angelis & Pecce, 2019; Furtado & Teresa de Risi, 2020; Furtado, Rodrigues, Arêde, & Varum, 2021; Bagnoli, Grande, & Milani, 2022; Sathurshan, Thamboo, Mallikarachchi, Wijesundara, & Dias, 2023). RC frame with unreinforced masonry (URM) infill wall is vastly used in North America and abroad for multi-storey buildings, generally for low- to –medium-rise residential, school, and government buildings. The RC moment-resisting frame (RC MRF) with URM infill walls is defined as a composite structure developed by combining the infill walls and a moment-resisting frame. The RC frame is commonly used as a gravity and lateral load-resisting system (Moehle, Hooper, & Lubke, 2008; Ahmad & Owais, 2016), while URM infill walls are widely used in RC frame buildings as internal partitions and exterior enclosure walls. 15 The masonry infill walls, generally considered non-structural elements, are built after the construction of the RC frame, in which the compressive and tensile strength of masonry play important properties that affect the structural performance. The URM infill walls should be installed with a sufficient gap and a good connection to the surrounding frames, which the interaction that was developed between them can influence both the local and global effects (Stylianidis, 2012; NBCC 2010). Despite their relatively well-known poor seismic behaviour, URM buildings continue to be used, even in areas prone to high seismic activity levels, due to their reliability against fire and moisture, good thermal and acoustic insulation, and low construction costs (Longo et al., 2018). The seismic performance of unreinforced masonry-infilled RC frame (URM RC frame) buildings has been a major topic of interest since the 1950s. Many researchers have studied the behaviour and performance of RC frame structures with URM infill walls. They have revealed that the presence of masonry walls in RC frames as an infill can change the behaviour of whole structures (Catherin Jeselia et al., 2013; Tarque et al., 2015; Alwashali, Sen, Jin, & Maeda, 2019), as illustrated in Figure 2.1. The infilled RC frame may have a potential positive or negative effect on the structure's seismic performance. The beneficial effects of infilled reinforced concrete (RC) frames on seismic performance include increased structural stiffness, strength, energy dissipation, reduced storey drift, and the addition of in-plane shear resistance. Most of the detrimental impact is attributable to poor earthquake design and construction detailing of infill walls, which, if taken into account, can positively impact the performance of new buildings (Vicente et al., 2012). Therefore, failure to consider infill masonry panels may result in inaccurate evaluations of RC frame buildings' lateral stiffness, strength, and ductility. However, many current design codes still do not, or very few, consider infills and their influence on the structural response. As evidenced by recent earthquakes worldwide, most buildings, either non-ductile or ductile, suffer significant damage after a major earthquake. This demonstrates that the seismic risk 16 assessment of infilled RC frames remains important to investigate whether future buildings will survive severe earthquakes. Accurately representing the performance of masonry infill walls in analytical assessments is crucial for understanding the overall seismic response of infilled-frame buildings. However, the most significant modelling of the masonry infill is the main issue for an accurate analytical assessment of the seismic performance of the infilled-frame buildings. This is due to the complexity of the interaction between the infill and the frame and the enormous number of parameters involved, as well as seismic codes often regard infill walls as nonstructural components. Therefore, a more reliable analytical model is required to evaluate the performance of masonry-infilled RC frame buildings appropriately. (a) (b) Figure 2.1: The effect of masonry infill on the modification of the lateral load transfer mechanism, (a) bare frame- predominant frame action, and (b) fully infill frame- predominant truss action (Based on work from Kaushik, Rai, & Jain, 2006). To yield a clear understanding of the structural behaviour of RC frames with masonry infill, an extensive literature review of several past studies is summarized in this chapter. Several analytical methods proposed by several researchers for evaluating the lateral strength and stiffness of masonry infill are also presented in this section to develop a reliable model in the current study. Although the target of the study is RC frames with unreinforced brick masonry infill 17 under seismic loading, the interaction between the soil and structure, which is considered an important parameter for the performance of the RC buildings, is also included to evaluate the significant effect on the building’s performance. 2.2 Seismic performance of RC frame buildings with URM infill wall: Lessons from earthquakes Recent and past earthquake assessment reports and damage and collapse surveys of RC buildings in severe earthquake areas highlight the significance of masonry infills in local and global seismic response (Humar, Lau, & Pierre, 2001; Braga, Manfredi, Masi, Salvatori, & Vona, 2011; Vicente et al., 2012; Piroglu & Ozakgul, 2013; Aguiar & Mieles, 2016; Idris et al., 2022 ). RC buildings with masonry infill exhibited better performance than bare-frame buildings. The observation results showed that masonry infill has a crucial role in preventing the collapse of such buildings. According to Humar, Lau, & Pierre (2001), several RC frame buildings in Ahmedabad were damaged or collapsed during the 2001 Bhuj earthquake. Multiple factors caused the damage. An open first storey, inadequate detailing, and varying material quality contributed to the damage. Many RC frames had masonry walls except on the first floor, which was for parking. Upper-storey masonry infills stiffen the building, increasing seismic forces. The high shears on the first-storey columns have damaged the visible hinge zones at the top of the columns, as shown in Figure 2.2. Buildings with brick-in-cement mortar survived and performed better, despite major cracks. In several cases, masonry infill panels saved RC buildings from collapse or major damage, especially when the infill filled throughout the building's height. Even if the infill wall is not attached to the surrounding frame, it could prevent the building from collapsing if it is uniformly distributed throughout the height. 18 (a) (b) Figure 2.2: Damaged or collapsed during the 2001 Bhuj earthquake, (a) The damage and hinge regions of the columns in the open first storey of this building, (b) infilled low-rise RC frame with uniform strength and stiffness experienced nearly uniform damage along its height. (From © Murty, Goel, Goyal et al., 2002. Reinforced Concrete Structures. Earthquake Spectra, 8(1_suppl), 149-185. Page 167. By permission from SAGE Publications). Doǧangün (2004) reported that the building collapses during the 2003 Bingol earthquake in Turkey were categorized as heavy damage/collapse, medium damage, and low damage. Multi-storey government buildings (schools, dormitories, state buildings) constructed with RC buildings with hollow-brick infill walls contributed to the most significant earthquake damage. Figure 2.3(a) and (b) show that the damages of RC frame buildings are related to the infill masonry walls, such as soft and weak storey collapses caused by the absence of infill masonry walls in the ground storey, failures due to a short column that formed as a result of a lack of structural design and openings in infill walls, and the presence of large and heavy overhangs. The building's collapses and damages were also caused by non-ductile factors such as a lack of transverse reinforcement (ties) in most of the damaged columns, poor concrete quality that split within the reinforcement cage, and strong beams-weak columns. 19 (a) (b) (c) (d) Figure 2.3: Observed damage cases of infill walls on RC frame structures during the 2003 Bingöl earthquake; (a) Failure ground stories and damaged buildings due to soft storey, (b) Diagonal cracks and separation of infill walls, (c) Failure columns due to short column effect, and (d) Captive column developed by partial height masonry wall (From © Doǧangün, 2004. Performance of reinforced concrete buildings during the May 1, 2003 Bingöl Earthquake in Turkey, Engineering Structures, 26(6), 841-856. Page 846,849,851. By permission from Elsevier). Nevertheless, Gur et al. (2009), who focused on the performance of school buildings in Turkey during the 1999 Düzce and 2003 Bingol Earthquakes, observed that the performance of the surveyed buildings with moment-resisting RC frames seems to be related to the number of stories since the column size is uniform in all of the schools. The two-storey buildings were able to withstand the earthquake without suffering any damage to their columns. The contribution of the masonry walls to the strength and stiffness of the structures was sufficient to control the first-storey drift in the buildings because the force and displacement requirement on these buildings was low during the Bingol earthquake. In three-storey buildings or higher, lateral strength exceeded the requirement, causing poor performance. Both the infill walls and the captive columns had significant damage. The masonry walls' degradation reduced the structures' lateral 20 stiffness and increased storey drifts. New captive columns were developed by crushing the masonry walls' corner regions. Many buildings with three stories or higher suffered shear damage to their columns; some collapsed because the columns failed in shear, as shown in Figure 2.3(c) and (d). During the 2008 Wenchuan Earthquake, many buildings constructed with RC moment-resisting frames (MRF) also experienced soft-storey failure on the ground or first floors, as shown in Figure 2.4 (Free et al., 2008). These resulted from the uneven distribution of infill walls between stories. This has been identified as a significant issue in many earthquakes throughout history. Figure 2.4: Six-storey RC MRF that is exhibiting a soft-storey failure mechanism at the ground storey (detail of ground floor columns, right) subjected to Wenchuan Earthquake (Free et al., 2008, Image reproduced under fair dealing for research purposes). However, Decanini, Liberatore, & Mollaioli (2012) reported several RC frame and masonry buildings collapsed and several out-of-plane failures of the non-structural wall due to weak connections between the frame and wall during the L' Aquila, Italy earthquake in 2009 (Vicente et al., 2012). The impacted region's RC frame buildings are mostly two- to four-storey and multi-storey up to eight-storey residential and office buildings, with regular and irregular layouts in plan 21 and elevation. All these constructions are infilled moment-resisting RC frames with one or two withes of hollow clay brick infill or concrete blocks (in the perimeter). Due to the brief period of ground shaking, the infill walls also prevented non-ductile framed constructions from collapsing. Various damage observations have shown that, regardless of storey level, the interior walls' quality and material significantly impact how they interact with the structural frame and can lead to different damage categories. More recent earthquakes, such as in Van earthquake in 2011 (Yön, Onat, & Öncü, 2019), Kefalonia in 2014 (Bournas, 2018), Nepal in 2015 (Chen et al., 2017) and Pidie Jaya in 2016 (Idris et al., 2022), reported a similar problem in infilled RC frame buildings, including total collapse, soft-storey collapse, and significant deformation on the ground columns. The collapse and severe damage suffered by many buildings were typically the results of poor structural design and insufficient detailing. Figure 2.5 shows the damage patterns of infill walls and RC frames, varying from minor cracks to significant damage gathered from previous earthquakes. 22 (a) (b) (c) (d) (e) (f) Figure 2.5: Damage pattern infill walls and RC frames; (a) out-of-plane failure, L’Aquila earthquake, 2009 (From © Augenti & Parisi, 2010. Learning from Construction Failures due to the 2009 L’Aquila, Italy, Earthquake, Journal of Performance of Constructed Facilities, 24(6), 536–555. Page 541. By permission from American Society of Civil Engineers), (b) and (c) beam shear and infill wall diagonal cracking failure, Nepal Earthquake, 2015 (From © Syakya & Kawan, 2016. Reconnaissance based damage survey of buildings in Kathmandu valley: An aftermath of 7.8 Mw, 25 April 2015 Gorkha (Nepal) earthquake. Engineering Failure Analysis, 59, 161-184. Page 171. By permission from Elsevier), (d) infill shear failure, Pidie Jaya earthquake, 2016 (From © Idris et al., 2022. Post-earthquake damage assessment after the 6.5 Mw earthquake on December, 7th 2016 in Pidie Jaya, Indonesia. Journal of Earthquake Engineering, 26(1), 409–426. Page 421. By permission from Taylor & Francis), (e) diagonal failure and partial collapse (OOP failure), Kefalonia earthquake, 2014 (From © Bournas, 2018. Concurrent seismic and energy retrofitting of RC and masonry building envelopes using inorganic textile-based composites combined with insulation materials: A new concept. Composites Part B: Engineering, 148, 166–179. Page 168. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)), and (f) tension strut failure, Van earthquake, 2011. (From © Yön, Onat, & Öncü, 2019. Earthquake damage to nonstructural elements of reinforced concrete buildings during 2011 Van Seismic sequence. Journal of Performance of Constructed Facilities, 33(6). Page 6. By permission from American Society of Civil Engineers). Field evidence from recent earthquakes above has demonstrated how infill masonry panels significantly affect the structural behaviour of RC buildings. Based on the damages observed during previous severe earthquakes, most of the damages and collapses of RC frame 23 buildings are often associated with the infill masonry walls. Damages in RC buildings that caused collapses or severe damage were primarily due to; (i) soft-storey and weak-storey collapses caused by the absence of infill masonry walls in the ground stories, (ii) short column failure due to structural arrangements or openings in infill walls between columns, (iii) insufficient reinforcing detailing in beam-column joints, and (iv) non-structural irregularities in plan or elevation. The most severe damage was recorded in a three- to six-storey RC building with masonry infill walls. Besides, there were several non-structural damages, mainly due to in-plane (IP) action, has also been recorded, which can be categorized as; (i) cracking due to detachments of the panels in masonry walls RC frame building, (ii) tension strut mechanism across the infill, (iii) infill wall crushing at the corner close to the window opening, and (iv) shear cracking of partition walls (Yön et al., 2019). Out-of-plane failure is another non-structural damage generally observed due to maximum drift value under in-plane damage or overturning effect due to the horizontal seismic action of shear failure in the in-plane direction. Nevertheless, perhaps most importantly, many RC frame buildings with infill walls were not designed in accordance with seismic design procedures or standards. The lack of comprehensive guidelines regarding the design and analysis of infill wall elements in RC frame buildings is an important contributing factor. Although guidelines, such as specified in the NBCC, do incorporate certain requirements, it does not offer a comprehensive framework for this particular aspect. As a result, the seismic performance of the infilled-RC frame buildings might not have been adequately considered in design and analysis, potentially leading to structural vulnerabilities or collapse during seismic events. Therefore, to reduce the loss of human lives and costs, as well as to prevent damage and collapse during a severe earthquake, the influence and involvement of infill masonry panels in the seismic behaviour of RC buildings should be considered when designing new structures and assessing existing structures, as they may contribute to structural stability or cause undesirable damage or collapse of RC buildings. 24 2.3 In-plane behaviour of URM infill walls As the focus of this study, this section will review and summarize the current knowledge concerning the different in-plane effects of the masonry-infilled RC frames and the analytical model of the masonry infill subjected to in-plane only. Integrating URM infill walls into an RC frame profoundly affects the behaviour of both components. In RC buildings, infill walls are not considered structural elements as they are not expected to carry loads under static conditions. However, when large lateral or vertical deformation in RC buildings develops, the infill wall is activated, altering the frame structure's response, reducing the bending moment, and increasing the axial loads on the columns and beams (Dias-Oliveira, Rodrigues, Asteris, & Varum, 2022). Overall, the behaviour of the infilled RC frame is subject to various uncertainties and cannot be predicted by simple means. Therefore, understanding the experimental response of the infilled frame and the corresponding bare frame is required to develop a reliable model for designing, analyzing, and assessing the seismic performance of infilled RC frame buildings subjected to in-plane lateral loads. 2.3.1 Experimental studies of infilled RC Frames subjected to in-plane lateral load Over the last two decades, numerous experimental studies have been conducted to investigate the impact of infill on the local effect due to interactions between the infill and the surrounding RC frame and the global lateral resistance of the RC frame. Mehrabi, Shing, Schuller, & Noland (1996) conducted in-plane cyclic tests on two types of frames, non-ductile and ductile, designed for Seismic Zone 4 per the 1991 Uniform Building Code. Twelve half-scaled single-storey one-bay RC frames with unreinforced masonry infill were tested. Two types of infill walls were considered, which are hollow and solid concrete blocks representing 25 strong and weak infill. The experimental results reveal that infill panels can significantly increase the performance of RC frames in terms of lateral strength, stiffness, and energy dissipation, particularly for specimens with a strong frame and infill wall. Brittle shear failure was observed in column specimens with weak frames and strong infills. Still, it showed better energy-dissipation capability than in a weak frame with a weak panel. This study shows that infill panels will improve the performance of RC frame buildings designed for strong seismic loads. Besides, Infill panels may also enhance existing non-ductile frame performance. In the same context, Lee & Woo (2002) tested 1:5 scale masonry infilled non-ductile RC frames with two bays and three stories under dynamic and static monotonic conditions. This study investigates the effect of masonry infills on low-rise reinforced concrete (RC) frames designed according to Korean non-seismic details. They also noticed a considerable increase in global structure stiffness, strength, and earthquake inertial force than a bare frame due to the presence of the masonry infill. They also observed that the infilled frame failed by shear due to bed-joint sliding of the masonry infills, whereas the bare frame appeared to fail with a soft-storey plastic mechanism on the first floor. They conclude that the masonry infills can improve the structure's seismic performance since the strength increase is more than the induced earthquake inertia forces and the global structure's deformation capacity is almost the same. To investigate the relationship between the observed cracking and the storey drift-storey shear response, Buonopane & White (1999) performed pseudo-dynamic tests (PSD) on a two-bay, two-storey, 1/2-scale masonry-infilled non-ductile RC frame. In this study, two openings have been considered in the second storey. The PSD tests revealed that the type of cracking was directly related to the structure's ability to withstand lateral loads without severe deformation by establishing and maintaining effective compressive strut action. The pattern of stepped cracks on the second floor stabilized, preventing severe deformations. In contrast, the first-storey infill 26 deteriorated and developed extensive bed joint cracks, leading to a soft-storey response. Infill panel sliding failures can produce brittle failures such as column shear cracking in non-ductile RC concrete frames. Hashemi & Mosalam (2006) used a shaking table to evaluate a ¾-scale one-bay masonry infilled RC frame as a model for a basement of a five-storey building with the top beams joined by a concrete slab. They concluded that the presence of unreinforced masonry infills significantly affects the strength and ductility of RC frame buildings and should be considered in both analysis and design. Besides, unreinforced masonry infills not only improved stiffness by 3.8 times but also reduced the structure's natural period by 50% and increased the damping coefficient from 4% to 5-12%, and increased the dissipated energy of the structure, which significantly increased the load demand and decreased the deformations demands. Later, Kakaletsis & Karayannis (2007, 2008, 2009) conducted a series of tests on 1/3 scale single-storey single-bay RC frame specimens under cyclic horizontal loading up to a drift level of 4%. This study investigates the effect of openings, including windows and doors with various locations, sizes, and shapes, on the hysteretic characteristics of infilled RC frames and to understand better the comparative performance of the window and door openings positions in the frame. The experimental program also investigated the effect of two types of infill compressive strength, weak and strong infill, on the seismic performance of infilled RC frames with openings. The RC frame is designed as a typical ductile structure per Greece standards. Kakaletsis & Karayannis (2007, 2008, 2009) reported that masonry infills with eccentrically positioned openings improve the seismic capacity of bare RC frames in terms of strength, stiffness, ductility, and energy dissipation. However, the experimental results demonstrate that the impact of different types of openings resulted in a reduced seismic capacity of the infilled RC frame, in which door openings demonstrated a higher impact than window openings. They observed that the infilled 27 frame performs better with the opening near the infill edge. On the other hand, specimens with strong infills outperformed those with weak infills. Stylianidis (2012) performed 38 tests with a 1/3 scale single-storey one-bay RC moment resisting frames to assess the seismic response based on structural uncertainties. The experimental tests were divided into three experimental programs. Testing parameters for the first program (P1) include the axial compressive load on the columns, the connection between the RC frame and the infill panel, the quality of the mortar, and the existence of an RC lintel beam. In contrast, the second program (P2) variables include column load, the frame aspect ratio, the columns and beam reinforcement ratio, and the thickness of the infill. The third program (P3) focused on low-cost strengthening techniques on ten damaged samples from the first program. The results obtained from programs 1 and 2 show that the failure modes of the infilled frames with weak infill are similar to bare frames; infilled frames had a comparatively higher pinching impact than bare frames; infill wall reduced the ductility of the infilled frame but provided strength, stiffness, and energy dissipation which depend on their strength relative to the frame; vertical loading applied on the column of infilled frame increased the resistance, initial stiffness, and energy dissipation but reduced ductility yet still satisfactory; vertical loading applied on bare frame column increased the ductility slightly of the system; the good contact conditions increase strength, initial stiffness, and energy dissipation capacity but the ductility is not affected; Strong mortar increases strength, initial stiffness, and energy dissipation, but not ductility; the concrete lintel beam reduced strength, initial stiffness and energy dissipation at low displacement level; the aspect ratio of the frame affects infilled specimens more than bare frames; strength, initial stiffness, and energy dissipation are all improved in both bare and infilled frames due to the increased reinforcement ratio of the columns and beam; increased masonry thickness slightly increases infilled frame strength, initial stiffness, and energy dissipation. 28 Similarly, Basha & Kaushik (2016) tested eleven 1/2-scaled RC frames under cyclic in-plane lateral loading. This study investigates the lateral load behaviour of an infilled RC frame with strong-frame and weak-infill, evaluates the effectiveness of earthquake standard design requirements in improving the shear behaviour of RC columns, and assesses the impact of T-beam action provided by the RC slab on the behaviour of RC beams. The tests were carried out in two phases, the first consisting of eight ductile and non-ductile RC frames with full and 1/2-scaled fly ash bricks and the second involving three ductile-infilled RC frames with improved detailing and full-scale bricks. The experimental result of the first phase revealed that full-scale and half-scale brick-infilled frames had better resistance, stiffness, and energy dissipation than bare frames, which varied from 7-10 times for stiffness, 1.6-2.5 times for strength, respectively and 1-2.3 times for dissipated energy. This study also observed that columns of infilled frame failed in shear due to the strong-frame weak-infill. The stiffening (T-beam) action generated by the RC slab did not appear to have caused significant damage to any of the specimens' beams. The results from the second phase of the experiment show that provisions in the current code of practice do not appear to prevent shear failure in RC columns of infilled frames, even when a strong-frame weak-infill system is adopted. As a result, they recommend improved design methodologies for RC frames with masonry infills. Jiang, Liu, & Mao (2015) conducted lateral reversal low-cyclic load experiments on seven full-scale, single-bay, and single-storey RC frame specimens, focusing on three connections between RC frame and infill: flexible, stiff, and without connections. Jiang et al. (2015) concluded that the contribution of a rigidly connected masonry infill wall to the frame increases the lateral strength, stiffness, and energy-dissipation capacity of the bare RC frame significantly while resulting in a significant reduction in the displacement ductility ratio. However, the strength, stiffness, and energy-dissipation capacity contributed by the infill wall with a flexible connection 29 are much lower when compared to the infill wall with rigid connection, while the displacement ductility ratio of the frame increases. Dautaj, Kadiri, & Kabashi (2018) examined the behaviour of masonry-infilled RC frames with various types of masonry units and varying lateral strength of RC frames. Eight 2/3-scale, single-bay, single-storey RC frames were tested. Six specimens were infilled with hollow clay block masonry units and RC frames of varied strengths, one with solid clay bricks and one without infill (bare frame). This study also revealed that the failure mechanism of masonry-infilled RC frames varied according to the masonry unit tested. The principal failure mechanisms of the RC frames with hollow clay blocks infill were masonry infill shear failure, beam-column joint failure, and flexural hinges in the RC frame. Masonry-infilled RC frames with solid clay bricks failed due to column and masonry infill shear failure. Experimental results suggest minimal lateral design strength criteria for RC frames infilled with hollow clay blocks to ensure controlled ultimate failure. More recently, Alwashali et al. (2019) performed a static cyclic lateral loading test on three 12-scale single-storey RC frames with masonry infill to investigate in-plane seismic capacity. The surrounding RC columns, beams, and masonry infill mortar strength were examined since design codes, and significance studies differ. The experimental results verified that the shear strength of the infill increased significantly with the strength of the surrounding frame. The measured parameters did not influence the initial stiffness. The specimen of a masonry panel built with low-strength mortar exhibited much-improved ductility and significantly less damage to the masonry infill panel and the surrounding frame. Alwashali et al. (2019) reported that the frame strength ratio could affect the shear strength of the masonry infill and the structure's ductility. They suggested that the new building design requirements should consider it. 30 Approximately two hundred RC frame experiments with various infills can be compiled from published research over five decades that can refer to studies by Dias-Oliveira et al. (2022) and Furtado & Teresa de Risi (2020). However, the present section summarized some of the experimental investigations carried out during the past two decades; each study concentrated on a different purpose. Some experiments investigated how the infill panel affected the overall lateral response of the frame and how that response varied depending on factors such as infill type (e.g., solid or hollow clay or concrete bricks), the strength of mortar, relative stiffness and strength of the infill to the frame, and the presence of openings (such as windows and doors) of varying size, shape, location, and eccentricity. Most experimental works used in-plane monotonic horizontal loading, in-plane cyclic loading, or seismic excitation through shake table tests. Among the other investigated parameters, numerous specimens tested were infilled frames with a reduced or full-scale one-bay and one-storey RC frame, and fewer infilled or bare RC frames with two or three storeys were tested. These experimental results demonstrated that the performance and behaviour of URM infill on RC frame buildings vary based on several parameters, including the level of lateral load applied to the structures. The current discussion covered the key findings of these experimental studies on URM infills on RC frames under in-plane actions, as follows: 1. URM infill walls increase frame rigidity due to their high lateral stiffness. Therefore, Infilled frames are stiffer than bare frames and can change damage behaviour where the infill acts as a diagonal strut. 2. URM infill wall has excellent lateral load resistance. As a result, URM-filled frames have higher strength than bare frames. 31 3. Compared to the bare frame, the infilled frame will exhibit reduced deformations along the height of the structure. 4. The infill material strength properties, infill-to-frame relative stiffness and strength, ductile detailing of the frame, and openings influence the ductility of the infilled frame. 5. URM infill wall dissipates energy on frame structures through friction at structural interfaces, enhancing dynamic behaviour. 6. URM infill wall can protect the structure against low to medium-intensity lateral loads. However, seismic loading, which involves large numbers of nonlinear reversed cyclic loads, reduces the infill wall's contribution to the frame's lateral stiffness. It should be noted that several specimens from the above-mentioned test programmes were used in the modelling, analysis, and calibration techniques developed throughout the course of this thesis. 2.3.2 Failure modes of infilled frames due to in-plane loads According to Asteris, Antoniou, Sophianopoulos, & Chrysostomou (2011), the observed failure mode has differed depending on the main geometrical and mechanical features of infills and frames. Based on the experimental and analytical results obtained over the past several decades, different failure modes of masonry-infilled frames were identified (Wood, 1958; Stafford Smith & Carter, 1969; Liauw & Kwan, 1985; Sobaih & Abdin, 1988; Mehrabi et al., 1996) and 32 categorised into several failure mechanisms (Wood, 1978; Paulay & Priestley, 1992; Mehrabi et al., 1996; El-Dakhakhni, 2002; Shing & Mehrabi, 2002; El-Dakhakhni, Elgaaly, & Hamid, 2003; Asteris et al., 2011; Medriosa et al., 2022), which are as follows: 1. The corner crushing (CC) failure (Figure 2.6(a)); represents that at least one of the loaded corners of the infill has been crushed by compression. This mechanism is commonly observed in infilled frames with a weak masonry-infill panel surrounded by a frame with weak joints and strong members. 2. The sliding shear (SS) failure (Figure 2.6(b)); represents by horizontal sliding-shear failure (single or multiple) along mortar bed joints of masonry infill. The single sliding shear is usually at mid-height to the panel, whereas multiple sliding-shear formations are distributed across the panel height. This mechanism is frequently related to the infill of weak mortar joints and a strong frame and is one of the most important failure types that can reduce panel stiffness and may cause local frame deficiencies. However, it does not cause total failure because the panel preserves some lateral strength for the infilled frame. 3. The diagonal crack (DK) failure (Figure 2.6(b)); represents by cracks along the infill compressed diagonals, which frequently co-occur with sliding shear, corner crushing, and frame failure. This mechanism is commonly related to a weak frame (or weak joints with strong members) infilled with a strong infill. 4. The diagonal compression (DC) failure (Figure 2.6(a)); represents by the infill crushing observed in the middle of the panel. This mechanism is associated with the presence of thin infill walls as well as out-of-plane buckling. 33 5. The frame failure (FF) - (Flexural or shear failure of the columns) (Figure 2.6(b)); occurs when plastic hinges form in the columns, or shear failure occurs in the beam-column joints or columns. This mechanism is related to a weak frame or a frame with weak joints and strong members infilled with a strong infill. A variety of factors could cause the failure caused by the infill walls. The axial stresses on columns can be increased by increasing the stiffness and the forces introduced by the infills. The infill's diagonal truss generates a concentration zone in which the wall transfers some stress around the joints. This increases the shear stresses in the columns and the beams. In this case, the joints may fail, which would cause the system to fail. Infill shear failure or openings that cause a short column may increase flexural and shear force demand. (a) (b) Figure 2.6: Infill Failure Modes; (a) Corner Crushing and Diagonal Compression, and (b) Shear Sliding, Diagonal Cracking, and Frame Failure. (From © Asteris et al., 2011. Mathematical macromodeling of infilled frames: state of the art. Journal of Structural Engineering, 137(12), 1508–1517. Page 1509. By permission from American Society of Civil Engineers). The most common failure types with only in-plane loads are sliding shear on mortar layers, corner crushing, and diagonal tension cracking (Dias-Oliveira et al., 2022). 34 2.4 Numerical Modelling of URM infill walls subjected to in-plane failure The practice of analytical or numerical analysis is frequently used due to the challenges, constraints, and high costs associated with testing RC structural systems. To this end, the seismic behaviour of masonry infills should be adequately defined to appropriately develop the fragility functions for this structural type. As a result, much effort has been made to develop analytical tools and computational models that can simulate the seismic behaviour of masonry infill and its interaction with RC frames. However, despite extensive research studies on the topic, the most significant modelling and guideline of the masonry-infilled frame remains an open issue due to the complexity of the interaction between the infill and the frame, which exhibits highly nonlinear behaviour. Furthermore, the vast number of parameters involved results in various failure mechanisms. As a result, there are no established guidelines for modelling or analysis to appropriately assess the performance of RC frame structures with masonry infill walls. In order to accurately represent the effect of infills on the overall behaviour of RC frames under seismic activities from the early stages of damage to collapse, reliable nonlinear modelling guidelines are required. In order to achieve this, the current section outlines the modelling techniques and analytical models proposed in the prior studies and implemented in the current study. The literature comprehensively evaluates various modelling techniques for masonry-infilled RC frames (Asteris et al., 2011; Asteris, Giannopoulos, & Chrysostomou, 2012; Asteris et al., 2013; Tarque et al., 2015; Trapani et al., 2015; Asteris, Cavaleri, Di Trapani, & Sarhosis, 2016; Dias-Oliveira et al., 2022). There are two distinct modelling approaches for masonry infills: micro (or local) - and macro (or simplified) - models. The micro-modelling method facilitates experts to consider local effects and define crack patterns, ultimate load, and collapse mechanisms. The use of micro models, considering their accuracy, is quite complex. The model discretizes the member into small (micro) interconnected elements (finite element) through cross sections and 35 along member length with nonlinear hysteretic constitutive properties considering many input parameters to represent the RC frame, infill wall, and interface, resulting in a long processing time (Deierlein, Reinhorn, & Willford, 2010). The micro model also poses the most difficulties in the calibration of model parameters process and the availability of computer resources. Consequently, micro-modelling methods are typically employed primarily for particular research objectives and scopes and are useful only for small structures (Basiouny & Ghobarah, 2008). Additionally, there are three categories of micro-modelling methods: detailed, simplified and meso-modelling (Tarque et al., 2015). In the detailed micro-modelling, the brick units and the mortar are represented by continuum (smeared) elements, and discontinuum interface elements simulate their interaction. While in the simplified modelling, the brick units are modelled by continuum finite elements with the brick-mortar interface and the mortar properties are combined into a single element. Meso-modelling, considered a one-phase material, is smeared material for the brick, mortar, and their interface, and the masonry is represented as a continuum though a homogenization process. Currently, equivalent strut models are the most prevalent macro-modelling method. The simplified or macro-modelling method provides a model that can simulate the global behaviour and effect of the masonry walls on the response of the building. Compared to micro models, macro models are simpler. The macro models require a minimal number of numerical parameters that can be calibrated from experimental results, with little computational effort to predict the overall force-displacement behaviour of the infill. 2.4.1 Local Method: Micro-modelling According to Smith (1962), masonry infill walls have the same effect as a diagonal compressive strut on the RC frame. This action is expected to develop under higher load when 36 the infill partially detaches from the surrounding frame. However, it demonstrated that the infill strength and stiffness related to the surrounding frame determine the extent to which this action develops. Therefore, the complexities related to the local behaviour and interaction of an infilled frame system are better captured by micro-modelling approach. The micro-modelling approach, which discretizes a physical domain into smaller elements, allows the modeling of multiple material types, testing of complex geometry, and offers a detailed stress and strain analysis. This approach also has the ability to capture local behaviour, interaction, and nonlinear effects acting on a small area of the design. Additionally, the element-level focus allows for a more in-depth evaluation of the responses of the different components within the structure. Thus, the micro-modelling approach (finite element modelling), which can focus on the individual element, does have the potential to provide a more in-depth explanation of the response of RC frames influenced by the presence of infill walls and can identify several potential failure mechanisms. Most of the techniques and strategies proposed for the micro-analysis of infilled frames are described in this section. The micro-model approach was initially employed to analyse infilled framed structures by Mallick & Severn (1967). The analysis focused on the interface between the frame and the infill panel. Infill walls were modelled using linear elastic rectangular elements with two degrees of freedom at each node, whereas the frame was simulated with beam elements neglecting axial deformation. Wall-frame slippage was considered for the interaction, defined by frictional shear forces in the contact zone. The results of the predicted stiffness of single-storey rectangular infilled frames were in good agreement with experimental data for the to-span ratio less than two. In the 1970s, Mallick & Garg (1971) and other researchers, i.e. Kost, Weaver, & Barber (1974) and Axley & Bertero (1979), continued to implement micro models to assess the stiffness and strength of infilled frames, as well as examine the impacts of various parameters, such as gaps, openings, the bond between wall and frame, and different finite element schemes. 37 Later, in the last few decades, the finite element approach was increasingly applied to investigate the performance of infilled RC frames. Other studies have been directed into various elements of the model. Liauw & Kwan (1985a, 1985b) numerically modelled monotonic loading experiments for good predictions. The infill-frame interaction used a bar element with slip and separation capabilities. In contrast, the infill used a triangular plain stress element with varied compression (nonlinear material) and tension properties (brittle material). The model identified different failure modes, such as infill corner crushing. Dhanasekhar & Page (1986) developed a finite element model that integrated elastic characteristics, inelastic stress-strain relations, and a failure surface to study brick masonry infill walls numerically. It was designed using nonlinear isotropic components with six nodes, with brick units and mortar joints modelled separately. Data from the pushover experiment can be analytically analyzed using a computer program developed by Dawe & Seah (1989). The frame modelled with nonlinear behaviour is grouped at the end of each member. The infill masonry is represented by a series of elastic and rectangular elements connected by joints with tensile and shear capacities. Virtual joints simulate bricks to capture tensile failure on elastic elements. On the other hand, the validity of continuous‐interface models regarding the behaviour of mortar joints, accounting for the interaction between normal and tangential stresses, has been tested by other researchers such as Lourenco (1996), Mehrabi & Shing (1997), Dawe, Seah, & Liu (2001), Shing & Mehrabi (2002), Asteris (2003), Al-chaar & Mehrabi (2008), Stavridis (2009), Stavridis & Shing (2010), and Cavaleri, Zizzo, & Asteris (2020). Each study used different modelling techniques and components, separately for concrete, ties, bars, masonry, and mortar. Typical micro-modelling techniques for actual masonry walls involve a three-phase system material (Figure 2.7(b)) in which units and mortar in the joint and their contact are modelled as continuous and discontinuous elements (Rivero, 1982; Lourenco, 1996; Al-Chaar & Mehrabi, 2008). 38 Lourenço (1996) suggested combining coulomb friction, tension cut-off, and compression cap and proposed a simplified micro-modelling. The proposed model would combine the interface and mortar into a single discontinuous element while units are still represented by continuous elements, as shown in Figure 2.7(c). Damage was concentrated at the mortar joint and the pure tension surface in the middle of the masonry unit. This method is computationally efficient and can simulate masonry behaviour, such as bed joints, head joints, and masonry unit cracking. Mehrabi and Shing (1997) also used a simplified micro-model to investigate the behaviour of RC frames infilled with concrete masonry walls. The frame and the masonry units were modelled using a smeared crack element, while the mortar joints were accounted for using constitutive models that assumed elastic behaviour under compression pressures at the interfaces. The model assessed cracking, crushing, and sliding under cyclic and monotonic analysis. Using bond-slip elements between the frame and infill yielded more accurate results compared with the experiment rather than neglecting the element. Peak capacity was close to experimental data. However, system behaviour was not accurately predicted. In order to simulate the interface conditions between the infill and the frame in terms of a bond, friction, separation, and re-contact, as well as the capacity to evaluate the failure on the interfaces, Dawe et al. (2001) proposed a simplified linear finite element model using spring elements. The model also included the non-linear behaviour caused by the infill cracking under tension, crushing, and shear failure. Shing and Mehrabi (2002) used plasticity theory to study masonry wall element nonlinear behaviour. The possibility of brick–mortar, and mortar-frame cracking was taken into consideration. Based on the Rankine/Von Mises crack criterion, the system was assumed to be homogenous and isotropic until cracking occurred, followed by elastoplastic material behaviour. Asteris (2003) mainly focused on infill frame contact conditions, where the geometrical equilibrium conditions of the system were obtained by an iterative procedure using a finite element approach. With only two interface conditions—contact or 39 separation—the equilibrium prevents the infill from overlapping the frame. The approach can predict how contact conditions affect infill stiffness. Al‐Chaar et al. (2008) developed the micro-modelling of infilled RC frames using commercial DIANA software (DIANA 2011) through a combination of continuum and interface constitutive models. The continuous elements used for masonry units and the concrete in RC frames were modelled using the smeared-crack constitutive model, and the interface element to simulate the mortar joints were adopting the proposal of Lourenço (1996). The commercial program Diana used in Al-Chaar et al. (2008) also has been utilized in the study conducted by Sattar (2013) because it is more suitable for computing effort than other availability of multiple software packages. In the same context, Stavridis and Shing (2010) and Stavridis (2009) employed the potentialities of the finite element analysis program (FEAP) proposed by Taylor (2007) to develop the nonlinear finite element model. The complete system was modelled by a combination of discrete- and smeared-cracking models that can capture different failure modes, including the shear and flexural failure of RC members, crushing and splitting of brick units, and the mixed-mode fracture of mortar joints. However, Sattar (2013) claimed that the model presented by Stavridis (2009) is computationally demanding and inappropriate for practical use. Later, Mohyeddin, Goldsworthy, & Gad (2013) developed a meso-model to stimulate the in-plane and out-of-plane behaviour of infilled RC frames using the ANSYS program (ANSYS, 2012). Smeared-crack solid elements were used to model the RC frame and masonry wall, and surface contact elements were used to model the interaction between the brick units and the RC frame. The model can anticipate and analyze the infilled frame's behaviour over a wide range of lateral displacements and in-plane or out-of-plane loading. However, there are several limitations identified from this model, which are; i) the model requires the middle elastic mortar band, ii) unable to describe debonding between reinforcing bars and concrete, and iii) instability of contact elements when underlying elements are fully cracked/crushed. Zhai, Kong, Wang, & Chen (2016) modelled their experimental testing on RC frames with brick infill using the ABAQUS programme (ABAQUS, 2011). The model technique used in this study accurately 40 predicts the test specimens' seismic behaviours. Yuen, Kuang, & Ali (2016) used the same software to study the interaction between IP and OOP effect through a finite element approach. Cavaleri et al. (2020) recently used detailed finite element modelling for infilled RC frames to study the OOP behaviour of infilled panels that had been damaged previously subject to IP cyclic motions and developed equations for strength and stiffness degradation. Overall, the simulation of brick masonry is quite challenging due to the numerous influencing parameters, which include brick dimension and their different directional properties, joint width, and arrangement, the material properties of brick and mortar, and workmanship quality. For this reason, nonlinear structural finite element analysis can make use of a variety of masonry modelling techniques depending on the simplicity and accuracy level, as follows (Lourenco,1996): 1. Detailed micro-modelling - Masonry is modelled based on a three-phase material involving continuum elements representing units and mortar in the joints, and discontinuum elements used to represent the unit–mortar interface (Figure 2.7(b)). This allows for the investigation of the combined action of the unit, mortar, and interface. However, this model is suitable for small panels and structural details because of the numerical convergence complication and computation time. 2. Simplified micro-modelling – Masonry is modelled based on two-phase material in which the units are still represented as continuous elements. However, the mortar and interfaces are integrated into discontinuum elements, as shown in Figure 2.7(c)). Following this method, each joint needs to be represented with a single "average" interface based on a combination between the mortar and two unit-mortar interfaces. 41 In contrast, the units must be represented by an expanded element to maintain their geometric form. 3. Semi macro-micro (Meso)-modelling –Masonry is modelled based on one-phase material. Figure 2.7(d) shows the homogenous and continuous element used for units, mortar, and the unit-mortar interface. Masonry is a homogeneous anisotropic continuum with no difference between individual members and joints. This approach is unsuitable for the local stress study of a small panel due to the challenges in capturing all of the failure modes. The impact of mortar joints acting as weak planes is undefined. (a) (b) (c) (d) Figure 2.7: Finite element modelling strategies for masonry; (a) masonry sample, (b) detailed micro-modelling, (c) simplified micro-modelling, and (d) macro (meso)-modelling (Lourenco, 1996, Image reproduced under fair dealing for research purposes). The micro-model, which involves finite element modelling of RC frame, infill wall, and interfaces, can be most accurate to simulate their response. However, simplified strut models are 42 currently best suited for research due to the large number of parameters that need calibration for the material constitutive laws and competency in the finite element method. 2.4.2 Simplified method: Macro-modelling As mentioned in the preceding section, using micro-modelling techniques for large systems is not practicable due to the high computing required. Macro models, also known as simplified models, are one of the most effective techniques for capturing the global behaviour of infill panels, particularly in design and performance assessment, because of their simplicity and require less computational resources and time during the run of the analysis. The URM infill wall is traditionally represented by an equivalent pin-jointed diagonal strut system, as shown in Figure 2.8. Typically, the diagonal strut is connected to the intersection points of the beam and column centerlines, indicating that the numerical strut length is greater than the actual diagonal infill length. Galli (2006), on the other hand, observes that this additional length does not affect the validity of the seismic response evaluation. Figure 2.8: Macro model of equivalent diagonal strut and its related parameters (From © Panthi, Dahal, Shrestha, & Thapa, 2021. Fundamental period of RC buildings with infill walls in Nepal. Asian Journal of Civil Engineering, 22, 983-993. Page 987. Adapted with permission from Springer Nature). 43 Several macro models that represent by equivalent strut model are proposed to reproduce the major aspects of the infill-frame interaction mechanism (Polyakov, 1960; Flanagan, Bennett, & Department, 1993; Bennett, Fowler, & Flanagan, 1996; Crisafulli, 1997; Chrysostomou, Gergely, & Abel, 2002; El-Dakhakhni et al., 2003; Amato, Fossetti, Cavaleri, & Papia, 2009; Kadysiewski & Mosalam, 2009; Rodrigues, Varum, & Costa, 2010; Burton & Deierlein, 2013; Yekrangnia & Asteris, 2020; Yekrangnia & Mohammadi, 2017; Van, Lau, & Mohamed Nazri, 2022). Macro modelling with equivalent diagonal struts was initially designed to facilitate numerical analysis of infilled frames with higher lateral stiffness. However, as it improved, the diagonal strut element took into account the strength and post-peak behaviour of the wall in addition to lateral stiffness. In order to simulate the overall behaviour of entire infilled-RC frames, the proposed models vary from single- to multiple-struts models (Asteris et al. 2011) and eccentric to concentric (Tarque et al., 2015), as illustrated in Figure 2.9 (for further details, see chapter 3). (a) (b) (c) Figure 2.9: Macro model techniques: (a) Single-, (b) double-, and (c) triple-strut model (From © Furtado et al., 2015. Modelling of masonry infill walls participation in the seismic behaviour of RC buildings using OpenSees. International Journal of Advanced Structural Engineering (IJASE), 7(2), 117–127. Page 119. Creative Commons Attribution License (CC-BY 4.0)(https://creativecommons.org/licenses/by-nc/4.0/)). The diagonal strut model has different parameters depending on the type of analysis (for example, linear elastic or nonlinear) and the loading protocol (monotonic, cyclic, or transient). In a linear elastic analysis of a diagonal strut, the length and cross-section size of the strut and its modulus of elasticity is required as parameters. However, the entire force-displacement behaviour 44 of the strut is required when the nonlinear behaviour is considered. When dealing with monotonic loads, only one compression diagonal strut is required. The parameter required for the diagonal strut may become more complicated in cyclic and dynamic load situations. Therefore, extensive studies have been conducted to define the key structural parameters of the diagonal strut, including its width, stiffness, the behaviour of the diagonal strut (constitutive law), and the number of diagonal struts (Holmes, 1961; Stafford Smith & Carter, 1970; Mainstone, 1974; Thiruvengadam, 1985; Decanini & Fantin, 1987; Paulay & Priestley, 1992; Saneinejad & Hobbs, 1995; Panagiotakos & Fardis, 1996; FEMA-356, 2000; Al-chaar, 2002; Al-Chaar, Lamb, & Issa, 2003a; Asteris, 2003; Crisafulli & Carr, 2007; Amato, Fossetti, Cavaleri, & Papia, 2009; Asteris et al., 2013) (details are presented further ahead in this section and Chapter 3). Overall, macro-models can be considered the most effective method for modelling the infill panel's behaviour, especially for large buildings or when global and multiple assessments are required. The review presented in Chapter 3 (sections 3.2.2 and 3.2.3) indicates that the single strut model adequately captures the contribution of the infill walls to the global structural behaviour despite its simplicity. However, the single strut model cannot provide a realistic evaluation of the interaction between the frame and the infill wall. Alternatively, the multiple strut models may provide a reliable depiction of the behaviour during this interaction. However, because of the complicated interaction between the frame and the infill, reliable analytical approaches are required to assess infilled framed structures. Macro models, which involve replacing the masonry infill with one or more equivalent struts, offer a tremendously reasonable option between efficiency and precision, provided adequate guidelines for defining the mechanical properties of the struts are applied. However, a valid constitutive law is difficult to identify, and using different equations to estimate the equivalent strut properties may result in considerable changes in the response of infilled frames. Therefore, adopting appropriate models for assessments of masonry-infilled RC frames is essential. 45 2.5 Behaviour of masonry infill panels in RC frames subjected to pure out-of-plane effect and combination between in- and out-of-plane effect Failure of the masonry infill wall in the out-of-plane (OOP) direction is another important failure that needs to consider during the seismic assessment. The OOP collapse of infills can happen suddenly and destructively, risking human safety. However, the study of the OOP behaviour of the masonry infill wall is not as popular as the research done on the in-plane loading direction and is not the focus of this study. Previous analytical and experimental investigations on the OOP response of masonry infill panels concentrated on the pure OOP effect and the combined effect of infill walls in both IP and OOP directions, where collapse may also occur due to prior in-plane damage during earthquakes (Manfredi & Masi, 2014; Furtado, Rodrigues, Arêde, & Varum, 2015; Asteris, Cavaleri, Di Trapani, & Tsaris, 2017; Longo et al., 2018; Ricci, Di Domenico, & Verderame, 2022). Most results from the previous experimental studies show that the infill panels displayed an arching action that can be represented as hinges provided that proper connection with the surrounding frame element is applied (McDowell, McKee, & Sevin, 1956; Angel, Abrams, Shapiro, Uzarski, & Webster, 1994; Abrams, Angel, & Uzarski, 1996; Vougioukas, 2012; Tu, Liu, & Lin, 2007; Manfredi & Masi, 2014; Furtado et al., 2015; Türkmen, Wijte, De Vries, & Ingham, 2021; Pradhan, Zizzo, Di Trapani, & Cavaleri, 2022). This arching action minimizes the frame resistance to out-of-plane influences. The out-of-plane strength to resist the lateral load is proportional to the compressive strength of the masonry, the boundary condition around the perimeter, and the panels' slenderness (infill length to height ratio). The out-of-plane strength, stiffness, and ductility capacity of the infills can be reduced due to the ineffective connection of masonry infill with the surrounding RC frames (Pender & Pranjoto, 1996; Calvi & Bolognini, 2001; Kadysiewski & Mosalam, 2009; Yuan, Xiaobin, & Shulu, 2015; Ricci, Di Domenico, & Verderame, 2018) and the prior in-plane damage, which infills damaged by the IP displacement demand are more vulnerable 46 to OOP actions (Angel & Abrams, 1994; Calvi & Bolognini, 2001; Stavridis, 2009; Vicente, Parodi, Lagomarsino, Varum, & Silva, 2011; Manfredi & Masi, 2014; Anic, Penava, Abrahamczyk, & Sarhosis, 2020; Ricci et al., 2022). According to Braga et al.( 2011), the out-of-plane responses of infills in the RC frames can be associated with two limit conditions of infill seismic responses: 1) depending on the arching mechanism, which is when the infill wall is effectively confined in frame with no prior in-plane damage (Figure 2.10(a)), and 2) represented by a rigid-body mechanism, which is infill panels having a weak connection with the adjoining frame elements and/or prior in-plane damage or for untied surface wall construction (Figure 2.10(b)). Furthermore, according to Gabrielsen & Kaplan, (1978), arching action occurs in two categories: rigid arching on an infill panel that is perfectly bonded between supports and gapped arching occurring on an infill panel that has a small gap between itself one support. (a) (b) Figure 2.10: Infill seismic response conditions; (a) Arching behaviour with three hinges mechanism and (b) Rigid-body mechanism with the hinge at the bottom of the panel (From © Braga et al., 2011. Performance of non-structural elements in RC buildings during the L’Aquila, 2009 earthquake. Bulletin of Earthquake Engineering, 9(1), 307–324. Page 319. By permission from Springer Nature). 47 The out-of-plane experimental studies of the masonry infilled frames have been conducted using three different methods. The first method applies a blast loading on the masonry-infilled wall. For example, Angel & Abrams (1994) reported that in 1958, Monk studied the behaviour of the infill walls by detonating a high explosive at the center of the infill walls. Then, in 1977, Gabrielsen & Kaplan (1978) used the same technique to a shock tunnel surface. The second method that many researchers have used is static testing, in which the concentrated and uniform lateral load will be applied to the central portion of the infill walls using a hydraulic actuator or airbags to simulate the dynamic inertia loads (Drysdale & Essawy, 1988; Dawe & Seah, 1989; Abrams et al., 1996; Tu et al., 2007b). The third method for the dynamic testing of the infill walls is by using a shake table, which represents and simulates the performance of the masonry infilled walls subjected to ground motion in the out-of-plane direction of the structure (Bashandy, Rubiano, & Klinger, 1995; Bennett et al., 1996). The analytical model has also been developed based on the arching action either using an empirical or purely theoretical approach by several numbers of researchers, such as McDowell, McKee, & Sevin (1956), Dawe & Seah (1989), Klingner & Bertero (1978), Angel & Abrams (1994), and Bashandy, Rubiano, Klingner, & Klinger (1995) . Flanagan & Bennett (1999) claimed that the equation proposed by Dawe and Seah (1989) is the best to represent the available data in their comparative study of the analytical methods. Flanagan & Bennett (1999) have proposed a similar equation to Dawe and Seah (1989) with a 0.93 correction factor. Conversely, Calvi & Bolognini (2001) adopted the expression by Angel et al. (1994) and achieved a good agreement with their experimental results. Al-Chaar (1998, 2002) has generalized the Angel et al. (1994) model by considering the presence of openings in infills. Table 2.1 shows the capacity models based on the arching action that the above researchers proposed to estimate the out-of-plane strength of the infill panels. 48 Table 2.1: Capacity model referring to the arching mechanism (All expression is derived based on deformation sensitivity). Reference Equation Boundary Condition McDowell et al. (1956) 𝑞𝑢 = 1.7 (𝑓𝑚′(ℎ𝑡)2) (1 −𝑓𝑚′𝐸𝑣𝜀𝑣)2 One-way action Strip panel fully restrained at two opposite edges Dawe and Seah (1989) 𝑞𝑢 = 800. 𝑓𝑚′0.75. 𝑡2. (𝛼𝑙2.5+𝛽ℎ2.5) Two-way actions Panels restrained at all four sides and frame rigidities Angel (1994) & Angel et al. (1994) 𝑞𝑢 =2𝑓𝑚′ℎ𝑡. 𝑅1. 𝑅2. 𝜆 Strip panel fully restrained at two opposite edges Bashandy et al. (1995) 𝑞𝑢 =8ℎ2𝑙𝑀𝑦𝑣[(𝑙 − ℎ) + ℎ. 𝑙𝑛2]+ 𝑀𝑦ℎ . (𝑥𝑦𝑣𝑥𝑦ℎ) 𝑙𝑛 (𝑙𝑙 −ℎ2) . 𝑙 Based on yield-line approach and generalized McDowell model Panels restrained at all four sides EC6 (Tomaževič, 2009) 𝑞𝑢 = 𝑓𝑢. (𝑡ℎ)2 FEMA-356 (2000) 𝑞𝑢 =0.7𝑓𝑚′ 𝜆2ℎ𝑡. 144 Al-chaar (2002) 𝑞𝑢 =2𝑓𝑚′ℎ𝑡. 𝑅1. 𝑅2. 𝑅3. 𝜆 Panels restrained at all four sides Tu, Liu, & Lin (2007) 𝑃 = 𝑇. 𝑠𝑖𝑛 𝛾, 𝑇 = 𝑓𝑏 . 𝐴𝑇= 𝑓𝑏 (𝑏𝑐𝑜𝑠 𝜃. 𝑐𝑜𝑠 𝛾. 𝑊) . 𝑠𝑖𝑛 𝛾 Applied at the floor level and correspond to certain drift angle Without constraint Based on the numerical approaches developed in previous studies, several analytical models have been proposed and developed to assess the performance of the masonry infill wall 49 subjected to out-of-plane force. Hashemi & Mosalam (2007) developed strut and tie (SAT) model that can be used to analyse both in-plane and out-of-plane response. The proposed model consists of eight compression-only struts connected with a tension-only tie at the center point of the infill panel. However, Kadysiewski & Mosalam (2009) found that the SAT model has certain problematical behaviours under certain conditions in SAT model. Consequently, they have proposed a new infill model representing a single diagonal beam-column member, composed of two beam-column elements, with a node at the mid-span (Figure 2.11(a)). The main limitation of this model is that it is not shown if it effectively captures the behaviour of actual infill in the post-elastic deformation range. Second, the calculated global response of the building model gives an error because the “collapsed” infill will still be carrying the load in the analysis, which models are unable to account explicitly for the arching response. As a result, the load in other infill and RC frame members are often underestimated. Furthermore, the column shear failure was not considered in this model. Mosalam & Günay (2015) overcome the limitations by introducing the removal element in progressive collapse simulations and nonlinear shear spring model at the ends of the column, respectively. However, applying one diagonal strut element with both tension and compression strength may lead to a less accurate assessment of infill when subjected to the seismic load, given that this configuration is unreliable with the actual structural system (Asteris et al. 2017). Furtado, Rodrigues, & Arêde (2015) and Furtado, Rodrigues, Arêde, & Varum (2016) developed the simplified macro-model to evaluate the out-of-plane behaviour of the infill wall, with the corresponding interaction between the in- and out-of-plane loading due to the biaxial cyclic loading. The proposed model is an improvement from the model proposed by Rodrigues, Varum, & Costa (2010), which used the equivalent bi-diagonal-strut model. This model consists of four diagonal struts with rigid behaviour, and one central element with non-linear hysteresis was used 50 to simulate each masonry infill wall (2.11(b)). To represent the out-of-plane behaviour of the masonry infill wall, the OOP model integrates two central nodes to distribute the panel mass. However, this model is unable to capture the short column effect due to the presence of the infill walls. (a) (b) Figure 2.11: Three-dimensional masonry infill wall model; (a) model proposed by Kadysiewski and Mosalam (2009) (From © Mosalam, & Günay, 2015. Progressive collapse analysis of reinforced concrete frames with unreinforced masonry infill walls considering in-plane/out-of-plane interaction. Earthquake Spectra, 31(2), 921–943. Page 927. Image reproduced under fair dealing for research purposes), and (b) Simplified model proposed by Furtado et al. (2015) (From © Furtado et al., 2015. Influence of the in plane and out-of-plane masonry infill walls’ interaction in the structural response of RC buildings. Procedia Engineering, 114, 722–729. Page 724. Creative Commons Attribution License (CC-BY-NC-ND 4.0) (https://creativecommons.org/licenses/by-nc-nd/4.0/)). In summary, out-of-plane failure is identified as one of the factors that may significantly affect collapse safety. However, it is pertinent to mention that this study does not center around this topic. Nonetheless, for future investigations, it is imperative to consider the possible influence of out-of-plane failure on collapse safety assessment. This necessitates an extensive analysis of various factors, such as the combined impact of in-plane and out-of-plane forces, the interaction between infill and frames, and the characteristics of materials, construction techniques, and geometrical configurations that impact the behaviour of RC frames with infill walls. 51 2.6 Effects of soil-structure interaction on the seismic response of buildings Studying the seismic performance of RC frames considering the soil-structure interaction (SSI) effect is an important research topic in earthquake engineering analysis. Building damage during the 1964 Niigata earthquake in Japan clearly shows that structural damage depends on not only the behaviour of the superstructure but also the substructure surrounded by soil underneath the ground (Ohsaki, 1966). The earthquake that struck Mexico City in 1985 is another example that required the evaluation of the SSI effect in the presence of soft soil conditions during severe ground motion (Sanchez-Sesma, Chavez-Perez, Suarez, Bravo, & Perez-Rocha, 1988). SSI is a phenomenon that occurs when an earthquake affects the soil and the structure to interact. The ground shakes and moves during an earthquake, causing the soil to deform and exert forces on the foundation of a building. These forces can be transmitted to the building structure, affecting the building's response to the earthquake. In addition, due to the supporting soil's flexibility, the structure's global lateral stiffness reduces, leading to an increase in natural period and damping (Wong & Luco, 1992; Stewart, Seed, & Fenves, 1998; Mylonakis & Gazetas, 2000; Arefi, 2008; Rajeev & Tesfamariam, 2012b; Vivek & Raychowdhury, 2017; Zafarkhah & Dehkordi, 2017; Oz et al., 2020). The response of the building to the earthquake can depend on a number of factors, including the stiffness and strength of the soil, the depth of the foundation, the shape and size of the building, and the properties of the building materials. Therefore, it is an essential consideration in the design and construction of buildings, as it can significantly impact the building's response to seismic events. The study of the influence of SSI provides an in-depth analysis of the dynamic response of RC frames, accounting for all effects related to kinematic and inertial interaction for surface or embedded structures. Kinematic interaction deviates ground motion due to a stiff foundation 52 with/without mass, while inertial interaction is the deformation of foundation soil caused by induced base shear and superstructure moments. The foundation and wave field determine these components' relative importance. Kinematic interaction effects are much more challenging to evaluate than inertial interaction effects. Shallow foundations in a seismic environment with vertically propagating shear or dilatational waves experience little kinematic interaction, which can be neglected (NEHRP Consultants Joint Venture, 2012; Bapir, Abrahamczyk, Wichtmann, & Prada-sarmiento, 2023). However, the seismic performance of RC frames considering SSI is not as widely studied as other aspects of seismic performance due to several factors. Firstly, SSI is a complex phenomenon that includes both soil and structure components, and various elements must be considered, making it challenging to model and analyze accurately. Secondly, the assessment of SSI requires the use of sophisticated numerical modelling techniques and data-driven approaches, which increase the complexity and cost of the analysis. Finally, the limited availability of field data makes assessing SSI effects on seismic performance challenging. As a result, less research has been conducted into the seismic performance of RC frames considering SSI effects, which most studies commonly practice to analyze and design buildings by assuming fixed-based conditions at the building base (fixed-based approach). On the other hand, even is still evident that the design community is reluctant or has no attention to incorporate SSI into the structural analysis or practical design (Vivek & Raychowdhury, 2017), probably due to a lack of details or even general guidelines and the common belief that SSI usually has positive effects on structures behaviour (Bapir et al., 2023). Nevertheless, recent and past studies have found that ignoring the SSI effect may result in an unsafe design. In general, the seismic response of a building considering soil-structure interaction (SSI) effects can be assessed by assuming a fixed-based condition based on the fact that the SSI effect may not significantly affect the response of a building if the structure is sufficiently rigid and the soil is relatively stiff or founded on solid rock (Bielak, 1974; Stewart, Seed, & Fenves, 1999). 53 Under these conditions, the building can be treated as a rigid body fixed to the ground, and the building's foundation essentially absorbs the seismic waves transmitted through the soil. This assumption can simplify the seismic response analysis, allowing the engineer to focus on the building's dynamic properties and ignore the soil's influence. However, in many cases, the SSI effect cannot be neglected, and it is necessary to consider the dynamic interaction between the building and the soil. This is particularly true for buildings with flexible foundations, structures built on medium to soft soil, and structures subjected to strong ground motions (Bielak, 1974; Chau, Shen, & Guo, 2009; Magade & Patankar, 2009; Ceroni, Sica, Pecce, & Garofano, 2012; Zafarkhah & Dehkordi, 2017Shahbazi, Mansouri, Hu, & Karami, 2018). In such cases, the seismic response of the building can be significantly affected by the soil's response, and a more reliable analysis of the soil-structure interaction is necessary. In the past five decades, numerous research efforts have been made to study and assess the influence of SSI on structural responses in different focus areas to develop improved design strategies for buildings that can better withstand seismic loading. There are several studies have focused on the different modelling techniques and improvement (Noorzaei, 1996; Stewart et al., 1998; Raychowdhury, 2008; Pulikanti & Ramancharla, 2014; Galvín & Romero, 2014; Mohamadi & Tahghighi, 2019), the influence of SSI on the period and damping of buildings (Magade & Patankar, 2009; Vivek & Raychowdhury, 2017; Ozmen & Tarakci, 2022), and the effect of SSI on the performance of the building based on various parameters such as different buildings type and configurations, the strength and stiffness of the buildings, soil type, foundation type, and the stiffness of the foundation and soil using numerical simulations and experimental testing (Bielak, 1974; Arefi, 2008; Galal & Naimi, 2008; Tabatabaiefar, Fatahi, & Samali, 2011; Rajeev & Tesfamariam, 2012b; Hokmabadi, Fatahi, & Samali, 2013; Jayalekshmi & Chinmayi, 2014; Jayalekshmi, Jisha, Shivashankar, & Soorya Narayana, 2014; Li, Lu, Lu, & Ye, 2014; Chinmayi, 2016; Hokmabadi & Fatahi, 2016; Tomeo, Bilotta, Pitilakis, & Nigro, 2017; Vivek & Raychowdhury, 54 2017; Zafarkhah & Dehkordi, 2017; Kazemi, Asgarkhani, & Jankowski, 2023; Mohamadi & Tahghighi, 2019; Oz et al., 2020; Requena-Garcia-Cruz et al., 2022; Shahbazi et al., 2018; Tahghighi & Mohammadi, 2020). Bielak (1974) and Stewart, Fenves, & Seed (1999) reported that the soil foundation's flexibility reduces the structures' overall stiffness, leading to expansion in the fundamental period of the system. Determination of the fundamental period of the buildings is one of the main steps during seismic design and assessment. Considering the response of SSI allows the structural engineer to design the building by accounting for the adequate deformation of the overall system under seismic motion effect. Assuming a fixed base at the bottom of the structure in the seismic analysis may not discover this problem. Magade & Patankar (2009) carried out a parametric study to determine the lengthened lateral natural period of the building frame due to incorporating the effect of SSI. The study includes the building with isolated footing on soft, medium, and hard soil, infill wall, and shear wall in the frames. The study demonstrates that considering several parameters, such as soil structure interaction, soil types, infill wall stiffness, and wall location, significantly impacts a building frame's period, displacement, and base shear. Later, Vivek & Raychowdhury (2017) investigates the period and damping of steel moment-resisting frame buildings with shallow footings on dry sand deposits concerning the effects of soil-structure interaction (SSI). Impact hammer tests on 3-storey and 6-storey model steel frames with loose and dense sand beds, surface and embedded footings, and heavily or lightly loaded footings are used in the study. FEMA and finite-element model results are compared to experimental results. The results show that short and stiff buildings are more sensitive to SSI than taller ones, and heavily loaded 3-storey buildings on loose sand have 21% and 330% period and damping amplifications, respectively. Analytical results match the experiment. However, FEMA provisions overstate reactions, especially for the 6-storey building. 55 Recently, Sharma, Dasgupta, & Dey (2018) investigated the effect of SSI on the fundamental period of a reinforced concrete building frame supported by a pile foundation. The finite element software OpenSees is used to construct and analyze the superstructure-foundation-soil continuum model. Fast Fourier Transform (FFT) analysis of the time history response of the superstructure was used to obtain the natural periods of the frames with shear walls based on variations in the structural configuration and foundation and soil properties. The frame supported on loose sand was observed to have a lower natural frequency than that on dense sand. The natural frequency of a soil-pile foundation construction decreases as the supporting soil stiffens. TSSI/TF quantifies SSI's effect on the building frame's natural period with the shear wall. TSSI is the foundation of SSI-influenced building frames with shear walls. The fixed base frame's fundamental period is TF. SSI increases the frame's natural period with higher ratios. At the same time, soft soil increases the natural period for short and tall building frames. Lower values suggest that SSI decreases as soil stiffens. Ozmen & Tarakci (2022) conducted a nonlinear static pushover analysis using the SAP2000 analysis program for the twenty-five 4-storey RC frame buildings with different foundation types: raft and continuous foundation and having different soil bearing coefficients and soils having different bearing coefficients. The stiffness of the models are observed to be significantly affected by the foundation dimensions and the soil bearing coefficient. A period increase of up to 44% is observed per fixed base case. The foundation size and soil bearing coefficient impact the models' stiffness substantially. In the soil-structure interactive models, the primary natural vibration periods of the buildings are longer than in the reference fixed base model. Up to 44% period increases are reported depending on the foundation and soil stiffness. Overall, previous research reveals that soil and foundation flexibility significantly lengthens the fundamental period of the soil-structure system and increases damping. A study conducted by Galal & Naimi (2008) on unbraced frames under the influences of SSI founding on-site classes shows that when the buildings supported by soil with shear wave 56 velocity (Vs) less than 600 m/sec that is comprising site class E, D, and lower limit of site class C (360 m/s <Vs< 600 m/s), SSI effect on structural response need to be considered (Veletsos & Meek, 1974). El Ganainy and El Naggar (2009) showed that lateral deformation of the buildings founded on soil class C (360 m/s <Vs< 600 m/s) and E (Vs< 180 m/s) significantly influenced SSI in comparison to the fixed base. However, a study conducted by Tabatabaiefar, Fatahi, & Samali (2011) and Tabatabaiefar, Fatahi, & Samali (2014) on a full range of mid-rise unbraced buildings found that SSI extensively affects the seismic response of the buildings resting on subsoils with Vs less than 320 m/s and no significant difference between building resting on soil class C from a fixed base. Myat (2008) investigated the seismic performance of low-rise buildings resting on a strip footing. This study showed that the shear wall's axial and shear forces and bending moments with the SSI effect are more significant than the fixed base condition. Lopez-Caballero, Modaressi-Farahmand-Razavi, & Tabbakhha (2011) assessed seismic damage by considering nonlinear SSI effects on masonry structures supported on a rigid shallow foundation. The researcher implemented probabilistic numerical analysis to evaluate seismic response by taking SSI into account and considering the different data recorded with and without including the effect of SSI on masonry structures. Parametric studies showed that the response of the soil-structure system depends significantly on the intensity of the input motion. A minor earthquake keeps the soil relatively stiff and damping low, while a severe recorded ground motion can cause the soil foundation to become inelastic, reducing stiffness and increasing damping (Arefi, 2008). Besides, the masonry structure's structural drift without SSI was lower than when SSI was considered. The influence of SSI on the seismic behaviour of the buildings is also affected by the soil condition, which includes hard, medium, and soft soil (Magade & Patankar, 2009; Priyanka, Anand, & Justin, 2012). 57 Rajeev & Tesfamariam (2012b) assessed the effect of uncertainty of soil characteristics and foundation parameters on the seismic fragility of 3-, 6-, and 9-storey non-ductile RC frames with shallow foundations resting in the dense silty sand. The study showed that SSI significantly affects the fragilities curve shape compared to the fixed base model. Ceroni et al. (2012) numerically studied the response of an old structure consisting of moment frames in one direction and shear walls in the other. Fragility curves have been developed by considering the effect of SSI and showed a reduced seismic demand. However, research conducted by Stewart et al. (1999) on the structural design of braced framed buildings concluded that SSI could be ignored in the seismic design of braced buildings, especially buildings on rock or stiff soil (Carbonari, Dezi, & Leoni, 2012). Similarly, Jiang et al. (2010) studied the vulnerability of RC buildings with consideration of SSI. Displacement-damage curve and probability of each damage level were derived from a single 4-storey building. A related study was also conducted by (Zhang & Tang (2008) for slender shear walls. This study showed that the probability of each predefined level of damage decreased when SSI was taken into account. Their study also found that the friction angle of soil highly influenced the maximum inter-storey drift. Overall, the seismic response of RC frame structures can be significantly affected by SSI, and hence it is essential to consider this effect while designing and analyzing such buildings. Ignoring SSI can lead to inaccurate predictions of the structural behaviour and potentially underestimate the seismic hazard. Previous studies have shown that the soil properties can significantly affect the building's natural frequency, damping, and mode shapes, leading to a shift in the structural response spectrum. Additionally, the interaction between the soil and the structure can change the distribution of seismic forces, which can affect structural deformation, stresses, and energy dissipation. It was found that the stiffer the foundation, the higher the seismic performance of the RC frame. The abovementioned studies also revealed that the height of the frame and the type of earthquake also impact the RC frames' seismic performance. To certain 58 site conditions and ground motion characteristics, SSI can have a negative impact on some moderately flexible building. Therefore, considering the SSI effect can help to ensure the safety and reliability of the building against earthquakes. It can also help optimise the structural design and mitigate potential damage, leading to cost-effective and sustainable building solutions. In conclusion, SSI is a crucial factor in the seismic response of RC frame structures, and it should be accounted for in the design and analysis process. However, until recently, there has been little interest in seismic risk analysis of infilled RC frames, including the SSI effect concerning the effect of embedded shallow foundations. Literature has also emerged that offers debatable findings of SSI effects on buildings to consider in design and assessment. Therefore, further study is required to assess the seismic risk of the effect of SSI on buildings with masonry infill walls to get specific requirements to enhance the safety of RC buildings, focusing on the effect of foundation embedment depth. 2.6.1 A computational method for modelling SSI system under seismic loading Based on the available literature, the seismic response of buildings considering SSI can be evaluated using two commonly used methods: the substructure approach and the direct approach, as shown in Figure 2.12. These approaches can be divided into two modelling solutions developed for soil domains: the equivalent linear and the nonlinear methods (presented in section 2.6.2). 59 (a) (b) Figure 2.12: Schematic illustration of the numerical model of the SSI;(a) Direct analysis approach using continuum modelling, and (b) Substructure approach using rigid foundation or flexible foundation assumptions (From © Li et al., 2014. Influence of soil–structure interaction on seismic collapse resistance of super-tall buildings. Journal of Rock Mechanics and Geotechnical Engineering, 6(5), 477–485. Page 478. Creative Commons Attribution License (CC-BY-NC-ND 3.0) (https://creativecommons.org/licenses/by-nc-nd/3.0/)). The direct approach, also known as the finite element method, is a numerical method that models the entire system as a single system, including the soil, the foundation, and the structure (Figure 2.12(a)). The direct approach can capture the complexity of the soil-structure interaction and provide detailed information about the response of the building and the soil, including stresses and strains in the soil and the building's deformation. However, it is computationally intensive, which may limit the size of the model that can be analyzed. Moreover, it is inefficient during the initial design phases of a project. As a result, a substructure approach is frequently adopted, with all degrees of freedom of the supporting medium lumped at the soil-foundation interface. The substructure approach, also known as the multiple-step approach, is a widely used to evaluate the seismic response of buildings considering soil-structure interaction (SSI) effects. This approach divides the building and the surrounding soil into two separate components, the superstructure (above the ground level) and the substructure (below the ground level), and solves the equations of motion separately for each substructure following superposed steps. The superstructure is modelled as a flexible structure which also can be modelled using simplified 60 constitutive models, and the substructure, the foundation, and adjacent soil are simplified into a series of springs and dashpots to consider the SSI effect, as shown in Figure 2.12(b). The interaction between the soil and the structure or total effects is then incorporated through interface conditions between the substructures or using superposition principles. The superposition associated with this method requires an assumption of linear behaviour for the soil and structure. The substructure approach used in the evaluation of the SSI problem involved three main steps (Kramer & Stewart, 2004; NEHRP Consultants Joint Venture, 2012), as illustrated in Figure 2.13: 1. Compute the Foundation Input Motion (FIM)- FIM is the motion that would take place on the base slab when the structure and the foundation have no mass. Before defining FIM, the free-field soil motions and related soil material properties should be evaluated first. Foundation stiffness and soil geometry show the difference between the FIM and free-field motion. This process also includes evaluating transfer functions to convert the Free-Field Motion (FFM) to FIM based on foundation stiffness and soil geometry. Rotational and translational components in this motion represent the applied seismic demand to the foundation and structural system. 2. Evaluation of the impedance functions of the foundation - The impedance functions define the stiffness and damping properties of the interaction between the soil and the foundation. This is typically represented by simple function models or a series of springs and dashpots specified by the foundation soil's horizontal (Ku) and rotational (Kθ) stiffness. The dynamic impedance functions are frequency-dependent and damping characteristics of the soil-foundation interaction. 3. Seismic response analysis of the structure – The superstructure is modelled on the flexible base represented by the impedance function (or a series of distributed springs and dashpots) and subjected to a base excitation consisting of the FIM. Then, the seismic response 61 of the structure is assessed using one of two methods—response spectrum analysis or time history analysis. This step represents the effects of inertial interaction. (b) Step 1 (c) Step 2 (a) SSI problem (d) Step 3 Figure 2.13: Schematic illustration of a substructure approach steps to analysis of the soil–structure interaction problem; (a) Structure response problem, (b) Evaluation of FIM, (c) Estimation of impedance function, and (d) Analysis of structure on compliant base subjected to FIM (Kramer & Stewart, 2004, Image reproduced under fair dealing for research purposes). In summary, the substructure approach and the direct approach are two common numerical methods used to evaluate the seismic response of a building considering the soil-structure interaction effect. The substructure approach divides the soil and the structure into separate substructures, while the direct approach models the entire system using finite element analysis. Both methods have advantages and disadvantages and can provide valuable information about the building's response during seismic events. The substructure approach is more computationally efficient and easier to implement but may not capture the detailed SSI effects in the soil. The direct approach is more accurate but computationally expensive and 62 requires more expertise in numerical modelling. Both approaches require a thorough understanding of the properties of the soil and the building and appropriate modelling techniques. The approach chosen depends on the analysis's specific requirements and the available resources. In the present study, the substructure approach is adopted. 2.6.2 Soil domain modelling techniques based on the substructure approach Contact pressure distribution is an important characteristic of the foundation-supporting soil interface. The variance in pressure distribution is determined by the foundation behaviour (i.e., stiff or flexible: two extreme cases) and the underlying soil type (clay or sand etc.). Modelling the soil domain is the most challenging part when dealing with SSI problems. Several approaches are available for modelling the soil domain, especially for the substructure approach based on spring-type models, including the Winkler model, Lumped parameter models, and Beam on Nonlinear Winkler Foundation (BNWF) model. The Winkler model is a simplified mathematical model and the simplest model used to model the soil domain when analyzing SSI in structural engineering. It is often used in the preliminary design stage to estimate foundation systems' stiffness and load capacity. The Winkler model assumes that the soil behaves like a series of closely spaced independent springs, with each spring representing the stiffness of a small element of the soil attached to the foundation, and the soil response is linearly elastic. These springs are often referred to as "Winkler springs". The Winkler model assumes that a load acting at a specific position on the foundation only causes soil displacement at that point. This assumption is incorrect because, due to the continuity of the soil medium, displacements at one point are influenced by forces at other points (Al-hussaini, n.d.). The loads applied to the foundation are calculated, and the response of the soil is calculated as a series of vertical deflections. The Winkler model has another limitation: it assumes that the 63 soil is homogeneous and isotropic, which is not always the case in practice. It also assumes that the soil is linearly elastic, which may not be accurate for soils with high deformability or where nonlinear soil behaviour is observed. Besides, for uniform loading used in the Winkler foundation, the settlement of a flexible foundation on Winkler springs is assumed uniform is incorrect. Therefore, it must be carefully determined numerically to utilize it in a practical application since the modulus of subgrade reaction (also known as the modulus of springs) is the only parameter in the Winkler model idealizing the physical behaviour of the subgrade. Despite these limitations, the Winkler model helps analyze SSI problems, especially for preliminary design purposes. It provides a simplified approach for practical purposes to estimate the stiffness and load capacity of the foundation system. Several improved versions of the Winkler model are available in the literature to overcome this model's shortcomings and limitations. Lumped parameter model represents the frequency-dependent SSI of a massless foundation and is one common approach used in SSI analysis, which simplifies the behaviour of the soil-structure interaction problem by assuming that the soil and foundation resting on or embedded in homogeneous elastic half-space can be modelled using a set of discrete masses, springs, and dashpots. These lumped parameters represent the dynamic properties of the soil and foundation, such as their stiffness, damping, and inertial effect generated by the SSI phenomenon (Kechidi, Colaço, Alves Costa, Castro, & Marques, 2021). Different lumped parameter models have been developed using different arrangements and formulations of foundation impedances, which two common physical models used are spring and dashpots by Gazetas and the discrete element cone model by Wolf (Bapir et al., 2023). The first model was proposed by Gazetas in 1983 and has been widely used in engineering practice till the present. The spring and dashpot model associated with impedance function, offered for each vibration mode under a rigid but massless foundation, consists of a series and/or parallel arrangement of springs and dashpots to represent the stiffness and damping properties of the soil system under 64 or around the foundation. Generally, a rigid foundation has six vibration modes (three translational and three rotational), with dynamic spring stiffness K and dashpot damping coefficients C replacing the soil in each mode. The value of the foundation impedances represented by springs and the dashpots in each mode can be calculated using simplified methods proposed by Gazetas (1991). A complete set of algebraic formulas and dimensionless charts is provided to compute the dynamic stiffnesses (K) and damping coefficients (C) (springs and dashpots) of foundations on/in a homogeneous half-space for all the significant translational and rotational modes of vibration. The static springs and dashpots are initially estimated using this method based on foundation geometry, soil stiffness, and soil density. The static impedance is then multiplied by a frequency-dependent factor to calculate the frequency-dependent impedances. These formulas were applicable to practically all surface foundation geometries and partially and fully embedded foundations in homogeneous soil. According to Bowles (1996), this model's frequency-dependent effects and additional damping coefficients have a more significant impact on the whole structural response than the frequency-independent springs of the Winkler model. However, it has been determined that this approach is insufficiently accurate in analysing complex SSI problems. The second physical model from the lumped parameter family that is commonly used is the discrete element cone model developed by Wolf (1994). This model is based on truncated cone theory that replaces the soil domain with a semi-infinite truncated cone for translational and rotational motion. A system of springs and dashpots are placed under each foundation to connect the rigid circular base of the building to the soil medium. Translational and rotational springs represent sway and rocking DOFs, while soil and foundation radiation damping is considered with viscous dampers. In contrast to the spring-dashpot model, the vertical component of the base foundation in this model is assumed to be non-moving. Spring stiffness and damping coefficients are defined similarly to the static characteristics by Gazetas (1991). However, the SSI system's configuration and the number of input parameters differ from the spring-dashpot concept. Also, the definition of dynamic impedances differs. Previous studies suggest various practical applications for cone 65 model discrete elements. Many have used cone models to study SSI impacts on structural dynamics with different foundations and structural models. However, because the cone model is based on elastic half-space soil, discrete elements cannot capture plastic deformations in the soil under the foundation (Yang, 2016). This model cannot calculate residual displacement or settlements. The model also cannot show foundation-soil separation. Hence, the model may not work for light, slender structures on sandy soil. The cone model also cannot effectively handle material and geometric nonlinearity (Jabini Asli, Saffari, Zahedi, & Saadatinezhad, 2021). Hence, complex and important structures require more advanced soil models for soil and structural non-linearity. The beam on Nonlinear Winkler Foundation (BNWF) model is another simplified spring-type model to evaluate SSI effects. The Beam on Nonlinear Winkler Foundation (BNWF) approach is a mathematical modelling technique widely used to assess reinforced concrete (RC) frame buildings. The BNWF model has been employed in engineering practice due to its relative simplicity and ease of calibration (Requena-Garcia-Cruz et al., 2022). This approach was initially used for many years until the present to analyse the response of foundations, most notably the determination of piles (isolated) or pile group foundations behaviour (Boulanger et al., 1999; Harden, 2005). Later, the BNWF model was also developed for shallow foundation analyses (Raychowdhury, 2008) and has been used for several studies but still less, especially for moment-resisting frame structure (MRFs) assessment (Raychowdhury, 2008; Rajeev & Tesfamariam, 2012b; Tomeo et al., 2017; Vivek & Raychowdhury, 2017; Ali Mohamadi, 2019; Requena-Garcia-Cruz et al., 2022;). This model idealizes the soil domain by numbers of one-dimensional nonlinear springs, which include a series of vertical and horizontal nonlinear springs distributed along with the interface between soil and foundation (Raychowdhury, 2008). Based on this set of spring systems, the model allows measuring the soil domain's plastic deformations and energy dissipation. The increased pressure under the foundation caused by its rocking and sliding 66 motions during strong earthquake events makes it likely that the soil under the foundation may undergo plastic deformation (Yang, 2016). As a result, the system stiffness gradually decreases as the foundation's contact with the soil decreases. Raychowdhury & Hutchinson (2008) incorporated the BNWF model into OpenSees using elastic beam-column elements for structural foundation behaviour and independent zero-length soil elements for soil-foundation behaviour. It is currently only being developed for two-dimensional analysis. Thus, the one-dimensional beam-column elements utilised for the foundation possess three degrees of freedom per node (i.e., horizontal, vertical, and rotation). Figure 5.4 (see in Chapter 5) depicts the usage of one-dimensional uniaxial springs to model vertical load-displacement (q-z), horizontal passive load-displacement against the side of a foundation (p-x), and horizontal shear-sliding (z) behaviours at the foundation (t-x). Distributing vertical springs along the base of the foundation captures the moment-rotation behaviour of the system. The BNWF model is applicable for all surface and embedded foundation types. Regardless of the structural model, it might also be utilised for clay and sand soil deposits. Thus, the model is appropriate for various structural engineering SSI problems. This method is basically restricted in that it only has one dimension. The reaction of the spring is only affected by loads that apply in the same direction as the springs; loads that act in a direction that is perpendicular to the spring axis do not influence the springs' reaction. In general, the BNWF method is an effective tool for engineers, particularly for assessing the seismic performance of RC frame buildings due to its ability to simulate and predict various problems. It also provides a comprehensive understanding of the soil-structure interaction by allowing engineers to model the complex behaviour of the building and the soil-structure interaction in a simpler way. Therefore, in assessing RC frame buildings that will conduct in this study, the BNWF approach will be used, which can provide a more realistic representation of the building's response to seismic loading. 67 CHAPTER 3: Development of a computational model of masonry-infilled RC frames subjected to cyclic loading The previous chapter highlights literature reviews on the performance of infilled RC frame buildings, type of failure, and modelling. This chapter presents the development of a general guideline to evaluate the parameters to define the infill wall response. Past research on experimental and analytical studies focused on the in-plane response on infilled frame buildings is extensively reviewed, followed by a summary of relevant numerical and analytical modelling approaches used to predict the in-plane cyclic response of RC frames with URM infill walls. Details of the development of the computational model are described in this chapter. 3.1 Background Reinforced concrete (RC) frame buildings with unreinforced masonry (URM) infill walls, henceforth denoted as masonry-infilled RC frame structures, are widely used in building constructions. Damage observation from past earthquakes (e.g. (Decanini, Liberatore, Mollaioli, & Desortis, 2005; Zhao, Taucer, & Rossetto, 2009; Decanini et al., 2012) show that the seismic response of these buildings is strongly affected by the presence of masonry infill walls. The URM infills may increase lateral stiffness, strength, and energy dissipation capacity of the bare RC frame (Asteris, Antoniou, Sophianopoulos, & Chrysostomou, 2011; Campione, Cavaleri, Macaluso, Amato, & Trapani, 2015; Martinelli, Lima, & De Stefano, 2015). The presence of the infill walls on the bare frame might induce unexpected forces distribution and lead to local collapse when it is subjected to cyclic loading (Asteris et al., 2013). These effects depend on the infill geometrical distribution in plan and elevation, infill mechanical properties, infill aspect ratio, the configuration of openings, and construction methods (Asteris et al., 2011; Skafida, Koutas, & Bousias, 2014). 68 The seismic behaviour of masonry-infilled RC frame buildings has been investigated since the 1950s. Many experimental studies were conducted (e.g. (Pires, 1990; Pires & Carvalho, 1992; Mehrabi et al., 1996; Kakaletsis & Karayannis, 2007, 2008, 2009; Karayannis, Favvata, & Kakaletsis, 2011; Kyriakides, 2011; Sigmund & Penava, 2012; Stylianidis, 2012) to investigate the response of infill walls and their interaction with the surrounding RC frame. Concurrently, analytical studies have been carried out by researchers (e.g. (Schmidt, 1989; Decanini, Mollaioli, Mura, & Saragoni, 2004; Mondal & Jain, 2008; Asteris, Antoniou, Sophianopoulos, & Chrysostomou, 2011; Burton & Deierlein, 2013; Campione, Cavaleri, Macaluso, Amato, & Trapani, 2015; Liberatore & Mollaioli, 2015; Martinelli, Lima, & De Stefano, 2015; Tarque, Candido, Camata, & Spacone, 2015; Bârnaure, Ghita, & Stoica, 2016) to model and evaluate the performance of these buildings under both monotonic and cyclic loads. Despite numerous studies in the literature, assessing and modelling masonry-infilled RC frames remains an issue. The lack of a standardized guideline for properly determining important infill wall parameters of infill walls in global seismic analyses of masonry-infilled RC building frames is the primary issue affecting the accurate assessment and evaluation of seismic performance in RC frame buildings. Besides, the infill influence on the seismic behaviour of framed structures is widely recognized, but how it is incorporated into the design process differs noticeably from one country to another (Kaushik et al., 2006). Nevertheless, masonry infill walls are often neglected in the design process and analytical modelling and are considered non-structural elements. Reliable analytical methods are needed for the assessment of infilled framed structures (Asteris et al., 2011). This task is rather challenging due to the complex interaction between the frame and the infill, particularly in the nonlinear range. Moreover, the selection of the most appropriate model is related to the analysis overall objectives. To evaluate local interaction effects, the adoption of detailed models is essential. It should be noted that these detailed models can also serve for evaluating global responses. Nevertheless, simpler models, capable of 69 combining simplicity and accuracy, are more appropriate when assessing the global response of structures.. In this regard, macro models, which involve replacing the masonry infill with one or multiple equivalent struts, offer a good compromise between efficiency and precision (Asteris et al., 2011; Mondal & Jain, 2008), provided that proper rules are adopted for the definition of the struts mechanical characteristics. As the masonry wall is a nonhomogeneous anisotropic material, a valid constitutive law is difficult to find. Previous studies highlighted that the application of different equations to estimate the equivalent strut parameters led to noticeable differences in the infilled frames response (Asteris, Cotsovos, Chrysostomou, Mohebkhah, & Al-Chaar, 2013). Consequently, selecting adequate models for the analyses of masonry-infilled RC frames is imperative. The aim of this study is to develop general guidelines for evaluating the parameters to define the monotonic and hysteretic response of the masonry infill walls, specifically for the in-plane lateral cyclic response. The outline of the study is as follows. First, various modelling approaches available in the literature are reviewed. Specific attention is devoted to the single-strut modelling method, in which the many different formulations are discussed and compared. Afterwards, numerical analyses of several one-storey, one-bay infilled RC frames tested experimentally are performed through the Open System for Earthquake Engineering Simulation (OpenSees) software package (Mazzoni, McKenna, Scott, & Fenves, 2006) offers a wide range of advanced material models, elements, and analysis procedures that can accurately capture the behaviour of these structures. OpenSees provides robust capabilities for nonlinear analysis, including the modeling of material nonlinearity, geometric nonlinearity, and contact interactions These analyses are dual-purpose: (i) identify the most appropriate formulae for the definition of the strut constitutive law and (ii) verify the suitability of numerous material models available in the OpenSees (Mazzoni et al., 2006). From the comparison among different models and between 70 numerical and experimental results, suggestions are made to properly model the in-plane non-linear response of masonry infilled frames. 3.2 Modelling approaches for masonry infilled RC frame Comprehensive reviews on the experimental, analytical, and numerical research works by Crisafulli, Carr, & Park (2000), Shing & Mehrabi (2002), Asteris et al. (2011, 2013), and Tarque et al. (2015) categorized five main failure mechanisms of the infilled-frames: (1) the corner crushing (CC) mode; (2) the sliding shear (SS) mode; (3) the diagonal cracking (DK) mode; (4) the diagonal compression (DC) mode, and (5) the frame failure (FF) mode. The first failure mode, CC, occurs when a weak masonry infill panel is surrounded by strong frame members and the connection between the infill and the frame is weak. The second failure mechanism, SS, which is given by the horizontal sliding through multiple bed joints at approximately mid-height of the panel, occurs when the strength of mortar joints is low, and the infill is surrounded by a strong frame. This failure mode also introduces the short column behaviour, in which plastic hinges develop at the mid-height of the columns. This can also lead to the shear failure of the columns. The third failure mechanism, DK, which takes place when the frame is more flexible than the masonry infill, consists of a crack along the compressed diagonal of the masonry infill panel, which might be joined with a horizontal crack at the mid-height of the panel. The fourth mechanism, DC, displays crushing at the center of the masonry infill panel due to high compression forces. Masonry crushing may also develop when a slender flexible infill experiences large out-of-plane deformations. The last mechanism, FF, consists of a purely flexural mode, in which there is no separation between the infill and the frame under a low load level. Under a moderate load level, if the infill panel and bounding frame are not adequately tied together, the infill panel will separate partially from the frames, and flexural hinging at the top and bottom of the column will develop. This failure mode is particularly important when investigating the existing structures, which in 71 many cases, display frame weaknesses. The general conclusion from these studies is that different failure modes may develop depending on the infill and frame relative stiffness. The possible failure mechanisms described above are only for solid infill walls (without openings). Previous studies also involved experimental work on masonry infill walls with openings (Mosalam, White, & Gergely, 1997; Shing & Mehrabi, 2002; Al-Chaar et al., 2003; Kakaletsis & Karayannis, 2007, 2009; Stavridis, 2009; Tasnimi & Mohebkhah, 2011). Experimental results highlighted that masonry infills wall with openings can still enhance the performance of RC frames in terms of resistance, stiffness, ductility, and energy dissipation capacity, but to a lesser extent than a solid infill wall. An experimental study by Kakaletsis & Karayannis (2007, 2009) reported that masonry infills with an opening crack and detach from the bounding frame at an early stage before the column yielding. The location of the openings also influences global performance (Mosalam et al., 1997; Al-Chaar et al., 2003;). Moreover, when the frames are only partially infilled, a short column effect consisting of a brittle shear failure may develop. However, inconsistent evidence was accumulated on whether the openings lead to a more brittle or ductile behaviour than the solid infill wall (Zhai et al., 2016). Theoretically, the knowledge of both the geometric properties of the infill and of the cyclic behaviour of the masonry material should allow straightforward modelling. The intricate infill frame interaction leads to various possible modelling assumptions characterized by different computational efforts and accuracy (Lima, De Stefano, & Martinelli, 2014). Different approaches have been developed and validated with experimental test results for the modelling of masonry infills in order to capture the different possible failure mechanisms that take place in infilled RC frames. They are divided into two main groups based on the modelling approach: micro-modelling technique, e.g. (Campione et al., 2015; Lourenço, 1996) and macro-modelling technique (Decanini et al., 2004; Dolšek & Fajfar, 2008). A third approach, which has similar precision to 72 micro-modelling technique, is known as the meso-modelling technique (Asteris et al., 2013; Tarque et al., 2015). These approaches differ mainly in the degree of their infill panel modelling detail, as described in the following sections. 3.2.1 Micro-modelling and meso-modelling The micro- and meso-modelling approaches using nonlinear finite element (FE) methods are able to provide an accurate description of the interaction between the frame and infill at the local level (Campione et al., 2015). The micro-modelling approach includes two different modelling strategies: the detailed and the simplified micro-modelling (Lourenço, 1996). The former is based on the use of continuum elements for masonry units and mortar joints. In contrast, the unit mortar interface is represented by discontinuous elements (three-phase material) for the simulation of fracture behaviour in brick units and mortar joints (Asteris et al., 2013; Mehrabi et al., 1996; Zhai et al., 2016). The latter resorts to expanded units represented by continuum elements and the discontinuous elements (two-phase material) for the mortar joints and the unit-mortar interface (Asteris et al., 2013; Skafida, Koutas, & Bousias, 2014). The response of each element is described through proper constitutive relations. Chiou, Tzeng, & Liou (1999) developed several plasticity-based continuous interface models to capture the shear sliding in the joint. In the meso-modelling approach (one-phase material), units, mortar, and their interface are smeared out and the masonry is treated as a continuum through a homogenization process (Asteris et al., 2013). Contact, gap, or spring elements can be considered for modelling the interface infill frame, allowing the separation of the infill from the bare frame (Liberatore, Bruno, AlShawa, Pasca, & Sorrentino, 2016). Smeared crack elements can be used to model both reinforced concrete frames and brick infills. For instance, in the analyses reported in (Schmidt, 1989; Attard, Nappi, & Tin-Loi, 2007), infill panels are modelled as a homogeneous material 73 before fracture, and the effect of mortar joints is smeared out (Shing & Mehrabi, 2002; Stavridis & Shing, 2010). Overall, the above-mentioned methods are quite complex due to the large amount of information required for the constitutive models and the high computational effort involved, leading to delayed assessment, particularly for large structures. The micro-modelling approach is usually suitable for small buildings or sub-assemblages and focuses on assessing the interaction between bricks and mortar. 3.2.2 Macro-modelling The complexity and computational effort required by the micro-models led to the development of macro-models. Macro models use few elements and do not consider any distinction between the masonry units and joints. This approach provides simple and efficient tools to describe the global response of masonry-infilled RC frames. The diagonal equivalent strut model, which considers only the compressive force, is often adopted for the in-plane seismic analyses of solid masonry infilled frames (Decanini et al., 2004; Dolšek & Fajfar, 2008), and it has been updated to account for the out-of-plane/in-plane interaction (Asteris et al., 2017). The identification of the mechanical characteristics of the equivalent strut depends on the actual system properties. The macro model should represent all the important properties of the masonry wall, including strength, stiffness, and deformation capacity. Polyakov (1960) first suggested that masonry infill walls subjected to lateral loads could be represented by a diagonal no-tension strut element with appropriate mechanical properties. The idea was based on the observation that the infill wall separates from the surrounding frame at a moderate drift level, so that a compression diagonal path develops along two opposite corners 74 of the wall. Since then, many researchers have developed this model, by estimating the width, the mechanical properties, the number, and the configuration of the equivalent struts. For the evaluation of the strut parameters, e.g. the strut width, various predictive equations have been proposed. For example, Holmes (1961) continued the idea of a single pin-jointed diagonal strut and proposed that the effective width of the strut model should be 1/3 of the diagonal length. Afterward, numerous researchers continued to study the determination of the effective strut width considering other characteristics, e.g., the relative stiffness parameter, kh, the uncracked or cracked condition of the panel, etc., to control the stiffness and strength of the masonry infill (detail of the proposed equation can be found in Tarque et al., (2015) and Asteris et al., (2011). The stiffness is expressed as a function of the effective width of the strut, whereas the maximum capacity is related to a predefined failure mode. However, Amato, Cavaleri, Fossetti, & Papia (2008) and Amato, Fossetti, Cavaleri, & Papia (2009) introduced a new equation for the stiffness of the equivalent strut, which takes into account also the vertical load transferred from the bounding frame to the masonry infill walls. The influence of vertical load is integrated into the equivalent strut width estimation. A single diagonal strut in each direction, as shown in Figure 3.1, can be used to represent the behaviour of the infill walls under lateral loads in global effect. However, the single diagonal strut cannot be used to model and describe in detail the complex behaviour of the RC frame with infill walls subjected to cyclic loading. Observation from previous studies highlighted that a single diagonal strut cannot be used to adequately capture the bending moments and shearing forces in the RC frame members (Thiruvengadam, 1985; Crisafulli, 1997; Al-chaar, 2002; El-Dakhakhni, Hamid, & Elgaaly, 2004). The single-strut model was improved by introducing multiple struts to overcome this drawback. However, using different numbers of strut and strut configurations might lead to a different result of the overall response of the infilled frames. The strut model was also extended to infills with openings according to two different methods: (i) the use of several diagonal 75 struts around the opening as in (Thiruvengadam, 1985; Hamburger & Chakradeo, 1993); and (ii) the application of proper coefficients to modify the strut stiffness and strength (Al-chaar, 2002; Asteris, 2003; Mondal & Jain, 2008; Decanini, Liberatore, & Mollaioli, 2014). Figure 3.1: Schematic diagram of the equivalent strut model for infilled frames (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). Crisafulli (1997) investigated the influence of the different multiple strut configurations in the structural response of masonry-infilled frames. Afterwards, Crisafulli & Carr (2007) developed a new multi-strut macro-model including two parallel off-diagonal struts and a special shear spring to account for the diagonal tension failure and shear mechanism in the infill walls (Figure 3.2(a)). This model, however, involves complicated calibration for the required parameters, which are difficult to define in many cases. El-Dakhakhni et al., (2004) proposed an analytical method to estimate the stiffness and the ultimate load capacity of concrete masonry-infilled steel frames by using multiple struts model. The proposed analytical method is based on the nonlinear behaviour of the steel frame and 76 masonry panel. To estimate the bending moments and shearing forces in the frame members, two additional off-diagonal struts are introduced at the points of maximum moments in the beams and the columns, which approximately occurred at the end of the contact lengths. The whole panel is, therefore, represented by three struts, as shown in Figure 3.2(b). In this method, each strut is defined by force-deformation laws based on the orthotropic behaviour of the masonry panel. The use of a multi-strut model also simplifies the modelling of the interaction between different panels in multi-storey buildings. Figure 3.2: Multiple strut model proposed by: (a) Crisafulli (1997); Crisafulli & Carr (2007), (b) El-Dakhakhni et al. (2004), and (c) Sattar & Liel (2016a). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). Sattar & Liel (2016a) proposed a FE-enhanced strut model approach that can simulate the in-plane seismic response of structures up to ultimate failure. Two diagonal compression 77 struts (in each direction) are adopted to represent the behaviour of the infill wall (Figure 3.2(c)). The proposed model also focuses on the modelling of RC-frame elements in order to study the interaction between the infill wall and the frame. However, the model is not able to capture completely the infill-frame interaction that might lead to shear failure at the bottom of the columns and near the beam-column joints. To overcome the problem of capturing shear failure in the column, Burton & Deierlein (2013) developed a simple model by utilizing a pair of inelastic compression only strut in each direction (dual-strut model) (Figure 3.3). The dual-strut model can capture the infill wall strength and stiffness deterioration by using a peak-oriented hysteretic model and the shear failure of the column. Reinforced concrete columns and beams by elastic elements with zero-length flexural plastic hinges combined with a rigid softening shear degradation model. This approach can capture loss in the axial (gravity) load-carrying capacity due to column shear failure. Figure 3.3: Schematic diagram of typical infill frame model proposed by Burton & Deierlein, (2013). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). 78 3.2.3 Single strut modelling The simplest modelling option to simulate the behaviour of infills is using a single- or double-diagonal strut for monotonic or cyclic loading, respectively (Tarque et al., 2015). In this study, the cyclic response of the diagonal struts is reproduced by using different hysteretic materials available in OpenSees (Mazzoni et al., 2006) software. The main differences among these material models are discussed and shown with examples in the following section. The OpenSees software is used in this study due to its open source nature and object-oriented design. The Opensees framework is designed for the earthquake analysis of structures, which offers a wide range of advanced material constitutive models, elements, and analysis procedures that can accurately capture the behaviour of the structures. Additionally, the open-source nature of the software allows users to easily add or modify its code to integrate the current state-of-the-art models. OpenSees provides robust capabilities for nonlinear analysis, including the modeling of material nonlinearity, geometric nonlinearity, and contact interactions (McKenna 1997; Scott et al., 2008). The present study aims to select the simplest and most accurate model in terms of input parameters and characterization of hysteretic curves, respectively. The following section briefly summarizes the main important task that need to consider during the equivalent strut calibration, which include selection of the force-displacement relationship definition and cyclic behaviour, and the evaluation of input strut parameters (e.g. equivalent strut width), the stiffness and the strength. 3.2.3.1 Backbone curve – Constitutive law The selection of reliable constitutive models (force-displacement relationships) to describe the equivalent strut behaviour is required to conduct nonlinear analyses of masonry-infilled RC frames. Numerous constitutive hysteretic models or semi-empirical relationships have been 79 proposed, mostly based on experimental parametric studies. The constitutive law for a single equivalent strut can be described via a multi-linear relationship (Decanini & Fantin, 1987; Bertoldi, Decanini, & Gavarini, 1993; Panagiotakos & Fardis, 1996; Liberatore, 2001; Decanini et al., 2004; Stavridis, 2009; Liberatore & Decanini, 2011b; ) or via a combination of linear and nonlinear branches (Panagiotakos & Fardis, 1996; Cavaleri, Fossetti, & Papia, 2005; Cavaleri & Di Trapani, 2014). However, many studies used the monotonic constitutive model as the backbone curve for the cyclic response. The constitutive law is used to represent the initial stiffness, the strength and the panel post-peak behaviour in compression. The tensile strength is often neglected in the analyses. If the multiple strut model is adopted in the analysis, the evaluation of the constitutive law is necessary for each strut. To investigate the effect of different strut constitutive models available in the literature, three monotonic constitutive laws are discussed: Liberatore (2001); Liberatore & Decanini (2011b), Panagiotakos & Fardis (1996), and Dolšek & Fajfar (2008). In this study, these models have been tested and compared to experimental test data. The best-fit model is used to further investigate the suitability of various hysteretic laws. The model proposed by Liberatore (2001); Liberatore & Decanini (2011b) assumes a four branches skeleton curve of the lateral force-displacement (Hm-d) relationship (Figure 3.4(a)). The first segment (line OF) represents the un-cracked phase up to the first cracking (Hmf at point F) of the infill. The second segment (line F-FC) of the envelope corresponds to the post-cracking phase up to the development of the maximum strength (Hmfc). The descending third phase (line FC-R) defines the post-peak strength deterioration of the infill up to the residual strength, Hmr, reached at the displacement ur. 80 (a) (b) Figure 3.4: In-plane lateral force-displacement envelope of the model proposed by: (a) Liberatore (2001) and Liberatore & Decanini (2011), and (b) Panagiotakos & Fardis (1996). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). The stiffness at complete cracking stage (Kmfc) and the strength (Hmfc), that are required for the proposed model, are estimated according to Bertoldi et al. (1993); Decanini & Fantin (1987). All parameters are defined as functions of geometric and mechanical characteristics of the infill and the surrounding frame. The width of the equivalent strut bm, which is needed for the stiffness calculation, as given in Equation 3-1, is determined through the relative stiffness parameter kh proposed by Stafford Smith (1967) and by two constants K1 and K2 calibrated based on the experimental tests: dKKbhm 21 (3-1) where 𝜆ℎ is a non-dimensional parameter depending on the geometric and mechanical characteristics of the frame-infill system, K1 and K2 are coefficients that change according to 𝜆ℎ, and d is the length of the equivalent strut. 81 The parameter 𝜆ℎ is defined by the following expression: hIhEtEmcmmh 4/14)2sin(  (3-2) where 𝐸𝑚 is the elastic modulus of the infill, 𝐸𝑐 is the elastic modulus of concrete, h is the slope of the strut with respect to the horizontal axis, 𝑡𝑚 and ℎ𝑚 are the thickness and the height of the masonry panel, h is the storey height, I is the moment of inertia of the columns, and  is the slope of the equivalent strut. Parameters K1 and K2 depend on the parameter𝜆ℎ, as shown in Table 3.1. Table 3.1: Coefficient value to calculate the properties of the strut (Decanini & Fantin, 1987). 𝝀𝒉 < 𝟑. 𝟏𝟒 𝟑. 𝟏𝟒 < 𝝀𝒉 < 𝟕. 𝟖𝟓 𝝀𝒉 > 𝟕. 𝟖𝟓 𝑲𝟏 1.3 0.707 0.47 𝑲𝟐 -0.178 0.010 0.04 (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). The lateral stiffness of the equivalent strut of 𝐾𝑚𝑓𝑐 (in the horizontal direction) at the complete cracking stage is given by the following relation: 2cosmmmmmfcdbtEK  (3-3) where 𝑑𝑚 is the length of the equivalent strut, the meaning of 𝐸𝑚, 𝑡𝑚, 𝑏𝑚 and h are the same as mentioned above. Bertoldi et al. (1993) and Decanini & Fantin (1987) calculate the strength of 𝐻𝑚 value by considering four possible failure modes and the corresponding failure stresses: (a) diagonal tension, 𝐻𝑑𝑡; (b) sliding shear, 𝐻𝑠𝑠; (c) corner crushing, 𝐻𝑐𝑐; and (d) diagonal compression, 𝐻𝑑𝑐. 82 The equivalent failure stresses for each failure mode are calculated as: dbHmmdt00 3.06.0   (3-4) dbHmss00 3.0)cos45.0sin2.1(   (3-5) 088.0)(212.0)(1cossin12.1mhKhKccH  (3-6) 021 )(tan16.1mhdcKKH  (3-7) where, τm0 is the vertical compression strength of the masonry measured on masonry specimens; σ0 is the total vertical stress in the base of the masonry panel due to working loads; σm0 is the shear strength obtained from the diagonal compression test; and τ0 is the slide resistance in the joints measured form the triplet test or obtained from the empirical relation τ0 = 0.7 τm0. Assuming that the failure mode corresponding to the minimum value of the four-failure stress will happen first, then the lateral strength of the equivalent strut (in the horizontal direction) is given by: cos)( min mmmfc btHH  (3-8) The stiffness of the uncrack infill K0, is evaluated using the elastic stiffness of the frame (Kt0) and the infill stiffness at a complete cracking stage Kmfc as the following equation (Cavaleri & Di Trapani, 2014): mfct KKK 43 00  (3-9) 83 where 30123261hIEKpct (3-10) and lhIIcolumnbeam (3-11) Ibeam and Icolumn are the moments of inertial of the cross section of the beam and column, Hmf takes the value around 80% of the Hmfc, and Hmr takes the value around 35% of the Hmfc, according to the coefficient value assumed by Cavaleri & Di Trapani (2014). The constitutive law proposed by Panagiotakos & Fardis (1996) also consists of four segments of skeleton curve model in four linear shapes to describe the behaviour of compression strut. It was directly derived by comparing the experimental results on the masonry walls, bare RC structures, and the corresponding infilled frames. Conceptually, the proposed model is based on four different states of stress, as shown in Figure 3.4(b): a) initial elastic and shear behaviour of the un-cracked panel; b) post-elastic linear response, characterized by a reduced value of stiffness due to the detachment of the infill from the surrounding frame; c) the softening response of panel after the maximum force; and d) the residual axial strength after a given value of displacement. To fully define the backbone curve of the (Panagiotakos & Fardis, 1996) model, the following parameters are needed: The initial shear stiffness R1 of the uncracked masonry wall can be evaluated as follows: mmmmhltGR 1 (3-12) where, tm, lm, and hm are the masonry panel thickness, length, and height, respectively, while, Gm is the shear modulus of the masonry infill obtained in the diagonal compression tests. 84 The lateral cracking strength Fy, assumed equal to: mmmsy ltfF  (3-13) where, fms is the masonry failure stress, as evaluated by the diagonal-compression tests. Then, the displacement at crack (yielding) δy can be determined as: 1RFyy  (3-14) The axial post-cracking stiffness can be calculated using the following expression: mmmmdbtER 2 (3-15) where, Em is the Young modulus of masonry and the width bm computed according to the Mainstone (1974), as reported by Klingner & Bertero (1978): mmhm dhb4.0)(175.0   (3-16) where, λh is defined as in Equation 3.2., and dm is calculated as follow: 22mmm lhd  (3-17 The lateral maximum strength, Fm, assumed equal to: ym FF 3.1 (3-18) 85 and the displacement δm is corresponding to the maximum force: 2RFF ymym   (3-19) The stiffness of the softening branch R3 can be taken within the range of 0.5% to 10% of the initial stiffness R1. The lateral residual force Fr can be assumed equal to 5% to 10% of the maximum strength. Finally, the ultimate displacement δr is corresponding to the residual force: 3RFF rmmr   (3-20) Dolšek & Fajfar (2008) proposed an alternative model, which is theoretically similar to the model proposed by Panagiotakos & Fardis (1996). The only key difference between the two models is the assumption of the zero-residual strength (Fr = 0). This model required four parameters as described below: 1. The lateral cracking strength Fy is assumed to be equal to 60% of Fm. 2. The displacement at crack (yielding) δy can be determined through simple analytical relationships similar in Equation (3-14), which is the initial stiffness is defined as R1 in Equation (3-12). 3. The maximum lateral force Fm is defined according to the proposal by Žarnić & Gostič (2019):  11818.0 2  IImmmsm CCltfF (3-21) where mmIhlC 925.1 (3-22) 86 The maximum horizontal displacement δm is defined as a percentage of the wall height (0.2% for plain walls, 0.15% for walls with a window, and 0.10% for walls with a door opening). The slope of the softening response R3 is evaluated through the model Panagiotakos & Fardis (1996), described in the previous subsection. 3.2.3.2 Cyclic behaviour The equivalent strut utilization to perform the nonlinear inelastic analyses requires a practical conceptual cyclic law model to simulate the hysteretic behaviour of the masonry infill walls under cyclic loading. Notably, the cyclic behaviour of the masonry-infilled frame is quite difficult to capture. A set of rules is needed to account for the actual behaviour. Klingner & Bertero (1978) proposed a model based on a dynamic test. Figure 3.5(a) shows the compression strength of the envelope curve, which exhibits an exponential degradation beyond the peak strength. Cavaleri et al. (2005); Cavaleri & Di Trapani (2014) introduced some modifications to the model developed by Klingner & Bertero (1978) to enhance the accuracy of loading and unloading branches (Figure 3.5(b)). The cycles of the modified model are based on the envelope strength curves of the strut. Besides, the model suggested by Cavaleri et al. (2005) and Cavaleri & Di Trapani (2014) consider the pinching effect during the reloading by a zero value of the restoring force before reloading. The prediction of a cyclic behaviour of the masonry infilled RC frames requires three parameters (β, px, and py). These parameters are related to the definition of the unloading and reloading branches. 87 (a) (b) Figure 3.5: Hysteretic law proposed for the equivalent struts: (a) Klingner & Bertero (1978), and (b) Cavaleri & Di Trapani (2014); Cavaleri et al. (2005). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). Panagiotakos & Fardis (1996) proposed a hysteretic inter-storey shear force-drift relationship (Figure 3.6), which has a multilinear curve in monotonic loading, to represent the cracking, ultimate strength, post-ultimate branch, and residual strength. The model requires three empirical parameters to control the loading and unloading branches. Figure 3.6: Hysteretic law for equivalent strut proposed by Panagiotakos & Fardis (1996). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). Crisafulli (1997) and Crisafulli & Carr (2007) developed a more detailed cyclic model that can simulate different failure mechanisms. The masonry behaviour under cyclic loading is 88 presented by different axial force-relationships. The most significant novelty of the model proposed by Crisafulli is the addition of a shear spring to account for the shear behaviour of the infill panel. However, this model is quite complex because it requires a very large number of parameters that are difficult to calibrate, especially when test results on the materials are unavailable. Liberatore (2001) proposed a simple hysteretic model, which takes into account the degradation of stiffness in the unloading branch and the degradation of strength under displacement cycles of constant amplitude through two parameters:  and β. The parameter  controls the stiffness of the unloading branch, and its value range from 0 to 1, for =1, the unloading stiffness is the same as the initial one, as shown in Figure 3.7(a). The parameter β enables the control of reloading stiffness degradation according to the following expression (Figure 3.7(b)): *1'"EEHH h (3-23) where Eh is the cyclic dissipated energy and E* is the area enclosed in the force-displacement envelope up to the attainment of the residual strength. The parameters calibration and the adopted model validation were made through the comparison between the numerical and test results of different types of masonry Liberatore (2001). 89 (a) (b) Figure 3.7: Hysteretic law for equivalent strut proposed by Liberatore (2001). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). 3.2.3.3 The Infill Material Properties Numerous studies proposed different models to estimate the stiffness and the strength of the diagonal strut. In the following, those adopted in this study are briefly discussed. a) Evaluation of the strut strength Several studies (Decanini & Fantin, 1987; Priestley & Calvi, 1991b; Paulay & Priestley, 1992; Saneinejad & Hobbs, 1995; FEMA-306, 1998) suggested that the evaluation of the strut maximum compressive strength should depend on the possible failure mechanisms of the panel, which appeared in both experimental tests and actual behaviour under seismic action. The final compressive strength of the strut is selected based on the minimum possible resistance calculated by a specific equation as described below. Comprehensive studies by Haldar, Singh, & Paul (2013) and Moretti, (2015) reported that the typical failure mechanism of the masonry infill can be classified into four groups: (i) bed-joint sliding/sliding shear failure; (ii) diagonal tension cracking; (iii) diagonal compression failure; and (iv) corner crushing of infill. Table 3.2 provides an overview of four models that considers at least three different failure modes and that are frequently 90 cited in the literature. The models are adopted in this study to define the adequate strength of the diagonal strut. Table 3.2: Failure modes of masonry infill. Reference Diagonal tension cracking, Rdt Sliding shear failure, Rss Corner crushing of infills, Rcc Diagonal compression failure, Rdc Decanini & Fantin (1987) (DF) Yes Yes Yes Yes Priestley & Calvi, (1991) and Paulay & Priestley (1992) (PC) Yes Yes No Yes Saneinejad & Hobbs (1995) (SH) Yes Yes Yes Yes FEMA-306 (1998) and FEMA-356, (2000) Yes Yes Yes No (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). Decanini & Fantin (1987) suggested that the axial strength of the strut based on the different failure modes can be determined using Equations 3.4 – 3.7. All parameters involved in these equations are defined in the previous section (Section 3.2.3.1). Priestley & Calvi (1991) and Paulay & Priestley (1992) defined the axial force that can initiate a diagonal tension cracking (Rdt), bed-joint sliding failure (Rss), and diagonal compression strength (Rdc) as: mmmdt fdtR2 (3-24) mmmss dtlhfR3.0103.0 (3-25)  sec32mmdc ftR  (3-26) 91 where α, vertical contact length between infill and column, is defined as h2 (3-27) Saneinejad & Hobbs (1995) defined the strength of the strut in the four common failure modes as: cos22 tmmdt fhtR  (3-28) mmmmossdtdtR83.0tan45.01min ' (3-29) cos))(())(1( bmbcmcccctlthR (3-30) cos5.0 ammdcfthR  (3-31) ft and  are the tensile strength of the infill material and load factor, respectively, and θ’ is depicted in Figure 3.8. Moreover, αch and σc are the contact lengths and contact stress between the column and infill, and αbh and b are the contact lengths and contact stress between beam and infill, respectively. af is the permissible stress and effl is the effective length of the strut (see Figure 3.8) and is computed as: meffmatlff40139.0 (3-32) 92 Figure 3.8: Geometrical parameters used in the model proposed by Saneinejad & Hobbs (1995). (From © Noh, Liberatore, Mollaioli, & Tesfamariam (2017). Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). In the model by FEMA-306 (1998), the diagonal tension strength is calculated the same as proposed by Saneinejad & Hobbs (1995) in Equation 3.25. The cracking strength of masonry infill is assumed equal to 1/10 of the compressive strength. The sliding-shear capacity of the infill is determined as follows: cos)( mmyossltR (3-33) whereas in FEMA-356 (2000), the shear strength of the infill is calculated as: vieniss fAR  (3-34) Ani is the area of net-mortared section and fvie is the expected shear strength of infill wall. The Ani and fvie are computed as: mmni lbA 6.0 and )75.0(75.0 oovief   (3-35) 93 Finally, the corner crushing failure, which is modified from the equation provided by Stafford Smith & Carter (1970) expressed as: 90mmmcc ftbR  (3-36) where fm90 is the compressive strength measured in horizontal direction. b) Evaluation of the equivalent strut width The width of the strut, bm is important parameter in the equivalent strut modelling method, and various methods are proposed in the literature (Decanini & Fantin, 1987; Priestley & Calvi, 1991; Paulay & Priestley, 1992; Saneinejad & Hobbs, 1995; FEMA-306, 1998) (see summarized in Table 3.3). Table 3.3: The equivalent width equations. Reference Equivalent width, bm Decanini & Fantin (1987) (DF) As in Equation 3-1 Priestley & Calvi (1991) Paulay & Priestley (1992) (PC) 4mmdb  Saneinejad & Hobbs (1995) (SH) cos5.0cos)())(1(mincamcbbccccmffhflfhb FEMA-306 (1998) mhmdb 4.0)(175.0   where; h as in Equation (3-2) or (3-15) (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). 94 3.3 Structural and non-structural modelling with OpenSees This section provides in detail the procedure adopted to select the most adequate models for both the RC members and the infill. The simulations and calibrations were performed in OpenSees. 3.3.1 RC Frame modelling The non-linear behaviour of RC frame structures subjected to cyclic loads can be characterized by the development of plastic hinges close to the element ends, even though the interaction between the infill and frame may lead to shear failure in the columns. Numerical approaches need to be utilized to simulate the various nonlinearities arising from the seismic cyclic demands. To this aim, the concentrated- (lumped) and distributed- (fibre-based) plasticity models are the most accepted due to their robustness, flexibility, and capability to simulate the global response of framed structures. 3.3.1.1 Fibre-based distributed-plasticity model The fibre-based distributed plasticity approach, permits the spread of the inelastic behaviour by numerical integration over the element cross-section and along the deformable region of the member length (Spacone, Filippou, & Taucer, 1996). This method requires the discretization of the element into fibres, as shown in Figure 3.9. For each element, five integration points are usually considered. The nonlinear hysteretic characteristics in the cross-sections are captured by defining the uniaxial materials, i.e. unconfined concrete, confined concrete or steel reinforcement. Several control parameters associated with the hysteresis model need to be considered to establish the rule for inelastic reversed cyclic loading. The numerical convergence issue can be improved by increasing the number of fibres in each cross-section. The fibre based-95 model captures the axial-moment (P-M) interaction and can be used where the cracking and tension-stiffening behaviours govern the response. However, this model is not able to properly represent the deterioration phenomena of the steel reinforcing bars due to buckling and low-cycling fatigue. Figure 3.9: RC frame modelling using distributed plasticity elements. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). 3.3.1.2 Lumped-plasticity modelling approach The lumped plasticity model can be introduced using an elastic beam-column with two zero-length elements at both ends (Figure 3.10). The zero-length elements corresponds to a rotational hinge having a hysteretic response. The rotational hinge behaviour is defined by uniaxial material models, which describe the moment-rotation or force-deformation relationship. 96 Figure 3.10: RC frame modelling using concentrated/lumped plasticity elements. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). The most recent OpenSees implementation, the peak-oriented hysteretic model developed by Ibarra & Krawinkler (2005) (modIMKmodel), can be used to describe the behaviour of the RC beam-column element. This model captures the four cyclic deterioration modes: the basic strength deterioration, the post-capping strength deterioration, the unloading stiffness deterioration, and the accelerated reloading stiffness deterioration. The model requires six parameters: elastic stiffness (Ke), effective yield strength (My), strain hardening ratio (Mc/My), pre-capping rotation (θcap), post-capping rotation (θpc), and cyclic deterioration parameter (λ). Figure 3.11 shows the moment-rotation law (backbone) according to Ibarra & Krawinkler (2005). All the parameters are determinable using the predictive equations and tool developed by Haselton, Liel, & Lange (2007), as shown in Table 3.4. 97 Figure 3.11: Monotonic behaviour of component model developed by Ibarra & Krawinkler (2005). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). Table 3.4: Model plastic hinge parameters. Model Parameter Predictive equations (Haselton et al., 2007) gyeEIEIK  6.02.007.059.007.0HLS ycMM cfcv units'01.0)91.0()89.0(25.1 plcap, cfcshvslunitsa'01.065.0 )57.0()4002.0()13.0)(55.01(13.0  pc 10.0)4002.0()31.0(76.002.1  shv   dsv )10.0()27.0(7.170 where v , HLs / , sh , cf', sla , and ds / is the axial load ratio  cfAP g', the shear span ratio, the lateral confinement ratio, the concrete strength, the slip term (=1), and the ratio of transverse tie spacing to the column depth, respectively. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). 98 This simulation approach can be used for collapse prediction, to capture deterioration of the steel reinforcing bars due to rebar buckling and low cyclic fatigue, and to record the strength and stiffness deterioration to assess the global collapse. Overall, this approach is simple, effective for interface effects, and computationally efficient. However, it requires the moment-rotation relationship instead of stress-strain relationships, and it is incapable of capturing the P-M interaction, which is particularly important for the columns. 3.3.2 Infill wall panel modelling In OpenSees, the equivalent diagonal struts are modelled using truss elements. Several parameters are required to define the strength degradation, and loading and unloading rules. This study adopts and compares three material models available in OpenSees: Concrete01 material, Hysteretic material, and Pinching4 material. These models are able to capture the strength and stiffness degradation, the loading and unloading cycles and the residual strength. Details of each material model are discussed below. 3.3.2.1 Concrete01 material The Concrete01 material is a zero-tensile strength material. It requires only minimum data to define the features of the nonlinearity of the stress-strain constitutive law. The parameters required are the maximum stress, the strain corresponding to maximum stress, the ultimate stress and the ultimate strain corresponding to the ultimate stress, as shown in Figure 3.12. In Concrete01 material, the tangent line of the first linear branch of the curve (Em) is evaluated as two times the maximum stress divided by the maximum strain (Em=2($fpc/$epsc0)). The strength degradation of this material object is degraded by the linear unloading/reloading stiffness. 99 Figure 3.12: Concrete01 Material model in OpenSees (Mazzoni et al., 2006). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). 3.3.2.2 Hysteretic material The Hysteretic material is a uniaxial trilinear hysteretic material object, which includes the pinching effect, the cyclic deterioration due to deformations and dissipated energy, and the degradation of the unloading stiffness based on ductility (Figure 3.13). The parameters, such as initial slope, maximum stress, failure strain, pinching factor and degraded unloading stiffness are needed to study the cyclic response of the infill wall. The pinching factor for strain during reloading (PinchX), pinching factor for stress during reloading (PinchY) and power used to determine the degraded unloading stiffness based on ductility (Beta) are determined through the comparisons with experimental data. Values equal to 1, 0.1 and 0.5, are found for the three parameters. Damage parameters are not considered. 100 Figure 3.13: Hysteretic Material model in OpenSees (Mazzoni et al., 2006). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). 3.3.2.3 Pinching4 material The Pinching4 material model simulates a pinched load-deformation response of structural components that exhibits flexural strength and stiffness degradation under cyclic loading (Figure 3.14). In the loading direction of interest (i.e. positive and/or negative), two parameters – rDisp/rForce – define the ratio of the deformation/force (in this case rotation/moment), in which the reloading begins at the maximum deformation/force demand of the previous loading cycle in the loading direction of interest. The parameter uForce defines the ratio of flexural strength developed upon unloading from the negative/positive load to the maximum flexural strength developed under monotonic loading. The cyclic deterioration in unloading and reloading stiffness and flexural strength are controlled with gKLim, gDLim, and gFLim, respectively. The values of cyclic degradation parameters (gKLim, gDLim, and gFLim) and pinching parameters (rDispP, rDispN, rForceP, rForceN, uForceP and uForceN) need to be adjusted to simulate the force-deformation history for selected specimens. 101 Figure 3.14: Piching4 Material model in OpenSees (Mazzoni et al., 2006). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). 3.4 Numerical simulation with OpenSees: Selection and calibration The numerical analyses performed in this section are aimed at calibrating and validating the response of the different models with experimental test data (both bare- and infilled-RC frames subjected to in-plane cyclic loading. 3.4.1 Experimental data Two sets of experimental tests available in the literature are used in this study to calibrate the response of the different models. The calibration process focuses specifically on the assessment of in-plane strength and stiffness of the infill wall without openings. For this purpose, only the tests that provide horizontal force (cyclic loading) versus horizontal displacement curves have been considered. Furthermore, the calibration is limited to a specific type of structure: single-storey RC frames with infills made of perforated/hollow clay brick units. The panel aspect ratio 102 chosen for calibration is less than 1, as it is considered representative of the sizes commonly found in existing infilled frame buildings (Liberatore, Noto, Mollaiolo & Franchin, 2017). Additionally, the calibration is conducted for specimens under the condition that vertical loading is applied to the columns. Therefore, the experimental studies selected here were conducted by Stylianidis (2012) and Pires (1990), denoted in this paper as Experiment 1 and Experiment 2, respectively. Stylianidis (2012) performed quasi-static cyclic tests on 1/3 scaled single storey-single bay bare and infilled RC frames. The infill walls were made of perforated clay brick units with dimensions 190 x 63 x 90 mm and a 7.5 mm thick mortar. The specimens FBN (bare frame) and F1N (masonry infilled frame) from the first program were selected for comparison. The loading program is based on displacement-controlled loading cycles, with increasing displacements up to 30 mm. An axial compressive load of 80 kN (14% of the column strength) was applied on the columns. Pires (1990) tested 2/3 scaled single storey-single bay bare (M1) and infilled (M2) frames. The brick units had dimensions 300 x 200 x 150 mm with 1:4 mortar’s proportion. These specimens were tested under alternated horizontal actions. The loading program consisted in displacement-controlled loading cycles that imposed increasing displacements up to 100 mm unless failure of both columns was observed. A vertical force of 100 kN was applied on both columns. Tables 3.5 and 3.6 summarize the geometric characteristics and mechanical properties adopted for the specimens considered in this study. 103 Table 3.5: Geometric characteristic (Stylianidis, 2012; Pires, 1990). Design Characteristics Experiment 1 Experiment 2 1:3 2:3 Length (cm)-axis to axis of the column 159 225 Height (cm) 106 172.5 Cross-section of the column (cm) 15 x 15 15 x 15 Cross-section of the beam (cm) 10 x 20 15 x 20 Longitudinal of reinforcement of the column 8Ø6 8Ø8 Tensile and compression reinforcement of the beam 3Ø6 3Ø8 Stirrups Ø2.7 Ø4 Spacing stirrups in critical regions (cm) 3.33 5 Spacing stirrups in non-critical regions (cm) 6.67 10 (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). Table 3.6: Mechanical Properties of the material (Stylianidis, 2012; Pires, 1990). Material Compressive Strength, (MPa) Shear Strength, (MPa) Yield Stress, (MPa) Ultimate Stress, (MPa) Concrete Experiment 1 26.5 Experiment 2 33.1(M1) 28.3(M2) Brick unit Experiment 1 (6.3 cm) 6.0 Experiment 2 - Mortar Experiment 1 (Type S-STM) 10.7 Experiment 2 6.3 Masonry Experiment 1 (Type S mortar) 4.2 0.33 Experiment 2 2.1 0.4 Longitudinal Steel bars Experiment 1 (Ø6) 348 457 Experiment 2 (Ø8) 523 552 Transverse Steel bars Experiment 1 (Ø2.7) 271 395 Experiment 2 (Ø4) 434 519 (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). 104 3.4.2 Numerical Model The experiments were reproduced as two-dimensional models. Two different models were developed for the RC elements (columns and beam): (1) distributed plasticity model and (2) lumped plasticity model (plastic hinges). Equivalent diagonal struts, modelled as truss elements, were used to study the influence of the effect of the infill panel on the frame response. The stiffness degradation of the equivalent strut in loading and unloading phases was modelled using the three different models available in OpenSees: (a) Concrete01 material, (b) Hysteretic material, and (c) Pinching4 material. Figure 3.1 illustrates the modelling scheme of the masonry infilled RC frame. The model properties were calibrated with the experimental test results. 3.4.2.1 RC Frame modelling: Model 1 and Model 2 The nonlinear behaviour of the RC beam and columns in Model 1 was modelled by utilizing the distributed plasticity elements in the first model. Particularly, the columns and the beam are represented by the nonlinearBeamColumn element (Mazzoni et al., 2006). The cross-sections are defined using the fibre discretization with distinct fibres for steel reinforcement. Each element has five integration points. Concrete material that includes unconfined (cover) and confined (core) concrete is modelled using the Concrete01 material model (Figure 3.12). The steel reinforcing bars were modelled using a Steel02 material, which is based on the uniaxial Giuffre Menegotto-Pinto steel material, with a 1% strain hardening ratio. Table 3.7 summarizes the mechanical properties adopted for the structural materials. The confinement degree of the RC frame members used is K = 1.3 for both experiments. 105 Table 3.7: Parameters for the material behaviour. Material Experiment ID fc [MPa] Ec [MPa] Concrete01 Experiment 1 26.5 4700(fc)1/2 Experiment 2 M1= 33.1 M2=28.3 - - fy, [MPa] Es, [GPa] b Steel01 Experiment 1 348 210 0.01 Experiment 2 434 0.006 (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). The model calibration is based on the comparison between numerical and experimental results in terms of total base shear-top displacement curves and cumulative energy dissipation. An iterative approach was used, which consisted in adjusting the model parameters until the simulated hysteretic curves reproduced the experiment behaviour appropriately. Figure 3.15 shows the comparison between the calibrated model and the experimental results for both experiments. A good agreement between the two is obtained. The pinching effect is captured with acceptable accuracy, whereas the reloading stiffness of the model of the real structure is less accurately predicted. The strength of the numerical models slightly underestimates the experimental strength, in which the numerical value is 10.3% and 10.5%, slightly lower than the experimental values of Experiment 1 and 2, respectively. 106 (a) (b) Figure 3.15: Bare frame, Model 1. Numerical and experimental results: (a) Experiment 1, and (b) Experiment 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). Model 2 is based on the lumped plasticity model. RC beam and columns are idealized using the elastic elements with zero-length flexural plastic hinges at both ends, developed by Ibarra & Krawinkler (2005). The model requires six parameters, as described in Section 3.1.2. The plastic hinge parameters of the RC beam and columns were determined using the semi-empirical equations developed by Haselton et al. (2007). Figure 3.16 shows the force-displacement comparison between the experimental results and the numerical predictions of Experiments 1 and 2. As depicted in Figure 3.16, the hysteretic curves obtained by the numerical analyses are in good agreement with the experiments except for the pinching effect, which is larger and slightly greater than those recorded in Experiments 1 and 2, respectively. The level of underestimation of the maximum force value obtained from the numerical model is 6.8% and 5.2% for Experiments 1 and 2, respectively. 107 (a) (b) Figure 3.16: Bare frame, Model 2. Numerical and experimental results: (a) Experiment 1, and (b) Experiment 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). A more detailed understanding of the calibrated models' performance is attained by comparing the cumulative displacement energy dissipated during the experimental tests and those evaluated numerically. The cumulative dissipated energy is defined as cumulative summation of the areas enclosed within individual hysteresis loops or cycles, each evaluated at the same target displacement level. The jumps observed in the cumulative dissipated energy graph, as shown in Figure 3.17, correspond to different phases of the loading and unloading cycles. During the process of loading, energy is gradually stored and accumulated within the system. As the loading phase transitions to unloading, the stored energy is dissipated, causing a jump in the cumulative energy graph. This comparison was conducted only for Experiment 1, since raw data for Experiment 2 are not available. Figure 3.17 shows that both Model 1 and Model 2 overestimate the dissipated energy, being the average error equal to 8.2% and 14% for Models 1 and 2, respectively. It is observed that the two models are capable of adequately capturing the response of the bare frame. Therefore, both models are used further to simulate the behaviour of the infilled frames. 108 Figure 3.17: Cumulative displacement dissipated energy: Experiment 1. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). 3.4.2.2 Infill strut modelling (Concrete01, Hysteretic, and Pinching4 material) In the numerical simulation of the test specimens, a single diagonal strut replaces the masonry infill wall in each diagonal direction (Figure 3.1). No-tension truss elements with a multilinear response were used to simulate the behaviour of the infill in terms of strength and stiffness. The stiffness degradation in the loading and unloading phases was implemented using three different material models (Concrete01 material, Hysteretic material, and Pinching4 material) available in OpenSees, as discussed in Section 3.3.2. The initial step in this process was the identification of the contribution of the masonry infill wall to the overall response recorded in the experimental tests. To this aim, the net response of the infill was determined by subtracting the response of the bare frame from the total response of the infilled frame, as shown in Figure 3.18 for both experimental tests. Figure 3.18 highlights the 109 significant contribution of the infill, which is, however, dependent on the geometric and mechanical properties of both the frame and the infill. (a) (b) Figure 3.18: Contribution of the frame and the infill in the experimental tests: (a) Experiment 1 and (b) Experiment 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). Next, the experimental force-deformation curves of the masonry infill were compared with the three different backbone curve models of the equivalent strut outlined in Section 3.2.3.1. The key element of this approach was to verify and select the most suitable constitutive model, which include estimating key force-deformation parameters of the infill walls, to reproduce the infill response. The key force-deformation parameters, in term of strength and stiffness, is estimated by using predictive equations proposed by Decanini & Fantin (1987), Panagiotakos & Fardis (1996), and Dolšek & Fajfar (2008). The comparison is shown in Figure 3.19, where the experimental and the estimated monotonic curves are reported. The backbone curves by Dolšek & Fajfar (2008) and Panagiotakos & Fardis (1996) give a higher value of the strength and a slightly greater value of the displacement at the peak compared to the model by Decanini & Fantin (1987) 110 (Decanini & Fantin, 1987; Cavaleri et al., 2005; Liberatore & Decanini, 2011; Cavaleri & Di Trapani, 2014). The model adequately predicts the post-peak branch by Decanini & Fantin (1987) (Decanini & Fantin, 1987; Cavaleri et al., 2005; Liberatore & Decanini, 2011; Cavaleri & Di Trapani, 2014). On the other hand, the models by Dolšek & Fajfar (2008) and Panagiotakos & Fardis (1996) show a steeper decrease of the strength. With reference to Experiment 2, all models overestimate the initial elastic stiffness. Overall, the backbone curve model proposed by Decanini & Fantin (1987) shows the best agreement with the backbone curve of both experimental tests (Decanini & Fantin, 1987; Cavaleri et al., 2005; Liberatore & Decanini, 2011; Cavaleri & Di Trapani, 2014). Hence, this model is used in the subsequent analyses to outline the backbone curve of the struts. For this model, the calibrated elastic stiffness K0, degrading stiffness K2, elastic strength Hmf, and residual strength Hmr are: K0 = 3Kt0+4Kmfc (3-37) K2 = 0.02Kmfc Hmf = 0.8Hmfc Hmr = 0.35Hmfc 111 (a) (b) Figure 3.19: Comparison of the equivalent strut backbone curves proposed by Panagiotakos & Fardis (1996), Dolšek & Fajfar (2008), and Liberatore (2001); Liberatore et al. (2016): (a) Experiment 1, and (b) Experiment 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). (a) (b) Figure 3.20: Force-displacement curves of masonry infilled RC frames obtained using various strength models: (a) Experiment 1, and (b) Experiment 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). Finally, the width and the strength of the struts were calculated also according to different models described in Section 3.2.3.3. As for the axial strength of the equivalent diagonal strut, each model takes into account various failure modes. The strength models by Panagiotakos & 112 Fardis (1996) and Dolšek & Fajfar (2008) were not included in this evaluation because these models were based on a single failure mechanism (shear failure). Figure 3.20 shows the comparison between the experimental results and numerical results obtained by estimating the strut width and strength by adopting the equations by Decanini & Fantin (1987) and Liberatore & Decanini (2011), Priestley & Calvi (1991) and Paulay & Priestley (1992), Saneinejad & Hobbs (1995), and FEMA-306 (1998). It is noted that the models proposed by Decanini & Fantin (1987) and Liberatore & Decanini (2011), and Priestley & Calvi (1991) and Paulay & Priestley (1992) provide an adequate estimate of the experimental results for both experimental tests. Concerning Experiment 1, the adoption of Saneinejad & Hobbs (1995) and FEMA-306 (1998) models provide a lower resistance. For Experiment 2, only the model by Saneinejad & Hobbs (1995) noticeably underestimates the strength, whereas the other three models provide a fairly good prediction of the observed experimental response. This is because of the model by Saneinejad & Hobbs (1995) used the permissible stress fa (Equation 3.32) instead of using the compressive strength fm as applied in the other models. Therefore, in this study, the strength model proposed by Priestley & Calvi (1991) and Paulay & Priestley (1992) is used combined with the backbone curve by Liberatore & Decanini (2011). The basic mechanical properties of the infill wall used in the model are presented in Table 3.8. Table 3.8: Mechanical properties of the infill assigned to the equivalent strut. Material Experimental ID fm [MPa] Em [MPa] τm0 [MPa] τ0 [MPa] Masonry brick 1 (F1N) 4.2 2.31* 0.33 0.231a 2 (M2) 2.1 1.84 0.4 0.532 athe value of the parameters Em and τ0 are not available –the value of Em was calculated based on 550fm suggested by FEMA-356, and 0 was been evaluated using empirical equation 0 = 0.7 m0. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). 113 The model adopted for the diagonal strut was further implemented in OpenSees by using the three different uniaxial material models in order to reproduce the hysteretic response of the infills. These material models are capable of capturing the cyclic strength and stiffness degradation, which are generally observed in experimental test a) Strut model using Concrete01 material result Table 3.9 shows the value of the parameters required for the Concrete01 material. It is worth mentioning that the actual strain at the peak stress was decreased by half of its actual value in order to obtain a realistic value of the elastic stiffness. The numerical results obtained using the Concrete01 material are shown in Figures 3.21 and 3.22 for Experiments 1 and 2, respectively. Overall, good agreement between experimental and numerical curves is obtained. The percentage errors in the peak strength of the masonry-infilled frame using the Concrete01 material for the infill, combined with Models 1 and 2 for the frame members, is about 2.8% and 0.4%, respectively. However, some differences are noted in the unloading phases, which are multi-linear in the numerical model. This indicates a limitation of the Concrete01 material, which does not allow for a smooth unloading response. Figures 3.21(b) and 3.22(b) clearly show that the infill wall model combined with Model 2 gives a better performance in terms of hysteretic loops shape, unloading and reloading stiffness and peak strength. Table 3.9: Concrete01 material parameters for the equivalent strut. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). Experimental ID Dimensionless cross section, w/d Strength envelope compressive strength-strain law values σm [MPa] εm σR [MPa] εR 1 0.1868 -1.881 -0.00018 -0.658 -0.0124 2 0.2500 -1.044 -0.00011 -0.365 -0.00028 114 (a) (b) Figure 3.21: Force-displacement comparison of Experiment 1 using Concrete01 Material for masonry infill with: a) Model 1 of RC frame, and b) Model 2 of RC frame. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). (a) (b) Figure 3.22: Force-displacement comparison of Experiment 2 using Concrete01 Material for masonry infill with: a) Model 1 of RC frame, and b) Model 2 of RC frame. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). 115 b) Strut model using Hysteretic material result To define the backbone curve of the Hysteretic material, three points in tension and compression are required. However, a very small value (1% of the compressive stress and strain) is assumed for the tension part in order to reproduce a no-tension response. The parameters defining the shape of the hysteretic cycles are: β, which controls the stiffness degradation during unloading, PinchX and PinchY, which control the pinching effect. These parameters are calibrated by comparing the numerical analysis to the experimental tests. The obtained values are equal to: 0.1, 0.9 and 0.1 for β, PinchX and PinchY, respectively. Damage parameters are not considered. The cyclic response is shown in Figures 3.23 and 3.24. Compared to the Concrete01 material, the Hysteretic material model provides a better agreement with the experimental response, especially in the unloading branches. For Experiments 1 and 2, the numerical model is able to adequately reproduce the actual strength; even though the adoption of the lumped plasticity (Model 2, Figures 3.23(b) and 3.24(b)) results in slightly greater strength values than those obtained with the distributed plasticity model (Model 1, Figures 3.23(a) and 3.24(a)). 116 (a) (b) Figure 3.23: Force-displacement comparison of Experiment 1 using Hysteretic Material for masonry infill with: a) RC frame Model 1 and b) RC frame Model 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). (a) (b) Figure 3.24: Force-displacement comparison of Experiment 2 using Hysteretic Material for masonry infill with: a) RC frame Model 1 and b) RC frame Model 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). 117 c) Strut model using Pinching4 material result The Pinching4 material was used due to its capability of modelling nonlinearity and degradation of stiffness and strength. The multi-linear envelope curve was defined by eight parameters including cracking, yielding, maximum and residual strength, and corresponding displacement. The strength and stiffness of the equivalent strut in tension are assumed very small, in order to obtain a no-tension strut. Damage parameters are assumed to be zero. The pinching coefficients calibrated with the experimental data are indicated in Table 3.10, where the coefficients used by Lima et al. (2014) for a masonry made out of artificial blocks of expanded clay are also reported. Table 3.10: Cyclic deterioration parameters for the Pinching4 Material hysteretic model. Value rDispP rDispN rForceP rForceN uForceP uForceN gKLim gDLim gFLim Lima et al. (2014) 0.5 0.5 0.25 0.25 0.05 0.05 0.9 0.5 0.9 Calibrated_E1 0.8 0.8 0.1 0.1 0.01 0.01 0.8 0.1 0.1 Calibrated_E2 0.8 0.8 0.1 0.1 0.01 0.01 0.9 0.1 0.1 (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). The numerical results (Figures 3.25 and 3.26) are similar to those obtained with the Hysteretic material (Figures 3.23 and 3.24). The model can properly capture the shape of the hysteretic loops. The percentage errors in peak strength values using this material combined with Model 1 (distributed plasticity for frame members) are equal to 4.3% and 6.9% for Experiments 1 and 2, respectively. Whereas, when adopting Model 2 for the frame (lamped plasticity) the percentage errors in peak strength values are equal to 1.6% and 2.9% for Experiments 1 and 2, respectively, indicating a satisfactory agreement between the experimental and the numerical results, although differences are observed in the reloading phases. 118 (a) (b) Figure 3.25: Force-displacement comparison of Experiment 1 using Pinching4 Material for masonry infill with: a) RC frame Model 1, and b) RC frame Model 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). (a) (b) Figure 3.26: Force-displacement comparison of Experiment 2 using Pinching4 Material for masonry infill with: a) RC frame Model 1, and b) RC frame Model 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). 119 In general, each of the models succeeds in reproducing the observed experimental behaviour with acceptable precision. However, the observation of the hysteretic curve shapes highlights some discrepancy in the reloading phases. As for the unloading branches, the Hysteretic and Pinching4 materials provide a better matching to the experimental plots, compared to the Concrete01 material model, which is not able to capture the unloading stiffness slope. Moreover, the use of the Pinching4 material allows to accurately estimate the maximum strength of the infilled-frames. Finally, a comparison is made also in terms of dissipated energy (Figure 3.27), for Experiment 1. Concerning Model 1 (distributed plasticity), the actual dissipated energy is underestimated until a displacement level of 12 mm for Hysteretic and Pinching4 material model, and 18 mm for Concrete01 material models, whereas is overestimated in the following cycles (Figure 3.27(a)). The models with Concrete01 material, Hysteretic material, and Pinching4 material reproduce fairly well for the experiment, being the average errors equal to 24%, 22%, and 21%, respectively. For Model 2 (lumped plasticity), a similar trend is observed. The models with Concrete01 material, Hysteretic material, and Pinching4 material overestimate the cumulative displacement dissipated energy after a displacement equal to 18 mm, 6 mm and 12 mm, respectively (Figure 3.27(b)) and the average errors are equal to 20.2%, 18.1%, and 17.8%, respectively. 120 (a) (b) Figure 3.27: Cumulative displacement dissipated energy, Comparison for Experiment 1: a) Model 1, and b) Model 2. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). In summary, the assessment of the above mentioned values and the comparison among all the force-displacement curves, indicate that the Pinching4 material is slightly superior to reproduce the cyclic response compared to Concrete01 and Hysteretic materials. However, given that the Concrete01 material is the simplest model, requiring a limited number of parameters, and it still gives reasonable estimates of the overall response. Therefore, both materials (Concrete01 and Pinching4) is used in combination with the lumped plasticity model for the frame members in the following analyses. 3.5 Verification of selected model In order to evaluate the accuracy and ability of the calibrated models, five additional experimental tests are selected and numerically reproduced using the Concrete01 and Pinching4 Materials. The specimens under consideration are mainly focused on single-storey RC frame with 121 URM infill wall without openings. The specimens have a panel aspect ratio of 1.5 and consist of two types of masonry compressive strengths: "weak" and "strong". The selection of the samples also includes specimens subjected to vertical loading conditions on columns. Tables 3.11 and 3.12 report the geometrical characteristics, the mechanical properties, and the predicted failure mechanisms of the infills. Table 3.11: Geometry of the investigated specimens. Specimen tpanel (mm) L (mm) H (mm) (bxh)column (mm) (bxh)beam (mm) SU1 (Kyriakides, 2011) 58.4 1099 629 108 ×165 165 × 140 Specimen S (Kakaletsis & Karayannis, 2008) 60 1350 900 150 × 150 100 × 200 Specimen IS (Kakaletsis & Karayannis, 2008) 52 1350 900 150 × 150 100 × 200 Specimen #4 (Mehrabi et al., 1996) 92 2337 1556.5 178 × 178 152 × 229 Specimen #5 (Mehrabi et al., 1996) 92 2337 1556.5 178 × 178 152 × 229 (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). Table 3.12: Infill Frame properties from Experimental Test. Testing Label Loading Lm (m) Hm (m) Lm/Hm Lateral Strength, (kN) Failure Mechanism Lateral Vertical SU1 (Kyriakides, 2011) Cyclic Yes 0.991 0.559 1.26 92.7 Bed joint sliding Specimen S (Kakaletsis & Karayannis, 2008) Cyclic Yes 1.2 0.8 1.5 81.46 Diagonal tension failure Specimen IS (Kakaletsis & Karayannis, 2008) Cyclic Yes 1.2 0.8 1.5 72.92 Sliding shear failure Specimen #4 (Mehrabi et al., 1996) Cyclic Yes 2.159 1.422 1.5 162.36 Sliding shear failure Specimen #5 (Mehrabi et al., 1996) Cyclic Yes 2.159 1.422 1.5 266.89 Diagonal tension failure (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). Table 3.13 shows a comparison of the predicted infill strength with the experimental results for each strength model (see Section 3.4.2.2). Based on the normalized root mean square error 122 (NRMSE) shown in Table 3.13, no significant difference is detected between the models. However, the approach used by Paulay & Priestley (1992) and Priestley & Calvi (1991) (PPC) provide the best estimate of the lateral strength (NRMSE = 0.15). The ratio of predicted to observed lateral strength for this model ranges from 0.69 to 1.67. The model by Saneinejad & Hobbs (1995) offers the least accurate prediction (NRMSE = 0.23), the ratio ranging between 0.41 and 1.72. Although all the models produced acceptable average errors in estimating the strength of specimens, the model proposed by PPC is used to calculate the strength of the infills. The parameters assigned to the struts were evaluated according to the procedure described in Section 3.2.3.3. Tables 3.14 and 15 provide the parameter values considered for the analyses. Table 3.13: Comparing Infill frame strength from model prediction to experimental result. Reference Measured Lateral Strength (kN) Predicted Lateral Strength (kN) DF SH FEMA 356/306 PPC SU1 (Kyriakides, 2011) 78.7 72 (0.92) 78 (0.99) 97 (1.23) 101 (1.28) Specimen S (Kakaletsis & Karayannis, 2008) 40 21 (0.53) 16 (0.41) 23 (0.59) 27 (0.69) Specimen IS (Kakaletsis & Karayannis, 2008) 28 43 (1.54) 48 (1.72) 42 (1.49) 47 (1.67) Specimen #4 (Mehrabi et al., 1996) 113 121 (1.07) 149 (1.32) 106 (0.93) 150 (1.32) Specimen #5 (Mehrabi et al., 1996) 196 139 (0.71) 163 (0.83) 153 (0.78) 172 (0.87) NRMSE 0.18 0.23 0.17 0.15 () Ratio of predicted to measured lateral strength. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). Table 3.14: Strut model parameters for Concrete01 material. Parameters Experimental test SU1 Specimen S Specimen IS Specimen 4 Specimen 5 m -4.590 -1.52356 -3.00000 -3.05916 -3.49480 R -1.610 -0.53325 -1.05000 -1.07071 -1.22318 m -0.000374 -0.001153 -0.000528 -0.000262 -0.000229 R -0.025059 -0.077255 -0.035423 -0.017545 -0.015358 (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). 123 The results, in terms of force-displacements curves, are shown in Figures 3.28–3.30. The comparison between the results obtained from the experimental tests by Kyriakides (2011) (Figure 3.28), Kakaletsis & Karayannis (2008) (Figure 3.29), and Mehrabi et al. (1996) (Figure 3.30), and those obtained with the numerical analyses indicates that the adopted model is generally adequate to simulate the response of the masonry infilled RC frames. Specifically, a satisfactory agreement with the experimental data is obtained for tests, IS Kakaletsis & Karayannis (2008), Specimens 4 and 5 Mehrabi et al. (1996), where the error in estimating the peak strength ranges from 0.5% to 16%. Higher errors are observed in Figure 3.29(a) for a specimen made of masonry defined as ‘‘weak” by the authors, which shows an unexpected resistance compared to the ‘‘strong” masonry (Figure 3.29(b)). Figure 3.28: Comparison between experimental and numerical results, specimen SU1 (Kyriakides, 2011). (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). 124 (a) (b) Figure 3.29: Comparison between experimental and numerical results, experimental data by Kakaletsis & Karayannis (2008): (a) specimen S, and (b) specimen IS. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). (a) (b) Figure 3.30: Comparison between experimental and numerical results, experimental data by Mehrabi et al. (1996): (a) specimen #4, and (b) specimen #5. (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). 125 Table 3.15: Strut model parameters for Pinching4 material. Parameters Experimental test SU1 Specimen S Specimen IS Specimen 4 Specimen 5 Positive Backbone ePf1 (kN/mm2) 0.3420 0.121885 0.240000 0.244733 0.279584 ePf2 (kN/mm2) 0.3844 0.137120 0.270000 0.275325 0.314532 ePf3 (kN/mm2) 0.4270 0.152356 0.300000 0.305916 0.349480 ePf4 (kN/mm2) 0.1490 0.053325 0.105000 0.107071 0.122318 ePd1 0.0000056 0.0000125 0.0000123 0.0000097 0.0000086 ePd2 0.0000179 0.0001215 0.0000590 0.0000310 0.0000272 ePd3 0.0000304 0.0002306 0.0001057 0.0000524 0.0000458 ePd4 0.0010170 0.0077255 0.0035423 0.0017545 0.0015358 Negative Backbone eNf1 (kN/mm2) -3.420 -1.21885 -2.40000 -2.44733 -2.79584 eNf2 (kN/mm2) -3.844 -1.37120 -2.70000 -2.75325 -3.14532 eNf3 (kN/mm2) -4.270 -1.52356 -3.00000 -3.05916 -3.49480 eNf4 (kN/mm2) -1.490 -0.53325 -1.05000 -1.07071 -1.22318 eNd1 -0.000056 -0.000125 -0.000123 -0.000097 -0.000086 eNd2 -0.000179 -0.001215 -0.000590 -0.000310 -0.000272 eNd3 -0.000304 -0.002306 -0.001057 -0.000524 -0.000458 eNd4 -0.010170 -0.077255 -0.035423 -0.017545 -0.015358 Pinching rDispP 0.8 0.8 0.8 0.8 0.8 fForceP 0.1 0.1 0.1 0.1 0.1 uForceP 0.01 0.01 0.01 0.01 0.01 rDispN 0.8 0.8 0.8 0.8 0.8 fForceN 0.1 0.1 0.1 0.1 0.1 uForceN 0.01 0.01 0.01 0.01 0.01 Unloading stiffness degradation gK1 0.8 0.9 0.8 0.8 0.8 gK2 0.7 0.3 0.7 0.7 0.7 gK3 0.7 0.4 0.7 0.7 0.7 gK4 0.7 0.3 0.7 0.7 0.7 gKLim 0.8 0.9 0.8 0.8 0.8 Reloading stiffness degradation gD1 0 0 0 0 0 gD2 0 0 0 0 0 gD3 0 0 0 0 0 gD4 0 0 0 0 0 gDLim 0.1 0.1 0.1 0.1 0.1 Strength degradation gF1 1 1 1 1 1 gF2 0 0 0 0 0 gF3 1 1 1 1 1 gF4 1 1 1 1 1 gFLim 0.1 0.1 0.1 0.1 0.1 Energy degradation (gE) 10 10 10 10 10 Damage type (Cycle/Energy) Cycle Cycle Cycle Cycle Cycle (From © Noh, Liberatore, Mollaioli, & Tesfamariam, 2017. Modelling of masonry infilled RC frames subjected to cyclic loads: State of the art review and modelling with OpenSees. Engineering Structures, 150, 599-621. By permission from Elsevier). 126 The Pinching4 material model, as defined in the calibration process, demonstrates higher efficiency in terms of unloading and reloading stiffness, strength degradation, force-displacement effect, and pinching effect for all experimental tests. Although the Concrete01 material model provides a lower accuracy at each cycle, it is still able to provide a good prediction of the global response. The single-strut model, which was developed by following to the guidelines proposed in this study, provides a good match to the experimental results, and, notwithstanding its simplicity, is a worth tool to be used in design practice. 3.6 Summary This chapter focused on the development of reliable analytical method for the assessment of infilled RC frame buildings. A brief review of possible failure mechanisms and different modelling approaches available in the literature is first presented. The definition of the equivalent strut constitutive laws and the equations used to estimate the strut properties are also described in detail. Based on the different failure mechanisms of the infill wall, an appropriate and a simple analytical model is identified. Specifically, the infill wall is modelled using a single strut element in both the diagonal directions. The backbone curve proposed by Liberatore (2001) and Liberatore & Decanini (2011) is adopted as it accurately represents the force-displacement curves of the experimental tests used in this study. The selected backbone curve model includes the stiffness and strength degradation during the cyclic loading process. In addition, based on a comparative evaluation, the strength of the masonry infill wall is calculated using the Paulay & Priestley (1992) and Priestley & Calvi (1991) model. 127 In the context of macro modelling for infill panel, three different hysteretic models, available in OpenSees, are investigated. As for the RC frame members, both the distributed plasticity model and the lumped plasticity model were considered. The calibration of the model is conducted by comparing the results of the numerical analyses with two sets of experimental tests concerning one-storey one-bay infilled frames. The efficiency of the calibrated numerical model was than verified with five additional experimental tests. The comparison between numerical and experimental results are conducted based on the force-displacement response and, whenever available, on the cumulative dissipated energy. The general conclusions that arise from the comparisons are as follow: 1. The selected model can adequately reproduce the response of the masonry infilled RC frames. 2. The distributed plasticity model adopted for the RC members (Model 1) showed its ability to capture the deterioration of strength and stiffness. The average error of the cumulative dissipated energy is 8.2%, while the average error obtained with the lumped plasticity model (Model 2) is 14%. 3. The Pinching4 material was found to be the most suitable to reproduce the cyclic response of infills. However, a good compromise between simplicity and accuracy was obtained with the Concrete01 material. The average error of the cumulative energy dissipated is, on average, equal to 20% and 17.8% for Concrete01 and Pinching4 materials, respectively. 128 4. The comparison between five additional experimental tests and the corresponding numerical models showed that the selected models can appropriately reproduce the response of masonry-infilled RC frames. The application of the simplest model, i.e. the Concrete01 material can be used for envelope analysis, while a more complex model, i.e. the Pinching4 material, is necessary to increase the hysteretic behaviour accuracy. This chapter successfully identified an adequately simplified macro-model to evaluate the global performance of masonry-infilled frames under in-plane cyclic loads. This model, calibrated considering one-storey one-bay frames, can be adopted for the assessment of new or existing buildings subjected to seismic loads. However, further studies are needed to include the interaction between in-plane and out-of-plane forces in the response of infill walls, especially with reference to collapse conditions. 129 CHAPTER 4: Seismic collapse performance of code-conforming RC MRF buildings The previous chapter highlights the evaluation of various parameters needed to define the monotonic and hysteretic response of infill walls modelled by equivalent struts. In order to select a simple and reliable analytical model that is suitable for representing the infill wall response, different strut formulations and hysteretic models have been analyzed in detail and used to reproduce several experimental tests available in the literature. The numerical analyses are performed using the OpenSees computer program. Three uniaxial material models available in OpenSees are used to assess their capability to reproduce the experimental hysteretic response. Finally, from comparing different models and numerical and experimental results, suggestions are made to model the in-plane non-linear response of infills properly. This chapter presents the collapse risk assessment of code-conforming reinforced concrete moment resisting frame (RC MRF) buildings in Vancouver, Canada. This assessment investigates the three- and six-storey regular RC MRF building systems, with and without unreinforced masonry infill wall, representing low- to mid-rise structures to identify the capability, equality, and/or difference of the seismic performance of these designed buildings. Nonlinear dynamic analysis is applied in the performance-based seismic assessment procedures to assess the collapse response of structural for the set of 50-pair ground motion records. Next, the seismic fragility curves are developed through incremental dynamic analysis. Finally, the mean annual collapse frequency is calculated through the fragility curve and hazard curve. 4.1 Background Collapse of buildings is identified as the main contributor to injuries, casualties, and economic loss from past earthquakes (Porter, 2016). Current seismic design philosophy of Canadian and other countries, under rare earthquake events, focuses on buildings collapse 130 prevention (DeVall, 2003; Haselton, Liel, Deierlein, Dean, & Chou, 2011; Iervolino, Spillatura, & Bazzurro, 2017). In the National Building Code of Canada (NBCC 2010), reinforced concrete (RC) frame structures can be designed for two different ductility levels, ductile and moderately ductile, and conventional construction (Mitchell et al., 2003; NBCC, 2010). The ductile and moderately ductile designs should have similar seismic performance under the site-specific design earthquake. However, the presence of unreinforced masonry infill (URM) infill walls, which is normally not considered in the analysis and design process, may affect the performance and risk of collapse of infilled-RC frames in a severe earthquake to be greater or lesser than bare RC frames depending on the characteristics of URM infill walls (Mehrabi et al., 1996; Asteris, Cavaleri, Di Trapani, & Sarhosis, 2016; Sattar & Liel, 2016b). Thus, designing the buildings by following a prescriptive design code, the collapse safety is uncertain (e.g., Burton & Deierlein, 2013; Jeon, Park, & DesRoches, 2015). In this chapter, the collapse risk of Canadian buildings is quantified, with the seismicity of Vancouver, British Columbia, for the two ductility classes (ductile and moderately ductile) and with and without consideration of the URM infill wall. Various studies are reported on code-conforming RC moment-resisting frames (MRF). Haselton et al. (2011) implemented performance-based earthquake engineering (PBEE) approach to assess the collapse risk of ductile RC-MRF buildings designed according to ASCE 7-02 (ASCE, 2002) and ACI 318-05 (ACI, 2005). All models were developed using the lumped-plasticity element to capture strength and stiffness degradation. Nonlinear dynamic analysis through incremental dynamic analysis (IDA) method was conducted to quantify collapse safety of 30 RC MRF varying from 1- to 20-stories. The collapse risk accounted for the effects of both record-to-record (RTR) variability and modelling uncertainty. The seismic assessment results show that the collapse probability of the buildings for the 2% in a 50-years hazard level, P(C|Sa2/50), ranges from 3 to 20%. The mean annual frequency of collapse (c) values range from 0.7×10−4 to 7.0×10−4 (i.e., probability of collapse in 50 years Pc = 0.4–3.4%). Koopaee, Dhakal, & 131 MacRae (2017) investigated the effect of the ground motion selection method on seismic collapse fragility of a 10-storey RC MRF representing a mid-rise building, designed to New Zealand standard (NZS 1170.5, 2004; NZS 3101, 2006). In this study, the fibre-based model was used to account for the loss in the vertical load-carrying capacity of columns. Nonlinear dynamic analysis was carried out using multiple stripe analysis, using ground motion records selected at various hazard levels. The results indicate that the case study building has a 23% of P(C|Sa2/50), which is higher than the value reported by Haselton et al. (2011), particularly when compared with the average value estimated from 8- to 12-storey RC frame buildings [i.e., P(C|Sa2/50) = 17.5%]. This study found that considering the loss of vertical load-carrying capacity in the structural model contributed to the higher value of the collapse rate. Iervolino et al. (2017) quantified the seismic risk of code-conforming RC MRF buildings designed with the Italian NTC 2008 (Italian building code, 2008) design code. All the structures are designed for five sites with increasing seismic hazards. The results show that the RC MRF buildings considered in this study have λc between 1.0×10−5 and 8.47×10−5 and on average c = 2.4 × 10−5 (i.e., Pc=0.12%). The studies highlighted that as the site hazard level increases, the probability of collapse increases for all building systems. Several studies focused on the seismic performance assessment of the RC frame with URM infill wall, which includes non-collapse or collapse, compared with bare RC frame buildings. Past earthquakes have indicated that most of the RC frames with URM infill wall buildings experience poor seismic performance (e.g., Zhao et al., 2009; Kam, Pampanin, Dhakal, Gavin, & Roeder, 2010). The presence of URM infill walls can increase the strength, stiffness and energy dissipation of the RC frame that lead to better seismic performance of buildings, but may introduce brittle or shear failure in the column due to interaction between infill and surrounding frame (e.g., Klingner & Bertero, 1978; Mehrabi et al., 1996; Stavridis & Shing, 2012; Stylianidis, 2012). The column shear failure is caused by the force from compressive diagonal strut in the URM infill wall. 132 The columns shear failure can lead to a loss of the axial gravity load-carrying capacity of the columns and typically occurs prior to flexural yielding of the columns at low drift levels (Burton & Deierlein, 2013). Neglecting columns shear failure due to the interaction between the infill and surrounding frame in the seismic collapse assessment may increase the uncertainty in the system response (Burton & Deierlein, 2013; Jeon et al., 2015; Sattar & Liel, 2016b). Therefore, numerical modelling of an infilled-RC frame that is capable to simulate the interaction between infill and frame and column shear failure is required to explicitly assess the collapse risk of RC frame with URM infill walls. In this chapter, the collapse risk assessment of code-conforming RC MRF buildings designed according to the 2014 Canadian building code is carried out. The collapse assessments are conducted for ductile and moderately ductile RC MRF buildings. Figure 4.1 shows four sets of building typologies considered in this study, focusing on two different ductility classes of RC MRF buildings with and without URM infill walls. The first step of this study is characterizing a typical structure by the concepts of archetypical buildings. The archetypical structures are selected based on the FEMA P695 guidelines (FEMA-P695, 2009) to quantify the building’s response and performance factor in the NBCC 2010 seismic design code. The details of the archetypical RC MRFs buildings with and without the masonry infill are outlined in the Selection of Buildings: Characteristics and Configuration and Seismic Design Procedure sections. Next, the nonlinear structural analysis model is developed based on the selected building designs by considering the typical and critical failure modes of the structures as described in the section Nonlinear Simulation Models: RC Frames and URM Infill Walls. Then, the ground motion is selected and scaled, corresponding to a target seismic hazard level, as discussed in the section Ground Motion Selection. Next, the nonlinear model is used to simulate the response of the building until structural collapse through incremental dynamic analysis (IDA) [section Incremental Dynamic Analysis (IDA)]. Finally, as described in the section Collapse Fragility Assessment, a 133 collapse fragility curve is developed using IDA results. For this study, the seismic collapse risk assessment involves; (1) the evaluation of the median collapse capacity [g]; (2) the collapse margin ratio (CMR), (3) the mean annual frequency of collapse, c, and (4) probability of collapse in 50 years. Figure 4.1: Collapse risk assessment of RC frame framework. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). 4.2 Code-Conforming RC Frame Structures and Ground Motion Selection 4.2.1 Selection of Buildings: Characteristics and Configuration For the seismicity of Vancouver, BC, two sets of office building occupancy code-conforming RC MRF buildings (ductile and moderately ductile detailing) and building heights (3- and 6-stories) are designed. These buildings are founded on soft rock, which is the reference 134 ground condition (class C) in the NBCC 2010. The Canadian code specifies that the design does not consider the contribution URM infill wall (DeVall, 2003). However, in this study, collapse risk assessment is carried out for the RC building with and without consideration of URM infill walls (Figure 4.2(b)). The building is regular in plan and elevation, as shown in Figure 4.2. The RC office building has 7–6 m bays in the N-S direction and three bays in the E-W direction consisting of 2–9 m and a bay (Figure 4.2). The storey height for each level is 3.65 m. The following section explains the seismic design procedure and detailing according to the NBCC and CSA A23.3-14 (CSA, 2014) standard provisions. Figure 4.2: Code-conforming RC frame buildings; (a) Frame plan, (b) Frame elevations and types, and (c) typical columns and beams detailing. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). 135 4.2.2 Seismic Design Procedure Each MRF RC building is designed based on the 2010 NBCC (NBCC, 2010)) seismic design provision. The minimum design base shear force of each studied building computed using the equivalent static force procedure (ESFP), as shown in Equation 4.1 (Mitchell et al., 2003): V =S(Ta)MvIEWRdRo (4-1) where, S(Ta) is design spectral response acceleration expressed as a ratio of gravitational acceleration, g, at the design period Ta, Mv is the factor to account for higher mode effects, IE is the earthquake importance factor, W is the seismic building weight including 25% of snow load, and Rd and Ro are the ductility-related and overstrength-related force modification factors. The empirical fundamental lateral period, Ta is given by 0.075hn^3/4, where hn is the height of the building. However, since the dynamic fundamental periods are usually greater than Ta value (more than 150%), the fundamental lateral period value used to select the design spectral response acceleration is taken as 1.5Ta. The buildings are designed with an importance factor, IE = 1.0, on very dense soil and soft rock (Soil class C) and assumed fixed at ground level. Two different levels of ductility factors, which are ductile (Rd = 4.0 and R0 = 1.7) and moderately ductile (Rd = 2.5 and R0 = 1.4), are also considered (Mitchell et al., 2003). Since there is no eccentricity in the buildings, the effects of accidental torsional eccentricity is calculated by applying the lateral forces Fx at an accidental eccentricity of ±0.1Dnx = 4.245 m, where Dnx is a plan dimension of the building in the computed eccentricity direction that is perpendicular to the direction of seismic loading. The same floor plan is used at all levels, as illustrated in Figure 4.2. Typical superimposed load values of 1.0, 0.5, and 0.5 kN/m2 are used as a partition, mechanical services, and roofing material. The office floor live 136 load of 2.4 kN/m2, and snow load of 2.2 kN/m2 are considered. Concrete compressive strength, f′c , and concrete modulus of elasticity, Ec was taken as 30 and 24,700 MPa, respectively. Mild-yielding strength deformed rebar with yield strength, fy = 400 MPa, is used. The E-W moment resisting frame was chosen for the current study, as shown in Figure 4.2(b). ETABS 2015, an option for the Canadian code CSA A23.14, is utilized to analyze and design a three-dimensional structure system. The modal response spectrum analysis procedure, including second-order P-Delta effects, is considered in the design. Table 4.1 provides a summary of the design characteristics for beams and columns. The interior and exterior column is 500 × 500 and 450 × 450 mm, respectively. The beams of both the N-S and E-W frames are 400 mm wide × 600 mm deep for the first three stories and 400 × 550 mm for other stories. The two-way slab floor system consists of a 210 mm thick slab. The URM infill walls are considered a non-structural element and are neglected in the structural design process for the infilled-RC frame buildings. The thickness and compressive strength of infill panels are 150 mm and 6.9 MPa, respectively. Table 4.1: Summary of design characteristics of Ductile and Moderately Ductile RC frames. Structure ID Ductility class Rd Ro Infill Beam size (mm) Column size (mm) 3S_D_NI Ductile 4.0 No Infill 400 × 600a 400 × 550b 500 × 500c 450 × 450d 3S_D_I 1.7 Full Infill 6S_D_NI No infill 6S_D_I Full Infill 3S_MD_NI Moderately ductile 2.5 No infill 400 × 600a 400 × 550b 500 × 500c 450 × 450d 3S_MD_I 1.4 Full Infill 6S_MD_NI No infill 6S_MD_I Full infill aBeam size for level 1-3 ,bBeam size for level 4-6, cInternal column size, dExternal column size. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). 137 4.2.3 Nonlinear Simulation Models: RC Frames and URM Infill Walls A two-dimensional (2-D) model of code-conforming RC frame buildings with and without URM infill walls (Figure 4.3(a)) is developed using the Open System for Earthquake Engineering Simulation (OpenSees) software package (Mazzoni et al., 2006). The 2-D model employs a leaning column to account for P-Δ effects. For the RC members, the model used lumped-plasticity element models and rigid beam-column joint zones. The lumped-plasticity model can be introduced using an elastic beam-column element with two zero-length elements at both ends, as shown in Figure 4.3(b). The zero-length elements are related to a rotational hinge model with a hysteretic response to represent the flexural behaviour of the elements. The rotational hinge behaviour is attached by the multiple uniaxial materials to display the moment-rotation or force-deformation relationship. This simulation approach is used for the collapse prediction to capture deterioration of the steel reinforcing bars due to the rebar buckling and low cyclic fatigue and to record the strength and stiffness deterioration in assessing the global collapse. In this study, the Rayleigh damping model is used to consider the energy dissipated. The critical damping ratio of 5% is assigned to the first and third modes of the structure, which commonly recommended for all reinforced concrete (RC) structures in practical seismic design (Malhotra, 2022; Lu et al., 2020). This choice of a 5% damping ratio offers practicality and simplicity in the design process. It is a widely accepted value that is easy to implement and provides a reasonable approximation for a broad range of structural systems. However, it is important to note that the assumption of a 5% critical damping ratio is a simplification and may not capture the precise damping characteristics of a particular structure. The actual damping of a structure can vary depending on its materials, geometry, and dynamic properties. The Newton algorithm is used for nonlinear dynamic analysis to solve the system equations. 138 To describe the flexural behaviour of the RC beam-column element, the most common OpenSees implementation of the peak-oriented hysteretic model developed by Ibarra, Medina, & Krawinkler (2005) (modIMKmodel), is adapted. This model captures four modes of cyclic deterioration, which include; (1) the basic strength deterioration, (2) the post-capping strength deterioration, (3) the unloading stiffness deterioration, and (4) the accelerated reloading stiffness deterioration. The hysteretic model requires six key parameters: elastic stiffness (Ke), effective yield moment (My), strain hardening ratio (Mc/My), pre-capping rotation (θcap), post-capping rotation (θpc), and cyclic deterioration parameter (). The moment-rotation law (backbone), according to Ibarra et al. (2005), is illustrated in Figure 4.3(c). All parameters are obtained using the predictive equations and tools developed by Haselton et al. (2007). The My was calculated for each element from the sectional analysis. Analytical methods to model infilled-frame buildings with consideration of shear failure are limited in the literature. Crisafulli & Carr (2007) developed a new macro model for the seismic response of infilled RC frames, which can be modelled by four-node element. This model was developed based on a multiple-strut formulation that includes two parallel off-diagonal struts and a special shear spring in each direction to account for the diagonal tension failure and shear mechanism in the infill walls. Although the model can represent a different types of failure modes in shear for URM infill wall, the bending moment and shear forces of the surrounding frame are not able to predict appropriately due to the model's simplicity. Jeon et al. (2015) adopted a three-strut model developed by Chrysostomou, Gergely, & Abel (2002) to assess the seismic fragility of lightly RC frames with URM infills. Fibre-type displacement-based model was used to capture the flexural response of the surrounding frame. Two off-diagonal struts and one central strut in each direction were employed to simulate the column shear failure. A contact length between the column and infill panel is computed using Stafford Smith's approach. Two types of column shear failure were considered: shear failure and flexure-shear failure. 139 The column shear failure was simulated using two zero-length springs at the face of the beam and the flexure-shear mode, the column shear strength model adopted from Sezen & Moehle (2004). The flexure-shear failure has been modelled using a zero-length spring at the center of the column incorporating the limit state model proposed by Elwood (2004). Burton & Deierlein (2013) applied a pair of central and off-diagonal compression-only struts in both directions with zero contact length to assess the seismic performance of the non-ductile RC frame with URM infill walls. Lumped-plasticity model that can be introduced using an elastic beam-column with two zero-length elements at both ends is used to idealize beams and columns response. The flexure hinge and shear spring in series were introduced at the top and bottom column to capture the column shear failure and have been modelled based on the flexure-shear failure type that occurred after infill failure. Sattar & Liel (2016b) assessed the collapse risk of masonry-infilled RC frame buildings using strut modelling enhanced by finite element (FE) analysis. Two struts in each direction were employed to simulate the column shear failure, and the contact length was determined through the FE model response. This study also implemented a lumped-plasticity model with spring in series at the top of the column. Burton & Deierlein (2013) and Sattar & Liel (2016a) also used a similar approach developed by Sezen & Moehle (2004) to calculate the column shear strength. Although all studies applied a similar approach to capturing the response of strut and column shear failure, the infilled-RC frame model developed by Burton & Deierlein (2013) is less sophisticated and able to simulate most of the seismic collapse mode of buildings. Therefore, in this study, the model and tools developed by Burton & Deierlein (2013) for the infilled-frame structures are adopted (Figure 4.3(b)). A pair of the off-diagonal strut, as presented in Figure 4.3(b), is used to capture shear failure due to the interaction between the column and the infill walls. 140 Figure 4.3: Schematic of RC frame modelling using lumped plasticity elements; (a) overview of the overall model, (b) detail model for infilled—RC frame, (c) monotonic curve for RC frame member developed by Ibarra et al. (2005), (d) in-plane lateral force-displacement envelope model proposed by Decanini et al. (2014), and (e) hysteretic curve (cyclic behaviour). (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). 141 As illustrated in Figure 4.4, the zero-length shear springs model with a rigid softening material model is attached in series with the flexural hinges at the face of the columns. The column shear strength is calculated using a model developed by Sezen & Moehle (2004). Whereas the column shear deformation is obtained from the modelling parameter and acceptance criteria offered in Tables 4.6–4.8 of ASCE/SEI 41 (2007), which a proposed supplement to ASCE/SEI 41 developed by Elwood et al. (2007). Furthermore, this study assumed that collapse generated by axial column failure occurs at ultimate shear deformation. Figure 4.4: Spring model for column shear failure. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). For the URM infill wall, an equivalent diagonal struts model is implemented to simulate the behaviour of the masonry infill in terms of strength and stiffness. The performance of the masonry infill wall subjected to the in-plane effect is simulated by using two opposing pairs of the diagonal compression-only strut in each direction (Figure 4.3(b)). The monotonic backbone curve, shown in Figure 4.3(d), proposed by Decanini et al. (2014), is applied to define the overall in-plane behaviour of URM infill walls. The strength of the infill model is calculated using the strength model 142 proposed by Priestley & Calvi (1991) and Paulay & Priestley (1992). The distribution amount of force and stiffness of the strut are adopted from Chrysostomou (1991), who has investigated the force and stiffness distribution of central and off-diagonal struts of infilled-frame buildings using the principle of virtual displacements. The author founds that the maximum force distributed to the off-diagonal strut is ~25% of the total strut force. Thus, in this study, the stiffness proportion assigned to the central and off-diagonal strut are 75 and 25% of the total strut stiffness, respectively (Figure 4.4). The available elements and materials in the OpenSees are used to define the model. The selection of the most appropriate hysteretic model used to calculate and capture the strength, stiffness, and behaviour of the URM infill walls are presented in Noh, Liberatore, Mollaioli, & Tesfamariam (2017). Figure 4.3(e) shows the cyclic behaviour of a single-storey infilled frame by executing monotonic curves of RC frame member and infill wall, as illustrated in Figures 4.3(c) and (d). Table 4.2: First three fundamental periods of 3- and 6- storey RC MRF buildings. Structure ID Building type Period (s) Mode-1 Mode-2 Mode-3 T1 [Tmin, Tmax] 3S_D_NI No Infill 1.30 0.225 0.20 1.5 [0.2,2.0] 3S_D_I Full infill 0.32 0.14 0.14 0.4 [0.1,1.0] 6S_D_NI No Infill 2.28 0.7 0.38 2.0 [0.2,3.0] 6S_D_I Full infill 0.59 0.204 0.20 0.6 [0.2,1.0] 3S_MD_NI No Infill 1.45 0.374 0.2 1.5 [0.2,2.0] 3S_MD_I Full Infill 0.33 0.20 0.14 0.4 [0.1,1.0] 6S_MD_NI No Infill 2.38 0.75 0.4 2.5 [0.2,3.0] 6S_MD_I Full Infill 0.61 0.21 0.2 0.6 [0.2,1.0] (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). Table 4.2 presents the first three mode period of vibration obtained through a modal analysis conducted in the OpenSees model. The dynamic fundamental period that calculated for 143 the code-conforming RC frame models is based on the effective cracked stiffness of the structural members (Table 4.2). As shown in Table 4.2, the spectral acceleration at 1.5 s is selected, and the time range used to select ground motion is between 0.2 and 2.0 for the 3-storey building without infill. For the 3-storey building with infill, the spectral acceleration is selected at 0.4 s. While for a 6-storey building without infill, the spectral acceleration is selected at 2.0 and 2.5 s for ductile and moderately ductile, respectively, ranging from 0.2 to 3.0 s. The spectral acceleration at 0.6 s is selected for a 6-storey building with infill, with ranges from 0.2 to 1.0 s. As reported in Table 4.2, the dynamic fundamental period obtained for the same building height is not constant, as suggested in the code provision. It is also observed that the fundamental period of the infilled-RC frame decreases due to the presence of URM infill wall. According to Banik & Halder (2016), the fundamental period of the RF frame buildings not only depends on the building height, but the fundamental period is also influenced by effective stiffness properties of structural members, bay width, number of bays and support conditions. 4.2.4 Ground Motion Selection The RC buildings in Vancouver, BC, Canada, were considered due to their location, population, and significant seismic activities (Onur, Ventura, & Finn, 2005; Atkinson & Goda, 2011). The selected building site consists of very dense soil and soft rock site condition (Site class C) with the average shear-wave velocity in the upper 30 m (Vs30) between 360 and 760 m/s—Sa (T1) of the buildings with 5% damping. In order to perform the nonlinear dynamic analysis, a set of 50 ground motion records (two horizontal components) is selected based on the seismic hazard of interest. The thorough selection of ground motion records is required for accurately assessing the seismic performance of structures, as it allows for the representation of regional dominating earthquake scenarios. In 144 this study, ground motion records were selected using the multiple conditions mean spectrum (CMS) method developed by Goda & Atkinson (2011). The application of the CMS as a target response spectrum provides an acceptable ensemble representation of ground motion records and is relevant for assessing the seismic behaviour of a structure at a specific seismic intensity level (Baker, 2011). This method expands on the standard CMS-based record selection procedure introduced by Baker (2011) by incorporating multiple CMS for different event types. The implementation involves the development of a specific target CMS for each type of earthquake, utilising the equation presented by Baker (2011) as a weighted average.The selected ground motion records that follow the same procedure reported in Tesfamariam, Goda, & Mondal (2015) and Tesfamariam & Goda (2015b, 2015a) considered three dominant sources of earthquake: shallow crustal, deep in-slab, and off-shore megathrust interface earthquakes type from the Cascadia subduction zone. The ground motion recordings used for IDA are selected from two major databases: the PEER-NGA database and the K-NET/KiK-NET database. The matching of response spectrum characteristics between a set of ground motion records and the target CMS reflects the relative contributions of three type of earthquake. This indicates that varying amounts of records are selected for each earthquake type based on their respective vibration periods. The process of matching the ground motion records with the target CMS over a range of vibration periods employed a least-squares approach. Figure 4.5 shows an example of the ground motion records selected for 3S_D&MD_NI buildings with T1 = 1.5 s. The spectral acceleration at the fundamental vibration period, denoted Sa(Tn), has been chosen as the seismic intensity measure for the structure. 145 Figure 4.5: Example of selected ground motion records for 3S_D&MD_NI (T1 = 1.5 s). Selected ground motion records for; a) 3S_D&MD_NI, b) 3S_D&MD_I, c) 6S_D_NI, d) 6S_MD_NI and e) 6S_D&MD-I. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). 146 4.3 Incremental Dynamic Analysis (IDA) A series of nonlinear dynamic analyses are conducted through IDA to evaluate the seismic response and collapse fragility (Vamvatsikos & Allin Cornell, 2002). The IDA was carried out based on multiple records of ground motions by increasing the scale factor of each ground motion amplitude until it caused a sideways collapse. In this study, the IDA is implemented on eight RC MRF building models using 50 pairs of ground motion records selected based on the 2% PE in 50 years. Collapse is defined as the dynamic instability point when the maximum inter-storey drift ratio of the buildings exceeds 0.10 (Haselton et al., 2007), and the IDA curve transforms to a horizontal line for each ground motion. The IDA curves correlate intensity measure level and maximum inter-storey drift ratio. In this assessment, collapse mechanisms due to column shear failure are not directly simulated in the analysis model. However, the columns are expected to experience critical shear failure when interacting with URM infill walls. Therefore, the shear critical failure mode, the so-called non-simulated collapse mode, is evaluated by post-processing IDA results. In this process, a force-based limit state check is applied to predict the median collapse drift ratio (𝐶𝐷?̂?) at which critical shear failure will occur. The median 𝐶𝐷?̂? is calculated based on the properties of the column. The capacity of the deformation increases with decreasing axial load or more shear reinforcement. The 𝐶𝐷?̂? is defined using Equation 4.2, developed by Aslani & Miranda (2005), 𝐶𝐷?̂?𝑠ℎ𝑒𝑎𝑟 =10.26 (𝑃𝐴𝑔𝑓𝑐′𝜌𝑠ℎ+ 25.4)≥1100 (4-2) where P is the axial load on the column, Ag is the gross cross-sectional area of the column, and ρsh is the transverse reinforcement ratio. Figures 4.6 and 4.7 show the IDA results for the 3- 147 and 6-storey RC MRF buildings. The circle marks on each IDA curve in Figures 4.6(c-d) and 4.7(c-d) show the shear failure that occurs predicted by Equation 4.2. For columns with ductile shear design and detailing, the predicted shear failure occurs at a 𝐶𝐷?̂? between 0.0295 and 0.0339 rad, while for moderately ductile the predicted shear failure occurs at a 𝐶𝐷?̂? between 0.0206 and 0.0275 rad. From the IDA results, the collapse fragility relationships, as described in the following section, are then developed to compute the median collapse capacity. Figure 4.6: Incremental dynamic analysis curves for 3-storey buildings; (a) 3S_D_NI, (b) 3S_MD_NI, (c) 3S_D_I, and (d) 3S_MD_I. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). 148 Figure 4.7: Incremental dynamic analysis curves for 6-storey buildings; (a) 6S_D_NI, (b) 6S_MD_NI, (c) 6S_D_I, and (d) 6S_MD_I. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). 4.4 Collapse Fragility Assessment The seismic collapse fragility curve shows the probabilistic relationship between the frequency of failure (collapse) of buildings and peak ground motion acceleration in an earthquake (Porter, 2017). In this study, a damage measure, which represents an actual response of the building under seismic excitation, is based on maximum inter-storey drift (i.e., the maximum inter-149 storey drift ratio is 0.1 for collapse). The collapse fragility curve that was constructed based on the IDA results can be represented by a lognormal cumulative distribution function (Baker, 2015), as shown in Equation 4.3. P(C|IM = x) = Φ (ln (xμ)β) (4-3) where P(C|IM = x) is the probability that a ground motion with IM = x will cause the structure to collapse, Φ () is the standard normal cumulative distribution function, μ is the median of the fragility function, and  is the standard deviation of ln (IM) (sometimes referred to as the dispersion of IM). Figures 4.8(a)&(b) show the collapse fragility curves for 3- and 6-storey RC MRF buildings derived from IDA and Equation (2). In this study, the collapse fragility assessment also accounted for both record-to-record (RTR) variability and structural modelling (M) uncertainties for comparison purposes. A modelling uncertainty of βln,M = 0.50 is assumed, as suggested by Haselton and Deierlein (2007). The total uncertainty, βln, is the total that accounts for both RTR and M and is computed by using the square root of the sum of the squares (Equation 4.4), βln,Total = √βln,RTR2 + βln,M2 (4-4) The dotted line is used to represent the RTR+M fragility curve. Figure 4.8 also illustrates the collapse fragility curve for RC MRF with and without consideration of shear failure, as shown by the solid and dashed curves. 150 Figure 4.8: Fragility curves of (a) 3-storey and (b) 6-storey MRF RC frame with and without URM infill walls. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). Based on these fragility curves, the collapse performance parameters, in terms of the median collapse capacity, can be obtained at the ground motion capacity with a 50% of probability of reaching the collapse targets. Figure 4.8 shows that the median collapse capacity for ductile bare RC MRF buildings ranges from 0.15 to 0.53 g, which is greater than the moderately ductile 151 buildings varying from 0.08 to 0.41 g. The presence of URM infill walls on the RC MRF frame considered in this study increases the median collapse capacity by 66–90% and 74 and 94% for ductile and moderately ductile building, respectively, as compared to the bare RC MRF buildings. As shown in Figure 4.8, the collapse fragility capacity with consideration of shear failure was significantly reduced by 8–30% compared to the sideways collapse mechanism. Overall, the median collapse capacity decreases with increasing building height. Median collapse capacity results are then expanded to the collapse median ratio (CMR) evaluation. The CMR is evaluated by dividing the median collapse capacity of the structure by the ground motion intensity, SMT. As recorded in Table 4.2, the ductile RC MRF buildings with and without URM infill walls induce higher CMR than moderately ductile RC MRF buildings, ranging from 0.65 to 2.25 and 0.45 to 1.92, respectively. Any CMR value <1.0 indicates that the median collapse capacities are lower than the SMT and vice-versa. 4.5 Mean Annual Frequency The mean annual frequency of collapse in seismic risk assessment (Porter, 2017 and Ellingwood & Kinali, 2009) is given by: λc = ∫ FR(x)dH(x)dxdx∞0 (4-5) where FR(x) is the cumulative distribution function of seismic capacity of structural (collapse fragility curve), and dH(x) is the differential of the seismic hazard curve. Equation 4.6 can be expressed as 152 λc = ∑ P[C|Q = x]P[Q = x] (4-6) where P[Q = x] denote the seismic hazard and P[C|Q = x] represents the seismic fragility of a structure with collapse damage. The ground motion hazard curves were selected at Vancouver, BC, Canada, for site classification C and a period according to the building model. Figure 4.9 shows the hazard curve for Vancouver at different periods. Figure 4.9: Ground motion hazard curve for Vancouver for different periods on soil Class C. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). 0.000010.00010.0010.010.01 0.1 1 10Probability of exceeding Sa in 50 yearsIM=Sa(T1) [g]T1=0.4T1=0.6T1=1.5T1=2.0T1=2.5153 The probability of collapse that will occur at least once in time, t (t = 50 years) is calculated using the following equation: P[C in 𝑡 years] = 1 − exp (−λ𝑐. 𝑡) (4-7) where λc is the expected value of collapse derived from Equation (5). Seismic collapse assessment results for 3-and 6-storey RC MRF buildings with and without URM infill walls, in terms of mean annual frequency of collapse and probability of collapse at 50 years, are reported in Table 4.3. Figure 4.10 shows this study's mean annual frequency of collapse, including results from different studies that used different codes during the seismic design process. Data in Table 4.3 also reported for both RTR and RTR+M uncertainties. Table 4.3: Result of seismic collapse assessment for ductile and moderately ductile RC MRF with and without URM infill walls. Structure ID Median collapse, Sa [g] SMT [g] CMR 𝛌𝒄 _RTR [×𝟏𝟎−𝟓] Pc[in 50 years] 𝛌𝒄 _RTR+M [×𝟏𝟎−𝟓] Pc[in 50 years] 3S_D_NI 0.63 0.31 2.03 9.05 0.0045 16 0.0078 3S_D_I 1.85 0.92 2.01 10.62 0.0052 20 0.0101 6S_D_NI 0.15 0.23 0.65 23.39 0.0116 39 0.0192 6S_D_I 1.51 0.67 2.25 8.53 0.0042 16 0.0080 3S_MD_NI 0.41 0.31 1.32 23.31 0.0116 36 0.0177 3S_MD_I 1.58 0.92 1.71 36.76 0.0182 80 0.0391 6S_MD_NI 0.08 0.17 0.45 130 0.0630 165 0.0794 6S_MD_I 1.29 0.67 1.92 11.69 0.0058 21 0.0105 (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). 154 Figure 4.10: Mean annual frequency of collapse for ductile and moderately ductile RC MRF buildings with and without URM infill walls comparison with other building design codes. (From © Noh & Tesfamariam, 2018. Seismic Collapse Risk Assessment of Code-Conforming RC Moment Resisting Frame Buildings Designed With 2014 Canadian Standard Association Standard A23.3. Front. Built Environ. 4:53. Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)). As reported in Table 4.3 and illustrated in Figure 4.10, the mean annual frequency of collapse for ductile RC MRF buildings is between 16 and 39 × 10−5, with the probability of collapse in 50 years ranging from 0.8 to 1.92%. For the moderately ductile RC MRF buildings, the calculated mean annual frequency of collapse is between 13 and 165 × 10−5, with the probability of collapse in 50 years ranging from 1.05 to 7.94%. These results reveal that the seismic safety level is higher for ductile RC MRF buildings than moderately ductile RC MRF buildings due to the special detailing of reinforcement during design in increasing resistance to structural collapse. Furthermore, this study also found that the 6-storey bare RC MRF buildings have a slightly higher mean annual frequency of collapse than the 3-storey bare RC MRF building, which have λc=39 to 165× 10−5, corresponding to 1.92 to 7.94% probability of collapse in 50 years. This study observes that the increase in building height will increase the overall mass of the building, 155 which becomes dominant over the increase in the lateral stiffness. Moreover, this is due to lower spectral acceleration based on the hazard site for longer periods during the building design stage, which in turn may affect the collapse capacity of the buildings. Comparison of the bare RC MRF and RC MRF with URM infill walls buildings illustrates inconsistent results among infilled-RC MRF buildings. As observed, the 6-storey RC MRF building with URM infill walls shows a lower collapse rate compared to the 6-storey bare RC MRF buildings, ranging from 16 to 21 × 10−5. In contrast, the collapse rate of 3-storey RC MRF with URM infill walls buildings is 20–80 × 10−5, illustrating a higher collapse rate compared to the 3-storey bare RC MRF buildings. The results of 6-storey bare RC MRF buildings and 3-storey RC MRF building with URM infill walls buildings are at least 2.5 and 1.2 times, respectively, to collapse compared to the 6-storey RC MRF building with URM infill walls. These results indicate that the presence of URM infill walls affects the collapse performance of RC MRF buildings based on the number of stories. As the number of stories increases, the URM infill walls contribute to a higher stiffness within the structure. On the other hand, the 6-story RC MRF building with URM infill walls benefits from its ductile design, which contributes to better collapse resistance and enhances the safety of the building. Overall, the findings highlight the importance of considering the specific characteristics and behaviour of URM infill walls, as well as the number of stories in RC MRF buildings, in order to accurately assess their collapse performance. Designing RC MRF buildings with ductile features can provide improved collapse resistance and enhance the overall safety of the structures. The results of the mean annual frequency of collapse of ductile RC MRF buildings are further compared with studies conducted by Haselton et al. (2011) and Iervolino et al. (2017), whereby each building is designed based on different code provision that includes the American code, and Italian code, respectively. For comparison purposes, the collapse assessment is 156 evaluated by considering record-to-record and modelling uncertainties. It can be observed that there is significant variation in the mean annual frequency of collapse for differently designed buildings, which may occur due to the differences in design spectra, response reduction factors, site location, ground motion selection method, and structural configurations. As shown in Figure 4.10, RC frame buildings designed based on Canadian code have calculated the mean annual rate of collapse between 1.6 and 3.9 × 10−4, whereas American code Haselton et al. (2011) have calculated the mean annual rate of collapse between 1 to 4.7 × 10−4. The mean annual rate of collapse for buildings designed based on the Italian code ranges from 0.13 to 0.85 × 10−4. The range value of the mean annual frequency of collapse for Canadian buildings is similar to the American buildings, which can considerably perceived to be within a reasonable range as reported in Haselton et al. (2011). In comparison, the buildings designed for Italian codes have significantly lower mean annual rate of collapse than the others buildings designed for Canadian and American codes. The decrease in collapse probability for Italian buildings is due to different response reduction factors during the design process, site location, and response history analysis. In addition, different approaches to nonlinear dynamic analysis are adopted, where Canadian and American buildings are assessed using the IDA method. In contrast, Italian buildings are assessed using multiple stripe analysis methods. 4.6 Summary This chapter evaluates the seismic collapse risk of two sets of code-conforming RC MRF buildings, considering ductile and moderately ductile design details and with and without URM infill walls. The code-conforming RC MRF buildings were designed according to the Canadian seismic design code, NBCC 2010, and detailing, CSA A23.3-14. IDA method is used to perform 157 nonlinear dynamic analysis. Collapse fragility relationships are developed from IDA results to represent the probability of building collapse as a function of ground motion intensity. The collapse mean annual frequency is determined by integrating seismic hazard and fragility function. The results from this assessment identified that the mean annual frequency of collapse varied between 16 and 165 × 10−5, corresponding to the collapse probabilities in 50 years from 1 to 7.9%. The ductile RC MRF buildings present better seismic collapse performance for both 3- and 6- storey buildings compared to moderately ductile RC MRF buildings. These results are expected since the ductile RC MRF buildings are designed based on special reinforcement detailing with higher over-strength, which is important to prevent structural collapse. It was observed that structural configuration might lead to a different result of collapse probability at 50 years. Seismic collapse assessments are also conducted to show seismic performance over building height. Comparative studies between 3- and 6-storey RC MRF buildings without infill demonstrate that the calculated mean annual frequency of collapse increases as the building height increases. This study would be helpful to extend by investigating the influence of the soil-structure interaction (SSI) effect, which may also contribute to collapse risk. The collapse response is expected to be different for RC frames with the SSI effect between building height and structural systems because the flexibility of the soil foundation reduces the overall stiffness of the structures, which may lead to expansion in the fundamental period of the system. This chapter also investigated the influence of URM infill walls on the seismic collapse risk of buildings. A comparative study of this building system shows that the RC MRF buildings with URM infill walls can resist higher ground motion of intensities. However, there is an inconsistency in terms of collapse rate, whereby the 6-storey RC MRF buildings have a higher collapse rate 158 when compared among the buildings considered. The presence of infill walls, material and geometric characteristics, and the number of building storey are considered the main factors associated with these outcomes. A more comprehensive study of URM infill walls is recommended to enhance understanding of the overall contribution of infill walls to collapse safety by considering both in-plane and out-of-plane URM infill walls effect. Further, this chapter compares the mean annual frequency of collapse of ductile RC MRF buildings for different codes. It has been observed that the RC MRF buildings designed by Canadian code are in the reasonable range of collapse risk for buildings. Further, there is significant variation in the mean annual frequency of collapse of the building designed for Italian codes. The results presented in this chapter only focused on low- to mid-rise buildings. However, the results obtained from this study help comprehend the seismic safety level of current Canadian buildings. This study can be extended by considering the SSI effect and both in-plane and out-of-plane URM infill walls effect to understand better the overall seismic collapse performance of buildings in Canada. 159 CHAPTER 5: Seismic vulnerability of RC frame buildings considering soil-structure interaction (SSI) effects In performance-based earthquake engineering, it is important to predict the seismic performance of structures accurately. Chapter 4 assesses the collapse risk of RC frame building based on different building configurations and ductility without considering the soil-structure interaction (SSI) effect. However, in reality, structures subjected to earthquakes are affected by their interaction with the foundation and soil. The SSI is often neglected in standard seismic building designs. Considering SSI can significantly impact structural seismic fragility through several mechanisms depending on the combined effects of soil properties and structural characteristics. Therefore, a seismic collapse assessment that includes the SSI effect consideration is needed to understand the potential factors that caused the buildings to collapse. The effects of SSI on the fragility curves of 2-dimensional bare RC frames and infilled RC frames are discussed in this chapter using a probabilistic method. The SSI analyses are used to determine the effect of various structure types and foundation conditions on the seismic response of structures. The interaction between the superstructure and substructure is studied by modelling the soil as simply as possible to capture the overall system response. A substructures approach was applied concerning the SSI modelling. Several response factors have been analyzed, and inherent issues have been outlined. This chapter provides reliable data and comments on the framework that facilitates the assessment of RC frame buildings while considering the SSI impact into account. The main objective of this current topic is to assist and enhance the understanding of practicing engineers and researchers in determining the importance of considering the complex dynamic interaction between superstructure, foundation, and soil to the seismic performance of superstructures. 160 5.1 Background The seismic response of buildings is complex due to the parameters and characteristics of ground motion, including epicenter, distance, depth, and local soil characteristics. It can also be affected by factors such as structure type, material, building height, ductility, etc. In principle, the ground moves rapidly back and forth during an earthquake, forcing the building's foundation to move along with it (Kramer & Stewart, 2004). Due to its mass of inertia, the top part of the building prefers to remain still, which causes the structure to vibrate strongly, resulting in resonance phenomena between the structure and the ground. This demonstrates a direct relationship between the movement of the building and the movement of the ground, with the structure's motion affected by the soil's response and the soil's response influenced by the structure's motion. The term "soil-structure interaction" (SSI) describes this phenomenon. It has been shown that the building design and its subsequent response to an earthquake are affected by SSI (Wolf, 1985). Nevertheless, practicing structural engineers usually do not consider SSI effects while designing and analyzing buildings. The soil-supporting structures are typically neglected in both design and seismic assessment, although SSI effects can significantly change the response of structures during earthquakes due to the soil's increased flexibility reducing internal stresses and the overall lateral stiffness of the building (FEMA, 2020; Wolf, 1985). Generally, it is well known that accounting for SSI effects involves respecting the fundamentally complicated procedure, and this is typically accomplished by taking into consideration inertial and kinematic interaction systems. Hence, the neglection of SSI will reduce the complexity of the structural analysis. In many countries, the current design code guidelines for structures do not require engineers to include SSI impacts, either constructing new buildings or evaluating the seismic performances of existing buildings. Instead, the guidelines suggested the “Fixed-Base Approach”, a simple and practical method for designing and evaluating buildings. 161 Furthermore, although a current code identifies the structure for which the SSI must be included in engineering practice, there is a lack of general guidelines on the SSI assessment (Requena-Garcia-Cruz et al., 2022). Thus, most of the related studies assessed seismic evaluation of the buildings only depended on the superstructures, which superstructures were restrained at the base, expecting that the attention to soil-structure interaction would produce conservative results. In certain cases, utilizing the data obtained from fixed-base buildings can lead to an unsafe design and cause an unreliable result (Mylonakis & Gazetas, 2000). The effect of SSI may be negligible in some cases but critical in others. As reported by FEMA 440 (FEMA-440, 2005) and ASCE/SEI 41-06 (ASCE/SEI, 2007), the seismic building performance depends on the stiffness and strength of the soil–foundation components. The supporting soil properties will not considerably influence the dynamic response of the structure during the earthquake if the ground is stiff enough, and the structure can be assessed under the fixed-base condition. On the other hand, the dynamic response of a structure resting on a flexible medium will differ from the fixed-base condition due to the interaction between the soil and the structure (Wolf, 1985; Shahbazi et al., 2018; Tahghighi & Mohammadi, 2020). The damage of numerous infilled RC frame buildings in an earthquake like Mexico City 1985, Kobe 1995, and Bhuj 2001, has been evidenced during the earthquakes due to the soil-related motion amplification (Figure 5.1). In the 1985 Mexico City earthquake, most buildings collapsed due to the soft soils that amplified the ground motion and modified the frequency of ground shaking (Abdel Raheem et al., 2015). During the Kobe 1995 earthquake, several buildings collapsed because of soil movement (Badry & Satyam, 2016). Similar behaviour was observed during the Bhuj 2001 earthquake, in which the collapse of buildings due to the local soil condition in which those buildings located on unconsolidated young sedimentary materials (Sairam et al., 2018). It is technically feasible that eliminating SSI mispredicts structural responses based on ground motion characteristics. Therefore, the flexibility of the foundation soil must be appropriately 162 considered in the building analysis; otherwise, the structures' dynamic characteristics and seismic performance may differ from their actual performance (Mylonakis & Gazetas, 2000; Pranjoto & Pender, 2003; Stewart, Kim, Bielak, Dobry, & Power, 2003; Mayoral & Romo, 2006; Arefi, 2008; Magade & Patankar, 2009; Oz et al., 2020). (a) (b) (c) Figure 5.1: Buildings Collapsed during;(a) the Mexico City earthquake of 1985 (From © Abdel Raheem et al., 2015. Evaluation of soil–foundation–structure interaction effects on seismic response demands of multi-story MRF buildings on raft foundations, Int J Adv Struct Eng, 7, Creative Commons Attribution License (CC-BY 4.0)), (b) the Kobe earthquake of 1995 (From © Badry & Satyam, 2016. An efficient approach for assessing the seismic soil structure interaction effect for the asymmetrical pile group. Innov. Infrastruct. Solut. 1, Creative Commons Attribution License (CC-BY 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)), and (c) the Bhuj earthquake of 2001 (From © Murty, Goel, Goyal et al., 2002. Reinforced Concrete Structures. Earthquake Spectra, 8(1_suppl), 149-185. Page 167. By permission from Sage Publication). 163 Numerous research studies have been conducted in the recent past to understand better and characterize the effect of SSI on structure performance. The significance of the SSI effect has been studied by comparing the responses of the system for fixed-base and flexible-base conditions. Many studies on the effects of SSI have focused on the seismic behaviour of buildings with shallow foundations considering different soil flexibilities (Bielak, 1974; Gazetas, 1983; Stewart et al., 1999; Galal & Naimi, 2008; Magade & Patankar, 2009; Tabatabaiefar et al., 2011; Sáez, Lopez-Caballero, & Modaressi-Farahmand-Razavi, 2013; Vivek & Raychowdhury, 2017; Ali Mohamadi, 2019; Ozmen & Tarakci, 2022). They conclude that the soil foundation's flexibility reduces the structures' overall stiffness, leading to expansion in the fundamental period of the system. Besides, because of the stiff nature of the structure and often soil softness, which can, in turn, cause an increase in base shear, the storey drifts/ displacements, and damping (Khalil, Sadek, & Shahrour, 2007; Lou, Wang, Chen, & Zhai, 2011; Vivek & Raychowdhury, 2017; Mohamadi & Tahghighi, 2019). A series of studies involving the response of SSI on RC frame buildings, among others, concluded that nonlinear SSI generally changes the force demands of the structure (energy dissipation) and ductility (Wolf, 1985; Khalil et al., 2007; Rajeev & Tesfamariam, 2012b; Shahbazi et al., 2018; Mohamadi & Tahghighi, 2019; Tahghighi & Mohammadi, 2020; Requena-Garcia-Cruz et al., 2022). Studies conducted by Pitilakis, Karapetrou, & Fotopoulou (2014) on the vulnerability of reinforced concrete (RC) moment-resisting frame (MRF) buildings have shown that the SSI effects might play a crucial role in modifying the seismic performance and fragility of RC MRF buildings. Previous studies also identified that the seismic behaviour of buildings supported on a pile foundation differs from that on a shallow or rigid foundation. Shallow foundations typically result in lower natural frequencies and greater displacement amplitudes for the superstructure and foundation (Nghiem, 2009). Van Nguyen, Fatahi, & Hokmabadi (2016) studied the effect of shallow foundation size on the seismic response of a typical mid-rise moment-resistant building frame. The study indicated that a shallow foundation larger shallow foundations limit SSI-induced lateral displacement and inter-storey 164 drifts. Changes in shallow foundation size also absorbed earthquake energy at the system's natural frequency. They also found that seismic excitations attract stronger inertial forces from larger shallow foundations. For researchers to take into account the SSI effect, various numerical methods have been used to model the structural behaviour on surface footings (Tabatabaiefar and Massumi 2010; Lou et al. 2011; Tabatabaiefar et al. 2013; Fatahi and Tabatabaiefar 2014) such as the Winkler model, the Elastic continuum model, or the finite element model. However, the most popular method used in design practice when modelling SSI is the beam-on-nonlinear-Winkler foundation (BNWF) approach. The update is chosen due to the familiarity of current engineering practice with the simplified Winkler approach. This was used to examine multiple assumptions. Winkler's idealization describes the soil medium as a system of identical but mutually independent springs that are closely spaced, discrete, and linearly elastic. The BNWF model describes the soil as a linearly elastic system. The soil characteristics, measured in terms of the elastic modulus/shear modulus and Poisson's ratio, have been assigned in terms of equivalent spring stiffness. This approach is the most simple one and has been in use for the longest (Raychowdhury 2011; Marzban et al. 2014; Tahghighi and Rabiee 2017). Despite extensive research that has been conducted, soil-structure interaction is still rarely used in engineering practice. The effect of SSI on RC frame-building performance is still debatable. To adequately assure structural sufficiency and safety for the benefit of the community, the SSI analysis should be conducted with various parameters to gain better insight into structural performance and to improve accuracy in the analytical simulation of important structural response quantities. Therefore, this chapter focused on investigating the probability that the SSI may influence the fragility curve and hence affect the building vulnerability of low- to mid-rise RC MRF structures. The study is conducted for RC frames with or without infill walls under fixed-base and flexible-base assumptions by considering the effect of variability in the depth of foundation embedment using nonlinear incremental dynamic analysis (IDA methods), as this 165 parameter influences the moment capacity and shear capacity increase with an increase in depth of embedment. In this study, SSI is modelled by implementing a substructure approach incorporating with BNWF model for the soil domain. Analyses are performed investigating the influence of the depth of embedment of the foundation on the seismic response and fragility of RC buildings. Finally, fragility functions are derived for the RC buildings considering SSI effects as a function of spectral acceleration at the structure's fundamental elastic period Sa(T1) for the collapse failure for the fixed-base and SSI models based on the methodology described in detail in Chapter 4. 5.2 Description of the methodological framework The proposed methodology in this research is organized into four phases: (1) characterizing the case study building and the soil; (2) numerically modelling the superstructure and the substructure (SSI system); (3) determining the parameters of the analysis; and (4) assessing the seismic fragility. An overview of the proposed framework employed to evaluate the seismic vulnerability of RC frame buildings is shown in Figure 5.2. 166 Figure 5.2: Methodological framework for the vulnerability analysis of the infilled RC MRF buildings with SSI. Different building configurations are considered by selecting RC MRF buildings on medium soil (site class C) with shear wave velocities less than 600m/s of differing typologies developed by various seismic code levels to derive generic fragility curves and increase the dependability of the results. The analytical simulation of the structural capacity is based on structural details, material properties, and plasticity modelling, while the infill wall is modelled using a diagonal equivalent strut approach. In the SSI system, the soil-foundation interface is represented by nonlinear Winkler springs. The OpenSees computer software was implemented to develop the entire model and conduct the dynamic analysis. The earthquake demand is defined based on selecting 50 pairs of actual earthquake recordings, such that the seismic input motion has different frequency content and duration characteristics. A series of two-dimensional IDA is performed on the structure under increasing ground motion intensity levels until it causes a sideways collapse to evaluate the seismic performance of structural systems. When the maximum 167 inter-storey drift ratio of the buildings reaches 0.10, this is the threshold of dynamic instability, and collapse will occur. RC MRF buildings' nonlinear response is investigated based on two comparable base conditions, fixed-based and flexible-based. The evaluation considers SSI effects with varying foundation embedment depth. The results of each analysis are used to develop a fragility curve that provides information on the probability of exceedance of collapse for the structure under consideration. The fragility curves are constructed in terms of the spectral acceleration at the structure's fundamental elastic period Sa(T1). Several uncertainties are included in the probabilistic approach given herein concerning the structural modelling and the seismic demand variability (record-to-record). The obtained results were investigated for fixed- and flexible-base conditions. The fragility curves can then be used to estimate the seismic performance of the structure, as well as to develop mitigation measures to improve its performance. 5.2.1 Structural and Geotechnical Details The SSI study considers a set of 3- and 6-storey RC MRFs representing low- and mid-rise RC buildings designed according to different seismic code levels and height classes—the frame structures designed based on modern seismic code provisions. In particular, two three-storey – three-bay RC frame models (Low-rise – moderately ductile and ductile) and two six-storey – three-bay frame models (Mid-rise – moderately ductile and ductile), both designed according to the NBCC 2010 and CSA A23.3-14 standard provision as special moment resisting frames in both the X and Y directions. This study has considered the prototype building model presented in Chapter 4 (see details in sections 4.2.1 and 4.2.2). The selected fixed structure models are illustrated in Figure 5.3. 168 (a) (b) Figure 5.3: Ductile and moderately ductile RC MRF models used for the seismic vulnerability assessment considering SSI; (a) 3-storey (Low-rise) building, (b) 6-storey (Mid-rise) building. 169 Overall, eight (8) typical RC MRF buildings are modelled with different heights and infill configurations supported by medium soil types, which are presented for site C (360 < Vs < 760 m/s) according to the NBCC 2010 Site Classification for Seismic Site Response. The lower limit of site class C (Vs = 360 m/s) was considered to evaluate the significance of the SSI effect in the building response. The nonlinear response of MRF buildings is investigated in this chapter using two comparable base conditions. First is the NSSI model, which is fixed–based, indicating the rigid foundation system. Second, the SSI model or considered a flexible-based model in which foundation movement and soil plasticity are integrated, and the soil-foundation interface is represented by nonlinear Winkler springs. These models are identified by the fact that the soil and foundation interact nonlinearly. For this study, internal and external columns are supported by the same size of an isolated square shallow footing at different embedment depths (or Df/B ratio). The characteristics of the footings employed in this study are summarized in Table 5.1 and Figure 5.4. Table 5.1: Foundation characteristics. Building Model Footing type Width of footing, B (m) Length of footing, L (m) Height of footing, L (m) Embedment depth of footing, Df (m) 3S-D-NI Isolated 2.0 2.0 1.0 0 and 1.0 3S-MD-NI 3S-D-I 3S-MD-I 6S-D-NI Isolated 2.0 2.0 1.0 6S-MD-NI 6S-D-I 6S-MD-I 170 Elevation (a) Plan (b) Figure 5.4: Schematic diagram of the isolated shallow footing (a) Elevation, and (b) Plan view. Parameters used in the geotechnical design include the shear wave velocity (VS), specific gravity (), shear modulus (G), Poisson's ratio (), modulus of elasticity (E), cohesion coefficient (C), and internal friction (). Table 5.2 shows the adopted soil parameters. Table 5.2: Details of soil parameters. Site Class  (degree) C (kPa)   (kN/m3) G0 (MPa) Vs (m/s) C 42 0 0.35 21 280 360 171 5.2.2 Nonlinear Modelling of Infilled RC frame buildings with SSI The OpenSees finite element software was used to create the computer model of the structure with fixed-based structure and flexible-based (the soil-foundation-structure systems). In this chapter, the substructure approach, which consists of two separate components, the superstructure (above the ground level) and the substructure (below the ground level), is used to study the influence of the SSI effect on the seismic response of buildings. The structural members (superstructure component), beams, and columns are represented as elastic beam-column elements with distributed and lumped plasticity elements with flexure-shear interaction, while equivalent diagonal strut element model the infill URM walls. The numerical modelling of the nonlinear structural models (superstructure model) has been described in detail in Chapter 4. In this study, the structures are assumed to be supported by isolated square footing (shallow foundation) embedded in various soil depths (soil site class C). The soil-foundation system (substructure system below the ground) is modelled by adopting the BNWF model upgraded by Raychowdhury & Hutchinson (2008) and implemented in the OpenSees, which accounts for the nonlinear interaction between the foundation and soil on the structural response, particularly for the shallow foundation. A detailed description of the selected modelling approach for the SSI system is presented in the next section of this chapter. Figure 5.5 illustrates a general schematic view of the sample two-dimensional structural models, which consist of RC frame, infill wall, and soil-foundation system modelling. 172 (a) (b) (c) Figure 5.5: Numerical model in OpenSees; (a) overview of the overall model, (b) Infilled RC frame model with lumped plasticity and strut model, and (c) BNWF schematic model proposed by Raychowdhury & Hutchinson (2009) (From © Raychowdhury & Hutchinson, 2009. Performance evaluation of a nonlinear Winkler-based shallow foundation model using centrifuge test results, Earthquake Engng Struct.Dyn, 38, 679–698. Page 682. Adapted with permission from John Wiley and Sons). 5.2.3 Soil-foundation Modelling: The BNWF model The Beam on Nonlinear Winkler Foundation (BNWF) approach is used to model the nonlinear SSI of a shallow foundation (an isolated square footing). The BNWF approach can provide a more realistic assessment of the structural response of RC frame buildings under seismic loading. It can deal with geometrical and material nonlinearities and capture the important identified in shallow foundation investigations. In this model, the foundation, a part of the structural member, is modelled similarly to RC beams, using an elastic beam-column element. In contrast, 173 the independent zero-length element (Figure 5.6(b)) represents the soil domain, consisting of a parallel series of nonlinear springs and dashpots, representing the soil stiffness and damping, respectively. In the BNWF model, the kinematic interaction was neglected as this assumption is commonly accepted in the case of shallow foundation resiting in/on the half-space. Figure 5.6 provides the schematic diagram of the shallow foundation and the BNWF model used in this study. (a) (b) Figure 5.6: The schematic diagram of; (a) Graphical representation BNWF model, and (b) Example series of Winkler springs below a rigid foundation represented by one-dimensional finite element (zero length element) (From © Raychowdhury & Hutchinson, 2009. Performance evaluation of a nonlinear Winkler-based shallow foundation model using centrifuge test results, Earthquake Engng Struct.Dyn, 38, 679–698. Page 682. Adapted with permission from John Wiley and Sons). As shown in Figures 5.5(c) and 5.6(a), vertical and horizontal soil flexibility is modelled by distributed vertical springs and concentrated horizontal springs, where the vertical q-z springs capture the vertical and rotational resistance. In contrast, two horizontal springs, t-x and p-x, are used to model the passive and sliding resistance of the foundation, respectively. In OpenSees, the q-z, t-x, and p-x springs are modelled using QzSimple, PxSimple, and TxSimple models material, respectively ( Harden, 2005; Raychowdhury, 2009; Rajeev & Tesfamariam, 2012b; Behnamfar & Banizadeh, 2016). These three material models are represented by nonlinear backbone curves calibrated against shallow foundation tests (Figure 5.7) (Raychowdhury & Hutchinson, 2009). 174 (a) (b) (c) Figure 5.7: Hysteretic behaviour of BNWF model springs; (a) q-z spring (axial and rotational), (b) p-x springs (passive resistance), and (c) t-x springs (sliding resistance) (From © Raychowdhury & Hutchinson, 2009. Performance evaluation of a nonlinear Winkler-based shallow foundation model using centrifuge test results, Earthquake Engng Struct.Dyn, 38, 679–698. Page 683. Adapted with permission from John Wiley and Sons). The equations developed by Boulanger, Curras, Kutter, Wilson, & Abghari (1999) to define the PySimple material model and are modified by Raychowdhury & Hutchinson (2009) to describe the QzSimple material model. The computation for the PxSimple and TxSimple material models is similar to that for the QzSimple material model with variation in the constants for Cr, n, and C. For more details regarding the material models, can refer to Boulanger et al. (1999), Raychowdhury( 2008) and Raychowdhury & Hutchinson(2009). 175 The soil springs equations proposed by Gazetas (1991) are used in the study. The vertical and horizontal spring stiffness for isolated square footing at embedment depth (Df) can be calculated by using the following equations; Vertical surface stiffness; 𝑘𝑣 = 𝐺𝐿1 − 𝜐[0.73 + 1.54 (𝐵𝐿)0.75] (5-1) Horizontal surface stiffness; 𝑘ℎ = 𝐺𝐿2 − 𝜐[2 + 2.5 (𝐵𝐿)0.85] (5-2) Vertical embedded stiffness; 𝑘𝑣,𝑒𝑚𝑏 = 𝑘𝑣 {1 + (121) (2𝐷𝑓𝐵) [1+ 1.3 (𝐵𝐿)]} [1 + 0.2 (𝐴𝑤𝐴𝑏)23] (5-3) Horizontal embedded stiffness; 𝑘ℎ,𝑒𝑚𝑏 = 𝑘ℎ [1 + 0.15 (2𝐷𝑓𝐵)0.5] {1+ 0.52 [(2ℎ𝐵) (4𝐴𝑤𝐿2)0.4]} (5-4) where 𝑘𝑣 and 𝑘ℎ are vertical and lateral stiffness of the surface footings; 𝑘𝑣,𝑒𝑚𝑏 and 𝑘ℎ,𝑒𝑚𝑏 are the vertical and lateral stiffness of the footing embedded at a depth 𝐷𝑓; 𝐴𝑤 is sidewall-soil contact area (h x perimeter of the footing); and 𝐴𝑏 is soil-foundation contact area. As stated in Section 5.2.1, G is the shear modulus of the soil; 𝜐 is the Poisson’s ratio of the soil; B and L are footing width and length, respectively. Each spring’s stiffness is assigned based on its tributary length, and the entire foundation stiffness is distributed along the length of the footing. The stiffness intensity and spacing along the footing length are defined by the equation recommended by Harden (2005) and supported by Raychowdhury(2008) and Raychowdhury & Hutchinson (2009). 176 5.2.4 Nonlinear Dynamic Analysis IDA is employed in this study to determine the seismic collapse level of RC MRFs for each record with increasing the amount of Intensity Measure (IM) to investigate the seismic performance and later assess the seismic vulnerability of RC MRF buildings influenced by the SSI effect. IDA was firmly dependent on the ground motion record selected, which is representative of the site-specific hazard and design criteria and covers a range of ground motion intensities. The building model must be consistently subjected to adequate seismic records. Hence, in this study, IDA is conducted using a set of 50 pairs of earthquake records selected based on the seismic hazard of interest that can cover the entire range of structural response, from elasticity to yielding, and finally, global instability. This study selects the spectral acceleration in the fundamental period of the RC MRF, Sa(T1), as IM ( for further details, see chapter 4, section 4.2.4). As described earlier, the IDA is applied to evaluate the collapse capacity of the selected models, where the total collapse of the structure can be achieved when the maximum inter-storey drift ratio of the buildings exceeds 0.10 (Haselton et al., 2007), and the IDA curve transforms into a horizontal line for each ground motion. The IDA curves establish a correlation between the intensity measurement level and the maximum inter-storey drift ratio. Several IDA curves are selected to study the general pattern of seismic demand. Figures 5.8 and 5.9 presented examples of IDAs of 3- and 6-storey bare RC MRF without and with SSI effects (Df = 1.0 m), under different scaled accelerograms. The pattern of the IDA results demonstrates several essential aspects of the building’s seismic performance, such as the level of the building that can resist high levels of ground motion before experiencing significant damage. Figures 5.8 and 5.9 show that the IM level decreased with building height and ductility. 177 The seismic collapse performance of each building model, described in section 5.2.1, based on the median IDA curves, is compared to evaluate the influence of considering embedment depth. Figures 5.10 and 5.11 present the median IDA curves considering two cases of embedment depth for different building heights, configurations, and designs. According to Figures 5.8 and 5.9(a–b), the SSI effects can significantly reduce the Sa(T1) values in the median IDA curves of all cases for 3-storey buildings and several cases for 6-storey buildings. The SSI models showed a more flexible behaviour, especially for low-rise buildings, affecting the system's overall rigidity. The noticeable difference in the IDA curves due to the decreased soil rigidity indicates that the foundation-structure system became more flexible due to utilizing a more significant number of springs. Furthermore, it was observed that decreasing the soil's rigidity caused an increase in the difference between the IDA curves in the NSSI and SSI models. In addition, it can be observed from Figures 5.10 and 5.11 that the surface foundation with a depth of 0.0 m exhibited a more flexible response, which demonstrates that it has greater flexibility compared to the embedded foundation with a depth of 1.0 m. As expected, the infilled RC frame significantly affects Sa(T1) values in median IDA curves in all models, where the infill walls can significantly increase the values of Sa(T1). Overall, these results emphasise the importance of considering SSI effects in evaluating seismic performance and designing the structure of buildings with different heights and configurations, particularly concerning the foundation's embedment depth. The consideration of these factors influences the degree of flexibility of the structure. Hence, it is recommended that designers consider these factors, along with the influence of infill walls and SSI to ensure more accurate and reliable seismic assessments for different building design and heights. 178 (a) (b) (c) (d) Figure 5.8: IDA curves of the 3-storey bare RC MRF; (a) 3S_D_NI without SSI, (b) 3S_MD_NI without SSI, (c) 3S_D_NI with SSI, and (d) 3S_MD_NI with SSI. 179 (a) (b) (c) (d) Figure 5.9: IDA curves of the 6-storey bare RC MRF; (a) 6S_D_NI without SSI, (b) 6S_MD_NI without SSI, (c) 6S_D_NI with SSI, and (d) 6S_MD_NI with SSI. 180 (a) (b) (c) (d) Figure 5.10: Median IDA curves of the 3-storey RC MRF with SSI (Df=0.0 m and 1.0 m); (a) 3S_D_NI, (b) 3S_D_I, (c) 3S_MD_NI, and (d) 3S_MD_I. 181 (a) (b) (c) (d) Figure 5.11: Median IDA curves of the 6-storey RC MRF with SSI (Df=0.0 m and 1.0 m); (a) 6S_D_NI, (b) 6S_D_I, (c) 6S_MD_NI, and (d) 6S_MD_I. The results of each IDA are used to generate a fragility curve that provides information regarding the probability of a structure exceeding a certain level of damage or failure (i.e collapse) given a specific intensity of ground motions. The fragility curves are then utilized to evaluate the 182 structure's seismic functionality, to assess the risk of failure to a building and develop strategies to enhance performance or mitigating risk of the structure. 5.3 Influence of SSI on Period of Buildings Supported by Shallow foundations In general, the fundamental period is the most important and dominant mode to evaluate the seismic demand of a structure. The effect of base conditions, including the fixed- and flexible-based buildings, on the fundamental period obtained from Opensees models is shown in Table 5.3 and plotted in Figure 5.11. As the base flexibility increase from a rigid foundation to a flexible foundation, the fundamental period increases monotonically. Furthermore, as shown in Table 5.3, the period decreases when the embedment of the footing change from 0 to 1.0 m as the embedment depth of the footing stiffens the system. However, the trend line presented in Figure 5.11 does not depict it because of the slight increment. From Table 5.3, it can be seen that considering the SSI raises the period value from 0.5% to 2.5%. In this regard, the fundamental relationships between the soil and the structure are related to SSI. Specifically, it can be seen from a comparison of flexible-based structures—which take into account the impacts of soil deformability—and fixed-based structures that the fundamental period of the flexible-based structures lengthens due to SSI effects. Table 5.3: Fixed- and flexible-based structure periods – 1st mode. Structure ID Building type Period (s) - 1st mode Fixed Flexible -Df=1.0m Flexible -Df2=0.0m 3S_MD_NI No Infill 0.970 0.985 0.995 3S_MD_I Full Infill 0.319 0.324 0.327 6S_MD_NI No Infill 1.884 1.894 1.899 6S_MD_I Full Infill 0.601 0.612 0.615 3S_D_NI No Infill 0.924 0.944 0.946 3S_D_I Full infill 0.315 0.322 0.323 6S_D_NI No Infill 1.819 1.830 1.836 6S_D_I Full infill 0.598 0.605 .612 183 (a) (b) Figure 5.12: Base flexibility effect on period; (a) moderately ductile RC frame, and (b) ductile RC frame. Period lengthening, also known as period elongation, is the ratio of the fundamental period of a flexible system to the fundamental period of a comparable rigid system. Table 5.4 and Figure 5.12 illustrate the period-lengthening pattern that is obtained when the SSI impact is considered. A general trend of lengthening period duration shown in Figure 5.12 is now more clearly visible. Based on the results, it can be seen that the lengthening of the period is more noticeable in the 3-storey building than in the 6-storey building. This demonstrates that short-height structures are more vulnerable to SSI effects. This is due to the fact that when a structure is short and stiff, the flexibility of the base has a more substantial impact on the overall stiffness of the system, whereas structural flexibility is dominant over foundation flexibility for tall and slender structures (Vivek & Raychowdhury, 2017). In addition, as previously demonstrated, the fundamental period of the infilled RC frame buildings decreases as a result of the presence of the infill walls. Overall, the average period elongation for the 3-storey buildings is approximately 1.9 % and 2.4% for embedment and surface foundations, respectively, whereas 1.0% and 1.6% for the 6-storey buildings. 184 Table 5.4: Period lengthening caused by SSI. Structure ID Building type Period elongation ratio (TF/TSSI) Flexible -Df=1.0m Flexible -Df2=0.0m 3S_MD_NI No Infill 1.015 1.026 3S_MD_I Full Infill 1.016 1.025 6S_MD_NI No Infill 1.005 1.008 6S_MD_I Full Infill 1.018 1.023 3S_D_NI No Infill 1.022 1.024 3S_D_I Full infill 1.022 1.025 6S_D_NI No Infill 1.006 1.009 6S_D_I Full infill 1.012 1.023 Figure 5.13: Base flexibility effect on the period-elongation ratio. 5.4 Comparison of SSI effects on the seismic performance of RC MRF frame buildings The results of the IDA (Sa(T1)- maximum inter-storey drift ratio values) are used to derive the fragility curves that can be represented by a lognormal cumulative distribution function (Baker, 2015), as shown in Equation 4.3 described in Chapter 4, Section 4.4: 185 P(C|IM = x) = Φ (ln (xμ)β) (5-1) where P(C|IM = x) is the probability that a ground motion with IM = x will cause the structure to collapse, Φ () is the standard normal cumulative distribution function, μ is the median of the fragility function and  is the standard deviation of ln (IM) (sometimes referred to the dispersion of IM). The log-standard deviation parameter β, which describes the overall dispersion associated with each fragility curve, includes the two primary sources of uncertainty, record-to-record variability (RTR-βRTR) and structural modelling (M-βM). The uncertainty in the structural modelling is assumed to be 0.5, as suggested by Haselton and Deierlein (2007), while for the seismic demand or RTR-related uncertainty is accounted by using the variability in the simulated data. The overall variability is calculated as the sum of the squares of the component dispersions, shown in Equation 4.4, assuming that these two variability components are statistically independent. Table 5.5 presents the lognormal distributed fragility parameters (median collapse capacity and log-standard deviation) for all study buildings. These buildings are founded on-site in class C and modelled with three different based conditions: fixed-based (no SSI effect –NSSI), and flexible-based with different embedment depth (Df), 0.0 m (SSI_Df0) and 1.0 m (SSI_Df1). For the reported structural model, the calculated log-standard deviation β values of the curves vary from 0.59 to 0.77. Figures 5.14 and 5.15 shows comparative plots of fragility curves for the eight representative buildings, which consist of different heights, ductility classes, and configurations derived as a function of Sa(T1) for the fixed-base and SSI models. 186 Table 5.5: The fragility function parameters for fixed-based and flexible-based models. Structure ID Foundation conditions Median collapse capacity, Sa(T1)[g] Dispersion, β 3S-D-NI Fixed-based (NSSI) 1.580 0.62 Flexible-based (Df= 1.0 m) 1.525 0.61 Flexible-based (Df= 0.0 m) 1.405 0.65 3S-D-I Fixed-based 4.281 0.67 Flexible-based (Df= 1.0 m) 4.029 0.66 Flexible-based (Df= 0.0 m) 3.828 0.68 3S-MD-NI Fixed-based 1.118 0.63 Flexible-based (Df= 1.0 m) 1.114 0.62 Flexible-based (Df= 0.0 m) 1.079 0.63 3S-MD-I Fixed-based 3.016 0.66 Flexible-based (Df= 1.0 m) 2.862 0.65 Flexible-based (Df= 0.0 m) 2.754 0.65 6S-D-NI Fixed-based 0.591 0.75 Flexible-based (Df= 1.0 m) 0.614 0.75 Flexible-based (Df= 0.0 m) 0.636 0.77 6S-D-I Fixed-based 2.964 0.66 Flexible-based (Df= 1.0 m) 2.871 0.67 Flexible-based (Df= 0.0 m) 2.755 0.69 6S-MD-NI Fixed-based 0.313 0.60 Flexible-based (Df= 1.0 m) 0.298 0.59 Flexible-based (Df= 0.0 m) 0.280 0.64 6S-MD-I Fixed-based 2.529 0.66 Flexible-based (Df= 1.0 m) 2.442 0.66 Flexible-based (Df= 0.0 m) 2.378 0.65 As demonstrated in Figures 5.14 and 5.15, it has been shown that the SSI model that considers nonlinear soil is more vulnerable to damage than the fixed-based model. This trend is more pronounced for the low-rise buildings designed with ductile class than in other cases. In the case of buildings considering the SSI effect with a foundation embedded at 1.0 m depth, the seismic failure probability of the 3-storey RC MRF with the ductile building design decreased from 3.5% to 5.9%, whereas it decreased from 0.4% to 5.1% for the moderately ductile building. The seismic failure probability for a 6-storey ductile RC MRF building considering the SSI effect with a foundation embedded at 1.0 m depth, is decreased by 3.1% for the infilled frame. In contrast, it 187 increased by 3.9% for the bare frame building. The moderately ductile 6-storey RC MRF buildings decreased from 3.4% to 4.8%. A significant increase in fragility is shown for the SSI with surface foundation (Df=0.0 m) models compared to the fixed base of the RC MRF building for both ductile and moderately ductile buildings, in which the seismic failure probability decreases between 3.5% to 11.1%. In addition, it has been demonstrated that the presence of infill walls to RC MRF structures resulted in a significant increase in the structure's fragility curves, with the buildings' seismic failure probability decreasing from 6% to 10.6%. However, the seismic failure probability of mid-rise buildings has a different failure pattern than low-rise buildings, indicating that building height may affect their expected seismic performance. Based on the findings of this study, it is demonstrated that the SSI model with a 1.0 m foundation embedment depth is less vulnerable than the SSI system with a surface foundation. This observation is more apparent in the model with mid-rise buildings than low-rise buildings. Nonetheless, all analysis cases certainly show an overall increase in the building's fragility compared to the fixed-based model. Hence, the SSI effect considering various embedment depths of the foundation, may have an important role in the predicted structural damage. In conclusion, the results indicate that fragility curves derived for RC MRF buildings with a fixed-based condition may underestimate the actual vulnerability of the structures under certain conditions. Thus, it is recommended that the SSI's effects be incorporated into the assessment, given its significant influence. The structural response of the assessed buildings is found to be altered when soil flexibility and foundation are incorporated, leading to increased vulnerability levels. The seismic structural vulnerability may decrease or increase depending on the characteristics of the buildings, the input motion, and the soil properties, so this should not be considered a general trend. 188 (a) (b) (c) (d) Figure 5.14: Seismic fragility curves of the 3-storey RC MRF considering different building configurations with and without SSI; (a) 3S_D_NI, (b) 3S_D_I, (c) 3S_MD_NI, and (d) 3S_MD_I. 189 (a) (b) (c) (d) Figure 5.15: Seismic fragility curves of the 6-storey RC MRF considering different building configurations with and without SSI; (a) 6S_D_NI, (b) 6S_D_I, (c) 6S_MD_NI, and (d) 6S_MD_I. 190 5.5 Summary The seismic vulnerability of eight typical RC MRF buildings designed with different ductility classes, heights, and configurations has been assessed considering SSI effects. The SSI system has been considered by implementing the substructure approach based on the BNWF model, which separates the building and surrounding soil into two independent components: the superstructure and the substructure systems. The SSI system is analyzed for different foundation depths of embedment at the same soil site Class C. The effect of SSI on the seismic performance of RC MRF buildings is investigated using IDA with 50 pairs of ground motion records selected based on the 2% PE in 50 years. Finally, probabilistic fragility functions for the collapse level for each case have been developed. The results are evaluated with the ones obtained from models with a fixed-based condition. The main focus of findings is the effects of foundation embedment depth and their significant impact on the fundamental period, seismic responses, and vulnerability of the buildings. The analysis results of this study identified that foundation flexibility has a slight effect on the fundamental period of RC MRF buildings. However, it is observed that the effect of SSI on the fundamental period is more noticeable in the 3-storey building than in the 6-storey building, indicating that low-rise buildings are more sensitive to SSI effects than medium ones. Besides, the fundamental period increase linearly when the foundation is on the ground surface (Df = 0.0 m) for both building height. For instance, 3-storey RC MRF buildings can be caused the fundamental period to increase by 2.5% and 0.61% on average with respect to fixed-based and flexible-based with Df = 1.0 m, respectively. Overall, each building type with a surface foundation (Df = 0.0 m) has a higher fundamental period. 191 A significant divergence is identified between the median IDA curves due to the foundation's flexibility. The findings of the median IDA curves indicate that the SSI effects may substantially reduce the Sa(T1) values, which can be observed in all cases for 3-storey buildings and several cases for 6-storey buildings. Finally, the probabilistic fragilities that show the seismic probability of collapse are derived from the fundamental mode spectral acceleration of the buildings for all cases. The results show that SSI under nonlinear soil behaviour may considerably influence structural performance and fragility compared to fixed-based buildings, increasing the structure's seismic vulnerability, especially in low-rise buildings. The obtained findings indicate that the vulnerability of the building increases when the SSI system has a surface foundation compared to a fixed-based model. However, the seismic performance of the buildings with embedded foundations does not change substantially because the foundation embedment depth stiffens the system and may decrease the seismic vulnerability of the structure. Thus, it is essential to consider the SSI effects on the seismic design of RC MRF buildings resting on the surface foundation. In general, it is observed that the derived fragilities for the SSI systems will differ from fixed-base systems due to the soil-structure nature. Overall, the current study demonstrates how SSI and embedment depth effects influence the seismic response and vulnerability of a building. The importance of SSI and embedment depth cannot be oversimplified. However, it should be noted that the results are only relevant to the case studies analysed, namely buildings consisting of RC MRFs founded on soil class C (Vs= 360 m/s). Therefore, additional research is required to develop generalised fragility functions applicable to various RC building typologies that would consider SSI and foundation depth of embedment effects for various soil conditions, particularly in soft soil sites, to improve the reliability of seismic vulnerability assessment studies. Moreover, vulnerability functions derived 192 for the same building should be related to varying foundation sizes. In conclusion, the findings obtained from this study will help assess how SSI affects the structural response. This will provide instrumentation for structural designers to be aware of the potential consequences of their decisions to accomplish a structural design that is both safe and cost-effective. 193 CHAPTER 6: Conclusions and Recommendations This chapter concludes and summarises the thesis by highlighting the important findings of the study. In addition, recommendations for future research are provided. 6.1 Summary and Conclusions The present thesis addressed the development of an improved conceptual framework and provided benchmark data for assessing the performance and risk of code-conforming RC frames due to severe seismic actions considering URM infill walls and SSI effects. The following is a summary of each chapter, including a selection of the most significant findings and conclusions. In order to adequately evaluate the assessment of infilled RC frame buildings using a reliable analytical method, a general guideline for evaluating the monotonic and hysteretic response of URM infill walls modelled by analogous struts, specifically for the in-plane lateral cyclic response, is developed. First, a literature review of failure mechanisms and modelling methods is discussed. The corresponding strut constitutive laws and equations for estimating strut attributes are also explained. Then, the backbone curve proposed by Liberatore (2001) and Liberatore & Decanini (2011) is adopted as it accurately represents the force-displacement curves of the experimental tests used in this study. Later, the strength of the URM infill wall is calculated using the Paulay & Priestley (1992) and Priestley & Calvi (1991) models. Next, the calibration of the model is conducted by comparing the results of numerical analyses with two sets of experimental tests concerning one-storey, one-bay infilled frames. Finally, the efficiency of the calibrated numerical models, which include a combination of the lumped plasticity model for the RC frame members (Model 2) with Pinching4 material, and Concrete01 material to reproduce the cyclic response of infills, were verified with five additional experimental tests. The best-simplified 194 macro-model, which effectively reproduces the URM infill wall behaviour, is selected to evaluate the global performance of masonry infilled frames under in-plane cyclic loads. The study then proceeded with the collapse risk assessment of code-conforming RC frame buildings in Vancouver, BC, Canada, varying in height from three- to six-storeys, and considering different levels of design details, ductile and moderately ductile, with and without URM infill walls. The assessment employed strut models proposed by Burton & Deierlein (2013), utilizing a pair of off-diagonal struts to simulate column shear failure resulting from the interaction between the column and the infill walls. The proposed guideline and calibrated model from Chapter 3 was utilized to identify the monotonic backbone curve and the infill model strength, and and accurately replicate the behaviour of the infill wall. However, the analysis model did not directly simulate collapse mechanisms due to column shear failure; instead, this mechanism was evaluated through post-processing IDA results. In this process, a force-based limit state check is applied to predict the median collapse drift ratio (CDR̂), indicating the critical point at which shear failure is likely to occur. Using a set of 50 ground motions selected based on the 2% PE in 50 years and employing the CMS method, collapse fragility datasets were generated for each structure. This study compared collapse fragility assessments using RTR variability and structural modelling (M) uncertainty. Based on these fragility curves, the median collapse capacity was computed at the ground motion capacity with a 50% probability of achieving collapse targets. Lastly, the annual frequency of collapse was calculated by integrating the seismic hazard curve and the fragility function. Finally, this study extends to the vulnerability assessment of RC MRF buildings by considering the influence of the SSI effect, which contributes to collapse risk. The investigation focuses on the effects of different isolated shallow foundation embedment depths, including surface-level and 1m depth shallow foundations, on the seismic performance of the buildings. The 195 study specifically concentrates on the same soil site class, denoted as medium soil site class C, with shear wave velocities less than 600m/s. To evaluate the significance of the SSI effect on the building response, the lower limit of site class C (Vs = 360 m/s) is taken into consideration. In the SSI system analysis, the study implemented the substructure approach based on the BNWF model. The BNWF model represents the soil-foundation interface using nonlinear Winkler springs and incorporates an appropriate material model to accurately capture the behaviour of the system. The study examines the nonlinear behaviour of MRF buildings under two comparable base conditions. The first condition involves the NSSI model, representing a fixed-based system with a rigid foundation. The second condition involves the SSI model, depicting a flexible-based system where foundation movement and soil plasticity are incorporated. Overall, this study provides a comprehensive investigation into the seismic performance of RC frame buildings with URM infill walls. It focuses on several key aspects, including the identification of predictive equations for estimating infill wall response parameters, the evaluation of moderately ductile and ductile RC frame buildings with URM infill walls, and the examination of the soil-structure interaction (SSI) effect. The results from this research are believed to contribute valuable guidance to seismic engineering practices, empowering structural designers to make informed decisions for achieving cost-effective and safe structural designs. The findings from this research are expected to significantly enhance the resilience and safety of buildings in earthquake-prone regions. Based on the findings of the literature review and seismic risk analysis on infilled-RC frame with consideration of SSI effect, the following major conclusions are drawn;  The published literature has highlighted three critical issues in the modeling and assessment of masonry-infilled RC frames: the lack of a standardized guideline to 196 determine reliable predictive equations for estimating key force-deformation parameters of URM infill walls in global seismic analysis, the need to comprehend seismic collapse risk assessment in code-conforming RC MRF buildings, and the importance of clearer conceptualization of soil-structure interaction (SSI) behaviour in infilled RC frame buildings, considering foundation embedment depth.  An appropriate and simplified analytical model is identified through a proposed guideline for assessing the overall performance of RC frames with URM infill walls under in-plane lateral loads. This guideline outlines the evaluation process for various parameters necessary to define the monotonic and hysteretic response of infill walls, which are modeled using equivalent struts.  Three monotonic constitutive laws, namely Liberatore (2001), Liberatore & Decanini (2011b), Panagiotakos & Fardis (1996), and Dolšek & Fajfar (2008), were carefully examined and compared against experimental test data. The chosen backbone curve models incorporate the effects of stiffness and strength degradation that occur during cyclic loading. Through a rigorous analysis and comparison, the most suitable strut constitutive model proposed by Liberatore and Decanini (2011) provided the most accurate representation of force-displacement curves observed in experimental tests.  Four commonly cited models from the literature were evaluated and compared, each considering at least three different failure modes, to determine the appropriate width and strength of the diagonal strut. The analysis revealed that the models proposed by Priestley & Calvi (1991) and Paulay & Priestley (1992) demonstrated a reliable and accurate estimation of the experimental results. This comparison provides valuable insights into the 197 performance and suitability of various models in predicting the strength of diagonal struts in structures with masonry infill walls.  In this study, the infilled-RC frame model was developed using Opensees software, which offers a wide range of elements, material constitutive models, and analysis algorithms. The distributed plasticity model (Model 1) employed for the RC members demonstrated its ability to capture the deterioration of strength and stiffness, with an average error of 8.2% in the cumulative dissipated energy. Comparatively, the lumped-plasticity model (Model 2) exhibited an average error of 14% in the same aspect.  Regarding the cyclic response of infills, through extensive analysis, the Pinching4 material incorporated with lumped-plasticity model was found to be the most suitable option. However, the Concrete01 material achieved a good compromise between simplicity and accuracy. The average error of the cumulative energy dissipated was found to be approximately 20% and 17.8% for Concrete01 and Pinching4 materials, respectively. These findings contribute valuable insights to the understanding and modeling of infill walls, enhancing the overall reliability of seismic analyses in structural engineering.  Assessing collapse risk of RC frame buildings in Vancouver, BC, Canada was found that the mean annual frequency of collapse for the studied buildings ranged from 16 to 165 × 10−5, corresponding to collapse probabilities of 1% to 7.9% in 50 years. Ductile RC MRF buildings exhibited superior seismic collapse performance compared to moderately ductile RC MRF buildings due to their special reinforcement detailing and higher over-strength, crucial in preventing structural failure. 198  The analysis of the influence of structural configuration highlights its significant impact on the probability of collapse at 50 years. Moreover, comparative studies between 3- and 6-storey RC MRF buildings without infill demonstrate that the calculated mean annual frequency of collapse increases as the building height increases.  The presence of URM infill walls in RC MRF buildings improved their ability to resist higher ground motion intensities. However, there was an inconsistency in the collapse rate, with 6-storey RC MRF buildings exhibiting a higher rate compared to other buildings. The presence of infill walls was identified as key factor affecting collapse outcomes. It was also observed that shear failure reduces collapse fragility when compared to sideways collapse. These findings underscore the importance of considering structural configuration in seismic risk assessment and design considerations.  By comparing the mean annual frequency of collapse for ductile RC MRF buildings designed according to Canadian, American, and Italian codes, it was evident that the buildings designed under the Canadian code fell within a reasonable range of collapse risk when compared to American codes. However, significant variation was observed for buildings designed according to Italian codes.  The substructure approach based on the BNWF model, which separated the superstructure and substructure components, was implemented to analyze the SSI effect on the seismic response of RC MRF buildings. The findings proved that the foundation flexibility had an effect on the fundamental period of RC MRF buildings. However, the effect of SSI on the fundamental period was more pronounced in 3-storey buildings compared to 6-storey buildings, indicating that low-rise structures are more sensitive to SSI effects. 199  The findings also showed significant divergence between the median IDA curves due to the foundation's flexibility. SSI effects were found to substantially reduce the spectral acceleration values (Sa(T1)). Further, analysis on the various of foundation embedment depth indicated that buildings with surface foundations (Df = 0.0 m) exhibited higher vulnerability, while embedment depth stiffened the system and reduced seismic vulnerability.  The probabilistic fragilities derived from the fundamental mode spectral acceleration of the buildings further demonstrated that SSI effects under nonlinear soil behaviour and foundation embedment depth can considerably influence structural performance and fragility, increasing the seismic vulnerability. Therefore, the results emphasized that considering SSI with different foundation embedment depth effects is important in seismic design and analysis to accurately assess structural response and vulnerability. 6.2 Originality and Contribution The findings presented in this thesis significantly contribute to our understanding of the uncertainties associated with assessing the collapse fragility of infilled RC frame buildings. This research stands out as one of the few studies that comprehensively investigates the seismic risk of RC moment-resisting frames (MRFs) with unreinforced masonry (URM) infill walls. Through a comprehensive examination of critical failure mechanisms of URM infill wall, this study has developed a systematic guideline. This guideline serves as a valuable tool for selecting appropriate monotonic and hysteretic parameters, as well as infill strength and stiffness formulations, to construct a reliable computational strut model. This model is specifically designed to accurately evaluate the seismic performance of infilled RC frames, with a specific focus on in-200 plane lateral cyclic response. Notably, a single strut modeling method is employed and analyzed through the OpenSees software package, further enhancing the precision and reliability of the assessments. In contrast to the majority of existing studies that focus on non-ductile infilled-RC frames while neglecting the soil-structure interaction (SSI) effect, this research shifts the focus to address these previously neglected issues. Consequently, it leads to the development of seismic risk assessment tools for modern infilled-RC frames, taking into account the SSI effect. The proposed framework, which includes two levels of ductility design, enables engineers to make informed decisions regarding structural design based on alternative provisions in modern building codes. Furthermore, this research provides additional evidence on the necessity of considering soil-structure interaction at certain embedment foundation depth when assessing RC frame buildings. This insight supports the need for enhancing structural systems to reduce building risk, thereby reducing the potential for severe damage, economic losses, and human casualties caused by future earthquakes. Overall, this study provides significant contributions by offering guidelines for modeling techniques used in masonry infill walls. This study also presents a comprehensive framework for assessing modern reinforced concrete frames with masonry infill walls, taking into consideration the effect of soil-structure interaction. Finally, the study establishes collapse fragilities as reliable indicators for collapse, further enhancing the field's understanding in this area. 201 6.3 Limitations The work of the present study has certain limitations. 1. In the infill strut model, the guidelines developed to select an adequate strut model only focused on the different masonry compressive strengths, i.e., “weak” and “strong” infill panels and without openings. 2. It must be noted that this study focused on assessing the collapse risk assessment for low- and mid-rise RC frame buildings designed with ductile and moderately ductile in the Vancouver region of British Columbia (BC), Canada. 3. The SSI effect in this study is restricted to site class C soil, in which the consequence of the study just focused on the surface and embedded foundation. 4. The overall assessment only focused on the 2D model, which only considered the in-plane effect rather than the combined effect between the in-plane and out-of-plane effect. 6.4 Recommendations for Future Research In consideration of the conclusions presented above, it is recommended that future studies be conducted in the following areas: 1. Given the guidelines' limitations to selecting an adequate strut model, the procedures must be further implemented for medium-strength infill panels with openings. Besides, a sensitivity analysis needs to perform on the various 202 parameters of the infill panel, such as wall mortar strength, w/d ratio, and slenderness (aspect) ratio, to compare and select the trend of the lateral strength. 2. Further research is required to extend the results obtained in this study by focusing on different countries or cities in BC with significant seismicities, such as Victoria and Nanaimo; different layouts and materials; different numbers of stories (medium- or high-rise buildings); and different numbers of records. 3. The findings provided for the SSI effect in this study are restricted to foundations embedded in site class C soil. 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(a) (b) (c) (d) Figure A.1: IDA curves of the 3- and 6-storey bare RC MRF with SSI (Df=0.0); (a) 3S_D_NI, (b) 3S_MD_NI, (c) 6S_D_NI, and (d) 6S_MD_NI. 239 (a) (b) 240 (c) Figure A.2: IDA curves of the 3-storey RC MRF without and with SSI (Df=0.0 m and 1.0 m); (a) 3S_D_I_NSSI (b) 3S_D_I_SSI_Df1, and (c) 3S_D_I_SSI_Df0. 241 (a) (b) 242 (c) Figure A.3: IDA curves of the 3-storey RC MRF without and with SSI (Df=0.0 m and 1.0 m); (a) 3S_MD_I_NSSI (b) 3S_MD_I_SSI_Df1, and (c) 3S_MD_I_SSI_Df0. 243 (a) (b) 244 (c) Figure A.4: IDA curves of the 6-storey RC MRF without and with SSI (Df=0.0 m and 1.0 m); (a) 6S_D_I_NSSI (b) 6S_D_I_SSI_Df1, and (c) 6S_D_I_SSI_Df0. 245 (a) (b) 246 (c) Figure A.5: IDA curves of the 6-storey RC MRF without and with SSI (Df=0.0 m and 1.0 m); (a) 6S_MD_I_NSSI (b) 6S_MD_I_SSI_Df1, and (c) 6S_MD_I_SSI_Df0.
Thesis/Dissertation
eng
Civil Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Tesfamariam, Solomon
Seismic risk assessment of code-conforming reinforced concrete moment resisting frame buildings : consideration of unreinforced masonry infill wall and soil-structure interactions
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