ISTANBUL TECHNICAL UNIVERSITY  GRADUATE SCHOOL M.Sc. THESIS SEISMIC RISK OF SUBSTANDARD RC FRAMES WITH FOUNDATION SETTLEMENT Shahin HUSEYNLI Department of Civil Engineering Structure Engineering Programme FEBRUARY 2022 Department of Civil Engineering Structure Engineering Programme ISTANBUL TECHNICAL UNIVERSITY  GRADUATE SCHOOL SEISMIC RISK OF SUBSTANDARD RC FRAMES WITH FOUNDATION SETTLEMENT M.Sc. THESIS Shahin HUSEYNLI (501191057) Thesis Advisor: Assoc. Prof. Dr. Ufuk YAZGAN FEBRUARY 2022 İnşaat Mühendisliği Anabilim Dalı Yapı Mühendisliği Programı ŞUBAT 2022 İSTANBUL TEKNİK ÜNİVERSİTESİ  LİSANSÜSTÜ EĞİTİM ENSTİTÜSÜ TEMEL OTURMASINA MARUZ KALMIŞ STANDART ALTI BETONARME ÇERÇEVELERİN SİSMİK RİSKİ YÜKSEK LİSANS TEZİ Şahin HÜSEYNLİ (501191057) Tez Danışmanı: Doç. Dr. Ufuk YAZGAN v Thesis Advisor : Assoc. Prof. Dr. Ufuk YAZGAN .............................. Istanbul Technical University Jury Members : Prof. Dr. Alper İLKİ ............................. Istanbul Technical University Prof. Dr. Serdar SOYÖZ .............................. Boğaziçi University Shahin Huseynli, a M.Sc. student of ITU Graduate School student ID 501191057, successfully defended the thesis entitled “SEISMIC RISK OF SUBSTANDARD RC FRAMES WITH FOUNDATION SETTLEMENT”, which he prepared after fulfilling the requirements specified in the associated legislations, before the jury whose signatures are below. Date of Submission : 13 January 2022 Date of Defense : 1 February 2022 vi vii To my family, viii ix FOREWORD I would like to express my sincere gratitude to my supervisor, Dr. Ufuk Yazgan, for his continuous patience and dedication throughout the whole process. I consider myself really fortunate to have had the opportunity to work with such a proficient professor in his field. His way of thoroughly explaining the matter was quite enlightening to me. Without his guidance, this work would not have been completed. I acknowledge the funding provided by the Disaster and Emergency Management Presidency (AFAD) as a part of the project UDAP-Ç-21-34: “Monitoring of Surface Deformation in the Elazığ Sivrice Using Radar Remote Sensing.” I'm also grateful to Feras Abla, a member of our study team, for his company and exchange of useful information. Finally, I would like to extend my thanks to my family for their love and support. In particular, I would like to thank my lovely niece, Maryam, for keeping me motivated amid the challenging periods of the COVID-19 pandemic. January 2022 Shahin HUSEYNLI (Structural Engineer) x xi TABLE OF CONTENTS Page FOREWORD ............................................................................................................. ix TABLE OF CONTENTS ......................................................................................... xi ABBREVIATIONS ................................................................................................. xiii SYMBOLS ................................................................................................................ xv LIST OF TABLES ................................................................................................. xvii LIST OF FIGURES ................................................................................................ xix SUMMARY ............................................................................................................ xxv ÖZET.....................................................................................................................xxvii 1. INTRODUCTION .................................................................................................. 1 Problem Statement ............................................................................................. 1 Objective and Scope ........................................................................................... 3 Literature Review ............................................................................................... 5 1.3.1 Previous research on differential support settlement .................................. 5 1.3.2 State-of-the-art in the seismic performance of the buildings with settlement ............................................................................................................. 5 Overview ............................................................................................................ 8 2. CONCEPTUAL FRAMEWORK ......................................................................... 9 Static Analysis .................................................................................................. 10 Pushover Analysis ............................................................................................ 11 Seismic Fragility Analysis ............................................................................... 12 Risk Analysis ................................................................................................... 12 3. CASE STUDY BUILDING AND ANALYSIS MODEL .................................. 13 Case Study Building ......................................................................................... 13 Numerical Model ............................................................................................. 15 3.2.1 Material definitions ................................................................................... 15 3.2.2 Section definitions .................................................................................... 16 3.2.3 Element definitions ................................................................................... 17 3.2.4 Gravity loading ......................................................................................... 18 Performance Criteria ........................................................................................ 18 Settlement Profiles ........................................................................................... 19 Capacities ......................................................................................................... 20 Compatibility .................................................................................................... 21 Ground Motion Set and Dynamic Analysis ..................................................... 22 Seismic Hazard ................................................................................................. 23 4. DISCUSSION OF RESULTS ............................................................................. 27 Impact of Settlement on Internal Force Distributions ...................................... 27 4.1.1 Internal force distributions prior to settlement .......................................... 27 4.1.2 Redistribution of axial force demands following settlement .................... 29 4.1.3 Redistribution of bending moment demand following settlement ............ 38 4.1.4 Redistribution of shear demand following settlement .............................. 43 Pushover Analysis Results ............................................................................... 47 4.2.1 Direction of pushover loading .................................................................. 47 xii 4.2.2 Pushover analysis results prior to settlement ............................................ 48 4.2.3 Post-settlement pushover analysis results ................................................. 48 Incremental Dynamic Analysis Results ............................................................ 53 4.3.1 Impact of vertical excitation component ................................................... 54 4.3.2 Impact of shear failure ............................................................................... 55 4.3.3 Seismic fragility curves ............................................................................. 56 Risk Analysis Results ....................................................................................... 59 4.4.1 Impact of vertical excitation component ................................................... 60 4.4.2 Impact of shear failure ............................................................................... 60 4.4.3 Change in annual probability of collapse .................................................. 61 5. CONCLUSIONS AND RECOMMENDATIONS ............................................. 63 Conclusions ...................................................................................................... 63 Recommendations ............................................................................................ 65 REFERENCES ......................................................................................................... 67 APPENDICES .......................................................................................................... 71 APPENDIX A......................................................................................................... 72 APPENDIX B ......................................................................................................... 73 APPENDIX C ......................................................................................................... 76 APPENDIX D......................................................................................................... 77 APPENDIX E ......................................................................................................... 84 APPENDIX F ......................................................................................................... 90 CURRICULUM VITAE .......................................................................................... 93 xiii ABBREVIATIONS AFAD : Afet ve Acil Durum Yönetimi Başkanlığı (Disaster and Emergency Management Presidency) CDF : Cumulative Distribution Function ELSA : European Laboratory for Structural Assessment ICONS : Innovative Seismic Design Concepts for New and Existing Structures IDA : Incremental Dynamic Analysis IDR : Inter-story Drift Ratio IM : Intensity Measure JRC : Joint Research Centre MFDR : Modified Flexural Damage Ratio OpenSEES : Open System for Earthquake Engineering Simulation PDF : Probability Density Function PEER : Pacific Earthquake Engineering Research PGA : Peak Ground Acceleration PGV : Peak Ground Velocity PHA : Peak Horizontal Acceleration P-M : Axial load-Moment PSD : Pseudo-dynamic PSHA : Probabilistic Seismic Hazard Analysis RC : Reinforced Concrete SSI : Soil-Structure Interaction TBDY : Türkiye Bina Deprem Yönetmeliği (Turkish Seismic Code) TS : Turkish Standard xiv xv SYMBOLS Ac : Total section area bs : Strain hardening ratio b : Width of the section cR1 : Curvature degradation parameter cR2 : Curvature degradation parameter D : Damage d : Damage level Ec : Initial elastic stiffness of concrete Es : Initial elastic stiffness of steel fc : Concrete compressive strength fck : Characteristic compressive strength of concrete fct : Concrete tensile strength fy : Steel yield stress h : Depth of the section Lp : Plastic hinge length Mw : Moment magnitude R0 : Initial value of the curvature parameter R Rjb : Joyner-Boore distance S : Settlement amount Φ : Lognormal cumulative distribution function λ : Median σ : Standard deviation εc : Concrete strain at compressive strength εcu : Ultimate concrete strain capacity in compression εt : Ultimate concrete strain capacity in tension ø : Diameter of reinforcement bar xvi xvii LIST OF TABLES Page Table 3.1: Material properties. .................................................................................. 15 Table 3.2: Plastic hinge lengths. ............................................................................... 17 Table 3.3: Performance criteria. ................................................................................ 19 Table 3.4: Ground motion set. .................................................................................. 23 xviii xix LIST OF FIGURES Page Figure 1.1: Tilted and settled buildings observed in the 2011 Christchurch earthquake (Courtesy: Cubrinovski et al, 2011). ................................................. 1 Figure 1.2: Differentially settled buildings due to the 1999 Kocaeli Earthquake observed in (a) Adapazari (Courtesy: Earthquake Engineering Field Investigation Team) and (b) Izmit (Courtesy: DHA). ......................................... 2 Figure 1.3: Excavation failure next to a residential building in Gebze (Courtesy: Milliyet). .............................................................................................................. 2 Figure 1.4: (a) Tilting and sinking Millenium Tower (Courtesy: Beck Diefenbach/Reuters) and (b) a transit station that was constructed next to it (Courtesy: Melia Robinson/Business Insider). .................................................... 3 Figure 1.5: Collapsed Champlain Tower South and a multistory building that was built next to it (Courtesy: The Visual Journalism Team/BBC). .......................... 3 Figure 2.1: Hypothetical representation of seismic fragility analysis: (a) settlement definition and (b) its impact on seismic fragility curves. ................................... 10 Figure 3.1: (a) ICONS bare frame (Courtesy: Pinto et al, 1999) and (b) elevation view. ................................................................................................................... 14 Figure 3.2: Plan view of the ICONS frame (unit are in mm). .................................. 14 Figure 3.3: Stress-strain curves for (a) steel and (b) concrete. ................................. 16 Figure 3.4: Section details and their locations on the frame. .................................... 16 Figure 3.5: Gravity loading. ...................................................................................... 18 Figure 3.6: Settlement scenarios. .............................................................................. 19 Figure 3.7: Yield moments prior to settlement [kNm]. ............................................ 20 Figure 3.8: Shear capacities [kN]. ............................................................................ 20 Figure 3.9: Pushover analysis results and the actual hysteretic cycles exhibited during the experiment at third story (Courtesy: Pinho and Elnashai, 2000). ..... 21 Figure 3.10: Artificially generated accelerogram with a return period of 475 years that was applied in the experiment (Courtesy: SeismoSoft, 2021). ................... 22 Figure 3.11: Compatibility of the displacement-time history at the top floor with the experiment. ......................................................................................................... 22 Figure 3.12: Locations of sites on the Turkey Earthquake Hazard Map (Courtesy: AFAD). .............................................................................................................. 23 Figure 3.13: (a) PSHA data acquired from AFAD and (b) the logarithmic curve- fitting results. ..................................................................................................... 24 Figure 3.14: (a) PSHA results converted to an annual rates and (b) probability of annual seismic hazard at the sites. ..................................................................... 25 Figure 4.1: Case 0 – normalized axial force demands in (a) beams and (b) columns. ............................................................................................................................ 28 Figure 4.2: Case 0 – (a) axial load-moment interaction and (b) moment-curvature diagrams for ground-floor columns. .................................................................. 28 Figure 4.3: Case 0 – bending moment demands normalized to yield moments in (a) beams and (b) columns. ..................................................................................... 29 xx Figure 4.4: Case 0 – shear force demands normalized to shear capacities in (a) columns and (b) beams. ...................................................................................... 29 Figure 4.5: Case A with 1 cm of settlement – (a) normalized axial force demands and (b) percentage change with respect to Case 0. ............................................. 30 Figure 4.6: Case A with 2 cm of settlement – (a) normalized axial force demands and (b) percentage change with respect to Case 0. ............................................. 30 Figure 4.7: Case A with 3 cm of settlement – (a) normalized axial force demands and (b) percentage change with respect to Case 0. ............................................. 31 Figure 4.8: Case A – (a) axial load-moment interaction and (b) moment-curvature diagrams for C101. ............................................................................................. 31 Figure 4.9: Case A – (a) axial load-moment interaction and (b) moment-curvature diagrams for C102. ............................................................................................. 32 Figure 4.10: Case A – (a) axial load-moment interaction and (b) moment-curvature diagrams for C103. ............................................................................................. 32 Figure 4.11: Case A – (a) axial load-moment interaction and (b) moment-curvature diagrams for C104. ............................................................................................. 32 Figure 4.12: Case B with 1 cm of settlement – (a) normalized axial force demands and (b) percentage change with respect to Case 0. ............................................. 33 Figure 4.13: Case B with 2 cm of settlement – (a) normalized axial force demands and (b) percentage change with respect to Case 0. ............................................. 33 Figure 4.14: Case B with 3 cm of settlement – (a) normalized axial force demands and (b) percentage change with respect to Case 0. ............................................. 34 Figure 4.15: Case B – (a) axial load-moment interaction and (b) moment-curvature diagrams for C101. ............................................................................................. 34 Figure 4.16: Case B – (a) axial load-moment interaction and (b) moment-curvature diagrams for C102. ............................................................................................. 34 Figure 4.17: Case B – (a) axial load-moment interaction and (b) moment-curvature diagrams for C103. ............................................................................................. 35 Figure 4.18: Case B – (a) axial load-moment interaction and (b) moment-curvature diagrams for C104. ............................................................................................. 35 Figure 4.19: Case C with 1 cm of settlement – (a) normalized axial force demands and (b) percentage change with respect to Case 0. ............................................. 36 Figure 4.20: Case C with 2 cm of settlement – (a) normalized axial force demands and (b) percentage change with respect to Case 0. ............................................. 36 Figure 4.21: Case C with 3 cm of settlement – (a) normalized axial force demands and (b) percentage change with respect to Case 0. ............................................. 36 Figure 4.22: Case C – (a) axial load-moment interaction and (b) moment-curvature diagrams for C101. ............................................................................................. 37 Figure 4.23: Case C – (a) axial load-moment interaction and (b) moment-curvature diagrams for C102. ............................................................................................. 37 Figure 4.24: Case C – (a) axial load-moment interaction and (b) moment-curvature diagrams for C103. ............................................................................................. 37 Figure 4.25: Case C – (a) axial load-moment interaction and (b) moment-curvature diagrams for C104. ............................................................................................. 38 Figure 4.26: Case A with 1 cm of settlement – bending moment demands normalized to yield moments in (a) beams and (b) columns. ............................ 39 Figure 4.27: Case A with 2 cm of settlement – bending moment demands normalized to yield moments in (a) beams and (b) columns. ............................ 39 Figure 4.28: Case A with 3 cm of settlement – bending moment demands normalized to yield moments in (a) beams and (b) columns. ............................ 39 xxi Figure 4.29: Case B with 1 cm of settlement – bending moment demands normalized to yield moments in (a) beams and (b) columns. ............................ 40 Figure 4.30: Case B with 2 cm of settlement – bending moment demands normalized to yield moments in (a) beams and (b) columns. ............................ 40 Figure 4.31: Case B with 3 cm of settlement – bending moment demands normalized to yield moments in (a) beams and (b) columns. ............................ 41 Figure 4.32: Case C with 1 cm of settlement – bending moment demands normalized to yield moments in (a) beams and (b) columns. ............................ 42 Figure 4.33: Case C with 2 cm of settlement – bending moment demands normalized to yield moments in (a) beams and (b) columns. ............................ 42 Figure 4.34: Case C with 3 cm of settlement – bending moment demands normalized to yield moments in (a) beams and (b) columns. ............................ 42 Figure 4.35: Case A with 1 cm of settlement – shear demands normalized to shear capacities in (a) columns and (b) beams. ........................................................... 43 Figure 4.36: Case A with 2 cm of settlement – shear demands normalized to shear capacities in (a) columns and (b) beams. ........................................................... 43 Figure 4.37: Case A with 3 cm of settlement – shear demands normalized to shear capacities in (a) columns and (b) beams. ........................................................... 44 Figure 4.38: Case B with 1 cm of settlement – shear demands normalized to shear capacities in (a) columns and (b) beams. ........................................................... 44 Figure 4.39: Case B with 2 cm of settlement – shear demands normalized to shear capacities in (a) columns and (b) beams. ........................................................... 45 Figure 4.40: Case B with 3 cm of settlement – shear demands normalized to shear capacities in (a) columns and (b) beams. ........................................................... 45 Figure 4.41: Case C with 1 cm of settlement – shear demands normalized to shear capacities (a) columns and (b) beams. ............................................................... 46 Figure 4.42: Case C with 2 cm of settlement – shear demands normalized to shear capacities in (a) columns and (b) beams. ........................................................... 46 Figure 4.43: Case C with 3 cm of settlement – shear demands normalized to shear capacities in (a) columns and (b) beams. ........................................................... 46 Figure 4.44: Case B with 2 cm of settlement – pushover curves in both directions. 48 Figure 4.45: Case 0 – (a) pushover curve and (b) plastic hinge formation diagram. 48 Figure 4.46: Case A with 1 cm of settlement – (a) pushover curve and (b) plastic hinge formation diagram. ................................................................................... 49 Figure 4.47: Case A with 2 cm of settlement – (a) pushover curve and (b) plastic hinge formation diagram. ................................................................................... 49 Figure 4.48: Case A with 3 cm of settlement – (a) pushover curve and (b) plastic hinge formation diagram. ................................................................................... 49 Figure 4.49: Case B with 1 cm of settlement – (a) pushover curve and (b) plastic hinge formation diagram. ................................................................................... 50 Figure 4.50: Case B with 2 cm of settlement – (a) pushover curve and (b) plastic hinge formation diagram. ................................................................................... 50 Figure 4.51: Case B with 3 cm of settlement – (a) pushover curve and (b) plastic hinge formation diagram. ................................................................................... 51 Figure 4.52: Case C with 1 cm of settlement – (a) pushover curve and (b) plastic hinge formation diagram. ................................................................................... 51 Figure 4.53: Case C with 2 cm of settlement – (a) pushover curve and (b) plastic hinge formation diagram. ................................................................................... 51 Figure 4.54: Case C with 3 cm of settlement – (a) pushover curve and (b) plastic hinge formation diagram. ................................................................................... 52 xxii Figure 4.55: Case D with 1 cm of settlement – (a) pushover curve and (b) plastic hinge formation diagram. ................................................................................... 52 Figure 4.56: Case D with 2 cm of settlement – (a) pushover curve and (b) plastic hinge formation diagram. ................................................................................... 52 Figure 4.57: Case D with 3 cm of settlement – (a) pushover curve and (b) plastic hinge formation diagram. ................................................................................... 53 Figure 4.58: Maximum strains in (a) compression and (b) tension prior to ground motion. ................................................................................................................ 54 Figure 4.59: Case A with 2 cm of settlement – axial load ratios in C302 (a) without and (b) with a vertical excitation component at 10 cm/s PGV during Kocaeli record. ................................................................................................................. 54 Figure 4.60: Case A with 1 cm of settlement – seismic fragility curves for complete damage level without and with a vertical excitation component. ...................... 55 Figure 4.61: Case 0 – seismic fragility curves for complete damage level without and with shear failure. ........................................................................................ 55 Figure 4.62: Case A – seismic fragility curves for (a) slight, (b) moderate, and (c) complete damage levels. ..................................................................................... 56 Figure 4.63: Case B – seismic fragility curves for (a) slight, (b) moderate, and (c) complete damage levels. ..................................................................................... 57 Figure 4.64: Case C – seismic fragility curves for (a) slight, (b) moderate, and (c) complete damage levels. ..................................................................................... 58 Figure 4.65: Case D – seismic fragility curves for (a) slight, (b) moderate, and (c) complete damage levels. ..................................................................................... 59 Figure 4.66: Change in the median collapse capacity for all cases. .......................... 59 Figure 4.67: Case B – annual probability of collapse at site B without and with a vertical excitation component. ........................................................................... 60 Figure 4.68: Case B – annual probability of collapse at site B without and with shear failure consideration. .......................................................................................... 60 Figure 4.69: Case A – annual probability of collapse at (a) site A and (b) site B..... 61 Figure 4.70: Case B – annual probability of collapse at (a) site A and (b) site B. .... 61 Figure 4.71: Case C – annual probability of collapse at (a) site A and (b) site B. .... 62 Figure 4.72: Case D – annual probability of collapse at (a) site A and (b) site B..... 62 Figure A.1: Boundary conditions and settlement definitions. ................................... 72 Figure B.1: Case A – yield moments after (a) 1 cm, (b) 2 cm, and (c) 3 cm of settlement. ........................................................................................................... 73 Figure B.2: Case B – yield moments after (a) 1 cm, (b) 2 cm, and (c) 3 cm of settlement. ........................................................................................................... 74 Figure B.3: Case C – yield moments after (a) 1 cm, (b) 2 cm, and (c) 3 cm of settlement. ........................................................................................................... 75 Figure C.1: Plan view of the foundation attached to the strong floor. ...................... 76 Figure C.2: Section details of the foundation attached to the strong floor. .............. 76 Figure D.1: Case 0 – pushover analysis results in positive (top) and negative (bottom) direction ............................................................................................... 77 Figure D.2: Case A with 1 cm of settlement – pushover analysis results in positive (top) and negative (bottom) direction. ................................................................ 77 Figure D.3: Case A with 2 cm of settlement – pushover analysis results in positive (top) and negative (bottom) direction. ................................................................ 78 Figure D.4: Case A with 3 cm of settlement – pushover analysis results in positive (top) and negative (bottom) direction. ................................................................ 78 xxiii Figure D.5: Case B with 1 cm of settlement – pushover analysis results in positive (top) and negative (bottom) direction. ............................................................... 79 Figure D.6: Case B with 2 cm of settlement – pushover analysis results in positive (top) and negative (bottom) direction. ............................................................... 79 Figure D.7: Case B with 3 cm of settlement – pushover analysis results in positive (top) and negative (bottom) direction. ............................................................... 80 Figure D.8: Case C with 1 cm of settlement – pushover analysis results in positive (top) and negative (bottom) direction. ............................................................... 80 Figure D.9: Case C with 2 cm of settlement – pushover analysis results in positive (top) and negative (bottom) direction. ............................................................... 81 Figure D.10: Case C with 3 cm of settlement – pushover analysis results in positive (top) and negative (bottom) direction. ............................................................... 81 Figure D.11: Case D with 1 cm of settlement – pushover analysis results in positive (top) and negative (bottom) direction. ............................................................... 82 Figure D.12: Case D with 2 cm of settlement – pushover analysis results in positive (top) and negative (bottom) direction. ............................................................... 82 Figure D.13: Case D with 3 cm of settlement – pushover analysis results in positive (top) and negative (bottom) direction. ............................................................... 83 Figure E.1: Case A – seismic fragility curves for slight damage level (a) without and (b) with a vertical excitation component............................................................ 84 Figure E.2: Case A – seismic fragility curves for moderate damage level (a) without and (b) with a vertical excitation component. .................................................... 84 Figure E.3: Case A – seismic fragility curves for complete damage level (a) without and (b) with a vertical excitation component. .................................................... 84 Figure E.4: Case B – seismic fragility curves for slight damage level (a) without and (b) with a vertical excitation component............................................................ 85 Figure E.5: Case B – seismic fragility curves for moderate damage level (a) without and (b) with a vertical excitation component. .................................................... 85 Figure E.6: Case B – seismic fragility curves for complete damage level (a) without and (b) with a vertical excitation component. .................................................... 85 Figure E.7: Case C – seismic fragility curves for slight damage level (a) without and (b) with a vertical excitation component............................................................ 86 Figure E.8: Case C – seismic fragility curves for moderate damage level (a) without and (b) with a vertical excitation component. .................................................... 86 Figure E.9: Case C – seismic fragility curves for complete damage level (a) without and (b) with a vertical excitation component. .................................................... 86 Figure E.10: Case D – seismic fragility curves for slight damage level (a) without and (b) with a vertical excitation component. .................................................... 87 Figure E.11: Case D – seismic fragility curves for moderate damage level (a) without and (b) with a vertical excitation component........................................ 87 Figure E.12: Case D – seismic fragility curves for complete damage level (a) without and (b) with a vertical excitation component........................................ 87 Figure E.13: Case A – annual probability of collapse at (a) site A (b) site B without and with a vertical excitation component. ......................................................... 88 Figure E.14: Case B – annual probability of collapse at (a) site A (b) site B without and with a vertical excitation component. ......................................................... 88 Figure E.15: Case C – annual probability of collapse at (a) site A (b) site B without and with a vertical excitation component. ......................................................... 88 Figure E.16: Case D – annual probability of collapse at (a) site A (b) site B without and with a vertical excitation component. ......................................................... 89 xxiv Figure F.1: Case A – seismic fragility curves for complete damage level (a) without and (b) with shear failure. ................................................................................... 90 Figure F.2: Case B – seismic fragility curves for complete damage level (a) without and (b) with shear failure. ................................................................................... 90 Figure F.3: Case C – seismic fragility curves for complete damage level (a) without and (b) with shear failure. ................................................................................... 90 Figure F.4: Case D – seismic fragility curves for complete damage level (a) without and (b) with shear failure. ................................................................................... 91 Figure F.5: Case A – annual probability of collapse at (a) site A (b) site B without and with shear failure. ........................................................................................ 91 Figure F.6: Case B – annual probability of collapse at (a) site A (b) site B without and with shear failure. ........................................................................................ 91 Figure F.7: Case C – annual probability of collapse at (a) site A (b) site B without and with shear failure. ........................................................................................ 92 Figure F.8: Case D – annual probability of collapse at (a) site A (b) site B without and with shear failure. ........................................................................................ 92 xxv SEISMIC RISK OF SUBSTANDARD RC FRAMES WITH FOUNDATION SETTLEMENT SUMMARY Foundation settlement is one of the most common problems in buildings. Situations such as poorly administered deep excavations and soil liquefaction cause ground deformation and thus trigger the settlement of nearby buildings. Substandard RC buildings may suffer substantial damage from foundation settlements, and seismic effects exacerbate the problem. Although the seismic risk of buildings exposed to settlement has been studied by some researchers, in the majority of them, interstory drift ratios (IDRs) have been used as the key response parameter. However, because settlement causes considerable strain on structural elements, the stresses in critical regions of structural elements may approach their flexural capacity even when lateral deformations are very low. Therefore, the strain-based approach was employed in the study. As the case study building, a substandard RC frame with poor concrete quality and inadequate tranverse reinforcement is studied. It is numerically modelled using OpenSees software framework, and the simulated response is validated using data from an earlier experiment. Elements are defined using a force-based approach, and fiber-sections are used in the section definitions to capture the axial force-moment interaction. A number of settlement profiles are applied to the frame, each with a specific range of settlement amounts. First, the redistribution of internal forces following settlement is examined. The findings of the static analysis show that the internal force distributions change substantially following the settlement. Members near the settled area experience a significant increase in axial, shear, and bending moment demands. In some cases, flexural and shear demands exceed capacity. The results of the pushover analysis lead to some remarkable observations as well. The direction of pushover loading has been demonstrated to have a considerable effect. The type of failure and the collapse mechanism are demonstrated to be dependent on the settlement profile. It is shown that the maximum base shear and drift ratio at ultimate displacement capacity decrease significantly as the settlement amount increases. Incremental dynamic analyzes (IDA) are performed using a ground motion set scaled to a specific intensity range. To construct seismic fragility curves, the amount of settlement is added as a new independent parameter to the conventional functional form. A set of damage states are defined based on resultant strains. Two sites with different seismic activity rates are chosen as the case study sites, and the seismic hazard associated with each is identified. Seismic fragility analysis data and seismic hazard information are combined to calculate the annual probability of collapse. The presence of a vertical excitation component as well as consideration of shear failure are found to have a significant influence on the seismic fragility analysis results. xxvi The median collapse capacity decreases by up to 26% due to foundation settlement. The annual probability of collapse increases by 0.5% as an outcome of this reduction in the median capacity. xxvii TEMEL OTURMASINA MARUZ KALMIŞ STANDART ALTI BETONARME ÇERÇEVELERİN SİSMİK RİSKİ ÖZET Temel oturması binalarda çok sık gözlemlenen sorunlardan biridir. Binanın yakınında iyi yönetilmeyen derin kazı bulunması ve deprem zamanı gerçekleşen toprak sıvılaşması gibi durumlar zemin deformasyonuna sebep olur ve dolayısıyla da yakındaki binaların temelinin oturmasını tetikler. Bu gibi olayların yüksek kaliteli malzemeden oluşan ve iyi tasarlanmış binalarda bile ciddi sorunlar oluşturduğu görülmüştür. Düşük dayanımlı ve yetersiz temel taşıma kapasitesi olan zeminlerde bulunan betonarme yapılarda bu konu daha da fazla ciddiyet kazanır. Binaların sismik davranışının temel oturmalarından nasıl etkilendiği yeterince araştırılmamıştır. Oturmaya maruz kalmış binaların deprem riski konusu bazı araştırmacılar tarafından incelense de, genelde bu çalışmarda hasar sınır durumu göreli kat ötelemeleri esas alınarak ifade edilmiştir. Ama, oturma gerçekleştiği zaman yapı elemanlarında önemli ölçüde gerinim oluşduğundan, yanal deformasyonlar çok düşük olduğunda bile kritik bölgelerdeki yapı elemanlarının gerinimleri kırılma kapasitesine yaklaşabilir. Bu etki, hasar seviyesinin yalnızca göreli kat ötelemeri sınırları esas alınarak tanımlandığı durumda göz önüne alınamamaktadır. Bu yüzden, çalışmada birim şekilde değiştirme esaslı yaklaşım kullanılmıştır. Özellikle gelişmekte olan ülkelerin bina stoğunun büyük bir kısmını düşük dayanımlı betonarme yapıları kapsadığından, bu çalışmada farklı oturmaların standart altı betonarme binaların sismik riski üzerindeki etkisi incelenmiştir. İtalyada ELSA laboratuvarında test edilmiş ICONS çerçevesi üzerine örnek olay incelemesi yapılmıştır. Bu çerçeve Güney Avrupa ülkelerinde 1950’lerde inşa edilmiş tipik standart altı betornarme binaları temsil etmektedir. Beton basınç dayanımı düşük ve sünekliğinin yetersiz olması nedeniyle ülkemizdeki standart altı yapıları da belirli bir oranda temsil ettiği söylenebilir. OpenSees yazılımı kullanılarak binanın sayısal modeli oluşturulmuş ve sonuçların deneyle uyumluluğu doğrulanmıştır. Eksenel kuvvetle eğilme momentinin etkileşimini incelemek için, eleman tanımında kuvvete dayalı yaklaşım ve fiber tabanlı bir sonlu eleman modeli kullanılmıştır. Oturma profiline özel bir analiz çalışmanın kapsamı dışında olmasına rağmen çerçeveye bir dizi potansiyel oturma profili uygulanmıştır. Dört farklı oturma durumu belirlenmiş ve her durumda üç farklı oturma miktarı seviyesi incelenmiştir. Elde edilen sonuçlar, oturmaya maruz kalmamış durumla karşılaştırılmıştır. İlk önce, oturmayı takiben iç kuvvetlerinin yeniden dağılımı incelenmiştir. Statik analiz bulguları, oturma sonrasında iç kuvvet dağılımlarının önemli ölçüde değiştiğini göstermektedir. Oturma bölgesi yakınındaki elemanlarda, eksenel kuvvet, eğilme momenti ve kesme kuvveti taleplerinde kayda değer bir artış gözlenmiştir. Oturma miktarı arttıkça, akma momentinin ve kesme kapasitesinin büyük bir kısmının xxviii tüketildiği görülmüştür. Bazı ekstrem durumlarda, eğilme ve kesme taleplerinin kapasiteyi aştığı gözlemlenmiş ve dolayısıyla oturmaların sismik etki olmaksızın bile göçmeye sebep olabileceği gösterilmiştir. Statik analizin yanı sıra, farklı oturmaların binanın yanal yükler altındaki davranışını nasıl etkilediğini incelemek için tüm oturma durumları için itme analizi yapılmıştır. Yanal yük hem pozitif hem de negatif yönde etkitilmiş ve elde edilen sonuçlar karşılaştırılmıştır. Sonuçlar, yükleme yönünün ciddi etkiye sahip olduğunu ve bu gibi çalışmalarda her iki yönü dikkate almak gerektiğini göstermektedir. Oturma miktarı arttıkça maksimum taban kesme kuvvetinde ve göreli kat ötelemelerinde sırasıyla %15 ve %44’e varan azalma gözlemlenmiştir. İtme analizi sonuçları esas alınarak oturmanın plastik mafsal oluşumu üzerindeki etkisi de araştırılmıştır. Kırılma türü ve göçme mekanizmasının, oturma profiliyle doğrudan ilgili olduğu görülmüştür. Bazı profiller için düşük oturma seviyelerinde eğilme kırımlası etkin olsa da ileri seviyelerde kesme kırılmasının daha etkin olabildiği tespit edilmiştir. Her oturma profilinde farklı plastik mafsal dağılımı gözlemlenmiştir. Kırılmanın gerçekleştiği bölgenin bile bazı durumlarda değiştiği görülmüştür. Bu değişimlerin binanın deprem riskini nasıl etkileyeceğini araştırmak için ilk önce sismik kırılganlık analizi yapılmıştır. Sismik kırılganlık eğrileri artımsal dinamik analiz sonuçlarından yola çıkarak oluşturulmuştur. Analizde, belirli bir şiddet aralığına ölçeklenmiş bir yer hareketi seti kullanılmış ve ivme kayıtlarının düşey bileşeni de dikkate alınmıştır. Genel kırılganlık fonksiyonuna ek parametre olarak oturma miktarı eklenmiştir. Performans seviyeleri hafif, orta ve ağır hasar olarak kategorize edilmiştir. Belli bir oturma miktarı ve şiddet ölçüsünde gerinimler hesaplanmış ve onların hasar sınırlarını ayrı-ayrı geçip geçmediği kontrol edilmiştir. Bundan başka her seviyede kesme taleplerinin kapasiteyi aşması durumu da araştırılmıştır. Kirişlerin kesme kırılması orta hasar, kolonların kesme kırılmasıysa ağır hasar olarak nitelendirilmiştir. Sonuçlardan yararlanarak sismik kırılganlık fonksiyonuna göre her hasar seviyesinin geçilme olasılığı hesaplanmış ve sismik kırılganlık eğrileri oluşturulmuştur. Yer hareketlerinin sadece yatay bileşeni kullanılarak hesap yapıldığında eksenel yük oranı sadece çerçeve etkisi yüzünden değişir. İvme kaydının düşey bileşeni de dikkate alındığındaysa eksenel yük oranı dağılımında ekstra etki gözlemlenir. Her iki durum karşılaştırıldığında bunun sismik kırılganlık üzerinde önemli ölçüde fark yarattığı gözlemlenmiştir. Her aşamada kesme kırılmasıyla eğilme kırılmasının hangisinin daha önce gerçekleştiği kontrol edilmiştir. Ağır hasar eğrileri daha erken gerçekleşen kırılma türü esasında belirlenmiştir. Kesme kırılmalarının da dikkate alınmasının sismik kırılganlık analizi sonuçları üzerinde önemli bir etkiye sahip olduğu görülmüştür. Tüm durumlar incelendiğinde, medyan göçme kapasitesinde temel oturması nedeniyle %26’ya varan azalma gözlemlenmiştir. Bazı durumlarda, göçme kapasitesindeki değişim az olsa bile, hafif ve orta hasar seviyelerindeki medyan kapasite ciddi oranda azalmıştır. Böyle durumlarda binanın göçme olasılığı pek fazla değişmese bile, çok düşük şiddetli depremler gerçekleştiğinde bile onarılamayacak duruma gelebilir. Elde edilen sismik kırılganlık analizi sonuçlarının binaların deprem riski üzerinde ne kadar etki yaratabileceği incelenmiştir. Türkiye dahilinde farklı sismik aktivite oranlarına sahip iki bölge seçilmiştir. Türkiye Deprem Tehlike Haritası üzerinden o bölgelerin ZB yerel zemin sınıfına denk gelen sismik tehlike verileri alınmıştır. Her iki bölgenin 50 yılda aşılma olasığı %2, %10, %50 ve %68 olan en büyük yer hızı xxix değerleri alınmıştır ve olasılığa dayalı sismik tehlike eğrileri oluşturulmuştur. Daha sonra, bu değerler Poisson’un yineleme modeli kullanılarak yıllık olasılıklara dönüştürülmüştür. Elde edilen yıllık tehlike sonuçları, sismik kırılganlık analizi verileriyle birlikte kullanılarak yıllık göçme olasılığı hesaplanmıştır. İvme kayıtlarının düşey bileşeninin ve kesme kırılmasının dikkate alınmasının sismik risk üzerinde de büyük etkisi oluğu gözlenmiştir. Tüm durumlarda, oturma miktarı arttıkça, yıllık göçme olaslığının da arttığı görülmüştür. Bazı ekstrem durumlarda, yıllık göçme olasılığında %132 daha yüksek rakamlara ulaşılmıştır. Sismik aktivite oranı düşük olan bölgede de benzer durum sözkonusu. Dolayısıyla, sismik aktivite oranı düşük bölgede yerleşse bile, oturma miktarı yüksek olan bir binanın deprem riski yine yüksek olacaktır. xxx 1 1. INTRODUCTION Problem Statement Foundation settlement in buildings is a well-known phenomenon. Settlement that develops uniformly along the supports does not constitute a significant risk. When the foundation shifts differentially into the soil, however, it creates a greater danger. Non- uniform (i.e., differential) settlements may be attributed to numerous conditions. They are usually triggered by earthquakes or nearby deep excavations, according to prevailing view. Earthquake-induced settlements occur when the soil liquefies or loses its bearing capacity. Differential settlements have been observed in the aftermath of many earthquake events (Bray and Dashti, 2014). The two instances of settlement that occurred during the 2011 Christchurch earthquake are displayed in Figure 1.1 (Cubrinovski et al, 2011). Both buildings were demolished following the incident because they were deemed unviable for repair. During the 1999 Kocaeli earthquake, similar occurrences were documented. Figure 1.2a shows the two buildings in Adapazari that were subjected to extreme levels of differential settlements (Bird et al, 2006). Figure 1.2b shows a building in Izmit that was tilted in the 1999 Kocaeli earthquake yet was occupied for a long period afterward (Ayaz and Koyuncu, 2021). Figure 1.1: Tilted and settled buildings observed in the 2011 Christchurch earthquake (Courtesy: Cubrinovski et al, 2011). 2 (a) (b) Figure 1.2: Differentially settled buildings due to the 1999 Kocaeli Earthquake observed in (a) Adapazari (Courtesy: Earthquake Engineering Field Investigation Team) and (b) Izmit (Courtesy: DHA). Poorly administered excavations that result in ground deformations are another key issue, as they may cause neighboring buildings to settle. Concerns about excavation- induced differential settlements are growing as the number of projects requiring deep excavations continues to expand. Figure 1.3 illustrates an example of such an incident. In Gebze, a landslide caused excavation near a building to fail (Koyuncu et al, 2021). Due to potential threats, including the structure's excessive settlement, the residents of the building have been evacuated. Figure 1.3: Excavation failure next to a residential building in Gebze (Courtesy: Milliyet). According to conjecture, some incidents may have occurred as a result of excavation- induced ground deformations. As indicated in Figure 1.4, the Millenium Tower in San Francisco has been tilted and sunk 5 cm in the northwest direction and 40 cm in the vertical direction, respectively (Bendix, 2018). Settlements allegedly began to grow following the construction of an adjacent transit station. What caused the collapse of the Champlain Towers South building in Surfside is still a matter of speculation. Two years before the building collapsed, a multistory 3 residential building (Eighty Seven Park) was constructed next to it, as shown in Figure 1.5 (BBC, 2021). It is postulated that ground deformations may have evolved at the time of the construction. (a) (b) Figure 1.4: (a) Tilting and sinking Millenium Tower (Courtesy: Beck Diefenbach/Reuters) and (b) a transit station that was constructed next to it (Courtesy: Melia Robinson/Business Insider). Figure 1.5: Collapsed Champlain Tower South and a multistory building that was built next to it (Courtesy: The Visual Journalism Team/BBC). As the data suggests, foundation settlement may occur even in structures with sufficient material quality and foundation details. Thus, substandard reinforced concrete buildings with poor foundations are far more vulnerable, and when the seismic effect is paired with the settlement effect, the consequences can be disastrous. Objective and Scope The core objective of this study is to assess the impact of foundation settlements on the seismic vulnerability of substandard RC frames. The research's other key objective is to analyze how the change in seismic fragility affects the seismic risk of buildings. 4 The existence of relative settlement is not taken into account in the conventional seismic assessment frameworks. Structural engineers rely on geotechnical engineers for sufficient details on the foundation to be constructed. For the new buildings, there are new tools for improving the ground and new machinery for building very strong foundations. However, soil conditions are often very poor, and the foundations of existing buildings are often quite weak. Thus, relative settlements occur, and infill walls exhibit cracks (in a single direction) as a result of these settlements. Because they are not structural elements, this is frequently overlooked. However, as a result of differential settlement, the axial loads in the adjacent columns rise, the system's entire hinge mechanism shifts, and the internal forces imposed by relative settlement distort the view. As a result of the shift in moment distribution, the structure gets pre- deformed prior to any ground motion, which changes the fragility substantially. Hence, the quantity of settlement has a direct influence on fragility, but it is not well quantified in the literature. Some preliminary research has been done to investigate this behavior, but it is insufficient to quantify the relationship. This has yet to be quantified in seismically active regions with substandard reinforced concrete structures. The main purpose of this study is to quantify this impact. This study investigates a substandard RC frame used as a case study building. In seismic fragility analysis, conventionally, inter-story drift ratios (IDRs) are used as the response parameter for defining damage limits. However, strain-based performance assessment was employed in this investigation. Because differential settlements may generate large strains in the members, even when lateral deformations are comparatively small. There are some limitations of the study. The studied impact of foundation settlements is limited to a single case. Loads are defined only by their equivalent regular distribution. Stochastic live load combinations have not been investigated. This research does not examine the geotechnical aspects of settlement profiles. However, a variety of settlement profiles have been considered. The redistribution of internal forces is the starting point for the study, and the impact of creep effects is beyond the scope. The influence of SSI, which takes into consideration soil and foundation flexibility, is also outside the scope of this research. It should also be highlighted that there is no experimental validation for the settlement analysis. Settlement values are just applied as an additional degree of freedom in the numerical model. 5 Literature Review 1.3.1 Previous research on differential support settlement The response of buildings to ground movements has been the central theme of many studies. Some researchers have investigated the particular impact of excavation and tunneling work on buildings. Others, on the other hand, concentrated on soil liquefaction and structural damage following an earthquake. The common concern of these studies, however, has been differential support settlements. Earlier research on this topic focuses on settlements caused by the building's own weight or nearby excavation and tunneling. The damage assessments of differential settlements have been widely discussed in the literature. Several damage categories were specified by Skempton and Macdonald (1956), Boscardin and Cording (1989), Burland (1997), and Day and Boone (1998). The criteria developed by these researchers are still employed in investigations studying the impacts of settlements. Differential settlements caused by liquefaction have also been investigated in the past decades. Bird et al. (2005) have developed a framework to assess the structural damage due to liquefaction-induced ground deformations. Several recommendations have been made by Bray and Dashti (2014) for predicting liquefaction-induced differential settlement of buildings. The effect of liquefaction-induced differential settlements on the fragility of low-code RC frames has been investigated by Fotopoulou et al. (2018). Despite the fact that fragility curves were created using a strain-based approach, the study is based on static analysis results. According to the results, the probability of damage drastically increases as the settlement amount increases. Even when a building is only subjected to gravity loads, it is clear that differential settlements may cause significant damage. 1.3.2 State-of-the-art in the seismic performance of the buildings with settlement Some researchers have also studied the seismic behavior of buildings that have experienced foundation settlements. These studies are reviewed in the following paragraphs. Mo and Hwang (1997) investigated the seismic response of a reinforced concrete structure to deep excavation-induced settlements. A comparative study was carried out at various stages of the excavation construction. They discovered that as the excavation 6 progresses, the adjacent structure's settlement increases. In the analysis, four different cases of material properties have been examined. The structure was subjected to the 1940 El Centro record, and damage was assessed in terms of roof displacements and MFDRs proposed by Roufaiel and Meyer (1987). The results suggest that as the excavation advances, the roof displacement rises by up to 30% and the number of steel yielding points increases. Steel yield stress has been shown to have a larger impact on a structure's seismic behavior than concrete compressive strength. The seismic vulnerability of differential settlements in an eight-story reinforced concrete building near a deep excavation was studied by Castaldo and Iuliis (2014). The authors created a comparative analysis for a real-world case study's before and after excavation scenarios. First, geotechnical and excavation system models were developed to estimate the foundation settlement. Then non-linear dynamic analysis was performed on the structural model to evaluate the seismic response of the superstructure. The 1980 Irpinia earthquake record has been applied to the structure, and the seismic vulnerability has been evaluated using seismic damage indices and maximum inter-story drifts. The seismic damage index developed by Park and Ang (1985) was employed for cumulative damage, and ductility demand in terms of rotations was utilized for non-cumulative damage. After excavation, rotations have been shown to increase at all plastic hinge regions. The findings of the damage indices reveal a 4.26% increase in the cumulative damage and a 6.35% increase in the non-cumulative damage. Interstory drifts are likewise greater at all levels for the post- excavation configuration. The authors argue that the variations in the parameters used to quantify seismic vulnerability are too great to be ignored. Another real-world case study has been investigated by Yeganeh et al. (2015). The dynamic response of a 17-story RC frame adjacent to a deep excavation was investigated. Tiltmeters were installed in a column of the building and load cells were mounted on the anchors of the excavation wall to validate the numerical model. The study looked at three types of models: fixed-based, soil-structure-interaction, and soil- structure-excavation interaction. The settlement profiles for the latter two scenarios have been determined, and the models have been subjected to three different ground motions. The study employed several damage categories to measure the associated damage induced by differential settlement. The findings reveal that the damage category shifts from 0 to 1 based on the Day criterion. Very slight and slight damage 7 have been detected, according to Burland and Boscarding and Cording criteria, respectively. Akhtarpour and Mortazaee (2018) analyzed the same case study building utilizing similar methodology as in Yeganeh et al. (2015). Based on static and dynamic analysis results, the authors first address the change in internal force distributions following the settlement. The distributions of axial force and bending moment exhibited significant variations. In the interaction models, base shear, PHA, and inter-story drifts were found to be up to 43%, 78%, and 35% lower, respectively. The nonlinear dynamic response of 5, 10, and 15-story RC frames next to a deep excavation was studied by Fadavi and Mortezaei (2017). The fixed base, before excavation, and after excavation models were employed in this investigation. Seven ground motions were applied to the frames. According to the findings, base shear, maximum drift, maximum story acceleration, and plastic hinge formation all change in the post-excavation scenario. The greatest impact was observed on the 15-story building. Seismic vulnerability analysis was performed on a five-story steel frame subjected to differential settlement in a study conducted by Bao et al. (2019). The ground motion set of 10 records was scaled to range between 0 and 2.0 g of PGA levels for IDA. As a key response parameter, IDRs have been employed. The frame has been subjected to five different settlement amounts, and the seismic fragility curves illustrate that the median collapse capacity diminishes as the settlement amount rises. Different aspects of the same study are discussed by Bao et al. (2020). The quantity of settlement has been shown to have a direct influence on the structure's plastic hinge formation and energy dissipation. In another study by Bao et al. (2021), a similar analysis has been performed on a 10- story steel frame. The ground motion set includes 10 records, but 7 distinct earthquake events. Five different settlement amounts were applied in six different areas of the frame, with the corner zone having the greatest impact. Seismic fragility curves have been produced for cases with and without settlement. In the scenario with settlement, 25 mm of settlement is applied in the corner zone. The median collapse capacity has been demonstrated to drop from 0.54 g to 0.47 g, a reduction of 13%. 8 There are a number of other studies that deal with the seismic response of structures with foundation settlements. Raychowdhury (2010) investigated the impacts of soil- structure interaction effects, including differential settlements, on the seismic response of low-rise steel frames. Bray and Luque (2017) analyzed a building that was differentially settled due to liquefaction in the aftermath of the Christchurch earthquake. Gómez-Martínez et al. (2020) proposed a broader framework for quantifying flexural and shear demands generated by liquefaction-induced differential settlements in RC frames. Couto et al. (2020) examined the seismic fragility of a typical masonry structure in Lisbon that has experienced foundation settlements. According to the literature review, foundation settlements have a considerable role in a building’s seismic behavior. The majority of studies focus on the consequences for RC structures, but settlements have also been found to affect steel and masonry structures. As can be observed, the combination of settlement and seismic effects has not been adequately researched for substandard RC structures. There has not been any seismic fragility study using strain-based performance assessment criteria in particular. The majority of previous research utilized IDRs, or damage indices, as a response parameter, but they can only capture a tiny portion of the influence of settlement-induced strains on the building's seismic capacity. Overview The thesis consists of five chapters. The remaining part of the thesis is structured as follows. The conceptual framework for performing seismic fragility and risk analysis is provided in the second chapter. The methodology for obtaining preliminary observations is also included. The case study building and numerical model are presented in Chapter 3. This chapter also covers the settlement profiles and the performance criteria that were used. The results of the study are reported in Chapter 4. All of the findings of the analysis have been discussed at length. The conclusion and recommendations based on the discussion of results are outlined in the thesis's concluding chapter. References and appendices are provided at the end of the thesis. 9 2. CONCEPTUAL FRAMEWORK This chapter discusses the methodology used to study the impact of foundation settlements on seismic risk. The annual probability of collapse for a structure that has sustained settlement can be obtained by taking the integral of the multiplication of the seismic fragility function with the annual seismic hazard rate. For a structure with differential settlement, S reaching y, this relationship can be represented as follows: P[D > c|S = y, 1 yr] = න P[D > c|IM = x, S = y]P[IM = x|1 yr] dx ஶ ଴ (2.1) where D is the damage, c is the complete damage level, S is the settlement level, and x is the PGV level. In essence, the integral in equation 2.1 is a modified version of the commonly utilized ‘risk integral’. The only modification is that the structural fragility is expressed here as a function of both the ground motion intensity, IM, and the level of settlement, S. As seen in equation 2.1 above, the impact of settlement on the collapse risk is directly associated with the change in seismic fragility of the structure. Seismic fragility analysis has been widely applied by researchers to analyze the seismic reliability of structures. The tool is used to evaluate the probability of damage, D, being greater than a predetermined damage level, d, at a certain intensity measure level, IM. As stated in equation 2.1, a new parameter, settlement amount, S, has been added to the general formulation. When the settlement amount is introduced as a new independent parameter, the lognormal cumulative distribution function, Φ, that is commonly used to construct fragility functions, takes the following form: P[D > d|IM = x, S = y] = Φ ൤ ln(x) − λ(y, d) σ(y) ൨ (2.2) where x is the intensity level of input motion, λ(y,d) is the median, and σ(y) is the standard deviation of the intensity measure linked to the initiation of damage, d in a frame with a support settlement level of y. Figure 2.1 is a hypothetical illustration of the technique. Fragility curves in the diagram represent different settlement levels. The 10 damage probability at a given level of intensity measure rises, and the median capacity decreases as the curve moves to the left. Hence, a leftward shift is anticipated in these curves as the settlement amount increases. (a) (b) Figure 2.1: Hypothetical representation of seismic fragility analysis: (a) settlement definition and (b) its impact on seismic fragility curves. In order to understand the fundamental mechanisms that cause the changes observed in the seismic fragility with the onset of settlement, the issue was investigated at multiple levels (i.e., from individual plastic hinges to the structure as a whole) and at multiple stages (i.e., before the earthquake and during the earthquake). The sample substandard case study frame that is presented in the next chapter was considered in the investigation. First, static analysis has been performed to reveal the variation in the internal force distributions. Then a pushover analysis was done to assess how the capacity and plastic hinge formation change. Finally, incremental dynamic analysis (IDA) was performed to generate seismic fragility curves, after which, a risk analysis was conducted to investigate the impact of seismic fragility changes. Analyzes were carried out using the Open System for Earthquake Engineering Simulation (OpenSees) software framework (Mazzoni et al, 2006). The procedures for all of these analyzes are detailed in the following sections. Static Analysis The settlements have been applied by the load control integrator in small increments, and the norm displacement increment test was used to obtain convergence. The reverse Cuthill-McKee (Cuthill and McKee, 1969) numberer and the transformation constraint type have been found to be suitable for settlement analysis. To solve the system of 11 equations, the BandGeneral system type was employed, and the nonlinear equation was solved using the Newton solution algorithm. Axial force diagrams were created based on the findings of the static analysis to visualize the redistribution after settlement. The axial force demands were normalized to Aୡfୡ୩ (where Aୡ is the total section area and fୡ୩ is the characteristic concrete compressive strength) and presented in terms of axial load ratio. Moment curvature and axial load-moment interaction diagrams have been generated at multiple axial load levels to better understand the variance due to settlement. The bilinear idealization technique that was developed by Priestley et al. (2007) has been used to conduct moment-curvature analysis. The redistribution of bending moments following the settlement has been investigated. In the diagrams, bending moment demands have been normalized to yield moments to indicate which portion of the yield moments are already consumed at the plastic hinging regions by the onset of settlement prior to any shaking. The impact of foundation settlements on shear force demands in the elements was also examined. To determine how far away each member is from the shear failure, shear force demands were normalized to shear capacities. The Turkish Seismic Code (TBDY, 2018) and the Turkish Standard for Design and Construction of Reinforced Concrete Structures (TS500, 2000) were used to compute shear capacities. Pushover Analysis At each floor level, inverted triangular loads have been applied laterally until the maximum displacement is attained. Because earthquakes are cyclic events and the highest demand direction is unknown prior to the event, pushover loads were applied in both positive and negative directions. A displacement control integrator was used with small increments. The nonlinear residual equation was solved using modified Newton-Raphson and regular Newton algorithms. The correlation between pushover curves and the development of plastic hinges has been documented. On the diagrams, the points at which yielding starts and the point at which ultimate flexural capacity is attained are marked. The analytical model does not include any post-shear behavior modeling. As a result, the simulation in the aftermath of the shear failure is questionable. In the numerical model, the frame retains its full 12 shear capacity, but in reality, it will degrade significantly and the stiffness of the damaged element will drop, which is not reflected in the numerical model. The findings do show the points when the shear capacity is surpassed, but post-shear failure data is presented as well. Seismic Fragility Analysis Seismic fragility curves were plotted using incremental dynamic analysis results. The maximum compressive and tensile strains in all members have been recorded and assessed using the performance criteria outlined in Section 3.3. The damage levels are adapted from Crowley et al. (2004), which is based on Priestley (1997) and Calvi (1999). Shear forces have also been recorded at each PGV level to identify when the capacity is being reached. Risk Analysis Fragility curves by themselves do not reveal anything about the risk directly. It makes no difference whether the structure is extraordinarily strong or incredibly fragile if PGV is zero. Buildings that are more robust and located closer to the fault are more likely to experience high-intensity shaking. Weak buildings located further away from the fault, on the other hand, are more prone to experiencing low-intensity shaking. Strong buildings may sustain greater damage than weak buildings, implying that site hazards differ. Hence, seismic fragility evaluation is not very informative without risk calculation. The risk analysis was carried out to determine the annual probability of collapse. The study consists of a combination of seismic fragility data as well as the probability of seismic hazard at a given location. In order to demonstrate the impact of seismic hazard levels, the annual probability of collapse obtained at different seismic hazard rates is evaluated and compared. 13 3. CASE STUDY BUILDING AND ANALYSIS MODEL The case study building and the numerical model used to simulate the building's behavior are covered in this chapter. The characteristics of the structure and its suitability are discussed first, followed by the numerical model and accompanying assumptions. Then, damage assessment categories based on the material properties of the buildings are provided. The investigated settlement profiles are outlined in the fourth section. Following that, the flexural and shear capacities are presented. The numerical model's validity based on experimental evidence is also examined in this chapter. In the last sections, dynamic analysis and seismic hazard data are provided. Case Study Building The ICONS bare frame, which was tested at JRC's ELSA laboratory, was selected as the case study building for this study. It is designed to be representative of typical buildings constructed in Southern European countries in the 1950s (Pinho and Elnashai, 2000). As seen in Figures 3.1 and 3.2, it is a four-story, three-bay structure. Every level has the same height (2.7 m), but the third bay (2.5 m) is shorter than the other two bays (5 m). The longitudinal beam and the transversal beams are 12.5 meters long and 4 meters long, respectively. This structure was chosen for its seismically deficient features. Still, however, it may be considered to have fewer deficiencies than the highest risk portion of Turkey's substandard RC building portfolio. Issues such as soft story, insufficient anchorage, or lap splice, for example, are not covered. Nonetheless, it is determined to be the best- suited model among the available options for which direct experimental evidence is available. It is relevant as a substandard building because of its lack of confinement and relatively lower concrete strength (i.e., 16 MPa) as compared to modern buildings. Besides, the presence of uneven span dimensions—like in real buildings—makes it a suitable frame to investigate settlement effects realistically. In the experiment, the pseudo-dynamic (PSD) testing approach was used (Pinho and Elnashai, 2000). Displacements were applied to the structure with actuators. Two input 14 motions have been applied consecutively, one with a return period of 475 years and the other with a return period of 975 years. Although—for safety reasons—the experiment was not carried out until the structure collapsed, the findings indicated that the structure would fail due to soft-story on the third level or shear failure on the ground floor. The third-story columns had reduced section dimensions as compared to the lower stories. This change in stiffness caused the soft story mechanism. Shear capacity, on the other hand, depends on transverse reinforcement, its spacing along the column and shear demand. It is not really a concern when the elements are slender. However, because stiffer elements are present in this structure, the shear demand was considerable. Further details can be found in Pinto et al. (1999), Carvalho et al. (1999), and Pinho and Elnashai (2000). (a) (b) Figure 3.1: (a) ICONS bare frame (Courtesy: Pinto et al, 1999) and (b) elevation view. Figure 3.2: Plan view of the ICONS frame (unit are in mm). 15 Numerical Model The Open System for Earthquake Engineering Simulation (OpenSees) software framework has been used to model the frame (Mazzoni et al, 2006). It was developed by the Pacific Earthquake Engineering Research (PEER) Center at the University of California, Berkeley. The ICONS bare frame is already documented in SeismoStruct (SeismoSoft, 2021) as a verification structure. It has been used as a reference while modeling the structure in OpenSees. The Tcl command language was used to create scripts, and the data was post-processed using MATLAB (MathWorks, 2021). 3.2.1 Material definitions Stress-strain curves and material properties are provided in Figure 3.3 and Table 3.1, respectively. Material properties are acquired from the SeismoStruct verification model (SeismoSoft, 2021) and Pinho and Elnashai (2000). For steel, the Menegotto and Pinto (1973) model has been utilized, which is represented by the material model, SteelMPF (Kolozvari et al, 2015) in OpenSees. Steel has a mean yield stress (fy) of 343 MPa, an initial elastic stiffness (Es) of 200 GPa, and a strain hardening ratio (bs) of 0.24%. Curvature parameters (R0, cR1, cR2) are taken as recommended in Kolozvari et al. (2015). Table 3.1: Material properties. Steel Concrete f୷ 343 MPa fୡ -16.3 MPa Eୱ 200 GPa Eୡ 18.754 GPa bୱ 0.0024 εୡ -0.002 R଴ 20 εୡ୳ -0.004 cRଵ 0.925 fୡ୲ 1.9 MPa cRଶ 0.0015 ε୲ 0.001 Popovics (1973) material is used for concrete, which is represented as Concrete04 in OpenSees. The model is nearly identical to that of Mander et al. (1988). Concrete has an initial stiffness (Ec) of 18.754 GPa and an average concrete strength (fc) of 16.3 MPa. Concrete strains at compressive strength (εc) and ultimate capacity (εcu) are 0.2% and 0.4%, respectively. The number proposed by Priestley et al. (2007) for unconfined concrete is used for the strain at ultimate capacity because the confinement effectiveness of the sections are negligible (≤1.01). The concrete’s tensile properties are also defined. Concrete has 0.1% of strain (εt) at a tensile strength (ft) of 1.9 MPa. 16 The compressive strength of the concrete is lower than the design code requirement. However, it is greater than the average value of Turkey's existing RC buildings, which is about 10 MPa (Arslan and Korkmaz, 2007). (a) (b) Figure 3.3: Stress-strain curves for (a) steel and (b) concrete. 3.2.2 Section definitions Figure 3.4 depicts section details and their respective positions on the structure (Pinto et al, 1999). In order to study axial load-moment interaction, fiber sections were used in the discretization of the cross-sectional area. Figure 3.4: Section details and their locations on the frame. 17 There are five different column sections. The first and third columns are the same size (20 cm x 40 cm), but the third column has two additional longitudinal rebars on the lower levels. The second column is a strong column with larger dimensions (60 cm x 25 cm), but on higher levels, the width of the column decreases to 50 cm and there are fewer longitidunal reinforcement bars. The section along the fourth column is smaller than the other sections (20 cm x 30 cm). Beam sections have been defined using T-sections. Because the intermediate sections are not as critical, only the sections around the plastic hinge regions are shown in Figure 3.4. The size of the beam sections is the same (25 cm x 50 cm), but the rebar layout varies. The reinforcement details in the shorter bay are less than those in the other two bays. The effective widths and thicknesses of slabs in all sections are 40 and 15 cm, respectively. 3.2.3 Element definitions The column and beam members are defined using the force-based beam with hinges elements (Scott and Fenves, 2006; Scott and Ryan, 2013). It allows the user to specify plastic hinge lengths, allowing for the simulation of nonlinear behavior with fewer nodes than a displacement-based method. In all elements, HingeRadau is employed as a hinge integration approach. Plastic hinge lengths were determined using the approach defined in Priestley et al. (2007). The calculated values are provided in Table 3.2. To account for the in-plane rigidity of the slabs, equal-degree-of-freedom constraints (Cook et al, 2002) were used at each level of the frame. Due to the axial load-moment interaction of the fiber section, rigid-diaphragm constraints generate extra axial forces in the beams. A less stiff (i.e., flexible) material was defined and its axial behavior was applied to the beam sections with Section Aggregator command available in OpenSees to prevent this from happening. To account for second-order effects, P-Delta geometric transformations are used in all beam-column elements. Table 3.2: Plastic hinge lengths. Section ID L୮ Section ID L୮ Section 1 0.1811 Section 5 0.1811 Section 2 0.2415 Section 6 0.2415 Section 3 0.2415 Section 7 0.2415 Section 4 0.1811 Section 8 0.1811 18 3.2.4 Gravity loading In order to account for masses such as the weight of the slabs, finishings, and live load, in addition to the self-weight of the structure, mass blocks, sand bags, and water containers were used in the experiment (Pinho and Elnashai, 2000). In the numerical model, additional masses are calculated and imposed as distributed loads on the beams and point loads at the beam-column connections. Figure 3.6 illustrates the details of gravity loading as reported by Carvalho et al. (1999). An equilibrium check is performed to confirm the reaction forces. The total weight of the structure is 1705 kN. Figure 3.5: Gravity loading. Performance Criteria The performance levels that were used to interpret the obtained data are listed in Table 3.2. It is adapted from the structural damage bands proposed by Crowley et al. (2004). In that study, quantitative values were determined based on Priestley (1997) and Calvi (1999). The specified limits were excessive for the substandard RC structure used in this study. Therefore, some adjustments have been made. Up to the structural yield point, damage is characterized as none to slight. Steel strain at yield (0.172%) controls the slight damage level. The proposed moderate and extensive damage bands are beyond the ultimate capacity of the concrete employed in this study. Hence, the moderate and extensive damage bands are grouped together under the same category, with the top limit set at concrete strain at compressive strength (0.2%) or beam failure in shear. The complete damage threshold is 19 characterized by the ultimate compressive strain capacity of concrete (0.4%) and the shear failure of a column. Table 3.3: Performance criteria. Damage Level Steel strain Concrete strain Description References Slight 0.00172 - steel bar yielding point Crowley et al. (2004) Moderate - 0.002 concrete spalling initiation point or beam failure in shear Crowley et al. (2004) Complete - 0.004 concrete ultimate strain capacity or column failure in shear Crowley et al. (2004), Priestley et al. (2007) Settlement Profiles Five distinct settlement profiles, including a zero-settlement scenario, have been investigated, as illustrated in Figure 3.12. Three different settlement levels have been defined: (i) 1 cm, (ii) 2 cm, and (iii) 3 cm of settlement. Case 0 Case A Case B Case C Case D Figure 3.6: Settlement scenarios. Case 0 denotes a case where no settlement occurred. In Case A, only the fourth column settles, while the other columns stay in their original locations. In Case B, the third and fourth columns both settle to the same degree, but the other two columns remain fixed. In Case C, only the first column maintains its original position while the remaining 20 columns all settle by the same amount. In the final settlement profile, Case D, all columns settle linearly with the same rotation angle. Appendix A contains the Tcl scripts of each settlement profile that were used to apply constraints to the supports. Capacities The bilinear idealization approach described by Priestley et al. (2007) was used to perform moment curvature analysis. At nominal yield and ultimate points, moment and curvature capacities have been determined. The analysis was carried out at multiple axial load levels. The nominal yield point’s compressive strain limit is set at 0.4%, which corresponds to the ultimate compressive strain capacity of the concrete employed in this study. Hence, the behavior beyond this point is governed by the tensile strain boundaries set for steel. Figure 3.10 shows the yield moments for the zero-settlement scenario. The capacities for other settlement profiles can be found in Appendix B. Shear capacities of beams and columns are displayed in Figure 3.11. They are calculated using Turkish Seismic Code (TBDY, 2018) and Turkish Standard for RC Structures (TS500, 2000). Figure 3.7: Yield moments prior to settlement [kNm]. Figure 3.8: Shear capacities [kN]. 21 Compatibility The numerical model’s compatibility with the experiment has been examined. The largest IDR was discovered on the third story in the experiment (Pinho and Elnashai, 2000). Hysteretic curves produced in that story during input motion with a 975-year mean return period were reported. A pushover analysis was performed, and the corresponding story drift and story shear results have been added to the diagram, as shown in Figure 3.7. It is noticeable that the experimental results have been accurately captured. The figure also shows the point at which shear capacity is surpassed. Because the design code shear capacity is a conservative value, the curve exhibited in the experiment extends beyond that threshold. Figure 3.9: Pushover analysis results and the actual hysteretic cycles exhibited during the experiment at third story (Courtesy: Pinho and Elnashai, 2000). The numerical model’s accuracy was also verified by comparing the time history analysis results with the experiment. Figure 3.8 depicts the artificially generated accelerogram that was applied to the frame in the experiment, which has a mean return period of 475 years. The displacement-time history of the fourth story is reported by Pinho and Elnashai (2000). As illustreated in Figure 3.9, the same input motion is applied to the frame, and the resulting displacement-time history is added to the diagram to compare the results. It can be observed that, despite minor differences, the numerical model accurately reflects the experimental behavior. 22 Figure 3.10: Artificially generated accelerogram with a return period of 475 years that was applied in the experiment (Courtesy: SeismoSoft, 2021). Figure 3.11: Compatibility of the displacement-time history at the top floor with the experiment. Ground Motion Set and Dynamic Analysis Table 2.1 lists the 12 individual records that make up the ground motion set. The particular records were selected based on a study conducted by Akkar et al. (2005). The analysis only included records with high magnitudes. The moment magnitudes of the selected records range between 6.19 and 7.62. In the table, the moment magnitude scale and the Joyner-Boore distance are denoted by M୵ and R୨ୠ, respectively. The ground motion records were first scaled to a range of 1 cm/s to 30 cm/s PGV, in 1 cm/s increments. Then, time series were defined and uniform excitations were applied. To account for the vertical excitation component's extra influence on axial force distribution, uniform excitations included both horizontal and vertical components. The same analysis commands as in static analysis were utilized. This time, however, the Newmark integrator and transient analysis types were used. The equations were solved using modified Newton-Raphson and regular Newton algorithms. 23 Table 3.4: Ground motion set. Event Date Station Comp Mw Rjb (km) Site Class PGA (g) PGV (cm/s) Cape Mendocino 4/25/1992 Petrolia 000 7.01 0.00 D 0.589 48.4 Chi-Chi 9/20/1999 TCU076 N 7.62 2.74 D 0.416 64.2 Coalinga 5/2/1983 Pleasant Valley P.P. - Yard 045 6.36 7.69 D 0.592 60.2 Duzce 11/12/1999 Duzce 270 7.14 0.00 D 0.535 83.5 Gazli 5/17/1976 Karakyr 090 6.80 3.92 D 0.718 71.6 Imperial Valley 10/15/1979 Parachute Test Site 315 6.53 12.69 C 0.204 16.1 Kocaeli 8/17/1999 Arcelik 000 7.51 10.56 C 0.219 17.7 Loma Prieta 10/18/1989 Gilroy Array #6 090 6.93 17.92 C 0.170 14.2 Morgan Hill 4/24/1984 Gilroy Array #3 090 6.19 13.01 D 0.201 12.7 Northridge 1/17/1994 Newhall 360 6.69 3.16 D 0.590 97.3 Parkfield 6/28/1966 Cholame #5 085 6.19 9.58 D 0.441 24.7 Superstition Hills 11/24/1987 El Centro Imp Co Center 000 6.54 18.20 D 0.358 46.4 Seismic Hazard This study focuses on two sites with different seismic activity rates in order to estimate the sensitivity of the settlement in the region. Figure 2.2 depicts the locations of the sites on the Disaster and Emergency Management Presidency's Turkey Earthquake Hazard Map (AFAD, 2018). Site A is in Adapazari, a seismically active zone where the 1999 Kocaeli earthquake resulted in a large number of examples of differential settlement. Site B, on the other hand, is in a less seismically active region, Konya, and is farther away from the fault. Figure 3.12: Locations of sites on the Turkey Earthquake Hazard Map (Courtesy: AFAD). The ZB soil type has been chosen for both sites. Because the ZA soil type is extremely hard, it would be a poor choice. While ZC is a suitable choice since it is softer, ZB 24 type soil was found to be more effective because the supports are assumed to be fixed. Despite the relatively rigid conditions of the ZB soil class, improper excavation might result in settlements. Seismic hazard data has been collected from the Turkey Earthquake Hazard Maps (AFAD, 2018) interactive web application. The probabilities have been converted into rates and interpolated in the log-log space. The acquired probabilistic seismic hazard analysis (PSHA) data, as well as the logarithmic curve fitting results, are shown in Figure 2.3. (a) (b) Figure 3.13: (a) PSHA data acquired from AFAD and (b) the logarithmic curve- fitting results. The data is provided in terms of the probability of exceeding (2%, 10%, 50%, and 68%) a specified intensity level, x, within 50 years. It is assumed that it is a Poisson process and everything is based on the rate of occurrence of the event. Then, by using those rates, probabilities of occurrence can be calculated in other time frames. Hence, it was converted into an annual rate using the Poisson's recurrence model presented by Kramer (1996), as indicated in equation 3.1. The resulting annual rates are provided in Figure 2.4a. P[PGV > x|1yr] = − ln(1 − P[PGV > x|50yr]) 50 (3.1) The cumulative distribution function (CDF) was then constructed using the annual rates. The probability distribution function (PDF) of the seismic hazard was obtained by taking the derivative of the CDF. The final results are displayed in Figure 2.4b. 25 (a) (b) Figure 3.14: (a) PSHA results converted to an annual rates and (b) probability of annual seismic hazard at the sites. 26 27 4. DISCUSSION OF RESULTS This chapter deals with the numerical analysis results for all settlement scenarios. The discussion starts with the redistribution of internal forces following the settlement. The results of the pushover analysis, including the change in plastic hinge formation, are covered in the second section of the chapter. In the third section, the seismic fragility curves are examined. The concluding section of the chapter discusses the risk analysis results. Impact of Settlement on Internal Force Distributions The static analysis results presented in this section look at the internal force distributions to get a sense of the state before lateral loading. The pre-settlement distribution is displayed first, followed by the redistribution in each settlement scenario. 4.1.1 Internal force distributions prior to settlement Axial load ratios for the case without settlement are shown in Figure 4.1. Because of the in-plane rigidity of the slabs, there is no axial force in the beams. But the demands are quite large in the columns. The highest demands are exhibited in the first-story columns. The axial load ratios on those elements range from 24 to 34%. The demand tends to decrease on the upper floors. Values are about five times lower on the fourth floor than they are on the first. In Figure 4.2, P-M interaction and corresponding moment-curvature diagrams for the ground-floor columns are displayed. The yield moments are normalized to fcbh2 (where fc is the compressive strength of concrete, b is the width of the section, and h is the depth of the section), and the ultimate curvatures are multiplied by the depth of the section. The axial load levels in all columns are around the balanced condition. The largest yield moment capacity is observed in the second column (49%), yet it also has the lowest curvature capacity (0.4%). Even though the yield moment capacities are lower (8–12%) in the rest of the columns, the curvature capacities (1.5–2%) of the members are higher than in the second column. 28 (a) (b) Figure 4.1: Case 0 – normalized axial force demands in (a) beams and (b) columns. (a) (b) Figure 4.2: Case 0 – (a) axial load-moment interaction and (b) moment-curvature diagrams for ground-floor columns. Figure 4.3 depicts the distribution of bending moments in the frame prior to settlement. The values provided in the diagram are normalized values (with respect to the corresponding yield moment capacities). The yield moments at the ends of beams differ from those in the middle section. As a result, normalizing bending moments to yield moments causes discontinuity around the plastic hinge regions. At the connections with the second column, the bending moment demands on the beams vary between 14% and 19%. At the opposite ends of these beams and at the third bay, smaller ratios are observed (1–5%). The largest demands in the columns are found on the fourth level, with values ranging from 2 to 9%. The second column, which is also the stiffest column, consumes only 0–2% of the yield moment. The findings reveal that in some members, a considerable portion (up to 19%) of the yield moment is consumed under gravity loading, even before any ground motion or settlement occurs. 29 (a) (b) Figure 4.3: Case 0 – bending moment demands normalized to yield moments in (a) beams and (b) columns. The ratios between shear force demands and shear capacities are shown in Figure 4.3. In the beams, the ratios are quite high. The second column’s beam-column connections have the highest demands, with values ranging from 21 to 31%. The demands of the columns are smaller than those of the beams. The ratios range from 0% to 4%, with the largest demands observed on the fourth floor columns. The results show that the presence of strong beams causes non-negligible shear demands. (a) (b) Figure 4.4: Case 0 – shear force demands normalized to shear capacities in (a) columns and (b) beams. 4.1.2 Redistribution of axial force demands following settlement Even when considerably lower settlements occur, the distribution of axial forces has been seen to vary significantly. Figures 4.5, 4.6, and 4.7 demonstrate the change in Case A when the fourth column is exposed to 1 cm, 2 cm, and 3 cm of settlement, respectively. There is negligible change in beams, whereas in columns the situation is different. The largest variation is observed in the settled column and the one next to it. 30 At ground level, the axial load ratio of the third column keeps increasing and reaching a value as high as 80%. Axial forces in the fourth column, on the other hand, experience a significant decrease. They even become tension members after the settlement occurs. The axial load ratios of these members get to a level as low as 17% after 3 cm of settlement. It was calculated whether it is actually possible for such an axial tensile force to occur, taking into account the foundation and ground floor loading. The same loading is assumed at the ground level as in the first story. Appendix C shows the details of the foundation attached to the strong floor. Due to the absence of the exact details, the weight of the foundation used in the test unit has been added to the ground floor weight. It was determined that in tension, an axial load ratio of up to 10% is reasonable. The values that are higher than this level may still be justified in the event of additions such as gardening structures. However, 3 cm of settlement should be regarded as an extreme condition for Case A. (a) (b) Figure 4.5: Case A with 1 cm of settlement – (a) normalized axial force demands and (b) percentage change with respect to Case 0. (a) (b) Figure 4.6: Case A with 2 cm of settlement – (a) normalized axial force demands and (b) percentage change with respect to Case 0. 31 (a) (b) Figure 4.7: Case A with 3 cm of settlement – (a) normalized axial force demands and (b) percentage change with respect to Case 0. After settlement, the P-M interaction of the first-floor columns, as well as variations in the moment-curvature diagrams, were analyzed. Figures 4.8, 4.9, 4.10, and 4.11 illustrate the change in the first, second, third, and fourth columns, starting from the left. In both C101 and C102, there have been very slight changes. The changes in the column that is subjected to settlement and the column adjacent to it are substantially higher. A 136% increase in the third column’s axial load ratio resulted in yield moment and curvature capacity reductions of up to 36% and 47%, respectively. The interaction diagram shows that axial load levels reach extremely high values, even exceeding the compression control point. The yield moment capacity drops by up to 70% in the column subjected to settlement, whereas the curvature capacity rises by 3.5–4.5 times. Axial load levels move towards the pure axial tension point in the P-M interaction diagram, which is the highest tensile force that the column can resist. (a) (b) Figure 4.8: Case A – (a) axial load-moment interaction and (b) moment-curvature diagrams for C101. 32 (a) (b) Figure 4.9: Case A – (a) axial load-moment interaction and (b) moment-curvature diagrams for C102