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Seismic strengthening of unreinforced masonry walls using sprayable Ecofriendly Ductile Cementitious… Soleimani-Dashtaki, Salman 2018

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SEISMIC STRENGTHENING OF UNREINFORCED MASONRY WALLS USING SPRAYABLE ECOFRIENDLY DUCTILE CEMENTITIOUS COMPOSITE (EDCC) by  Salman Soleimani-Dashtaki  B.A.Sc. with Minor in Commerce, The University of British Columbia, 2011  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Civil Engineering)   THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  April 2018  © Salman Soleimani-Dashtaki, 2018 ii  The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled:  Seismic strengthening of unreinforced masonry walls using sprayable Ecofriendly Ductile Cementitious Composite (EDCC)  submitted by Salman Soleimani-Dashtaki  in partial fulfilment of the requirements for the degree of Doctor of Philosophy (PhD) in The Faculty of Graduate and Postdoctoral Studies (Civil Engineering)  Examining Committee: Prof Nemkumar (Nemy) Banthia Co-supervisor Prof Carlos Estuardo Ventura Co-supervisor  Prof Patrick McGrath Supervisory Committee Member Prof W.D. Liam Finn University Examiner Prof Farrokh Sassani University Examiner   Additional Supervisory Committee Members: Prof Adam Lubell Supervisory Committee Member N/A Supervisory Committee Member  iii  Abstract  Due to their good sound and thermal insulation properties, unreinforced masonry (URM) walls are widely used in partitioning many of the commercial and residential buildings worldwide, either as in-fill or stand-alone.  URM is considered one of the most common types of partition wall systems in many of the mid-age, low-rise to mid-rise, school and hospital buildings in North America.  URM is still a very common and major building material, in many of the developing countries, being used in many residential and commercial buildings.  URM partition walls are known to have very low drift capacity in seismic events and the failure mechanisms are known to be mostly brittle and of catastrophic nature, during earthquake ground motion.  Compared to other partitioning systems, URM walls tend to perform poorly during earthquake events, leaving many injuries, casualties, and fatalities behind.  This dissertation elaborates on development of a novel, effective, and practical methodology for a robust out-of-plane seismic strengthening technique toward seismically upgrading URM partition walls, using a thin plaster layer of sprayable Ecofriendly Ductile Cementitious Composite (EDCC).  The EDCC layer is devoted to secure such walls, which exist in most parts of the world; specially, in developing countries, where world’s most population density is concentrated.  In many of these countries, retrofit is the only option, since building replacement is not practical nor an economically feasible solution.  The EDCC material can be applied in three different methods: hand troweled, hopper sprayed, or pump sprayed.  The thickness of the layer can vary between 10mm to 20mm, depending on the design variables. iv  Full-scale URM walls are built, strengthened, and tested on a shake table, using the strongest real historical earthquake records.  The EDCC layer is providing nearly full out-of-plane detention for the wall’s building blocks, as well as minor but uniform shear capacity enhancements for the in-plane action; therefore, holding the masonry units together from falling apart and being thrown during an earthquake generated ground motion.   The newly developed high performance material is sprayable, ductile, and resilient, while being affordable, and easy to apply, with much less carbon footprint compared to other similar repair materials. v  Lay Summary  Every year hundreds of thousands of lives are taken away worldwide by natural disasters such as earthquakes. Walls made of concrete blocks or bricks, are amongst the most vulnerable type of walls, which tend to collapse during an earthquake. Debris from collapsing walls fall on pedestrians and building occupants, leaving behind a great deal of injuries and fatalities, even if the building frame is still standing. This research work has been devoted to develop an effective, practical, and affordable technology to help secure such walls, which exist in most parts of the world and, specifically, in developing countries, where the world’s highest population density is concentrated. Through this doctoral work, a novel sprayable material, called Ecofriendly Ductile Cementitious Composite (EDCC), has been developed, used to strengthen real-scale versions of such walls, which were subsequently tested on a shake table, using the strongest actual historical earthquake records. The developed technology aims to save millions of lives worldwide. vi  Preface  This thesis, entirely produced and drafted by Salman Soleimani-Dashtaki, presents the conducted research, as part of a doctoral work, under the primary supervision of Prof. Nemy Banthia, and co-supervision of Prof. Carlos E. Ventura, both professors of civil engineering at UBC. The entire tests are done by Salman Soleimani-Dashtaki and data collection, analysis, result presentations, and the writings are done by Salman Soleimani-Dashtaki.  The material testing portion of this doctoral work is primarily performed at the UBC laboratory of SIERA: Sustainable Infrastructure Research Group, under the supervision of Dr. Banthia. This includes the work presented in Chapters 3 and 6 of this dissertation.  The structural full-scale and half-scale experimental work, including the shake table testing of large size wall specimens, are done at the Earthquake Engineering Research Facility (EERF) at UBC, under the supervision of Dr. Ventura. This experimental work is primarily presented as part of Chapters 4 and 5 of this thesis.  Two conference papers are already published from this conducted research and there will be two journal papers, which are currently being prepared for submission from the research work presented in this thesis. The mentioned publications, with their titles and dates, are listed below, in a bullet-point format, with reference to the corresponding chapters of the thesis.  vii  (1) Soleimani-Dashtaki, S., Soleimani, S., Wang, Q., Banthia, N., & Ventura, C. E. (2017). Effect of high strain-rates on the tensile constitutive response of Ecofriendly Ductile Cementitious Composite (EDCC). PROTECT2017: The 6th International Workshop on Performance, Protection & Strengthening of Structures under Extreme Loading. Engineering Procedia. Guangzhou (Canton), China: ELSEVIER (Engineering Procedia). Retrieved from www.elsevier.com/locate/procedia - Part of Chapter 6 of this thesis includes parts of this paper. The paper is drafted by Salman Soleimani-Dashtaki, and presented at PROTECT 2017. The static testing part of the data in the paper, shown for comparison in Chapter 6 with proper citations, are from the work done at UBC by Ms. Qiannan Wang, a visiting PhD student from Southeast University of China. In addition, Ms. Saghar Soleimani-Dashtaki, as an undergraduate research assistant, has helped with running the dynamic tests, as presented in the paper, and included in Chapter 6 of the thesis.  (2) Soleimani-Dashtaki, S., Ventura, C. E., & Banthia, N. (2017). Seismic Strengthening of Unreinforced Masonry Walls using Sprayable Eco-Friendly Ductile Cementitious Composite (EDCC). 6th International Workshop on Performance, Protection & Strengthening of Structures under Extreme Loading, PROTECT2017, 11-12 December 2017. Procedia Engineering. Guangzhou (Canton), China: ELSEVIER (Engineering Procedia). Retrieved from www.elsevier.com/locate/procedia - Salman Soleimani-Dashtaki produced this paper, including the text, data, and the analysis. Part of this paper is included in some segments of Chapter 4 and Chapter 5 of this thesis. viii  (3) Soleimani-Dashtaki, S., Banthia, N., & Ventura, C. E. (in preparation, 2018 expected). Investigation and modeling of the Effect of high strain rates, as measured during an earthquake shaking, on the tensile constitutive response of EDCC, when applied as a strengthening material for URM Walls. - This will be an extraction from Chapter 3 and 6 of the thesis.  (4) Soleimani-Dashtaki, S., Ventura, C. E., Banthia, N. (in preparation, 2018 expected). Shake Table Testing of six full-scale EDCC strengthened URM Walls; a robust retrofit technique for prevention of out-of-plane failure. - This will be an extraction from Chapter 4 and 5 of the thesis.  ix  Table of Contents  Abstract ......................................................................................................................................... iii Lay Summary .................................................................................................................................v Preface ........................................................................................................................................... vi Table of Contents ......................................................................................................................... ix List of Tables .............................................................................................................................. xvi List of Figures ........................................................................................................................... xviii List of Abbreviations ............................................................................................................... xxiv Acknowledgements ....................................................................................................................xxv Dedication ................................................................................................................................ xxvii Chapter 1: Introduction ................................................................................................................1 1.1 Research Program Incentives and Structure ................................................................... 1 1.1.1 Problem Statement ...................................................................................................... 1 1.1.2 Goals, Objectives, and Scope...................................................................................... 2 1.1.3 Tasks and Thesis Overview ........................................................................................ 3 1.2 Need and Necessity for Development of New Retrofit Technologies ............................ 3 1.2.1 Demand for Higher Practical Performance Levels ..................................................... 4 1.3 Introduction to the Developed Retrofit Methodology .................................................... 5 1.3.1 Introducing Ecofriendly Ductile Cementitious Composite (EDCC) .......................... 5 1.3.2 Sprayability of EDCC ................................................................................................. 6 1.4 Testing Program and Deliverables .................................................................................. 6 1.4.1 Material Level Investigations ..................................................................................... 7 x  1.4.2 Dynamic Testing of Full-Scale EDCC Retrofitted Specimens ................................... 7 1.4.3 Development of a Vibration-Based Damage Assessment Technique ........................ 8 1.5 Translation of the Technology to Real Life Applications .............................................. 8 1.5.1 Technology Inclusion in the Seismic Retrofit Guidelines .......................................... 9 1.5.2 Real-World Application of EDCC through a Demonstration Project ........................ 9 1.5.3 Market Size and Industry Demand for the Technology ............................................ 10 Chapter 2: Background and Literature Review .......................................................................11 2.1 Background on Development of Ductile Cement Based Composites .......................... 12 2.1.1 Conventional Fiber Reinforced Mortar and Concrete .............................................. 12 2.1.2 Introduction to Different Advanced Types of FRC .................................................. 13 2.1.3 Behavioral Classification of Fibrous Cementitious Composites .............................. 15 2.1.4 Factors Affecting Overall Consecutive Response of FRCC ..................................... 15 2.1.4.1 Micromechanism Involved in Fiber-Matrix Interaction ................................... 16 2.1.4.2 Contributions of the Matrix to the Bond-Slip Response ................................... 17 2.1.4.3 Contributions of the Fiber System to the Bond-Slip Response ........................ 18 2.1.4.4 Effect of Fiber Content and Geometry on Behaviour of FRC .......................... 19 2.1.4.4.1 Fiber Content - Volume Fraction (Vf) ......................................................... 20 2.1.4.4.2 Fiber Length (L) .......................................................................................... 24 2.1.4.4.3 Effect of Locally Bent Fibers on Post-Cracking Response of FRC ............ 25 2.1.4.5 Effect of Fiber Deformations and Surface Modifications on FRC ................... 27 2.1.4.5.1 Fiber Geometry and Coating ....................................................................... 27 2.1.4.5.2 Fiber Surface Modification ......................................................................... 28 2.1.4.6 Effect of Crack Band Formation and Crack Branching on FRC ...................... 29 xi  2.1.4.6.1 Crack Band Formation and Theories .......................................................... 30 2.1.4.6.2 Crack Branching During the Crack Propagation......................................... 31 2.1.4.7 Effect of Matrix Modifiers on Bond-Slip Behaviour of Fibers ........................ 33 2.1.4.7.1 Silica Fume .................................................................................................. 33 2.1.4.7.2 Fly Ash ........................................................................................................ 34 2.1.4.7.3 Methylcellulose ........................................................................................... 35 2.1.4.8 Effect of Proper Mixing on Mechanical Behaviour of FRC ............................. 36 2.1.5 Existence or Extent of Multiple Cracking as a Function of Fiber Content ............... 36 2.1.6 Micromechanics of Ductile Fibrous Cementitious Composites ............................... 38 2.1.7 Effect of Applied Stress-Rates on Bond-Slip Behaviour of FRC ............................. 41 2.2 Background on Sprayable EDCC ................................................................................. 42 2.3 Background on Retrofit of URM Walls ........................................................................ 44 2.3.1 Different Modes of Failure for URM Walls ............................................................. 44 2.3.2 Mathematical Modeling of the Out-of-plane Failure Mechanism ............................ 46 2.3.2.1 Backbone Curve for Out-of-Plane Walls .......................................................... 49 2.3.3 URM Retrofit: Conventional Techniques and Ongoing Studies .............................. 52 Chapter 3: Development of Sprayable EDCC and its Applications........................................55 3.1 EDCC with High Volume of Fly Ash ........................................................................... 55 3.2 The Hybridized Fiber System of EDCC ....................................................................... 56 3.2.1 Poly-Vinyl Alcohol (PVA) Fibers ............................................................................ 56 3.2.2 Poly-Ethylene Terephthalate (PET) Fibers ............................................................... 57 3.2.3 Cementophilic Fibers ................................................................................................ 57 3.3 EDCC Final Mix Designs ............................................................................................. 57 xii  3.4 The EDCC Spray System and Specifications ............................................................... 59 3.5 The Application Methods for EDCC ............................................................................ 62 3.5.1 Available Finishes for EDCC ................................................................................... 62 3.6 Bond Performance of EDCC to Masonry ..................................................................... 64 3.6.1 Previous Bond Investigations at UBC ...................................................................... 64 3.6.2 Disk Pull-Off Test: Equipment and Setup ................................................................ 65 3.6.3 Bond Investigation Results and Statistics ................................................................. 67 3.6.4 Discussion on the EDCC-CMU Tensile Bond Results ............................................. 70 3.7 Preliminary Cost Analysis: Strengthening Using Sprayable EDCC vs. FRP ............... 72 Chapter 4: Shake Table Testing of EDCC Strengthened URM Walls ...................................75 4.1 The Shake Table Testing Program ................................................................................ 75 4.1.1 The Inventory and Specifications of the URM Wall Specimens .............................. 77 4.1.2 Ground Motion Selection and Use ............................................................................ 81 4.1.3 Shake Table Setup and Calibration ........................................................................... 85 4.1.4 Ground Motion Characteristics and Spectral Content .............................................. 86 4.2 Experimental Procedure and Details ............................................................................. 90 4.2.1 Instrumentation and data acquisition ........................................................................ 90 4.2.2 Test Arrangements and Setup ................................................................................... 93 4.3 Shake Table Testing Summary Results and Discussions ............................................. 96 4.3.1 Effects of Aftershocks on a Partially Damaged Wall ............................................. 107 4.3.2 Force Distribution and Motion Amplification Factors ........................................... 108 4.3.3 Displacement Pattern and Damage Model .............................................................. 111 4.3.4 Stability and Displacement Capacity Enhancements .............................................. 117 xiii  4.3.5 Discussion on Performance Comparison ................................................................ 120 4.4 Detailed Studies of the Shake Table Testing Results ................................................. 122 4.4.1 Shake Table Testing Results: Load-Deflection Curves .......................................... 122 4.4.2 Shake Table Testing Results: Moment-Rotation Diagrams.................................... 124 4.4.3 Shake Table Testing Results: Multiple Curvature Bending Deflections ................ 126 4.4.4 Shake Table Testing Results: Moment-Curvature Diagrams ................................. 128 4.5 Final Discussion on the Overall Shake Table Testing Results ................................... 129 Chapter 5: Vibration Based Characteristics Assessment of the Specimens .........................131 5.1 Vibration Assessment of EDCC Retrofitted Walls ..................................................... 131 5.2 Multi-Degree-of-Freedom Modal Analysis for Retrofitted Walls .............................. 139 5.3 Possible Amplification Effects by the Test Setup....................................................... 143 5.4 Operational Modal Analysis using ARTeMIS Modal Pro .......................................... 146 5.4.1 Damage Model by Monitoring Modal Parameters using ARTeMIS Modal Pro .... 151 5.4.2 Discussion on the Damage Assessment Results of Operational Modal Analysis .. 154 Chapter 6: Effect of High Strain Rates on Constitutive Response of EDCC .......................156 6.1 Targeted Strain Rates .................................................................................................. 156 6.2 Experimental procedure .............................................................................................. 157 6.2.1 Preparing the specimens ......................................................................................... 157 6.2.2 Dynamic Tensile Testing ........................................................................................ 159 6.3 EDCC Dynamic Test Results...................................................................................... 161 6.3.1 Dynamic vs. Static Tensile Testing ........................................................................ 164 6.3.2 Discussion on the Dynamic Test Results ................................................................ 168 6.4 Actual Dynamic Loading Rates for EDCC from Shake Table Testing ...................... 170 xiv  6.4.1 Isolating the Impact Cycles from the Data ............................................................. 170 6.4.2 Peak Strain Readings – Rates and Values from Shake Table Testing .................... 177 6.4.3 Discussion on Actual Strain Rates for EDCC from Shake Table Testing .............. 183 Chapter 7: Conclusions, Recommendations, and Future Work ...........................................187 7.1 Scope of the Research Work and Related Contributions ............................................ 187 7.1.1 The Overall Contributions of the Thesis ................................................................. 188 7.2 Significance of the Experimental Work and Notable Results .................................... 190 7.3 Technology Transfer through Demonstration Project ................................................ 191 7.3.1 Inclusion of EDCC as a URM Retrofit Option in SRG III ..................................... 191 7.3.2 Retrofit of a URM Wall at Annie B. Jamieson Elementary School ....................... 192 7.4 Recommendations for Future Investigations .............................................................. 193 7.4.1 Static Monotonic and Cyclic Testing of EDCC Retrofitted Wall Panels ............... 193 7.4.2 Effect of Bi-Directional Motions on Full-Scale EDCC Retrofitted Walls ............. 194 7.4.3 Investigation on In-Plane Capacity of Full-Scale EDCC Retrofitted Walls ........... 195 7.4.4 Spray Process Characterization and Testing ........................................................... 196 7.4.5 Tensile and Flexural Testing of EDCC in High Dynamic Rates of Loading ......... 196 7.4.6 Recommended Numerical and Analytical Modeling .............................................. 197 References ...................................................................................................................................198 Appendices ..................................................................................................................................208 Appendix A - Retrofit Details as Presented in Volume 7 of SRG III ..................................... 208 A.1 SRG III – URM partition walls (# 11) – Restraint of Wall using Sprayed EDCC . 208 Appendix B - Additional Graphs and Data for Chapter 6: ..................................................... 210 B.1 EDCC Premium Mix - 2% PVA Fibers .................................................................. 210 xv  B.2 EDCC Mix with 2% PET Fibers ............................................................................. 211 B.3 Regular EDCC Mix – Hybrid of 1% PVA + 1% PET Fibers ................................. 212 B.4 Additional Detailed Combined Graphs for all EDCC Mixes ................................. 213 Appendix C - Raw Materials’ Specifications of the Masonry Specimens.............................. 217 C.1 Concrete Masonry Unit (CMU) Specifications and Details ................................... 217 C.2 Clay Bricks Specifications and Details ................................................................... 219 C.3 The mortar used for the Specimens ........................................................................ 220 Appendix D - Out-of-Plane Panel Tests: Specimens, Setup, and Instrumentation ................. 222 D.1 Concrete Masonry Unit (CMU) Wall Panel (wallet) Specimens............................ 222 D.2 Clay Brick Wall Panel Specimens .......................................................................... 224 Appendix E Monotonic and Cyclic Testing of EDCC Strengthened URM Wallets .............. 226 E.1 Overall Specimen Dimensions and Mounting Configuration ................................. 226 E.2 Instrumentation Details and Data Collection .......................................................... 227 E.3 Monotonic Testing of Half-Scale EDCC Strengthened URM Walls ..................... 228 E.4 Cyclic Testing of Half-Scale EDCC Strengthened URM Walls ............................ 229 Appendix F - Selected Photos from the Demo Project at Jamieson Elementary School ........ 230 Appendix G - Library of Generated MATLAB Codes, Scripts, and Functions ..................... 233 G.1 Import Functions and Scripts for Data Import from ASCII Files ........................... 233 G.2 Pre-Processing and Data Conditioning Scripts and Functions ............................... 236 G.3 Post-Processing and Plotting Scripts and Functions ............................................... 262 G.4 Peak Value Extraction and Data Input Creator for ARTeMIS Modal Pro ............. 297 xvi  List of Tables  Table 2-1: Resistance Functions for Out-of-plane Rocking Wall Prototypes (SRG III, 2017) .... 47 Table 3-1: The Final EDCC Mix Designs .................................................................................... 58 Table 3-2:  Data Statistics for the EDCC-CMU Tensile Bond Tests ........................................... 69 Table 3-3: Test Data on EDCC-CMU Bond for 20mm Thickness (Yan, 2016) .......................... 70 Table 3-4: Cost Estimation (/m2) for the EDCC Retrofit Option, (Material & Labour) .............. 72 Table 4-1: Summary of the Specimens Tested on Shake Table ................................................... 78 Table 4-2: Mass Calculation Guide – Total Mass per unit Surface Area of Specimen ................ 79 Table 4-3: Summary of Ground Motions Used & Their Corresponding Designation Number ... 81 Table 4-4: Peak Values and Details of the Selected Ground Motions .......................................... 82 Table 4-5: Outline of all the Result Summary Tables .................................................................. 96 Table 4-6: Summary of the Shake Table Testing for Wall # 1 ..................................................... 97 Table 4-7: Summary of the Shake Table Testing for Wall # 2 ..................................................... 99 Table 4-8: Summary of the Shake Table Testing for Wall # 3 ................................................... 102 Table 4-9: Summary of the Shake Table Testing for Wall # 4 ................................................... 104 Table 4-10: Summary of the Shake Table Testing for Wall # 5 ................................................. 105 Table 4-11: Summary of the Shake Table Testing for Wall # 6 ................................................. 106 Table 4-12: Effect of Aftershocks on Damaged Wall # 3 - Shake Table Testing Summary ...... 107 Table 4-13: Parametric Study Values for Wall-2 from Run-1 to Run-4..................................... 115 Table 4-14: Equations of the Trend Lines and Fitted Curves for Deflections of Wall-2 ........... 116 Table 5-1: Natural Frequencies, Periods, and Damping Ratios from Short Vibration Cycles ... 135 Table 5-2: Peak Modal Base Shear and Overturning Moment for all Modes of Wal1-1 ........... 142 xvii  Table 5-3: Modal Combination of Forces, Moments, and Displacements for Wall-1 ............... 142 Table 5-4: Wall-1 ARTeMIS Natural Frequencies and Modal Damping Ratios for all Runs ... 152 Table 5-5: Wall-2 ARTeMIS Natural Frequencies and Modal Damping Ratios for all Runs ... 153 Table 6-1: Summary of the Calculated Parameters .................................................................... 166 Table 6-2: Table of Peak Strain Values for Wall-1 during Run-7 and Run-22 to 25 ................. 179 Table 6-3: Domain of Strain Rates for Concrete Material under Different Loading Cases ....... 185 Table 7-1: Inventory of the Half-Scale EDCC Strengthened Wall Panels ................................. 193 Table 7-1: Unit Data for 10cm Standard CMU from Concrete Masonry Products .................... 218 xviii  List of Figures  Figure 2-1: Schematic Comparison between Different FRC Classes ........................................... 13 Figure 2-2: Schematic of a Single Fiber Pullout at Crack Opening (Bentur et al, 2007) ............. 17 Figure 2-3: Schematic Stress-Strain with Vf Above and Below Vf (Cr.) (Bentur et al, 2007) ........ 21 Figure 2-4: Schematic for Tension-Softening vs. Strain-Hardening (Li V. C., 2007) ................. 22 Figure 2-5: Three Tensile Stress-Strain Curves of a Typical ECC (Wang, Wu, & Li, 2001) ...... 23 Figure 2-6: Effect of Fiber Length and Bond on FRC strength (Bentur & Mindess, 2007) ......... 25 Figure 2-7: (a) Fiber Bending at Crack and (b) Crack Bridging Forces (Leung & Chi, 1995) .... 26 Figure 2-8: Optimal Range of Frictional Bond to Achieve Strain Hardening (Li et al, 2002) ..... 28 Figure 2-9: Effect of Surface Coating on Stress-Strain Response of ECC (Li V. C., 2003) ........ 29 Figure 2-10: Crack Band Formation and Branching - an R/ECC member (Li V. C., 2003) ........ 32 Figure 2-11: Typical σ-δ Curve with the Complementary Energy Shaded (Li V. C., 2003) ....... 38 Figure 2-12: Steady State Crack Analysis, Griffith Type Crack (Li & Leung, 1992) .................. 39 Figure 2-13: Steady State Crack Analysis, Steady State Flat Crack (Li & Leung, 1992) ............ 40 Figure 2-14: Typical Behaviour of URM Walls in Earthquake Generated Ground Shakings ..... 44 Figure 2-15: In-Plane Failure Modes of URM Walls (ElGawady, Lestuzzi, & Badoux, 2005) .. 45 Figure 2-16: Principal OP Failure Mechanisms for URM Walls (D'Ayala, et al., 1997) ............. 45 Figure 2-17: Acceleration Profile of Test Wall – GC2-1.32 (Meisl, 2006) .................................. 47 Figure 2-18: Physical & Analytical Models of OP Rocking Prototypes (SRG III, 2017) ............ 48 Figure 2-19: Backbone Curve for Out-of-Plane Prototypes (SRG III, 2017) ............................... 49 Figure 2-20: Force Displacement Relationship for Out-of-Plane Prototype (SRG III, 2017) ...... 50 Figure 2-21: Semi-Rigid OP Force Displacement Relationship for URM Walls (Meisl, 2006) .. 51 xix  Figure 3-1: Mass Proportions (Left); Mass Proportions of CM vs. Water and Sand (Right) ....... 59 Figure 3-2: EDCC Spray Pump (left), Spray Gun (top), and UBC Spray Chamber (bottom) ..... 60 Figure 3-3: Different Application Methods for EDCC ................................................................. 62 Figure 3-4: Applying EDCC onto URM Walls: Surface Pre-Miniaturization to Final Finishes .. 63 Figure 3-5: Schematic Setup for Standard Disk Pull-Off Test (Adopted from ASTM C1583) ... 65 Figure 3-6: Post-Impact Investigation of the Masonry-EDCC Tensile Bond Performance ......... 66 Figure 3-7: Schematic of Failure Modes of a Disk Pull-Off Test (ASTM C1583) ...................... 67 Figure 3-8: EDCC-CMU Tensile Bond Strength Data from Wall-1 after Collapse ..................... 68 Figure 3-9: Statistics for the Tensile Pull-Off Tests on Wall-1 .................................................... 69 Figure 4-1: Drawing from Bush, Bohlman & Partners (left) and the Six URM Walls (right) ..... 76 Figure 4-2: Wall Specimens – Six Specimens, 1.6m Wide by 2.8m Tall..................................... 77 Figure 4-3: Acceleration and Displacement Time-Histories for GM-1 @ 100% ......................... 84 Figure 4-4: Idealized Mass-Spring-Damper System Schematic for LST & Specimen ................ 85 Figure 4-5: Spectral Content of GM-1 @ 100% as Recorded on LST (5% Damping Ratio) ...... 86 Figure 4-6: Spectral Content of GM-4 @ 100% as Recorded on LST (5% Damping Ratio) ...... 87 Figure 4-7: Acceleration and Displacement Time-Histories for GM-4 @ 100% ......................... 88 Figure 4-8: Schematics of the Instrumentation of the Wall Tests; Wall # 1 is Shown Above ..... 92 Figure 4-9: Wall-2 during Run-4, being Tested at 150% Actual Intensity of GM-1 .................... 93 Figure 4-10: Views of Wall-2 before Collapse at Extreme Deformations during Run-5 ............. 94 Figure 4-11: Displacement Trace of Wall-2 from 133rd to 134th Second of Run-4 .................. 100 Figure 4-12: Displacement Trace of Wall-1 from 126th to 127th Second of Run-9 .................. 101 Figure 4-13: Acceleration profile at the impulse on Wall-3 at Run-13 ...................................... 103 Figure 4-14: Acceleration Traces for all Channels along the Height of Wall-2 at Run-4 .......... 108 xx  Figure 4-15: Acceleration Traces for all Channels along the Height of Wall-1 at Run-9 .......... 109 Figure 4-16: Acceleration and Displacement Amplification Factors for W-1 vs. Wall-2 .......... 110 Figure 4-17: Deflections of Wall-2 at its Mid-Height Point at Run 1 ........................................ 111 Figure 4-18: Deflections of Wall-2 at its Mid-Height Point at Run 2 ........................................ 112 Figure 4-19: Deflections of Wall-2 at its Mid-Height Point at Run 3 ........................................ 113 Figure 4-20: Deflections of Wall-2 at its Mid-Height Point at Run 4 ........................................ 114 Figure 4-21: Idealization of Out-of-Plane Rocking by Doherty et al. (2002) ............................ 118 Figure 4-22: Trilinear Force-Displacement Rocking Model ( Ferreira et al., 2014) .................. 119 Figure 4-23: Base Shear vs. Mid-Height Drift for all the Runs of Wall-2 ................................. 123 Figure 4-24: Overturning Moment vs. Average Rotations at Supports for Wall-2 .................... 125 Figure 4-25: Double-Curvature Bending Deflections for Wall-2 during Run-4 ........................ 126 Figure 4-26: Multiple Curvature Deflections for Wall-2 ............................................................ 127 Figure 4-27: Moment-Curvature Diagram for all the runs of Wall-2 ......................................... 128 Figure 5-1: Vibration Cycle at Mid-Height of Wall-2 for 30th to 36th Second of Run-4 .......... 131 Figure 5-2: Damped Free Vibration at Mid-Height of Wall-2 at 60th Second of Run-4 ........... 132 Figure 5-3: PSD for Six Seconds of Vibration of Wall-2 at 30th Second of Run-4 ................... 133 Figure 5-4: Damping Assessment using Bandwidth Theory (Carrillo et al., 2012) ................... 134 Figure 5-5: Fundamental Frequencies and Fitted Curves for Wall-2 ......................................... 136 Figure 5-6: Damping Ratios for Wall-2 after all the Runs, from Short Vibration Cycles .......... 137 Figure 5-7: Damped Force-Displacement Cycle for Wall-2 at 30th Second of Run-4 .............. 138 Figure 5-8: Normalized Mode Shapes for the Double Sided Walls ........................................... 140 Figure 5-9: Spectral Acceleration for the Blue Frame during Run-7 of Wall-1 ......................... 143 Figure 5-10: Spectral Velocity for the Blue Frame during Run-7 of Wall-1 .............................. 144 xxi  Figure 5-11: Spectral Displacement for the Blue Frame during Run-7 of Wall-1 ..................... 145 Figure 5-12: ARTeMIS Model Showing Wall-1 at Run-3 Vibrating at 1st and its 2nd Modes . 146 Figure 5-13: Singular Values of Spectral Densities of Wall-1 at Run-3 .................................... 147 Figure 5-14: Coupled Modes with Frame Components for Wall-1 at Run-2 in ARTeMIS ....... 148 Figure 5-15: Singular Values of Spectral Densities of Filtered Data of Wall-1 at Run-6 .......... 149 Figure 5-16: Mode Shapes 1–6 for Wall-2 before Run-5 using ARTeMIS Modal Pro ............. 150 Figure 5-17: Monitoring Natural Frequencies for all the Runs on Wall-1 ................................. 151 Figure 5-18: Monitoring Natural Frequencies for all the Runs on Wall-2 ................................. 154 Figure 6-1: Sample’s Dimensions (mm) ..................................................................................... 157 Figure 6-2: Measuring & Mixing Equipment (left); Mixture of PVA + PET Fibers (right) ...... 158 Figure 6-3: Casting, Consolidating, and Demolding EDCC Specimens (from left to right) ...... 158 Figure 6-4: Apparatus (left), grip mechanism (top right), and Air Chamber (bottom right) ...... 159 Figure 6-5: Tested Specimens (right) and the Fiber Pull Out at the Crack Opening (left) ......... 161 Figure 6-6: Average Curves for Load vs. Time .......................................................................... 162 Figure 6-7: Average Curves for Stress vs. Stain ......................................................................... 163 Figure 6-8: Coefficient of Variation (Load vs. Displacement) ................................................... 163 Figure 6-9: Static vs. Dynamic Stress-Strain Response of Premium EDCC Mix ...................... 164 Figure 6-10: Static vs. Dynamic Stress-Strain Response of EDCC Mix with 2% PET ............. 165 Figure 6-11:  Static vs. Dynamic Stress-Strain Response of Regular EDCC Mix ..................... 165 Figure 6-12: Acceleration and Displacement Peaks in Time-History of Wall-2 at Run-3 ......... 170 Figure 6-13: The Largest Six Impact-Like Load-Deflection Cycles for Wall-2 ........................ 171 Figure 6-14: Force-Time Curves for the Six Highest Impact Loads for Wall-2 ........................ 172 Figure 6-15: Deflection-Time Curves Corresponding to the Selected Load Peaks for Wall-2 .. 173 xxii  Figure 6-16: Displacement Rates for Wall-2 at six Major Peaks (Run-4 and Run-5) ................ 174 Figure 6-17: Load Rates for Wall-2 at six Major Peaks (Run-4 and Run-5) .............................. 175 Figure 6-18: Load-Deflection Rate Variation Curves for the Six Load Peaks of Wall-2 ........... 176 Figure 6-19: Strain Gages for Strain Sensing of EDCC on the Full-Scale Specimens .............. 177 Figure 6-20: Average EDCC Strain Readings at Mid-Height of Wall-1 at Run-22 ................... 178 Figure 6-21: Strain Trace for SG_6 from 22nd to 24th Second of Run-25 for Wall-1 .............. 180 Figure 6-22: A Short 0.2 Second Long Strain Trace with Trends for Wall-1 at Run-25 ........... 181 Figure 6-23: Calculated Strain Rates for 2-Sec Trace of SG_6 Strains on Wall-1 at Run-25 .... 182 Figure 6-24: Schematic Representation of Smeared Strain Readings over the Gage Length .... 184 Figure 7-1: SRG III – Retrofit Details for URM Partition # 11 – EDCC Technique ................. 209 Figure 7-2: Dynamic Load-Time Representative Curves for EDCC Premium Mix .................. 210 Figure 7-3: Dynamic Stress-Strain Representative Curves for EDCC Premium Mix ................ 211 Figure 7-4: Dynamic Load-Time Representative Curves for EDCC Mix with 2% PET ........... 211 Figure 7-5: Dynamic Stress-Strain Representative Curves for EDCC Mix with 2% PET ......... 212 Figure 7-6: Dynamic Load-Time Representative Curves for EDCC Regular Mix .................... 212 Figure 7-7: Dynamic Stress-Strain Representative Curves for EDCC Regular Mix .................. 213 Figure 7-8: Dynamic Load-Time Average Curves for EDCC Mixes ......................................... 213 Figure 7-9: Dynamic Stress-Strain Average Curves for EDCC Mixes ...................................... 214 Figure 7-10: Coefficient of Variation for Dynamic Load-Displacement for EDCC Mixes ....... 214 Figure 7-11: Dynamic vs. Static Stress-Strain Response for EDCC Premium Mix ................... 215 Figure 7-12: Dynamic vs. Static Stress-Strain Response for EDCC Mix with 2% PET ............ 215 Figure 7-13: Dynamic vs. Static Stress-Strain Response for EDCC Regular Mix ..................... 216 Figure 7-14: Concrete Masonry Products - 10cm Standard CMU Dimensions ......................... 217 xxiii  Figure 7-15: CMU delivered for building the specimens ........................................................... 218 Figure 7-16: Standard Clay Brick for Half-Scale Wall Panels ................................................... 219 Figure 7-17: The overall shape and dimensions of the CMU wall panels .................................. 222 Figure 7-18: Framed up CMU wall specimens at UBC .............................................................. 223 Figure 7-19: The Overall Shape and Dimensions of the Clay Brick Wallet Specimens ............ 224 Figure 7-20: Secured Clay Brick Wallet Specimens at UBC ..................................................... 225 Figure 7-21: Half-Scale Wall Specimens for Static OP Tests .................................................... 226 Figure 7-22: Instrumentation Details for the Half-Scale Specimens for Static OP Tests ........... 227 Figure 7-23: Static Tests Top Frame Supporting Condition Details .......................................... 227 Figure 7-24: The Test Setup for the Static-Monotonic OP Testing of Half-Scale Walls ........... 228 Figure 7-25: The Test Setup for the Static-Cyclic OP Testing of Half-Scale Walls .................. 229 Figure 7-26: The UBC Crew Setting Up and Getting Ready to Start at Jamieson School ......... 230 Figure 7-27: Design Specifications Being Reviewed and EDCC Getting Prepared .................. 231 Figure 7-28: Mixing EDCC with a Typical 60L Mortar Mixer at Jamieson School .................. 232  xxiv  List of Abbreviations  CMU Concrete Masonry Unit ECC Engineered Cementitious Composite EDCC Ecofriendly Ductile Cementitious Composite  EERF Earthquake Engineering Research Facility FRC Fiber Reinforced Concrete FRP Fiber Reinforced Polymer IC-IMPACTS Canada-India Research Centre of Excellence IP In Plane LDRS Lateral Drift Resisting System LLRS Lateral Load Resisting System LST Linear Shake Table MAST Multi Axis Shake Table OP Out of Plane PET Poly-Ethylene Terephthalate PVA Poly-Vinyl Alcohol SIERA Sustainable Infrastructure Research Group SRG Seismic Retrofit Guidelines UHPFRC Ultra High Performance Fiber Reinforced Concrete URM Unreinforced Masonry VF Volume Fraction xxv  Acknowledgements  First and foremost, I would like to sincerely acknowledge and appreciate the encouragement, support, and guidance of Professor Nemy Banthia, the primary supervisor of this doctoral work, as well as Professor Carlos Estuardo Ventura, the co-supervisor of the thesis. Without their support, care, and cooperation, this work would have not been possible with such a high quality, contribution, and impact.  Secondly, I would like to also acknowledge the assistance and guidance, which I received from both Dr. Patrick McGrath and Dr. Adam Lubell, the highly supportive thesis supervisory committee members, who dedicated their time over the past few years to provide me with top quality and very constructive advices and comments.  Special thanks would go to the administrative and technical staff at the Civil Engineering Department of the University of British Columbia for the great help and support through the past few years. Specially, the kind support of Mr. Harald Schrempp and Mr. Doug Hudniuk, whose assistants and contributions in setting up such a heavily experimental work has been remarkable.   Additionally, sincere thanks to Mr. Scott Jackson, Mr. John Wong, and Mr. Simon Lee, who helped me a great deal with instrumentation, data acquisition, and running the shake table and other related material and structural testing setups; as well as Dr. Mehrtash Motamedi, Dr. Armin Bebamzadeh, and Dr. Martin Turek. Furthermore, the kindness and continued support of Glenda Levins, Nadelene Nagamos, and other departmental administrative staff is appreciated. xxvi  I owe a great deal of recognition and appreciations to my beloved family for their countless, endless, and unconditional support, without whom, this journey would have never been started. To my sister Saghar and my brother Sasan, my awesome supports, who have always fulfilled me with love and care, and for always being there for me. Then of course, to the most special people in my life, whom this entire thesis is dedicated to, my lovely mother Mahin Lotfi, who patiently dedicated her entire life to us, and my role model of life, my father, Alborz Soleimani, who always unconditionally stood behind me and spoiled me with ultimate love, care, and attention.  My acknowledgements and appreciations extend to all of my colleagues and friends who provided me with tons of moral and physical courage and care throughout the past many years. Specially, I would like to thank Ferya Moayedi, who has been a moral and physical support to me over the past several years, all the way to the end of this journey; and also, for proof reading this long document, so patiently. In addition, many thanks go to my close friends Babak Ahmadi, Milad Mesbah, Amir Pourkeramati, Arash Tavakoli, Pouya Dehghani, Kasra Bigdeli, Saeid Allahdadian, Negar Roghanian, and Tahmineh Teymourian; as well as my great colleagues Yan (Joey) Zhou, Mohammed Farooq, Brigitte Goffin, Jane Wu, Ricky Ratu, Obinna Onuaguluchi, Aamer Bhutta, and many others, with whom I experienced such an enjoyable journey.  Finally and most importantly, I would like to greatly acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) and BrXton Construction LP, through the Collaborative Research and Development (CRD) grant. In addition, I would like to express special thanks to IC-IMPACTS, the UBC hosted Canada-India Research Centre of Excellence for the dedication and support throughout the project. xxvii  Dedication  This dissertation is dedicated to my beloved family, especially my parents, Alborz and Mahin, for their endless love, support, and encouragement.1  Chapter 1: Introduction The research focuses on development of a cost effective novel methodology for seismic retrofit of low-rise masonry buildings, using sprayable Ecofriendly Ductile Cementitious Composite (EDCC), which is a form of fiber reinforced engineered cementitious-based composite material. In particular, this retrofit strategy is targeting unreinforced, non-grouted, and unconfined non-loadbearing masonry walls of up to 6m tall. This type of wall would mainly be a common type of partition wall system used in many of the mid-age low-rise school and hospital buildings.  1.1 Research Program Incentives and Structure Due to their good sound and thermal insulation properties, unreinforced masonry (URM) walls are widely used in partitioning many of the commercial and residential buildings worldwide, either as in-fill or stand-alone. Therefore, URM is considered one of the most common types of partition wall systems in many of the mid-age, low-rise to mid-rise, school and hospital buildings in North America. This also extends out to the large number of offices, university buildings, and commercial facilities, which have a large number of URM partition walls, not only in Canada but also throughout the world. It should also be noted that slender URM walls made of Concrete Masonry Units (CMU) are still the main building blocks in many residential and commercial structures, in developing countries across the globe. This is mainly due to the availability and cost effectiveness of using CMUs in buildings.  1.1.1 Problem Statement URM partition walls are known to have very low drift capacities in seismic events and the failure mechanisms are known to be mostly brittle and catastrophic during earthquake shaking. 2  Compared to other partitioning systems, URM walls generally perform poorly during earthquake events, leaving many injuries and fatalities behind by collapsing. As fully elaborated in Section 1.2, need and necessity for development of modern retrofit technologies for such walls is clear.  At this time, removal of URM walls and replacing them with a different partitioning system, such as metal studs and gypsum panels is the most practical solution during school retrofits across the province of BC. Although this can sometimes be due to a change in space use, the main driving factor for such decisions by the building owner can be the negligible cost difference between the price of keeping and strengthening a URM partition wall, versus its replacement cost. For instance, there are currently miles of corridor walls existing in school building across the province, to be addressed during the ongoing seismic upgrade projects. However, securing URM partition walls, in a large scale, is currently very costly and difficult, considering the currently available techniques.  1.1.2 Goals, Objectives, and Scope The goal of this doctoral work was to develop a cost effective novel methodology for seismic retrofit of non-structural URM partition walls. The objective of the research work, however, is to develop and optimize a ductile material, targeted specifically for seismic applications, which has low cost and carbon footprint, with an easy, affordable, and practical application technique. The scope of the work includes providing out-of-plane restrain for URM partition walls to prevent failure and collapse of such walls during earthquakes, and is limited to the walls built of concrete masonry units (CMUs) with no surcharge. The following sections would provide an overview of the performed experimental tasks, with respect to the scope of the investigation. 3  1.1.3 Tasks and Thesis Overview The material is first tested, at the small-scale material level and through mesoscale experiments, to ensure an optimized material with high performance under dynamic rates of loading. Thereafter, practical application techniques are investigated and established, suitable for the material, with respect to its intended use. The material is then used to retrofit large-scale specimens, using the developed application methods. The specimens are instrumented at the materials level and monitored for structural response when tested on a shake table, using real earthquake ground-motion data, in order to investigate the overall out-of-plane behaviour of the retrofitted wall specimens in large scale. The test data is then used to determine the effectiveness of the retrofit, as well as development of operative damage detection techniques for the walls, during and after an earthquake. Section 1.4 elaborates on the performed tasks within the thesis and the details of the deliverables.  1.2 Need and Necessity for Development of New Retrofit Technologies While there is a significant body of research evidence on in-plane retrofit of in-fill, load bearing, and unconfined masonry, there is considerably less work done on out-of-plane retrofit strategies for URM walls. The main factor is that some of the URM walls highly affected by out-of-plane motions are partition walls or heritage facades, both of which are considered non-structural elements, and sometime are overlooked by structural research work.   In the context of the renewed interest and need toward multi-disciplinary research in today’s world, there is also need for cross-disciplinary investigations between structural studies and building material research fields. Therefore, devolvement and use of a novel type of ductile 4  cementitious composite for this intended application, out-of-plane strengthening of slender URM walls, is considered a needed and unique aspect of this doctoral work.  1.2.1 Demand for Higher Practical Performance Levels Although in-plane failure of URM walls, in the context of “life safety” or “collapse prevention,” may also be an issue, the out-of-plane collapse of these walls can create a great deal of casualties. Furthermore, both in-plane and out-of-plane failure of such walls becomes an important issue when considering higher performance criteria such as “damage mitigation” or “immediate occupancy”. Indeed, due to their very low displacement capacity, the URM walls have low allowable drift limits and a high probability of drift exceedance (SRG III, 2017). Such walls, if they do not collapse due to the out-of-plane failure, can have high levels of in-plane damage by formation of diagonal cracks, sliding close to the base, or toe-crushing, as shown in Figure 2-15. Therefore, after a seismic event, the wall is not repairable and most likely would need to be fully replaced. Considering the huge inventory of URM walls around the world, this can have a high net cost.  Unfortunately, building codes in Canada and around the world, still only mandate minimum performance criteria of life safety or collapse prevention only when walls are upgraded or retrofitted. Other performance criteria, such as damage mitigation and immediate occupancy are still considered luxury, even in most of the developed countries around the globe. This means that damage to the building elements during an earthquake shaking is of the secondary concern during the structural design. As a result, partition walls, being non-structural components, can be given a secondary importance during a major seismic upgrade project. This can mainly be due to 5  the lack of affordable technologies for securing this type of walls. Therefore, these walls are often easier to be removed, and replaced by alternative partitioning systems, such as metal studs and dry-wall partitioning system.  1.3 Introduction to the Developed Retrofit Methodology The developed methodology within this research work aims to provide nearly full out-of-plane detention for the wall building blocks, and presumably minor but uniform shear capacity enhancements for the in-plane action as a side benefit; therefore, holding the masonry units together from falling apart and being thrown during an earthquake generated ground motion. The newly developed high performance material is sprayable, ductile, and resilient, while being affordable, easy to apply, and having a lower carbon footprint, compared to the similar repair materials. The developed technology promises less injuries, casualties, and fatalities from failure or collapse of the URM partition walls. The technique can be even more valuable for high importance buildings such as schools, gyms, hospitals, fire halls, and other post-disaster shelters.  1.3.1 Introducing Ecofriendly Ductile Cementitious Composite (EDCC) Ecofriendly Ductile Cementitious Composite or EDCC is a composite material explicitly developed for seismic applications (Soleimani-Dashtaki, Soleimani, Wang, Banthia, & Ventura, 2017). It is considered one specific class of engineered fiber reinforced cementitious composites with elastoplastic type behavior under tension. EDCC uses about 30% cement content of typical repair mortar mixes, contains only natural sand, and uses a hybridized fiber system, about 2% in volume fraction, for creating the elastoplastic and strain-hardening type behavior and achieving high ultimate strain capacities of up to 5%, under pure tension (Wang, Banthia, & Sun, 2013). 6  Achieving such unique tensile elastoplastic modus from a cementitious-based composite requires an elaborate design, using a micro-mechanical approach, which takes into account the fracture mechanics of the matrix, the mechanism in which a fiber is engaged within the matrix, and the interactions at the fiber-matrix interface. Not only does the achieved ductility make EDCC a perfect choice for seismic applications, but also the lower cement content and hybridized fiber system would make EDCC cost-effective, practical, and a more sustainable material, compared to the other conventional cement-based repair systems. There are two different EDCC mix designs considered in this research, called the “Regular EDCC Mix” and the “Premium EDCC Mix,” which is a higher performance mix of EDCC, as explained in section 3.3 of this thesis.  1.3.2 Sprayability of EDCC The uniquely developed spray system for this material, as shown in Figure 3-2, is a low velocity shooting mechanism, using a rotary type pump, which is fairly similar to the spray systems typically used for spraying cementitious-based plasters and fire proofing polymer coatings. Considering the low velocity shooting aspect in spraying EDCC, there will be fewer particles and fibers bouncing off the placement surface (i.e. rebound issues). Creating less material waste (due to the less rebound), makes the spray process of EDCC more sustainable, compared to the other types of repairs with high velocity spray systems (i.e. shotcrete).   1.4 Testing Program and Deliverables For this primarily experimental work, two different classes of tests are completed. The first set of the tests are dedicated to investigations on the pure material properties, effectiveness of the repair system, and the failure behavior of different EDCC mixes under different rates of loading. 7  In the second set, the material is applied directly to masonry wall specimens, as a strengthening layer, so that the combined behaviour is investigated in large-scale testing format. This real-scale experimental work includes shake table testing of full-scale wall specimens, for overall response. Damage assessment tools are developed to understand refined details about the damage states of the specimens during / after the tests. This section briefly elaborates on each experimental phase.  1.4.1 Material Level Investigations During the initial development phase of EDCC, the material is tested for its mechanical properties at slow rates of loading. However, many structures could be subjected to high strain rates of loading caused by earthquakes, impacts, or blasts. Since EDCC is targeted for seismic retrofit applications, the effects of high rates of loading are also investigated.  For this phase, a large number of small-scale specimens are cast and tested under pure tension with different rates of loading to investigate the ultimate stress and strain capacities, as well as rate dependency of the consecutive response of different EDCC mixes. Therefore, the optimized repair material, having desired ductility, strength, and bond properties can be selected while maintaining material rheology to allow sprayability (Kim, Kong, & Li, 2003).  1.4.2 Dynamic Testing of Full-Scale EDCC Retrofitted Specimens In order to investigate the effectiveness of this rehabilitation system for enhancing the out-of-plane response of URM walls, a series of full-scale walls are tested on a shake table, using natural recorded earthquake ground motions, scaled to the mean hazard spectra of NBCC 2015 for Vancouver, Victoria, and Tofino (NRC, 2015). 8  The full-scale wall specimens are completely instrumented, in order to collect information, in both material and structural levels. Accelerometers and displacement sensors are installed to monitor the global response, and strain gages are implemented into the repair EDCC layer in order to understand what the repair material is actually going through within an earthquake run.  1.4.3 Development of a Vibration-Based Damage Assessment Technique Not only are the shake table testing results used for overall performance assessment, but also are used to develop a simple damage assessment tool, which predicts the state of damage at different intervals during the test. Considering that each run of the shake table testing is usually a few minutes long, the test often cannot be interrupted to assess the specimen during the test. Therefore, important stages of the damage on the specimen can be easily missed within a single run. Thus, an ongoing assessment tool is created using vibration assessment techniques, which can estimate the damage state of a wall, during the test, from the recorded signals. Consequently, more information can be extracted from the vibration behaviour of the walls during shaking, on how the damage is progressing during a single earthquake run.  1.5 Translation of the Technology to Real Life Applications In order to ensure practicality of the technology, the experimental results and the retrofit details are peer reviewed by a committee of local senior structural engineers and, accordingly, approved by a third-party technical review board, as small part of the third edition of the BC Seismic Retrofit Guidelines (SRG III, 2017). A demonstration project is done, using the developed technology for retrofitting a URM wall at a BC public school, as described during the proceeding sections and shown through photo highlights in Appendix F  of this thesis. 9  1.5.1 Technology Inclusion in the Seismic Retrofit Guidelines It is worth mentioning that, as of July 2017, EDCC is an officially recognized retrofit option by the third edition of the BC Seismic Retrofit Guidelines (SRG III), for out-of-plane retrofit of URM walls. This retrofit technique, which is referred to as “URM # 11” in Volume 7 of SRG III, allows design engineers to use sprayed or troweled EDCC as a retrofit option for securing URM walls for out-of-plane failure, by providing out-of-plane restrain. The detailed design specifications and drawings for the EDCC retrofit option (URM#11) are provided in SRG III to allow the design engineers to prescribe this retrofit option for different projects, if desired. It is worth mentioning that SRG III, along with its web-based platform, is currently the only available unified tool for structural engineers working on assessment and retrofit of BC school buildings; this tool is developed through a joint effort by APEGBC and UBC. The guideline is requested and paid for by the BC Ministry of Education, to be explicitly used by design engineers working on projects related to the mentioned seismic upgrade program for BC schools (SRG III, 2017). Appendix A  provides the full information and design specs for EDCC (URM#11) option, as presented in Volume 7 of SRG III.  1.5.2 Real-World Application of EDCC through a Demonstration Project As part of the research plan, a public school in Vancouver, BC, Canada is selected for demonstration of the EDCC retrofit on a URM wall. Dr. Annie Jamieson Elementary School is owned by the Vancouver School Board and operates under the legislations of BC Ministry of Education. The school has been going through a seismic upgrade, for which Bush, Bohlman & Partners LLP is the structural design firm for the project and Heatherbrae Builders Co. LTD is the general contractor. The retrofit details are in accordance with the SRG III guidelines, as 10  presented in Appendix A  and the retrofit was completed on Nov 7, 2017. Highlights of the project are presented in Appendix F  .  1.5.3 Market Size and Industry Demand for the Technology According to the British Columbia (BC) Ministry of Education in Canada, with reference to the Seismic Upgrade Program for BC schools, currently there are about 346 school buildings, in the province of British Columbia alone, classified as high risk, which are in urgent need of seismic upgrade, half of which are still to be addressed (BC-MOE, Feb 2018). From these school buildings, there are a large number of them with URM partition walls, which need to be retrofitted as part of the BC seismic upgrade program. The ministry has prioritized the seismic upgrade program, for BC schools, and has secured funding for this seismic upgrade program, and all of the retrofit projects are lined up and prioritized to be completed by 2030. Aside from BC, there is a large number of buildings across the world, made of URM units, which are in immediate need for seismic strengthening. In many of these countries, affordable retrofit is considered the only real option, since building replacement is not practical nor an economically feasible solution. 11  Chapter 2: Background and Literature Review The scope of this doctoral work requires background information and proficiencies in two major areas of expertise, considering the multi-disciplinary nature of the thesis.  On one side, the thesis elaborates on development and optimization of a novel specialized material for seismic retrofit applications. This mandates working with a high performance material with great toughness, high ductility, good energy absorption, and high ultimate strain capacity. Then it expands on development of a practical spray system for this material, facilitating the application process in terms of speed and cost.   On the other hand, the ultimate objective of the thesis is development of a novel and practical technology to address the issues related to the high rate of collapse for unreinforced masonry (URM) walls during an earthquake-shaking event. Thus, the thesis expands upon an extensive experimental program to examine the retrofit technique, using the newly developed high performance material.  Accordingly, this chapter provides background information and elaborates on the literature search done on both of the aforementioned areas of investigation, organized in different sections. It is worth mentioning that in some instances it is necessary to provide some background information within the main chapters of the thesis, for discussion purposes. In particular, there are existing numerical modeling and response estimation models for URM walls, which are directly discussed in a different chapter of this thesis, so to avoid repetition they are only described briefly in this section. 12  2.1 Background on Development of Ductile Cement Based Composites Over the past few decades, the general use of Fiber Reinforced Concrete (FRC) has been constantly increasing within the construction industry due to its performance improvements in terms of crack control and toughness. In fact, FRC has some great structural and non-structural applications, such as shotcrete ground support, tunnel linings, and industrial slabs-on-grade.  2.1.1 Conventional Fiber Reinforced Mortar and Concrete Typically, a three-phase model is used to describe an FRC mix: matrix, fiber, and the aggregate phases. It is known that the overall impact resistance capacity of concrete is increased by introducing randomly distributed fibers into the mix. However, this capacity is limited due to the poor bonding and week interactions between the three phases within the fiber reinforced concrete. Also, the dominant failure mechanism is usually the fiber-matrix debonding caused by tensile and shear deformations. Therefore, the use of polymer-based fibers, such as polyester, is more effective than other types of fibers in increasing the energy absorption of the concrete because of their enhanced bond with the matrix (Xu, Toutanji, & Gilbert, 2010).  When incorporated into the matrix, polymer-based fibers are also effective in reducing the overall weight of a reinforced concrete structure, enhance ductility, toughness, and crack resistance (Jalal-Uddin, Araki, Gotoh, & Takatera, 2011). In addition, increased durability has been proposed because of reduction in permeability caused by the pore refinement and crack control from high fiber content addition (Banthia & Bhargava, 2007). 13  2.1.2 Introduction to Different Advanced Types of FRC As a quick background to different classes of high performance FRC and ultra-high performance cementitious-based composites, reinforced with different types of fiber systems, Figure 2-1 presents a schematic diagram, comparing typical tensile stress-strain responses for three distinct classes of these materials. The diagram intends to create a distinction between these types.   Figure 2-1: Schematic Comparison between Different FRC Classes  In Figure 2-1, representative stress-strain fundamental response curves are presented for regular Fiber Reinforced Concrete (FRC) and Ultra-High Performance Fiber Reinforced Concrete (UHPFRC) in comparison to EDCC type material. FRC, which is the basis of the other two types, shows a typical tension softening type behaviour, with lower capacities in both peak stress and ultimate strain. On the other hand, UHPFRC, having a very high cracking strength, usually shows a great deal of strain hardening, compared to other cementitious composites, but lacks ductility, has a relatively low ultimate strain capacity, and retains high modulus of elasticity 14  (Yoo D. , Banthia, Kang, & Yoon, 2016). Unlike the other two, an EDCC type material is micromechanically engineered to have an elastoplastic type response with high capacities in ultimate strain and elastic/first cracking strengths similar to its parent, FRC. Although EDCC is not known for showing strain-hardening type behaviour, some EDCC mixes, containing higher volume fractions of fiber composition, tend to show strain hardening, compression toughening, and flexural hardening (Li V. C., 2007).  One innovative type of FRC is called Engineered Cementitious Composites (ECC), which is a class of the ultra-ductile fiber reinforced cementitious composites, initially developed by Prof. Li at U. of Michigan for use in applications that require large volumes of material (Li V. C., 1993). EDCC is considered one specific type of Engineered Cementitious Composite (ECC), which is a class of fiber reinforced cementitious composite with elastoplastic response or even strain-hardening type behavior under tension, in some of its high-fiber content composition forms.  Considering the sustainability aspects, it should be taken into consideration that cement‐based repair materials like UHPFRC usually involve the use of large quantities of cement to facilitate ease of application and development of a strong interfacial bond with the substrate. Also, bearing in mind that, unfortunately, production of Portland cement is responsible for nearly 8% of total global anthropogenic CO2 emissions. In particular, one ton of cement production emits nearly one ton of CO2 into the atmosphere and requires over 4GJ of energy. Therefore, a primary challenge in creating an ecofriendly and sustainable repair material like EDCC is to reduce the Portland cement content in the material by replacing it with industrial by‐products such as fly ash, silica fume, or granulated blast-furnace slag (Banthia N. , 2011). 15  2.1.3 Behavioral Classification of Fibrous Cementitious Composites Multiple factors can affect the bond-slip behaviour of a single fiber when being pulled out of a cementitious matrix. When dealing with material design and modifications at micro level, it is important to understand these factors and their associated effects on the bond-slip behaviour, and subsequently, on the overall composite behaviour of FRC. This section discusses some of the factors, known to affect bond-slip behaviour, described in published literature.  In general, when the fiber contents are 2 - 3% or higher (by volume), in a suitable cementitious composite matrix, the overall stress-strain response and the fracture behaviour is distinctly different from lower fiber contents. Mainly, in such higher fiber contents, the composite starts to show strain-hardening type behaviour as in ECC rather than typical tension-softening response as usually seen in normal FRC under uniaxial tensile loads (Wang, Wu, & Li, 2001).    General behaviour of FRC can be characterized by the overall shape of the curve presenting the stress variations across a crack (σ), as a function of the crack opening (δ). In fact, the shape of the stress-strain response for this type of material is governed by many factors such as matrix composition, fiber volume fraction, diameter, length, strength, and modulus, in addition to the fiber-matrix interaction parameters, which include the interfacial chemical, and frictional bond properties (Lin, Kanda, & Li, 1999).  2.1.4 Factors Affecting Overall Consecutive Response of FRCC Extensive research over the past decades has shown that the fundamental property of any type of fiber reinforced cementitious composite material lies in the specific way fibers bridge the crack 16  and the stress transfer mechanism across the crack (Li V. C., 1992). This property is usually represented as a stress across crack (σ) versus crack opening (δ). In particular, the stress (represented by the symbol “σ”) is the average tensile stress transmitted across crack with uniform crack opening of δ as perceived from a uniaxial tensile specimen under loading (Li V. C., 2003).  2.1.4.1 Micromechanism Involved in Fiber-Matrix Interaction Following crack formation, fibers behave in one of the two manners. The fiber can debond and get pulled out of the matrix slowly, developing frictional surface stresses, or alternatively, it can fracture at the crack opening, and loose contact completely. The two cases are as follow:  Case I – Fiber being fully pulled out of the matrix Shear stresses can develop along the fiber length; this would follow by interfacial debonding of the fiber at the crack opening. After which, the rest is governed by the frictional properties caused by the fiber being pulled out of the matrix with means of an almost constant shear stress along the debond fiber length at the surface. Thus, a debonding follows by the mechanical forces, such as friction, happening at the fiber-matrix interface, as in Figure 2-2.  Case II – Fiber ruptured at the crack opening The interfacial bond, through shear stresses along the surface of the fiber, induces tensile stresses in the fiber. If the tensile stress exceeds the fiber ultimate strength, the fiber fractures and is ruptured at the crack opening. Thus, no pullout would happen after this point and the fiber gets fully unloaded. 17  Figure 2-2 demonstrates the interfacial debonding shear stresses as well as the mechanical frictional shear stresses discussed above. This graph also points out that the peak maximum shear stress at debonding on the surface is much higher than the frictional shear stress after debonding.   Figure 2-2: Schematic of a Single Fiber Pullout at Crack Opening (Bentur et al, 2007)  2.1.4.2 Contributions of the Matrix to the Bond-Slip Response Many variables of the cementitious composite matrix affect the bond-slip behaviour of fiber pullout. The interfacial transition zone (ITZ) is a weak, porous, calcium hydroxide rich zone that develops around solid boundaries such as between the matrix and the fiber or between the matrix and the aggregate (Banthia, Bindiganavile, Jones, & Novak, 2012).   There is a significant lack of reproducibility between replicate single fiber pullout tests that is attributed to changes in the nature of the ITZ caused by such things as concrete or mortar batching, mixing, casting, placement, and consolidation techniques as well as curing (Bentur & Mindess, 2007). 18  Moreover, aggregate properties including angularity, gradation, and chemical decomposition (i.e. alkalinity) can affect the fiber-matrix interface and the overall bond-slip behaviour. In addition, the aggregate angularity can influence the interlocking behaviour in any concrete or mortar matrix. The aggregate interlocking properties can also be manipulated by the sample size and can be greatly affected by different loading scenarios (tension vs. bending), strain rates, and fracture directions (Mindess, Young, & Darwin, 2003).  Furthermore, variations in chemical composition, or rate and nature of the reaction of the cementitious materials in the matrix binder can influence the bond interface properties between fibers and the matrix. Even ordinary Portland cement (e.g. Type GU) from different sources can have different hydration and chemical characteristics (Mindess, Young, & Darwin, 2003).  More significantly, use of Supplementary Cementing Materials (SCMs) in mortar or concrete mixes are fairly common in today’s concrete industry. These SCMs are mostly by-products of different industries such as iron smelting or coal burning. Thus, the consistency of their cementitious and pozzolanic capacities can be varied quite readily, since they are obtained from so many different sources (Mindess, Young, & Darwin, 2003). This fact can also affect the matrix composition, and accordingly, the bond-slip performance of the fibers, as discussed later.  2.1.4.3 Contributions of the Fiber System to the Bond-Slip Response The volume of the fibers (Vf) plays an important role in categorization of the total composite response, particularly post-cracking. This is most evident when moving from FRC to ECC or EDCC. In general, in Ductile Fiber Reinforced Cementitious Composite (DFRCC) systems, the 19  role of fiber content (Vf) in the micromechanism development of the fiber-matrix interaction becomes more significant (Li V. , 1998). In addition, significant improvements in toughness are obtained for mixtures of Ultra High Performance Fiber Reinforced Concrete (UHPFRC) with higher fiber contents (Kazemi & Lubell, 2012).  2.1.4.4 Effect of Fiber Content and Geometry on Behaviour of FRC From a micromechanical perspective, the fiber volume fraction (Vf) and the fiber length (L) in any FRC would have great influences on both the bond-slip behaviour of single fibers and the overall material response as a composite system (Yoo, Kang, & Yoon, 2014).  The relevance of fiber volume fraction (Vf) and fiber length (L) to the mechanical behaviour of FRC can be discussed from two different perspectives:  (i) The effect of each factor for single fibers isolated from the contribution of all the fibers; this is referred to as the bond-slip behaviour in a single fiber pullout.  (ii) The effect of each factor on the composite response of the system; this is when the fiber is put into action with all of the other fibers.  In this section, the effect of fiber volume fraction and the fiber length are investigated separately, through literature survey, and their dependence on the various factors are discussed separately. At the end, the effect of geometrical modifications on the bond-slip response is discussed.  20  2.1.4.4.1 Fiber Content - Volume Fraction (Vf) As discussed in preceding section, the volume of fiber as a fraction of the total mix volume is important for the total composite response. Traditionally, it was assumed that contribution of one fiber can be integrated across a crack length to find out the contribution of all the fibers. However, the crack propagation mechanism can potentially be completely different when all the fibers are acting all together (Yoo, Yoon, & Banthia, 2015).  As the fiber content increases, the fibers might cross over each other at the crack opening. This might limit the fiber-matrix contact and affect the bond-slip behaviour. The orientation of fibers with respect to the tensile loading direction and centroidal distance of the fibers from the crack plane are changed when dealing with higher fiber contents (Li V. C., 1992).   Higher fiber contents can also cause potential fiber dispersion issues, which are discussed in more details in the following sections. Research shows that there exists a critical fiber content, which can predict the overall behaviour of the FRC system (Bentur & Mindess, 2007).   The critical fiber content can be used to classify the fiber reinforced cementitious composite behaviour, based on four different fiber content ranges (Vf), as listed and discussed as:  ∗  𝐂𝐚𝐬𝐞 𝐈: 𝑊ℎ𝑒𝑛  𝑽𝒇  <  𝑽𝒇(𝒄𝒓𝒊𝒕𝒊𝒄𝒂𝒍)  ⟹ 𝐵𝑟𝑖𝑡𝑡𝑙𝑒 𝐵𝑒ℎ𝑎𝑣𝑖𝑜𝑢𝑟 𝑎𝑠 𝑝𝑙𝑎𝑛𝑒 𝑐𝑜𝑛𝑐𝑟𝑒𝑡𝑒 This mode of failure is by the propagation of a single crack, since there is an insufficient volume of fibers to support the load that was carried by the matrix as it cracks. Thus, the composite 21  system would behave very similar to a plain concrete where there is no fiber added. Figure 2-3 (b) shows a schematic description of tensile stress-strain curves of composite with Vf < Vf (Critical).   Figure 2-3: Schematic Stress-Strain with Vf Above and Below Vf (Cr.) (Bentur et al, 2007)  As shown in Figure 2-3 (b), there is no residual strain capacity left after the initiation of the first crack. In fact, the response is only from the elastic behavior at the pre-cracking region (Bentur & Mindess, 2007). In such case, the integration of the bond-slip of a single fiber across a crack results in over estimation of the material toughness and more comprehensive fracture toughness models or experimental examination of the composite under different cracking conditions are needed for better estimations of the material toughness values.  ∗ 𝐂𝐚𝐬𝐞 𝐈𝐈: 𝑊ℎ𝑒𝑛  𝑉𝑓(𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙) < 𝑉𝑓  ≪  𝑉𝑓(𝑢𝑙𝑡𝑖𝑚𝑎𝑡𝑒) ⟹ 𝑇𝑒𝑛𝑠𝑖𝑜𝑛 𝑆𝑜𝑓𝑡𝑒𝑛𝑖𝑛𝑔 𝐵𝑒ℎ𝑎𝑣𝑖𝑜𝑢𝑟 𝑎𝑠 𝐹𝑅𝐶 When Vf is more than Vf (Critical), but much less than the Vf (Ultimate), the typical tension softening type behaviour of FRC, as shown in Figure 2-1, is observed. Referring to Figure 2-3 (a), when 22  the fiber volume is more than the critical value, then concrete would start to show post-cracking toughness (Bentur & Mindess, 2007). The residual toughness energy is from the post-cracking deformations and multiple cracking. This energy depends on a variety of factors such as matrix composition and structure, fiber type, geometry, surface coating, end textures, chemical bond, physical friction, and other interfacial chemical or mechanical properties (Bentur & Mindess, 2007).  Figure 2-4 provides a schematic representation of tension softening (typical FRC) versus strain hardening (typical HPFRCC) in a typical cementitious composite (Li V. C., 2007).  This schematic representation demonstrates the tension-softening behaviour of a classic FRC when the post-cracking load carrying capacity decays as strain increases over the course of loading.   Figure 2-4: Schematic for Tension-Softening vs. Strain-Hardening (Li V. C., 2007) 23  It is worth mentioning that the typical tension-softening behaviour shown in Figure 2-4 is not only a function of the fiber content. In fact, the emphasis here is the role of the fiber volume, Vf, as one of the main criteria in achieving such behaviour.  ∗ 𝐂𝐚𝐬𝐞 𝐈𝐈𝐈: 𝑊ℎ𝑒𝑛  𝑽𝒇(𝒄𝒓𝒊𝒕𝒊𝒄𝒂𝒍) ≪ 𝑽𝒇 < 𝑽𝒇(𝒖𝒍𝒕𝒊𝒎𝒂𝒕𝒆) ⟹ 𝑆𝑡𝑟𝑎𝑖𝑛 𝐻𝑎𝑟𝑑𝑒𝑛𝑖𝑛𝑔 𝐵𝑒ℎ𝑎𝑣𝑖𝑜𝑢𝑟 𝑎𝑠 𝐸𝐶𝐶 When Vf  much more than Vf (Critical), but less than Vf (Ultimate), FRC starts to show ECC type behaviour, with potential strain hardening regime. As mentioned before, a 2-3% fiber content coupled with a good cementitious matrix can show high ductility tensile behaviour. Figure 2-5 represents uniaxial tensile stress-strain curves of a typical ECC reinforced with 2% oil-coated PVA-REC15 fibers, showing high tensile ductility of about 5% in pure tension (Wang, Wu, & Li, 2001).    Figure 2-5: Three Tensile Stress-Strain Curves of a Typical ECC (Wang, Wu, & Li, 2001) 24  ∗ 𝐂𝐚𝐬𝐞 𝐈𝐕: 𝑊ℎ𝑒𝑛  𝑽𝒇(𝒖𝒍𝒕𝒊𝒎𝒂𝒕𝒆) < 𝑽𝒇  ⟹ 𝑈𝑛𝑤𝑜𝑟𝑘𝑎𝑏𝑙𝑒 𝑚𝑖𝑥 𝑤𝑖𝑡ℎ 𝑓𝑖𝑏𝑒𝑟 𝑑𝑖𝑠𝑝𝑒𝑟𝑠𝑖𝑜𝑛 𝑝𝑟𝑜𝑏𝑙𝑒𝑚𝑠 When Vf is more than Vf (Ultimate), then FRC would likely become an unworkable mix with fiber dispersion problems. The ultimate fiber content that can be added to a cementitious composite, Vf (Ultimate), is not an absolute value, but it is a representative measure to illustrate the upper limits. In fact, the maximum amount of fiber that can be added to a cementitious composite mix depends on the characteristics of the actual mix such as w/c ratio, aggregate type, size, gradation, and fineness; as well as the fiber geometry, type, shape, size, and water absorption capacity (i.e. hydrophobic vs. hydrophilic nature of the fibers) (Bentur & Mindess, 2007). Addition of fibers beyond such limit would result in a mix, which is very unworkable, but most importantly there will be major fiber dispersion problems resulting in dropped mechanical performance.  2.1.4.4.2 Fiber Length (L) In general, the effect of fiber length can be analyzed in terms of the stress transfer mechanisms discussed in the preceding sections. A critical length parameter, Lc, can be defined as the minimum fiber length required for the build-up of stress or load in the fiber, which is equal to its strength or failure load. The calculated value of Lc depends on the assumptions made regarding the stress transfer mechanism such as the frictional stress transfer mechanism or the elastic stress transfer mechanism (Bentur & Mindess, 2007).  Hence, for the fiber lengths less than the critical value, there is insufficient embedded length necessary to generate a stress equal to the fiber strength and, therefore, the fiber is not utilized efficiently. Indeed, only if the length of the fiber considerably exceeds the critical length (Lc), the 25  stress along most of the fiber can reach its yield or tensile strength (Yoo, Kang, & Yoon, 2014). Figure 2-6 illustrates the effects of length and bond on the bond-slip properties of fibers.   Figure 2-6: Effect of Fiber Length and Bond on FRC strength (Bentur & Mindess, 2007)   As shown in Figure 2-6, it should be noted that the fiber length effects on the pull out property is a complicated measure, thus, more sophisticated means of accounting for fiber length are generally utilized in fracture modeling of high performance FRC (Li V. , 1998).  2.1.4.4.3 Effect of Locally Bent Fibers on Post-Cracking Response of FRC Depending on the type of the fiber being mixed, the fibers can become deformed, damaged, or even fractured during the processing phase, particularly, when using high shear mechanical 26  mixers with cross-rotating blades. This section briefly discusses the effect of fiber damage on post-cracking behaviour of FRC.   The influence of local bending of fibers in the post-cracking zone of the response have been studied (Leung & Chi, 1995). Figure 2-7 shows the bending of a single fiber across a crack and the components of the crack bridging force are represented.   Figure 2-7: (a) Fiber Bending at Crack and (b) Crack Bridging Forces (Leung & Chi, 1995)  This may result in unexpected lack of system efficiency, if the inclination angle only in a straight fiber is taken into consideration, for which only axial stresses are assumed. This in fact results in overestimation of the load carried by the fibers across the crack. The response is also dependent on the properties of the matrix in the vicinity of the fiber and its ability to withstand the additional local flexure without cracking (Bentur & Mindess, 2007).  27  2.1.4.5 Effect of Fiber Deformations and Surface Modifications on FRC Deformations, end textures, and surface coatings are the most important fiber properties with respect to fiber-matrix interaction. These fiber properties can be tailored to change the mechanical properties of the composite.  These attributes influence both the chemical and frictional bonds (Yoo & Banthia, 2016).  In fact, the contribution of all the fibers across a crack would be affected by volume fraction, diameter, length, strength, and modulus, in addition to the fiber-matrix interaction parameters, which include the interfacial chemical, and frictional bond properties (Lin, Kanda, & Li, 1999). Certainly, both the interfacial chemical and frictional bond properties are highly affected by fiber geometry and surface modifications (Bentur & Mindess, 2007).  2.1.4.5.1 Fiber Geometry and Coating The monofilament fibers, which are used for cementitious composite reinforcement, rarely have a cylindrical shape, but are deformed into various configurations, to improve the fiber-matrix interaction through mechanical anchoring. A range of complex geometries, ranging from twisted polygonal cross sections to ring-type fibers have been evaluated, to provide effective anchoring, while maintaining adequate workability (Bentur & Mindess, 2007).  In Figure 2-8, there is an optimal range of frictional bond for PVA fibers in order to achieve strain hardening with 2% fiber content (Li, Wu, Wang, Ogawa, & Saito, 2002). The optimal frictional bond, as mentioned before, is a function of many parameters, including but not limited to the matrix composition. In Figure 2-8 (a), more specifically, single fiber pullout testing shows 28  that this target range can be achieved, with fiber modifications through texturing or surface coating, in a specific range (Li, Wu, Wang, Ogawa, & Saito, 2002).   Figure 2-8: Optimal Range of Frictional Bond to Achieve Strain Hardening (Li et al, 2002)  Figure 2-8 (b) shows the ultimate strain achieved by providing different surface coating contents to the PVA fibers (Li, Wu, Wang, Ogawa, & Saito, 2002). Oil coating of PVA fibers allow slippage to happen, instead of fiber yielding or fracturing; resulting in an optimum bond to transfer stresses, from the fibers, back to the matrix, creating a multiple-cracking regime, which creates higher strain capacities (Li & Zhang, 2016).  2.1.4.5.2 Fiber Surface Modification Providing surface coatings for the fibers is one of the important design factors, which a material designer can utilize to achieve ultra-high ductility from an engineered cementitious composite. There is tremendous amount of work done at the University of Michigan on the pullout properties and overall ECC responses while using different surface coatings (Li V. C., 2003). 29  Figure 2-9 demonstrates that excessive bond strength and severe fiber rupture limit the tensile strain capacity when PVA fiber is used untreated, as shown in Figure 2-9 (a). Significant tensile strain hardening is revealed, see Figure 2-9 (b), when the PVA fiber is properly coated with guidance from micromechanical models for interface property control (Li V. , 1998).   Scanning Electron Microscope (SEM) images of fibers from the composite fracture surface are shown for untreated and surface coated fibers in Figure 2-9. Delamination damage during pullout is visible for the untreated fiber, whereas the surface coated fiber is protected from damage during the pullout (Li V. C., 2003).   Figure 2-9: Effect of Surface Coating on Stress-Strain Response of ECC (Li V. C., 2003)  2.1.4.6 Effect of Crack Band Formation and Crack Branching on FRC Whether discussed from a composite micromechanics approach or from a fracture mechanics perspective, the fundamental ductile behaviour of fiber reinforced cementitious composites is not possible to achieve without the occurrence of multiple cracking, as part of the typical post-30  cracking behaviour for FRC, HSFRC, or ECC (Li & Leung, 1992). The presented subsections here focus on both crack band formations and the theories behind it and then discusses the possibility of crack branching at the micro level.  2.1.4.6.1 Crack Band Formation and Theories A flat crack propagation theory was first analyzed by Marshall and Cox (1988), applying the J-integral approach. According to Marshall and Cox the complementary energy of the fiber bridging curve has to be larger than the matrix toughness (Marshall & Cox, 1988). The multiple cracking phenomenon can be justified by such theories (Mindess, Lawrence, & Kesler, 1977), explaining the crack bands formations.  Fracture of a heterogeneous aggregate material such as concrete (either fiber reinforced or not) can be assumed to occur by progressive micro cracking, resulting in a stress-strain relationship that exhibits strain-softening. Such behaviour is not very easy to explain without the appropriate energy approach methodologies (Banthia N. , 2011).  In some of the alternative theories presented in the literature, the predictive effective width of the crack band front is about three-times the maximum aggregate size and the length of the fully developed fracture process zone is about 12-times the maximum aggregate size (Bazant & Oh, 1983). Knowing the effective crack bandwidth, it is possible to determine the fracture energy in fiber composites by measuring the uniaxial tensile stress-strain curve, including the strain-softening segment of the curve (Bazant & Oh, 1983).  31  2.1.4.6.2 Crack Branching During the Crack Propagation Crack branching is also another phenomenon in most of the research models of ductile or semi-ductile crack propagation mechanisms, especially when plastic deformations are present at the macro level around the fracture area (Leung & Chi, 1995).  If the strain-softening formulation for FRC is based on the total stress-strain, it is applicable only when the direction of the principle stress within the fracture process zone does not rotate significantly during the passage of the fracture front through a given station. However, this cannot be assumed always true, especially when large deformations are involved (Yoo D. Y., Banthia, Kang, & Yoon, 2016). For instance, in the case of beam bending, there will be rotation of the crack faces resulting in rotation of the principal stress direction. The cracked beam, indeed, is assumed to attain rigid body motions on both sides of the initial crack, with respect to the initial beam position (Fischer, Fukuyama, & Li, 2002).  The typical zigzag crack pattern, observed on typical failure surfaces of any cementitious composite, illustrates how the fiber is not uniaxially tensile loaded,. In fact, this rotation of the stress direction would considerably affect the bond-slip behaviour (Bazant & Oh, 1983).  In addition, referring to the same mentioned zigzag crack pattern and by rotations in the stress elements, the strain would continue on a rotated plane. This can result in inclination of the crack bands and, eventually, branching of cracks within the fracture plane. In fact, the almost parallel crack bands are now rotated, so across the facture neck there would be closely spaced bands, 32  which can lead the cracks to jump from one band to the other, creating localized cracks perpendicular to the crack face (Fischer, Fukuyama, & Li, 2002).  Fundamentally, rotation of the stress planes leads to the decomposition of the shear forces across the crack, from the fiber pullout. This induces minor tensile stresses at the fracture face, perpendicular to the crack propagation path; thus, the existing cracks start to branch out (Fischer, Fukuyama, & Li, 2002). Figure 2-10 demonstrates the formation of crack bands and the excessive crack branching caused by rotation of stress planes and fixed-end deformations.   Figure 2-10: Crack Band Formation and Branching - an R/ECC member (Li V. C., 2003)  In conclusion, formation of the mentioned crack bands as well as the crack branching results in a large overall crack path in terms of complete length; thus, an enormous amount of energy is being dissipated as the material is undergoing plastic deformation. This would make this type of material an attractive choice for applications requiring high ductility and plastic deformations without failure of the member (i.e. seismic applications). 33  2.1.4.7 Effect of Matrix Modifiers on Bond-Slip Behaviour of Fibers Matrix modifiers, such as silica fume, fly ash, methylcellulose, etc., play significant role in the overall response of any fiber reinforced cementitious composite. Especially, matrix densifiers typically used for achieving higher levels of strength and durability in high performance concrete would greatly affect the fiber-matrix interaction. The general properties and effects of each modifier on the bond-slip behaviour in FRC is discussed.  2.1.4.7.1 Silica Fume Silica fume is an amorphous structure containing SiO2 content from 85% to 98%. The particle sizes are approximately 10 times smaller than cement, having the mean particle size in the range of 0.1 - 0.2 µm. The particles have spherical shapes containing a number of primary agglomerates (Sellevold & Nilsen, 1987).  Silica fume undergoes a pozzolanic reaction with the by-products of cement hydration converting calcium hydroxide to calcium silicate hydrate. Its small size results in a filler effect, which promotes cement reaction. As a result, silica fume reduces average pore radius and reduces the thickness of the interfacial transition zone (ITZ) in the vicinity of any inclusions in the matrix such as aggregates, reinforcing bars, or fibers. Silica fume would greatly improve the bond-slip behaviour in any fiber pullout including the single fiber pullout behaviour.  Silica fume has some cementitious capacity and a good extent of pozzolanic capacity. However, it is well known to be used as a filler material in the concrete matrix for densifying the cementitious binder. Not only does silica fume increase the density of the matrix, but it also 34  improves the interfacial transition zone (ITZ) in the vicinity of any intrusions in the matrix such as aggregates, reinforcing bars, or fibers (Mindess, Young, & Darwin, 2003). Silica fume would improve the bond-slip behaviour in any fiber pullout including the single fiber pullout behaviour.  It is worth mentioning that silica fume, due its particle size and configuration, in general increases the water demand in fresh concrete, so it can highly affect the workability of the mix, and consequently, the fiber dispersion, due to a decreased mixing quality.  2.1.4.7.2 Fly Ash Fly ash is an industrial by-product mostly obtained from the combustion of pulverized coal in thermal power plants. It has spherically shaped particles having an average particle size similar to cement. However, the particle size can widely vary from 1 to 150µm, depending on the type of dust collection equipment used (Berry & Malhotra, 1987).  Fly ash has pozzolanic capacity and some cementitious capacity (dependent on source), which has a great effect on the matrix properties, generally in a similar manner as silica fume. In addition, the spherical shaped particles creates a ball-bearing effect within the body of fresh concrete, so it adds to its workability and pumpability (Mindess, Young, & Darwin, 2003). This results in higher quality products of hydration within the matrix, which improves the interfacial properties between the fibers and the matrix, thus, improving the bond-slip behaviour. In addition, fly ash due its general particle shape decreases the water demand in fresh concrete and increases the workability (Berry & Malhotra, 1987). Therefore, it can help the fiber dispersion and make some enhancements in the mixing quality. 35  2.1.4.7.3 Methylcellulose Methylcellulose, having nanoparticle sizes, has been investigated in recent years for its effects on the matrix properties of the cementitious composites. These nano-sized particles, which are much smaller than silica fume act as fillers within the concrete matrix. The great advantage of having methylcellulose in the mix is the further refinement of the matrix microstructure (Fu & Chung, 1998). This matrix densification would also greatly enhance the bond-slip behaviour, by increasing the frictional bond between the fibers and the matrix and by improving ITZ (Bentur & Mindess, 2007).  Methylcellulose itself as an admixture to the cementitious matrix increases the bond strength between the concrete matrix and steel rebars, steel fibers, and carbon fibers. It has been noticed that addition of this admixture would also serve to help disperse the fibers in the mix (Fu & Chung, 1996). It has been also shown that methylcellulose in combination with silica fume has a great effect on the bond properties. This is due to silica fume increasing the matrix elastic modulus and methylcellulose adhesion (Fu & Chung, 1998).  Since the addition of methylcellulose creates a high performance binder, its effect on the fiber-matrix interaction is unavoidable. However, due to the hydrophilic nature of methylcellulose, a high water absorption and retention occurs, reducing workability and thus compromising mixing ability and fiber dispersion (Fu & Chung, 1998).  36  2.1.4.8 Effect of Proper Mixing on Mechanical Behaviour of FRC Proper fiber dispersion is one of the key factors in achieving the desirable response of any fiber reinforced cementitious composite. Visual inspection is often used as the methodology in order to distinguish between a good and a bad dispersion.  Additionally, monitoring the compressive strength of the concrete before and after addition of the fiber content can be a good approximate indication for the uniformness of the fiber dispersion. If fibers are well dispersed in the mix, addition of low volume fraction of fibers to the mix should not affect the compressive strength of the FRC compared to the original matrix without fibers (Bentur & Mindess, 2007). At higher fiber volume fractions (VF), however, a potential drop of the compressive strength of the matrix is possible, even with minor fiber dispersion issues. Specifically, when dealing with higher fiber contents in FRC, proper mixture is sometimes not easy to achieve. Imperfect mixing would result in fibers being clumped up in separate bunches within the mix. The clumped fibers would have a negative contribution to the composite response, and subsequently, would act as weak planes where fractures can more easily occur.  2.1.5 Existence or Extent of Multiple Cracking as a Function of Fiber Content Enough fibers need to exist in an FRC mix to obtain good strain capacity, which is achieved through multiple cracks and considerations related to the chemical bond and friction.  The probability of multiple cracking in the matrix increases as the volume fraction of the fiber increases in the composite. In particular, the total fiber content in the cementitious matrix and the 37  bond-slip behaviour are key in creation the multiple cracking regime. As fiber content changes, fracture mechanism of FRC and, accordingly, the overall composite behaviour including the fracture toughness changes. From a composite material approach, the rule of mixtures can only be applied in the elastic, pre-cracked zone of the fiber reinforced cementitious composite. However, one important factor driving the post cracking response, either tension-softening type or strain-hardening type, is the fiber content and its interactions with the cementitious matrix which the fiber is imbedded in (Bentur & Mindess, 2007).  For the fiber volumes which exceed a critical value, 𝑉𝑓(𝑐𝑟𝑖𝑡), the mode of failure is characterized by multiple cracking of the matrix. After first cracking, the load carried by the matrix is transferred to the fibers, which due to their sufficiently large volume can support this load without failure. Additional loading leads to more matrix cracking, which is still not accompanied by the failure of the composite. In contrast, in situations where 𝑉𝑓 < 𝑉𝑓(𝑐𝑟𝑖𝑡), the mode of failure will be by the propagation of a single crack, since there is an insufficient volume of fibers to support the load that was carried by the matrix as it cracks (Bentur & Mindess, 2007).  In short, micromechanics relate macroscopic and physical properties of cementitious composites to the microstructure of the composite. In order to achieve high ductility in FRCC it has to be ensured that combination of micromechanism including the interfacial chemical and frictional bond properties create conditions for formation of multiple cracking as much as possible. As discusses, unless there is no mechanism in place for multiple cracking, the stress redistribution regime will not allow for extraordinary ductility, as observed from ECC or EDCC type materials. The following sections elaborate on this principle, from a fracture mechanics approach. 38  2.1.6 Micromechanics of Ductile Fibrous Cementitious Composites The key factor in order to understand the reason for the strain-hardening type behaviour of ECC versus the tension-softening type behaviour of FRC is to distinguish the load bearing and energy absorption roles of fiber bridging. There are two central criteria involved accounting for the ultra-ductile behaviour of this material (Li V. C., 2003).  Criteria I: One of the necessary conditions for multiple cracking is that the matrix cracking strength, which includes the very first crack strength, must not exceed the maximum bridging stress. This ultimate matrix cracking strength is shown as σcu on the schematic curve presented in Figure 2-11. In other words, if the maximum stress being transferred across the crack by the fibers is less than the mentioned σcu on the curve, the fibers would not be able to induce further cracks in the matrix, so they would rupture at the crack opening.   Figure 2-11: Typical σ-δ Curve with the Complementary Energy Shaded (Li V. C., 2003) 39  Criteria II: The second necessary condition for multiple cracking to happen is concerned with the mode of crack propagation. This is usually referred to as the energy criterion, which explains the energetics of crack extension in the matrix. In fact, in conditions such that the complimentary energy (shaded area ladled C on the curve presented in Figure 2-11) is small in comparison to crack tip toughness (the energy needed to break down the crack tip material to extend the bridged crack), the crack will behave like a typical Griffith crack as shown in Figure 2-12.   Figure 2-12: Steady State Crack Analysis, Griffith Type Crack (Li & Leung, 1992)  The condition, which results in a small shaded area C, creating a Griffith type crack as shown in Figure 2-12, consists of two conditions: (i) The fiber-matrix interface is too weak and thus pullout of fiber occurs. In fact, fiber pullout occurs at such as low stress that sufficient tensile forces are not created at the crack tip to create multiple crack paths. This results in an σ-δ curve with low peak strength (σcu) which typically sits flatter than what is seen in Figure 2-11. 40  (ii) The interface is too strong that the spring forces cannot stretch and the maximum fiber strength is achieved. This would result in rupture of the fibers bridging the crack and a small value of critical opening (δp). In this case, the curve would stand steeper and closer to the vertical axis compared to the schematic response curve shown in Figure 2-11.  In this type of Griffith crack, as the crack propagates the fibers get unloaded at the middle of the crack (where the opening is maximum), i.e. when δm exceeds δp in Figure 2-12. This type of crack propagation would result in a tension-softening (or also called strain-softening) regime during which the composite will fail progressively with reduced load carrying capacity as a typical FRC behaviour (Li & Leung, 1992).   In contrast, if the complimentary energy explained above is large (compared to the crack tip toughness), the crack will remain flat as it propagates and, therefore, a steady state crack opening (δSS) would be achieved, like shown in Figure 2-13.   Figure 2-13: Steady State Crack Analysis, Steady State Flat Crack (Li & Leung, 1992)  41  In this type of crack propagation the fibers stay loaded all across the crack and they maintain their tensile load carrying capacity at all time when the crack is propagating. As a result, the load can be transferred from the crack plane back into the matrix and cause the formation of another crack. The repetition of this process back and forth would create a well-known phenomenon of multiple cracking (Li V. C., 2003).   To recap, the two criteria (strength and energy) need to be satisfied at the same time in order for multiple cracking to happen. Multiple cracking is the backbone of the ductile behaviour of all the fibrous cementitious composites that show strain-hardening type response.  2.1.7 Effect of Applied Stress-Rates on Bond-Slip Behaviour of FRC The reliance of bond-slip on the rate of loading highly depends on both the matrix and the fiber properties. In particular, how the frictional shear stresses are distributed on the fiber surface, affects the rate dependency (Banthia, Chokri, Ohama, & Mindess, 1994).  The tensile properties of any type of fiber reinforced cementitious composite such as FRC, HSFRC, or ECC materials are generally rate dependent (Soe, Zhang, & Zhang, 2013); this is also observed in the flexural rate dependency of UHPFRC (Yoo D. , Banthia, Kang, & Yoon, 2016).   In addition, it has been shown that for mixes containing lower fiber volume fractions, the specimens show a much higher sensitivity to strain rate compared to those with higher volume fractions in FRCC (Yu & Dai, 2009).  42  Generally, at higher strain rates there is less allowance for the redistribution of stresses within the microstructure of the specimen while being loaded. In contrast, slow loading rates would result in the stress-strain planes to reorient so many times in order to redistribute the stresses while the material is being deformed in its plastic range. This phenomenon can result in underestimation or overestimation of the material performance levels in some failure models (Callister, 2000), and any good prediction model need to investigate and include the effect of applied stress or strain rates (Yoo & Banthia, 2016).  2.2 Background on Sprayable EDCC EDCC is considered one specific type of Engineered Cementitious Composite (ECC), which is a class of fiber, reinforced cementitious composites with strain-hardening type behavior under tension. Standard ECC mixtures are typically produced with high volume of a single type of oil-coated polyvinyl alcohol (PVA) fibers and microsilica sand, 0.250 mm maximum grain size (Li V. C., 1993), in order to create multiple cracking by the random discontinuous fibers inside a brittle composite matrix (Li, Lepech, Wang, Weimann, & Keoleinan, 2004).  However, EDCC uses about 30% of the Portland cement content of a typical ECC mix, contains only natural sand (1.2 mm maximum grain size), and uses a hybrid fiber system (multiple fiber types). This allows use of only 1% non-oil coated PVA fibers while still exhibiting strain-hardening type behavior and achieving 4% to 5% ultimate strain capacity in pure tension (Wang, Banthia, & Sun, 2013) and (Soleimani-Dashtaki, Soleimani, Wang, Banthia, & Ventura, 2017).  43  This tensile strain hardening regime results from an elaborate design using a micro-mechanical model taking into account the interactions among fibers, matrix and the fiber-matrix interface (Kanda, Saito, Sakata, & Hiraishi, 2003).  Therefore, these attributes not only make EDCC a much more cost-effective material (Soleimani-Dashtaki, Ventura, & Banthia, 2017), but also make it a considerably more sustainable material (Soleimani-Dashtaki, Soleimani, Wang, Banthia, & Ventura, 2017), compared to ordinary ECC or any of the other conventional cement based repair systems (Sahmaran & Li, 2009).  Furthermore, if a cementitious repair can be applied by spraying, the process of repair may become highly efficient. Indeed, since its first inception in 1910 by Carl Akeley, the use of sprayed concrete (shotcrete) for new construction and repair has grown rapidly. Sprayed concrete is easy to apply, does not require complicated formwork or sophisticated equipment and is sufficiently durable when applied properly (Banthia N. , 2011).         44  2.3 Background on Retrofit of URM Walls In this section, a literature review in given on the failure mechanisms of unreinforced masonry (URM) walls, focusing on out-of-plane action (OP). It also provides some background information on different existing analytical rocking models, for typical OP behaviour of URM.  2.3.1 Different Modes of Failure for URM Walls In order to investigate retrofit options for Unreinforced Masonry (URM) walls, it is necessary to understand the major failure mechanisms of this type of walls during an earthquake. For URM walls in an earthquake shaking there are two types of collapse mechanisms considered, namely, in-plane and out-of-plane, as shown in Figure 2-14 (D'Ayala & Speranza, 2003).   Figure 2-14: Typical Behaviour of URM Walls in Earthquake Generated Ground Shakings 45  In-plane failure modes of a masonry wall, as in Figure 2-15, are classified into four distinct failure modes of: (a) through diagonal shear across the wall, (b) failure by sliding at the base, (c) failure by overall rocking of the wall, and (d) failure by toe crushing (ElGawady, Lestuzzi, & Badoux, 2005). Each mode of failure has its own unique mechanism and prevention technique.   Figure 2-15: In-Plane Failure Modes of URM Walls (ElGawady, Lestuzzi, & Badoux, 2005)  A URM wall’s potential collapse mechanism, as in Figure 2-14, and the corresponding OP capacity, are mainly controlled by wall’s geometry and boundary conditions. Figure 2-16 shows  various subclasses of OP failure of a URM wall (D'Ayala, Spence, Oliveira, & Pomonis, 1997).   Figure 2-16: Principal OP Failure Mechanisms for URM Walls (D'Ayala, et al., 1997) 46  2.3.2 Mathematical Modeling of the Out-of-plane Failure Mechanism The out-of-plane rocking walls are modeled by rigid body motion of the segments or the system of the wall hinged at a location where a crack forms and allows rotation. The location of the hinge depends on loading and boundary condition, connection and the form of the wall system (Ferreira, Costa, & Costa, 2014). With regards to the force distribution models, the shake table testing of clay brick walls in out-of-plane action at the Earthquake Engineering Research Facility (EERF), University of British Columbia, by Meisl C. S. (2006) indicated a linear variation of acceleration along the height of the wall, as shown in Figure 2-17.  During the initial development phases of the first edition of the current Seismic Retrofit Guidelines (SRG I, 2011), for the analysis of rocking out-of-plane walls to the earthquake loading, input acceleration is applied at the base of the wall system. The acceleration is assumed to be linearly varied from the wall ends to the hinge location. The wall system is modeled as single degree of freedom system (SDOF) which has lumped mass and spring system representing wall resistance to the movement.  Figure 2-18 illustrates different prototypes and their physical and analytical models subjected lateral loadings. For these prototypes, the effective height of the wall and effective instability displacement are listed in Table 2-1, for reference (SRG III, 2017).  Other researchers also have used model of rigid body motion of wall segments for out-of-plane rocking wall (Zhang & Makris, 2001), (Doherty, Griffith, Lam, & Wilson, 2002), (Griffith, Magenes, Melis, & Picchi, 2003). Lumped mass representation of URM walls and linear variation of acceleration along the height are also used by Doherty et al. (2002) in their work on 47  trilinear model for URM walls, in out-of-plane action. This idealized model is shown and fully discussed within the main chapters of this thesis, in Figure 4-21 and section 4.3.4.   Figure 2-17: Acceleration Profile of Test Wall – GC2-1.32 (Meisl, 2006)  Table 2-1: Resistance Functions for Out-of-plane Rocking Wall Prototypes (SRG III, 2017)  Out-of-plane Prototype Resistance Function (f*) Peak Resistance     ( P) Instability Displacement ( uins) Effective Height in SDOF Model Unreinforced Cantilever wall ( OP-1)     tutuTHWem )(sgn3223  HWT 32T 32H  Unreinforced Cantilever wall with surcharge        ( OP-2)    tutuTHSWem )(sgn322)2(3  HTSW )2(  32T 32H  Unreinforced wall constrained at top and bottom ( OP-3)    tutuTHSWee )(sgn32)2(6  HTSW )2(4  32T 3H  Reinforced cantilever wall with footing             (OP-4)     tutuwHWeme )(sgn3223  HWwe 32 ew 32H   48   Figure 2-18: Physical & Analytical Models of OP Rocking Prototypes (SRG III, 2017) Reinforced Cantilever with Footing    (OP-4)Unreinforced Cantilever  Constrained at Top and Bottom (OP-3)Unreinforced Cantilever with Surcharge (OP-2)Unreinforced Cantilever (OP-1)SDOF Analysis ModelPhysical ModelPrototypeüg2H/3Hingef *M*eügSTW/2mügügH/3Hingef *MeügHTWügm2H/3Hingef *MeügHTWügm2H/3Hingef *MeügH200mmWügmWe/2200mm49  2.3.2.1 Backbone Curve for Out-of-Plane Walls The backbone curve for an out-of-plane wall is characterized by a moderately high initial stiffness, a plateau of effective maximum resistance (Pe), and finally a uniform rate of degradation to zero resistance at a drift corresponding to effective instability displacement.   The equivalent resistance (Pe) is 85% of the peak resistance (P) for the walls with thickness greater than 140 mm, and 90% of P for thinner walls. The effective instability displacement is usually taken as 95% of uins, in order to account for the material loss and, thereby, reduction of effective thickness at hinge points (SRG III, 2017).   The failure criterion for an out-of-plane rocking wall is when the displacement at the effective height of the wall exceeds the effective instability displacement. Figure 2-19 shows the backbone curve for the out-of-plane prototypes.   Figure 2-19: Backbone Curve for Out-of-Plane Prototypes (SRG III, 2017)  50  Doherty et al. (2002) also used tri-linear backbone curve for SDOF model of rocking out-of-plane wall.  In section 4.3.4 of this thesis, in Figure 4-21, this idealized model is discussed. In addition, for the same prototype discussed for Figure 2-19, the curve for effective force as a function of displacement at effective height of the wall is presented in Figure 2-20.   Figure 2-20: Force Displacement Relationship for Out-of-Plane Prototype (SRG III, 2017)  In a test conducted at the University of Auckland (New Zealand), clay brick URM walls are subjected to one-way bending by air bag under various levels of pre-compression load and the results can be compared against the existing idealized trilinear models, mentioned during the discussions of this section (Derakhshan & Ingham, 2008). The results also show very similar backbone curves as the ones shown in Figure 2-19 (SRG III, 2017) and Figure 4-21 (Doherty, Griffith, Lam, & Wilson, 2002).  51  The experimental results for the cyclic out-of-plane testing of URM walls made of CMU units, conducted at UBC EERF (Motamedi & Ventura, 2010) are also used for some of the models discussed (SRG II, 2013). This experimental work, which is also consistent with all the mentioned tri-linear models by different researchers, is the basis of all the prototype backbones and numerical models in SRG III.  Lastly, similar backbone behaviour of this type of wall is also presented by Meisel C. S. in his thesis work (2006) at the University of British Columbia, Earthquake Engineering Research Facility (EERF), as shown in Figure 2-21.   Figure 2-21: Semi-Rigid OP Force Displacement Relationship for URM Walls (Meisl, 2006) 52  2.3.3 URM Retrofit: Conventional Techniques and Ongoing Studies There are currently a number of retrofit techniques used worldwide for improving both in-plane and out-of-plane seismic performance of masonry walls. While there is a significant body of research evidence on in-plane retrofit of in-fill, load bearing, and unconfined masonry, there is considerably less work done on out-of-plane retrofit strategies for URM walls.  Around the in-plane response of this type of walls and the available strengthening techniques, there are a number of work done and there are some ongoing studies in this topic. Different types of engineered cementitious composites have been tried on these walls, both in forms of hand applied and sprayed. Even though there are available data on this work, there is a great need for more work in this area toward a distinct conclusion (Banthia N. , 2011), (Kanda, Saito, Sakata, & Hiraishi, 2003), (Lin, Biggs, Wotherspoon, & Ingham, 2014), (Billington, et al., 2009), and (Li & Leung, 1992).  On the other hand, there has been tremendous amount of research done on the analysis of masonry wall subjected to out-of-plane loading, as also described in the previous section. Milani et al. (2006) have done a limit analysis and safety assessment of out-of-plane loaded masonry panels using a simplified homogenization technique, and many other models are developed for predicting the out-of-plane behaviour of such walls (Ferreira, Costa, & Costa, 2014). The limit analysis allow identification of the distribution of internal forces at critical sections of a URM wall, when loaded out-of-plane, and to obtain the collapse modes and the failure loads in such loading conditions (Milani, Lourenço, & Tralli, 2006).  53  In terms of retrofit solutions, there are a limited number of publications on out-of-plane retrofit techniques by using CFRP and SFRP, but there is much less work done on use of cementitious-based composites for this type of retrofit (Hamoush, McGinley, Mlaka, Scott, & Murray, 2001). In many of the mentioned research work, mesoscale specimens, usually built of clay bricks, are strengthened using resin-based fiber reinforced composites (e.g. FRP), with the retrofit layer applied on the tension side, tested in static out-of-plane loading. Some of the investigations conclude that composite overlays increase the flexural strength; however, the ultimate flexural strength is not achievable using the current test setup, unless the premature failure by shear at the support is controlled (Hamoush, McGinley, Mlaka, Scott, & Murray, 2001).  Furthermore, there are some investigations done on mesoscale beam specimens, strengthened with ferrocement overlays (welded wire mesh with mortar), by testing them in a flexural setup. In this study also, the overlay is applied on the tension side and is tested with a unidirectional monotonic push. The researchers indicate an increase in the flexural strength, as expected, and emphasize on the ductile mode of failure for the tested specimens (Sachin, Singh, & Li, 2015).  It is worth mentioning that there are some major work done on retrofit technologies for different types of clay bricks and heritage type masonry, mostly in Europe (Correia, Lourenco, & Varum, 2015) and New Zealand (Derakhshan & Ingham, 2008). However, there is considerably less work done on practical use of cementitious composites for out-of-plane retraining of slender partition walls, built out of concrete masonry units (CMU). This type of wall is a major type of partitioning system in many of the schools and hospitals across North America.  54  In particular, hardly any of the available techniques aim for mitigation of out-of-plane (OP) damage or failure for the URM partition walls. Precisely, the existing retrofit solutions enhance the response by altering the mode of failure of these walls in the out-of-plane action from OP1 to OP2 and OP3, as described in section 2.3.1, aiming to satisfy the life-safety provisions of the current building codes (SRG III, 2017). In fact, providing full confinement for these components would be costly, challenging, and not so effective at this time.  55  Chapter 3: Development of Sprayable EDCC and its Applications Eco-Friendly Ductile Cementitious Composites (EDCCs) are a newly developed class of engineered cementitious composites that contain reduced amounts of Portland cement (compared to the conventional mortar mixes used in repair), use very high volumes of fly ash (or other SCMs), and show very high ductility and elastoplastic response in pure tension (Wang, Banthia, & Sun, 2013). These characteristics make EDCCs a promising material for seismic retrofit applications (Soleimani-Dashtaki, Soleimani, Wang, Banthia, & Ventura, 2017).  3.1 EDCC with High Volume of Fly Ash Adding a high volume of fly ash to high performance fiber-reinforced cementitious composites helps to reduce the matrix-fiber interfacial bond strength and the matrix toughness; thus, contributing in the achievement of high strain capacities during tensile loading (Wang, Banthia, & Sun, 2013). This high capacity is obtained through development of the known phenomenon of multiple cracking (Soleimani-Dashtaki, Soleimani, Wang, Banthia, & Ventura, 2017).  As mentioned, EDCC is originated from a previously developed material, called ECC, which achieves multiple cracking by using 2% volume fraction of oil coated PVA fibers in a high cement content matrix (Li V. C., 2003). However, EDCC achieves similar attributes and capacities to ECC through 70% mass replacement of the cement content by industrial byproducts, such as fly ash and silica fume, along with use of only 1% (by volume) non-coated polyvinyl alcohol (PVA) fibers in conjunction with a mixture of 1% of polyethylene terephthalate (PET) and surface treated PET (henceforth referred to as Cementophilic fibers).   56  Accordingly, these major modifications have caused EDCC to be a much more sustainable and economically feasible material than ECC (Soleimani-Dashtaki, Soleimani, Wang, Banthia, & Ventura, 2017). In particular, compared to conventional ECC, EDCC is a more ecofriendly material, by using far less Portland cement content and is more cost effective by using much less volume of non-oiled PVA fibers (Wang, Banthia, & Sun, 2013). This type of ductile cementitious material has many great applications such as dam repairs, bridge deck overlays, and seismic retrofits (Wang & Li, 2007).  3.2 The Hybridized Fiber System of EDCC There are three types of fibres are often used in the development processes of EDCC. Hybrid is a term used to mean two or more types of fibers used together. These fibers are non-coated polyvinyl alcohol (PVA) fibres, polyethylene terephthalate (PET) fibres, and Cementophilic fibers, which are a more evolved version of PET fibers with additional hydrophilic coatings for a better bond with the cementitious matrix. A brief introduction for each of these fibre types is provided in the following sections.  3.2.1 Poly-Vinyl Alcohol (PVA) Fibers Poly-vinyl alcohol (PVA) fibers are produced through processing of polyvinyl alcohol, which is a nontoxic, water-soluble, and fully biodegradable polymer. During this process PVA fibers are made with a high crystallinity and crystal orientation, which results in them having excellent tensile strength of 0.9 – 1.9 GPa and the elastic modulus of 11 – 43 GPa (Jalal-Uddin, Araki, Gotoh, & Takatera, 2011).  57  In addition, PVA fibers have high alkali resistance, good adhesive properties, and great resistivity to hot weather. Therefore, they are a very good choice of fiber to be used in FRC mixes (Jalal-Uddin, Araki, Gotoh, & Takatera, 2011).  3.2.2 Poly-Ethylene Terephthalate (PET) Fibers Use of Poly-Ethylene Terephthalate (PET) fibers as a concrete reinforcement system is a relatively new concept. These polyester fibers have a high strength and stiffness while being resistant to creep. They also have a high resistance to weathering and stress cracking. Moreover, they can be produced through chemical modifications of recycled polyethylene terephthalate plastic waste, which makes them a sustainable and cost efficient choice of fiber for use in large-scale projects (Rebeiz, 1995).  3.2.3 Cementophilic Fibers Cementophilic fibers are an advanced format of polyethylene terephthalate fibers, which are coated with an additional thin layer of commercialized hydrophilic coating. Not only does the additional coating give the fibers a higher ability to develop a better bond with the cementitious matrix, but also they give the fibers a better mixability with the mortar at the fresh state, causing a much better fiber dispersion and material uniformity.  3.3 EDCC Final Mix Designs After iterative attempts, three of the mixes of EDCC, with optimum performances, are selected and used for the work done in this thesis. They use similar mix proportions with the exception of the fiber type used. The maximum aggregate size is 1.2 mm, passing sieve No. 16, and all the 58  mixes maintain a w/cm ratio of 0.27 and a sand/cm ratio of 0.375. As shown in Table 3-1, the initial mix is the plain mortar matrix, followed by three mixes of 2% PVA, 2% PET, and 1%PVA + 1%PET.   All the mix designs need 2.00 L/m3 of superplasticizer with solid to liquid ratio of about 0.33, to achieve workability levels suitable for “hand-application” and “hopper-sprayed” methods, as described in section 3.5. The mixes all result in EDCC with 28-day compressive strength (f’c) of about 50 MPa, cracking strength (fcr) of about 8MPa, and a unit weight of around 2050 kg/m3.  Table 3-1: The Final EDCC Mix Designs Mix Design Cement (kg/m3) FA (kg/m3) SF (kg/m3) Sand (kg/m3) Water (kg/m3) PVA     (%) PET     (%) No Fiber (Plain) 390 780 78 468 337 0 0 2% PVA 385 770 77 462 333 2 0 2% PET 385 770 77 462 333 0 2 1%PVA+1% PET 385 770 77 462 333 1 1  From Table 3-1, in this thesis, the mix containing 2% PVA fibers is consistently referred to as the “Premium Mix EDCC”, which is a more expensive mix, being “high-performance EDCC”, due to having a higher strain capacity. However, the hybrid PVA + PET mixture is called the “Regular Mix EDCC” throughout the thesis discussions and illustrations. Figure 3-1 shows the mass proportions and compares the amount of the cementitious materials to the water and the sand used in casting all the EDCC mixes used for studies within this thesis. 59   Figure 3-1: Mass Proportions (Left); Mass Proportions of CM vs. Water and Sand (Right)  3.4 The EDCC Spray System and Specifications As previously mentioned, if a cementitious repair can be applied by means of a spray system, the process of repair may become highly efficient. Indeed, since its first inception in 1910 by Carl Akeley, the use of sprayed concrete (shotcrete) for new construction and repair has grown rapidly. Sprayed concrete is easy to apply, does not require complicated form‐work or sophisticated equipment and is sufficiently durable when applied properly (Banthia N. , 2011).   The sprayed EDCC exhibits elastoplastic type behavior and high strain capacity in tension, despite containing low volumes of fibers, making it a great material for the seismic strengthening applications. Cast EDCC has been the main type of material used by all the studies presented in this thesis work. Cast EDCC shows great ductility and strain hardening type behaviour.   However, the main reason that cast samples were completed instead of sprayed is the difficulty encountered in overcoming challenges with the sprayability of the material. In order to make the 60  material sprayable and to ensure minimization of rebound, material slough-off, and to obtain a proper compaction at placement, iterative rheological modifications to the EDCC material were performed.  Figure 3-2 shows the EDCC sprayer (left photo), the EDCC spray gun (top right photo), and UBC SIERA Group’s spray chamber (bottom right photo). This machine, which is powered by a 5.5Hp Honda engine, is equipped with a built-in air compressor and uses an integrated hydraulic motor of 5500 in/lb power with a 3-way detent valve in order to provide power to the rotary type pumping system, to convey the EDCC material to the nozzle. The adopted spray gun then uses the provided air pressure to pneumatically shoot and compact the EDCC mix against the specimens, as shown in the lower right corner of Figure 3-2.   Figure 3-2: EDCC Spray Pump (left), Spray Gun (top), and UBC Spray Chamber (bottom) 61  To confirm that mechanical properties of the EDCC material would remain unaffected, it is recommended that a few small sprayed tension specimens, cut out from sprayed panels, are tested in pure axial load and the results are compared against the original EDCC properties (Kanda, Saito, Sakata, & Hiraishi, 2003). However, it is important to mention that, in this thesis, sprayed tension specimens are not fully examined, and only sprayed beam specimens and larger sprayed wall panels have been made, but not tested for mechanical behaviour. Therefore, this thesis at the last chapter is recommending that such investigation should be performed and results should be compared with the casted specimens.  It is also important mentioning that all the full-scale specimens tested on a shake table, discussed throughout Chapter 4: of this thesis, have been retrofitted using the hand-applied technique, as fully discussed in the next section. The hand-applied EDCC is believed to have properties equal to “cast EDCC,” and might be slightly different from “sprayed EDCC”. In fact, retrofitting the six full-scale wall specimens needed a high volume of material and, hence, a mass production of EDCC was needed. Due to the heavy weight of the specimens and space limitations at the UBC EERF, during that specific period, it was not possible to spray the full-scale walls.   However, there are another 20 half-scale wall specimens, from which 10 of them are sprayed with EDCC layers. These wall panels are built for the still ongoing testing program on EDCC retrofitted walls, which is out of the scope of this thesis. However, for discussion purposes, as part of the recommended future work on EDCC, this thesis presents the specifications of the designed and fabricated setup for static monotonic and cyclic out-of-plane testing of the EDCC sprayed half-scale walls. This information is presented in Appendix D  and Appendix E  . 62  3.5 The Application Methods for EDCC EDCC retrofit can be applied in three different methods: hand troweled (cast), hopper sprayed, or pump sprayed. The thickness of the EDCC layer, plastered over the height on the surface of a typical URM partition wall, can be either 10mm or 20mm, applied on either or both sides of the wall, depending on the design variables. Figure 3-3 shows the different application methods.   Figure 3-3: Different Application Methods for EDCC  3.5.1 Available Finishes for EDCC Whether the EDCC material is applied by hand or sprayed, the final product can look smooth or rough. However, there is a major component of cost difference between the two mentioned 63  finishes. Indeed, like any other finishing work, there is some extra labour-hour needed to trowel the wall for the final look. Figure 3-4 shows some photos of the process and available finishes.   Figure 3-4: Applying EDCC onto URM Walls: Surface Pre-Miniaturization to Final Finishes 64  3.6 Bond Performance of EDCC to Masonry Interfacial chemical bond between the substrate and a repair material is, undoubtedly, one of the most influential factors, affecting the overall performance of the repair system. Seismic strengthening of URM walls is not an exception, and for sure, one of the most important factors affecting the overall composite behaviour of an EDCC retrofitted specimen is the interfacial bond between the applied EDCC layer and the concrete masonry units.   This section provides a summary to some of the bond investigations, which were performed on tested retrofitted specimens after the shake table tests. The data is then compared against previous MASc test data on the bond performance performed at UBC.  3.6.1 Previous Bond Investigations at UBC This bond performance as investigated by two MASc theses at the University of British Columbia, as part of the same research project, under the supervision of Prof. Nemy Banthia at the SIERA group. Yan Y. investigated the bond strength and performances between hand-applied/overlaid EDCC layers and different types of masonry materials, with varied service preparations / surface conditions, and under different curing environments (Yan, 2016).   Yang Du (2016) has looked at the bond durability between EDCC layers and masonry substrates, both clay brick and CMU, considering time factors, maturity, and sever environmental conditions. Yang has also investigated the interfacial bond variations for sprayed EDCC, compared to hand-applied (Yang, 2016). 65  3.6.2 Disk Pull-Off Test: Equipment and Setup It is important that the EDCC does not undergo bond loss or bond weakening during the course of an earthquake shaking. If a bond loss happens during the period of earthquake shaking, the EDCC layer can delaminate from the masonry units, causing the wall to lose the intended composite strength, which can result in failure of the repair performance or even an immediate collapse of the retrofitted URM wall.  Figure 3-5 shows the schematic of the standardized test setup for measuring tensile bond strength between the substrate and a repair material (EDCC layer in this case) using disk pull-off testing technique (ASTM-C1583/C1583M-13, 2013). This method requires coring through the repair into the substrate to isolate the repair material and create a more uniform bond line tensile stress.   Figure 3-5: Schematic Setup for Standard Disk Pull-Off Test (Adopted from ASTM C1583) EDCC Layer 66  A large number of bond tests are performed, and samples are taken from different locations on the surface of the damaged wall, after the complete failure and collapse of the wall, as shown in Figure 3-6. The results give an envelope of bond values after the dynamic loading.   Figure 3-6: Post-Impact Investigation of the Masonry-EDCC Tensile Bond Performance Tension pull-off specimens are taken from both front and back of the tested double-sided walls 53 bond specimens are pulled in tension, around the strain gage locations after the shake table tests 67  3.6.3 Bond Investigation Results and Statistics As per requirements of ASTM C1583, EDCC layer is cored and isolated from substrate (CMUs), and an epoxy-glued disk is used to pull the EDCC layer off the masonry surface. As shown in Figure 3-7, four different failure cases are likely to happen, and each case would impose a different interpretation to the obtained values for pull-off forces or stresses.   Figure 3-7: Schematic of Failure Modes of a Disk Pull-Off Test (ASTM C1583)  It is worth referring to Table 4-1, presented in the following chapter, which discusses the specifics of the full-scale wall specimens, from which Wall-1 is selected for this study. This wall is evaluated for bond performance, after being tested on a shake table.  Wall-1 is a full-scale URM wall specimen, made of CMUs, covered on both sides with 20mm thick layers of hand-applied Premium Mix EDCC. Total of 53 disk specimens were pulled off from the surface of this wall, after being tested to failure and collapsed on the shake table. 68  As illustrated in Figure 3-6, the 53 pull-off disk specimens were taken from both front and back of Wall-1, which is already collapsed, laying on the ground, after experiencing 25 full runs of aggressive earthquake ground motions on a shake table. Out of 53 specimens, 13 of them are considered “invalid,” or outliers, due to the failure of the epoxy adhesive, and have to be discarded based on the requirements of the standardized procedure provided ASTM C1583. Figure 3-8 shows the tensile bond values across the 40 disk specimens pulled off from Wall-1.   Figure 3-8: EDCC-CMU Tensile Bond Strength Data from Wall-1 after Collapse  Looking at the bars and the average curve presented in Figure 3-8, it is evident, as expected, that data has a high coefficient of variation. In fact, the pull-off tests are performed on a highly Bond Strength (MPa) Specimen Number 69  damaged wall, so it is expected to see some non-uniformity from the data. The statistics for the bond strength values are presented in Table 3-2.  Table 3-2:  Data Statistics for the EDCC-CMU Tensile Bond Tests Average (MPa) Standard Deviation (MPa) Coefficient of Variation Median (MPa) Max Value (MPa) Min Value (MPa) 1.10 0.51 29.5 % 1.10 2.33 0.37   With reference to Figure 3-7, the distribution between different modes of failure for the entire 53 samples (valid and invalid) have been calculated and graphically presented in Figure 3-9.   Figure 3-9: Statistics for the Tensile Pull-Off Tests on Wall-1 70  3.6.4 Discussion on the EDCC-CMU Tensile Bond Results Before discussing the post-collapse bond values, it is helpful to recap some of the data from previous work done on EDCC-CMU bond by Yan. Y. (2016), summarized in Table 3-3. This data is for the exact matching case, a 20mm thick layer of EDCC over CMU, and the tests are performed using the exact same procedure and equipment.  Table 3-3: Test Data on EDCC-CMU Bond for 20mm Thickness (Yan, 2016) Number of Specimens Tested Average Strength Standard Deviation Coefficient of Variation Failure Modes ( a ) ( b ) ( c ) 6 1.86 MPa 0.28 MPa 13.5 % 83 % 0 % 17 %  Comparing the average values and maxima from Table 3-3 with it corresponding values from Table 3-2 should be done carefully, since they are based on the data from different number of specimens. In fact, the previous data is coming from only six pulled off disks, for the 20mm thick EDCC case, while the values tabulated in this section are based on 40 pulled off disks. However, the tested wall had a lower average bond strength and much higher standard deviation.  This could be explained by either higher pretest bond variability in the large specimens or more likely bond strength degradation during loading and collapse of the wall.  Looking at the specific locations of the specimen numbers, presented in Figure 3-8, it is observed that the disks pulled off from the vicinity of the localized mid-height crack of Wall-1 tend to show much lower bond values, compared the ones taken from locations away from the crack. 71  Referring back again to the pie chart, presented in Figure 3-9, it is noticed that almost half of the pulled off specimens failed within the EDCC layer; which is a failure mechanism shown in diagram (c) of Figure 3-7. This is a surprising outcome, but leads to very interesting conclusions.  The pull-off specimens are taken from Wall-1, retrofitted with the Premium Mix EDCC, which has an average compressive strength (f’c) of about 50 – 55 MPa and a tensile cracking or breaking strength (fcr) of about 7 – 9 MPa, as shown in Figure 6-9. Thus, the EDCC layer splitting apart in tension at average tensile stresses of around 1.1 MPa is a surprise. Re-inspecting the pulled-off disks, as illustrated in the top-left corner photo in Figure 3-6, the failure pattern at the EDCC layer has no clear sign of fracture; similar specimens show the same pattern. Going back to the construction notes, it is realized that retrofit process of Wall-1, with hand applied Premium EDCC, was interrupted on a Friday, and restarted on the following Monday. Inspecting the photos indicate that a “scratch coat” of EDCC is applied on both sides of Wall-1 on a Friday, and the “final coat” or the “finishing coat” is applied after 3 days, on the following Monday, creating a clear cold-joint within the 20mm thick EDCC layer.  More interestingly, looking at the test results, Wall-1 is one of the best performing walls during the tests on the shake table, as illustrated in Table 4-6. In addition, looking at the “post-inspection notes” of the final test day for Wall-1, the wall is fully inspected on the shake table, right after the collapse. The notes indicate, “The EDCC layer is fully intact, with no visible sign of delamination, even after trying to pull the EDCC layer off by applying force and by use of pry bars”. This can indicate a minor shear fellow within the 20mm thick EDCC layer, helping the repair layer survive during the shakings even with 1.1 MPa average tensile bond strength. 72  3.7 Preliminary Cost Analysis: Strengthening Using Sprayable EDCC vs. FRP What makes sprayable EDCC a more attractive retrofit option is the cost effectiveness of this material compared to the conventional techniques. In the current retrofit strategies there are often two independent systems specified for upgrading both in-plane and out-of-plane behavior of the unreinforced masonry partition walls.  Based on the common prices in the current local market (as of 2016 in Vancouver, BC, Canada), based on city of, the bulk material cost for the current EDCC mixes are around 500 $/m3 for the Regular Mix and 900 $/ m3 for the Premium Mix. Considering an average placement thickness of 10 – 20 mm, these average prices would be about 8 $/m2 and 13 $/m2, respectively.  In terms of the labour cost for application, in one full hour a crew of two would be able to hand apply (trowel on) EDCC to about 10 – 15 m2 or, using one of the spray systems (guns), the same crew would be able to roughly cover an area of 20 – 30 m2  with sprayed EDCC. Assuming a labour cost of about $25/hour per person, this would results in an average price of about $10 to $16/m2. Table 3-4 provides the summary of the stated total cost estimation (material + labour); please consider a price variation of at least ±25%, to allow for the location dependency, materials availability, and varied labour costs.  Table 3-4: Cost Estimation (/m2) for the EDCC Retrofit Option, (Material & Labour) Retrofit Option Sprayed Hand Applied EDCC Premium Mix $15 CAD $20 CAD EDCC Regular Mix $10 CAD $15 CAD 73  In order to provide some basis for the comparison, based on the current market price (as of 2014), the materials cost for the Steel Fiber Reinforced Polymer (SFRP) and the Carbon Fiber Reinforced Polymer (CFRP) sheets are about 35 $/m2 and 60 $/m2, respectively. Depending on the structural design of the retrofit, the targeted wall might need up to three layers of FRP sheets (3× materials cost) in order to achieve the desired performance (Abdelrahman & El-Hacha, 2014). It should be noted that SFRP and CFRP are generally used for providing in-plane strengthening of such walls, but the numbers are presented as a simple base for a rough cost comparison. Considering the defined scope for this thesis, it cannot provide technical comparison for the in-plane response of URM walls strengthened with EDCC, compared to the ones strengthened by SFRP and CFRP, as examined by Abdelrahman and El-Hacha (2014). However, use of fiber-reinforced polymers for out-of-plane strengthening has been done at UBC, as part of a shake table testing, and performance comparison provided later in this section.  In order to provide a simplified head-to-head comparison, using EDCC brings a significant reduction in the material cost, down to about one third (1/3). It should be kept in mind that FRP retrofit would mostly require substantial amount of surface preparation and grinding to get to the desired surface roughness, whereas, the EDCC layers are hand-applied on the full-scale wall specimens (in this thesis) only having a relatively clean and pre-moisturized surface.  As also discussed in section 4.3.5 of this thesis, the EDCC single-sided retrofit option, for out-of-plane restraining of URM walls, would result in performance enhancements of much higher degrees, compared to the alternative single-sided retrofit options. For instance, a URM wall 74  retrofitted on one side with FRP strips collapsed under 65% intensity of the Kobe Earthquake of Japan in 1995, as previously tested at UBC EERF on a shake table; details in section 4.3.5.  It is worth mentioning that EDCC retrofit, compared to other available techniques, would also add some in-plane strengthening which could potentially reduce or completely eliminate the need for providing additional Lateral Drift Resisting System (LDRS) to reduce the structure’s overall probability of drift exceedance (SRG III, 2017). There are some preliminary test data, which can easily verify this with further details, if need be. Further in-plane testing of EDCC retrofitted specimens are listed as part of the recommended future work in the last chapter of this thesis. 75  Chapter 4: Shake Table Testing of EDCC Strengthened URM Walls In Chapter 3: of this thesis, the development of Eco-Friendly Ductile Cementitious Composite (EDCC) and its response to uniaxial tension is described. In addition, Chapter 6: of the thesis elaborates on the tensile behaviour of EDCC under higher rates of loading, with reference to the actual strain rates that occur when the EDCC layer gets engaged to hold the URM units of a partition wall together during an earthquake ground shaking.   In this section, the composite performance of EDCC, when used as a strengthening coat on unreinforced masonry, is tested and evaluated. This chapter gives the results of the shake table tests on full-scale masonry wall specimens, each 1.6 m wide by 2.8 m high, retrofitted using hand-applied EDCC mixes. Details are given on the experimental setup, specifics of the data acquisition system, and a summary of the results of the out-of-plane shake table testing of full-scale URM walls. The shake table testing is done using the Linear Shake Table (LST) at the UBC Earthquake Engineering Research Facility (EERF).  4.1 The Shake Table Testing Program Dynamic testing of full-scale specimens is one of the most effective experiments, which can be performed to understand the out-of-plane behaviour of walls. In this type of test, the location of the plastic hinge formation fully depends on the overall behaviour of the wall, compared to a quasi-static test where the out-of-plane failure mechanism is predetermined prior to the test.  For this experimental study, six full-scale unreinforced non-grouted masonry wall specimens are assembled, and then strengthened using Sprayable EDCC. The walls are then tested at the UBC 76  Earthquake Engineering Research Facility (EERF), on the Linear Shake Table (LST), under different ground motions with varying intensities (Soleimani-Dashtaki, Ventura, & Banthia, 2017). The results are then compared to three bare walls previously tested at the same facility. This comparison was possible as the wall dimensions, building block sizes, and the test setup are purposely selected to be identical to the previous full-scale wall tests, which were performed in 2013 and 2014 as part of the ongoing testing program for the school project (SRG III, 2017).  It is worth mentioning that the wall dimensions, block sizes, and the boundary conditions were decided on by the Technical Review Board (TRB) of the school project, considering the school building inventory and their most vulnerable masonry prototypes in out-of-plane failure. The design and specifications used were originally prepared for the TRB by Bush, Bohlman & Partners LLP (a local structural engineering firm). A few of the senior structural engineers from this firm are also on the TRB (SRG III, 2017).   Figure 4-1: Drawing from Bush, Bohlman & Partners (left) and the Six URM Walls (right) 1,600 mm 2,800 mm 77  Figure 4-1 shows the six URM walls while undergoing retrofit (right); the walls are assembled as per drawings prepared by Bush, Bohlman & Partners LLP (left). The dynamic test variables for the shake-table tests (Chapter 4:) were carefully chosen based on earlier experimental test results on the EDCC. These earlier investigations are included the material development-optimization stage (Chapter 3:), micro-level or mesoscale tests (Chapter 6:), and the semi-scale experiments and other tests (not presented here). The full shake table tests are primary to this thesis and are thus presented first.  4.1.1 The Inventory and Specifications of the URM Wall Specimens The specimen dimensions (left) and the test setup (right) of the six full-scale retrofitted URM walls are shown in Figure 4-2.   Figure 4-2: Wall Specimens – Six Specimens, 1.6m Wide by 2.8m Tall CRS 14CRS 13CRS 12CRS 11CRS 10CRS 9CRS 8CRS 7CRS 6CRS 5CRS 4CRS 3CRS 2CRS 1CRS 14CRS 13CRS 12CRS 11CRS 10CRS 9CRS 8CRS 7CRS 6CRS 5CRS 4CRS 3CRS 2CRS 1DISPL. 2DISPL. 0 (Table)DISPL. 3DISPL. 1DISPL. 4DISPL. 5DISPL. 6DISPL. 7ACCEL. 2ACCEL. 1ACCEL. 3ACCEL. 0 (Table)ACCEL. 4ACCEL. 5ACCEL. 6ACCEL. 7ACCEL. 8 (Frame)Fixed BaseBolted on to the Shake TableCRS.  Brick CourseDISPL.  DisplacementACCEL.  AccelerometerSTRN.  Strain GageCRS 14CRS 13CRS 12CRS 11CRS 10CRS 9CRS 8CRS 7CRS 6CRS 5CRS 4CRS 3CRS 2CRS 12800 mm200 mm1600 mm400 mm2800 mm800 mmCRS 14CRS 13CRS 12CRS 11CRS 10CRS 9CRS 8CRS 7CRS 6CRS 5CRS 4CRS 3CRS 2CRS 11600 mm400 mm2800 mm800 mmInstrumentation DrawingSide ViewInstrumentation DrawingFront ViewInstrumentation DrawingRear View500 mm 500 mmSTRN. 1STRN. 2 STRN. 3STRN. 4STRN. 5STRN. 6 STRN. 7STRN. 80Base2800Top1400MidCRS 14CRS 13CRS 12CRS 11CRS 10CRS 9CRS 8CRS 7CRS 6CRS 5CRS 4CRS 3CRS 2CRS 11600 mm2800 mm78  The CMU are nominally 100 mm thick, 400 mm wide, and 200 mm tall (actual dimensions are 90 mm × 390 mm × 190 mm). As shown in Figure 4-2, the walls are measured 0.1m thick, 1.6 m wide, and 2.8 m tall. This is the same as the dimensions of the three previously tested bare walls.  Some of the walls have ladder like joint reinforcements, formally called “wall-locks”, which is normally laid flat on top of the full row of the CMUs, placed inside the mortar joints, between the two courses (rows) of the CMUs. This is adopted and tested in four of the walls, as it is known to be a practice for many of the masonry walls built in 1970s and 1980s across BC. The wall-locks are present at specific mortar joints throughout the height of the wall, starting from the top of the second course (row) of the CMUs. The drawing in Figure 4-1 shows the location of these joint reinforcements, consistent with the previous EERF wall tests (SRG III, 2017).  The specimens were retrofitted with either regular or premium EDCC mixes. The EDCC was hand applied (or troweled) to either one or two sides of the wall. Table 4-1 shows the inventory of all the dynamic testing specimens, with their “ID” designations, as referred to in this thesis.  Table 4-1: Summary of the Specimens Tested on Shake Table Specimen ID Wall-Lock Retrofit Material Single/Double Sided Specimen Total Mass Wall-1 Yes Premium EDCC Double-Sided 1,250 kg or 2,750 lbs. Wall-2 Yes Premium EDCC Single-Sided 1,050 kg or 2,300 lbs. Wall-3 Yes Regular EDCC Double-Sided 1,250 kg or 2,750 lbs. Wall-4 Yes Regular EDCC Single-Sided 1,050 kg or 2,300 lbs. Wall-5 No Regular EDCC Double-Sided 1,250 kg or 2,750 lbs. Wall-6 No Regular EDCC Single-Sided 1,050 kg or 2,300 lbs.  79  The total specimen masses presented in Table 4-1 play an important role throughout the data analysis and modeling. Table 4-2 gives the mass per unit area of each type of wall.  Table 4-2: Mass Calculation Guide – Total Mass per unit Surface Area of Specimen EDCC Layer Thickness Single Side Retrofitted Wall Double Side Retrofitted Wall 10 mm (not used here) 186 kg/m2 207 kg/m2 20 mm 227 kg/m2 248 kg/m2 *Mass of a bare wall with no retrofit is 166 kg per 1m2 of the wall surface area  All six wall specimens, were brick-laid (laid up, mortared together) in mid-January of 2016 and were field cured for a few weeks (ambient curing, no wetting). The specimens then were retrofitted or strengthened with hand-applied EDCC layers in February 2016, followed by another 56 days of field curing for EDCC, and subsequently tested over the course of the months of June and July 2016, one wall at a time.  For the retrofit, the EDCC mix designs presented in Table 3-1 are used and the mixing procedure similar to what is described in section 6.2.1 is adopted. Based on the previous bond investigation at UBC (Yan, 2016), it was decided to avoid any specific type of surface preparations for the masonry walls. The goal, in fact, was to keep the retrofit process as simple and as cost-effective as possible, so it was decided that an optimum bond for this retrofit would be achieved by only pre-moisturizing the wall’s surface. There is no need to create a full SSD (Saturated Surface Dry) condition for the masonry walls, but it was ensured that wall surface is fully wetted about 10 min before applying the EDCC layer. This methodology was adopted in the retrofit process of all the specimens, including the six tested full-scale walls in this thesis, as shown in Figure 3-4. 80  The hand application method, as described in section 3.5, is adopted by troweling the EDCC layer on the wall surface, using ordi0nary concrete “finishing tools” (i.e. trowel and float). The 20 mm thickness is applied in two layers, a scratch coat and a final coat. It is highly recommended that the final coat is applied no later than 60 minutes after the application of the scratch coat, to avoid formations of any cold joints. Wood strips were cut into size and attached to the sides of the walls, as a guide for maintaining the 20mm thickness. However, based on the guidelines provided in Volume 7 of SRG III, for large-scale applications, an uniform 60 cm  grid of masonry screws (~ 60cm × 60cm) should be used as a guide, to ensure uniformity of the thickness of the EDCC layer (SRG III, 2017). All of the six walls have the “smooth finish” look, as described in section 3.5.1 and shown in Figure 3-4.  The mentioned 56 days of curing is highly recommended as the repair material consists of high volumes of fly ash, which can delay the long-term hardening and maturity of the repair system. This means that walls were not tested on the shake table until after the 56 days period; however, normal field curing in ambient condition, with no specific wetting or watering, can be used for the EDCC retrofitted walls. The same is also provided as part of the instructions for the EDCC retrofit option included in the SRG III documents.   It is worth mentioning that EERF (the testing facility) is normally heated to an average temperature of about 20 degrees Celsius, with fans blowing hot air into the facility. Therefore, to avoid possible shrinkage induced cracking, the six retrofitted walls were mildly splashed with water (by hand using a brush) three times over the first seven days (on day 2, 5, and 7). Indeed, the six walls were the very first set of large-scale retrofitted specimens, so this was done as an 81  extra pre-cautionary measure. However, after retrofitting more specimens and from the demonstration project, it can be noted that moist curing is not necessary in prevention of surface cracks. This perhaps is due to the low cement content, high volume of fly ash, and the existence of the polymer-based fibers in EDCC.  4.1.2 Ground Motion Selection and Use There is a complete suite of ground motions used for this experimental work, in terms of type, nature, location, magnitude, and duration. This is kept aligned with the set of ground motions selected and used for the analytical work done for SRG III, previously developed as part of the seismic mitigation action and seismic upgrade program for schools in BC (SRG III, 2017). The selected ground motion records are then scaled to the mean hazard spectrum of different targeted cities across the province of British Columbia, based on the NBCC 2015 values (NRC, 2015). The scale factors are chosen in accordance with the SRG III guidelines, majorly from the ground motion records scaled for short period buildings for different locations. Table 4-3 lists the ground motions used in this experimental study of the URM walls with different OP retrofit cases.  Table 4-3: Summary of Ground Motions Used & Their Corresponding Designation Number Record ID # Earthquake Name Event Date Country / Region Recording Station GM-1 Tohoku Mar 11, 2011 Miyagi-Oki, Japan FKS0011 – EW GM-2 Tokachi-Oki Sep 25, 2003 Hokkaido, Japan Hombetsu: HKD 090 – EW GM-3 Chi-Chi (Jiji) Sep 21, 1999 Nantou, Taiwan CHICHI04_CHY074-N GM-4 Kobe Jan 16, 1995 Kobe, Japan Nishi-Akashi: KOBE_NIS090 GM-5 Landers – Joshua Jun 28, 1992 California, USA LANDERS_LCN260 GM-6 Nisqually Feb 28, 2001 Washington, USA Nisqually – Renton (RBEN) – EW GM-7 Verteq-II Waveform - - Verteqii Waveform – Synthetic 82  Additionally, Table 4-4 provides more information for each of the ground motions listed in Table 4-3, such as type, magnitude, and the peak values. For each ground motion, the depth of the rupture (D), radius to the recording station (R), peak ground acceleration (PGA), and peak ground velocity (PGV), and the shear wave velocity (Vs30) are provided. It should be noted that the tabulated scaling factors (SF) are for the representative cities with the highest seismicity in BC, as explained later in this section; i.e. they are not for the same location or city, and should not be directly compared as presented in Table 4-4.  Table 4-4: Peak Values and Details of the Selected Ground Motions Record ID # Short Name Type Magnitude (Mw) R (km) D (km) PGA (g) PSV1-2 (m/s) Vs30 (m/s) SF GM-1 Tohoku Subduction 9.1 Mw 82.7 24.0 0.55 0.42* 585.9 1.14 GM-2 Hokkaido Subduction 8.3 Mw 56.0 145.8 0.50 0.27 654.3 1.54 GM-3 Chi-Chi Crustal 7.7 Mw 20.6 18.0 0.35 0.38* 553.4 0.59 GM-4 Kobe Crustal 6.9 Mw 19.9 17.9 0.51 0.43 609.0 1.07 GM-5 Landers Crustal 7.3 Mw 44.6 7.0 0.73 1.47* 684.9 1.41 GM-6 Nisqually Sub-Crustal 6.8 Mw 74.4 59.0 0.19 0.21 347.2 1.92 GM-7 Verteq Synthetic - - - 1.2 - - - *Peak Ground Velocity (PGV) reported, instead of average spectral pseudo-velocity between 1 and 2 second period (PSV1-2)  The ground motion selection is done in accordance with SRG III, in which conditional spectra (CS), rather than Uniform Hazard Spectra (UHS), have been adopted for record selection and scaling. As mentioned, the scale factors presented in Table 4-4 are for different representative cities, with different seismicity, across the province of British Columbia, Canada. Therefore, comparing them head-to-head for PGA and SF will not represent a single design spectrum.  83  The ground motion selection and scaling strategy has been set to select the ground motions, which are good match to most of the cities across the province, in terms of overall shape and spectral content, but requiring different scale factors to match the targeted intensity. Thus, running the same ground motion with different intensities on the shake table can cover the required conditional spectra and possibly beyond, for most cases.   The database of SRG III records provides two sets of ground motions and associated scaling factors: one set for the short period (Tc = 0.5 sec) and another set for long period (Tc = 1.0 sec). The short period structures are typically of non-ductile low-rise buildings or prototypes, amongst all the considered structures or building prototypes in SRG. The long period structures are of mid-rise buildings or prototypes that are more ductile.  Considering the tested URM walls are slender, relatively short (2.8 m), and elastically stiff, almost all of the ground motions are selected from the record sets targeted for short period structures, Tc = 0.5 sec. To also consider a long period record, only GM-5, which is a crustal event, is selected from the sets scaled for Tc = 1.0 sec. The experimental results clearly revealed that long period motions would have minimum effect on the tested URM specimens.  The subduction records (GM-1 and GM-2) and two of the crustal records (GM-4 and GM-5) are selected and scaled for Victoria, which is classified in SRG III as “High Risk” or “High Seismicity Zone” for both subduction and crustal events in BC. However, the only sub-crustal record (GM-6) is selected and scaled for the city of Vancouver, which is of “High Seismicity” for the sub-crustal seismic hazard, based on the SRG III database. 84  For discussion purposes, a selected number of the ground motions are plotted and the additional characteristics of them have been illustrated here, such as frequency content, spectral density, and the peak values. Figure 4-3 shows the acceleration and displacement of the table, for GM-1 (Tohuku Eq. of Japan) at 100% actual intensity, as recorded directly on the table during the shake table testing of Wall-1 in Run-7, as listed in Table 4-7 in the following section.   Figure 4-3: Acceleration and Displacement Time-Histories for GM-1 @ 100%  85  4.1.3 Shake Table Setup and Calibration The Linear Shake Table (LST) is carefully calibrated for the scaled intensity of each of the ground motions prior to the test. However as expected, the input motion that is fed into the control system of any shake table is not necessarily identical to the output motion, recorded on the surface of the table during the test. As shown in Figure 4-4, the Linear Shake Table (LST) and a URM wall specimen mounted on it can be schematically represented as an idealized coupled mass-spring-damper system; and, each of the sub-systems independently has its own different mass, stiffness, and damping characteristics.   Figure 4-4: Idealized Mass-Spring-Damper System Schematic for LST & Specimen  Although the table properties might have much higher or different values, compared to the specimen, the two idealized systems principally feed energy to each other back and forth during the shake table testing. As the specimen undergoes damage during the test and progresses through its non-linear behaviour, its stiffness and damping matrices are changing all time or are becoming decoupled, if the specimen undergoes rocking. Therefore, the output signal, recorded on the surface of the table during the test, as shown in Figure 4-3 would be marginally different from the input signal, especially when dealing with higher levels of shaking. 86  4.1.4 Ground Motion Characteristics and Spectral Content The wall specimens, like any other structure, are more sensitive to some of the ground motions, due to the specific frequency contents of those motions, which excite the walls at their resonance frequencies. This section reveals the spectral content of the Tohoku (GM-1) and Kobe (GM-4) earthquakes, in Figure 4-5 and Figure 4-6, which are two representative examples of ground motions that were observed to be exciting the specimens more destructively.   Figure 4-5: Spectral Content of GM-1 @ 100% as Recorded on LST (5% Damping Ratio) 87   Figure 4-6: Spectral Content of GM-4 @ 100% as Recorded on LST (5% Damping Ratio)  As experimentally observed, the motions containing higher frequency contents and typically of longer durations tend to have more destructive effect on the short period specimens. Looking at the acceleration spectral contents of GM-1 and GM-4 in Figure 4-5 and Figure 4-6, respectively, it is evident that both motions have considerable amount of high frequency (low period) acceleration contents, thereby affecting the walls further by more closely matching their natural periods. This indeed should not be of a surprise, as both motions are selected from the suite of 88  SRG III records selected and scaled for Tc = 0.5 sec, as mentioned before. As it will be discussed later, it is observed that while large displacements are well handled by the EDCC retrofitted URM wall specimens, they show more sensitivity to the velocity content of the motions (PGV or PSV), than the acceleration content (PGA) or record duration (i.e. the “long duration effect”). For reference, Figure 4-7 shows the time histories and their envelopes for GM-4 @ 100% intensity, as recorded on the table surface during the shake table testing of Wall-2 in Run-2.   Figure 4-7: Acceleration and Displacement Time-Histories for GM-4 @ 100%  It is worth mentioning that despite of the complete different shapes of motions, for GM-1 and GM-4, the spectral content have many similarities. Hence, most of the walls react very similarly to GM-1 and GM-4, but considering GM-1 is almost as twice as long as GM-4, the duration effect is very evident looking at the global degradation of the wall after each motion. 89  Referring to the top-left and the top-right corner graphs of Figure 4-5 and Figure 4-6, with the assumed 5% critical damping ratios, there is almost no difference between the acceleration response spectrum and the pseudo acceleration response spectrum, and very minimal variance between the relative velocity response spectrum and the pseudo velocity response spectrum, especially at higher frequencies. However, as known, the difference between the actual and pseudo spectral values gets larger as the critical damping ratio increases.  In addition, looking at the lower-right diagrams in both Figure 4-5 and Figure 4-6, comparing the spectral displacements for both records at different critical damping ratios, the sensitivity of the displacement response of these motions to damping is evident. As expected, the variation in spectral displacements, from 0% to 5% critical damping ratios, is much larger than increasing the damping beyond 5%. Thus, special attention should be given to modeling the damping correctly, when it comes to future numerical investigations, for true drift predictions. It should be noted that the response spectra obtained for both ground motions, GM-1 and GM-4, which are shown in Figure 4-5 and Figure 4-6, respectively, are calculated and assembled based on the actual mass and stiffness properties of Wall-1; all the double sided walls have the same mass and stiffness.  Considering the high ductility of EDCC and the high composite energy absorption capacity perceived from the large displacements of the EDCC retrofitted specimens during the shaking, it is certain that a great deal of the motion is being damped during the test. The large damping whether coming from the shake table itself, its hydraulics system, its mechanical moving parts, or even the specimen being tested, can change the table calibration, motion characteristics, and the peak values throughout the tests; this is an unavoidable nature of the shake table experiments. 90  4.2 Experimental Procedure and Details The test was setup on the Linear Shake Table (LST), using the mounting frame assembly (called the “blue frame” in this thesis), which was previously fabricated and used at the Earthquake Engineering Research Facility (EERF) for testing URM wall specimens in out-of-plane (OP) action during the experimental phase of the BC schools project at UBC (SRG III, 2017). In this experimental work, the six full-scale walls are tested with uniaxial shaking out-of-plane under different ground motions with varying intensities, as described in the preceding section.  4.2.1 Instrumentation and data acquisition The wall specimens are each instrumented at different levels, data are collected using 30 different data acquisition channels including 10 accelerometers, 8 channels of displacement sensors, 8 strain gauges, and time synchronized video recording using four High Definition (HD) cameras. All of the tests are also well-documented using five HD video recording devices, four of which were camcorders recording the tests from four distinct angles and one GoPro camera is mounted directly on the LST, recording the test on the table, looking up at the wall.   It is important to note that all the double-sided walls (i.e. Wall-1, Wall-3, and Wall-5) are instrumented with strain gages; however, the single-sided walls (i.e. Wall-2, Wall-4, and Wall-6) do not have strain gages. The table acceleration and the table displacement are also recorded in all the tests, plus the acceleration at the top of the “Blue Frame,” which is the holding frame for mounting the wall specimens on the shake table. The Blue Frame is designed to hold the walls at the top using steel angle sections, to create a semi (‘non-ideal’) pin-pin boundary condition. At the bottom, the wall blocks are set on the base in a starter mortar layer. Based on the engineering 91  surveys and reports for SRG, provided by the local structural engineering consulting firms, this is assumed to be the best representation and fairly consistent with the current in-situ connection systems for the existing URM partition walls at most of the school buildings across BC, Canada.  A summary of the 35-channel data recordings, as part of the experiment’s instrumentation, data acquisition, and documentation are listed. A typical instrumented wall is schematically illustrated in Figure 4-8, which shows the instrumentation of Wall-1, as a representative specimen.  Accelerometers @ 10 channels o 7 accelerometer installed directly on the wall, on every second course (row) o 1 accelerometer installed directly on the shake table, to measure input motion o 1 accelerometer installed inside the shake table, for control feedback o 1 accelerometer placed on top of the testing frame, to monitor possible slippages  Displacement measurements using string pods @ 8 channels o 7 string pods measuring absolute displacements, behind each accelerometer o 1 LVDT installed inside the shake table, for displacement control feedback  Strain sensing using 3 inches long surface bonded strain gages @ 8 channels o 4 strain gages, installed at the front face of the wall, as shown in Figure 4-8 o 4 strain gages installed at rear face of the wall, behind each of the front gages  High Definition (HD) video recording by 9 cameras o 4 channel time-synchronized video recordings, using security camera system o 3 camcorders recording the tests from 3 angles, for documentation purposes o 1 camcorder recording the tests from a top corner angle, for documentation o 1 GoPro® camera mounted on the corner of the shake table in front of the wall 92  The diagram shown in Figure 4-8 represents the instrumentation of Wall-1, which is identical to Wall-3, in terms of instrumentation.   Figure 4-8: Schematics of the Instrumentation of the Wall Tests; Wall # 1 is Shown Above 93  4.2.2 Test Arrangements and Setup As mentioned in preceding sections, all of the six EDCC retrofitted specimens listed in Table 4-1 are made of unreinforced, 100 mm thick, CMUs and are tested under the ground motions of Table 4-3, which are of different types and characteristics, as listed in Table 4-4. For clarity and ease of discussion, each of the earthquake runs on any of the walls has been associated with a unique “Run-ID” number in this thesis; and, the Run-IDs are always referred to throughout the discussions in this document. A summary of all the associated Run ID numbers for each of the tested walls (Wall-1 to Wall-6) are listed in separate tables in this section, from Table 4-6 to Table 4-11, respectively. In addition, a separate “aftershock investigation” is done on Wall-3 only, and the corresponding results of this aftershock study is presented in Table 4-12. As an example, Figure 4-9 shows a single-sided wall with premium EDCC, Wall-2, during its fourth run, Run-4, flexing under 150% intensity of the Japan’s 2011 Tohuku earthquake, GM-1.   Figure 4-9: Wall-2 during Run-4, being Tested at 150% Actual Intensity of GM-1 94  Over the next run of Wall-2, it developed a major plastic hinge at about 40% height from the bottom, and a localized crack was formed at the EDCC layer, where the wall started to rock at the cracked joint and failed after four full rocking cycles. In order for the wall to be able to rock freely, there is an approximately 50mm gap at the top of the wall. This is because the URM wall increases in height when completing a rocking cycle. Figure 4-10 shows the failure sequence of Wall-2, at its final run (Run-5), under Tohuku motion (GM-1) at 180% of actual intensity.   Figure 4-10: Views of Wall-2 before Collapse at Extreme Deformations during Run-5 95  Generally, each wall is first tested with 100% of the actual intensity of the targeted scaled ground motions, the same records used throughout the analytical phases of SRG editions. Thereafter, the intensity was subsequently increased until the failure and eventually collapse of each wall.  For instance, the test schedule for Wall-2 started with Run-1, which is 100% intensity of GM-1, the Tohuku earthquake, proceeding with Run-2, the 100% level of GM-4, the Kobe earthquake. Each wall is fully inspected for cracks and induced damages after each run, and then the testing program proceeds based on the observed results. The testing program for Wall-2 continues with Run-3, testing the wall at 120% intensity of GM-1 followed by 150% intensity of the same record, labeled as Run-4, which is shown in Figure 4-9. At its Run-4, Wall-2 went through very large cycles of displacement and experienced large accelerations at the mid height. After this run, there are obvious signs of induced damage, with by multiple micro cracks into the EDCC layer, but no major localized crack is observed. The wall proceeds with Run-5, which results in collapsing of this wall, as shown in Figure 4-10. A summary of the mentioned runs and discussed outcomes for Wall-2 is provided in Table 4-7.  The collapse of Wall-2 happens during Run-5 at 180% scale of the actual intensity of GM-1, the Tohuku earthquake, recorded at the Miyagi-Oki Station. This ground motion is considered a long duration subduction event with significant strong motion components. This induces a great fatigue factor for the retrofitted wall during the motion. In particular, the GM-1 record is a shortened version of the actual recorded ground motion, which was originally 6 min long. In fact, GM-1 is a 3 minutes long truncated section of this record, but it is truncated such that it contains the entire strong motion part of the original Tohuku record, as listed in Table 4-3. 96  4.3 Shake Table Testing Summary Results and Discussions As shown in Table 4-1, three walls are retrofitted on one side with a single 20mm thick hand-applied layer of EDCC, and three walls are double-sided (20 mm each side) retrofit. Two of the top performance mixes of the EDCC material are identified from the pure materials testing results and used in this full-scale testing program; the two selected mixes are the “Premium Mix” and the “Regular Mix,” as discussed in Chapter 3: of this thesis. It is worth to refresh here again, that the detailed summary of all the tests, their associated Run ID numbers, and the corresponding outcomes for each of the tested walls (Wall-1 to Wall-6) are listed in separate tables in this section, from Table 4-6 to Table 4-11, respectively. For further clarifications, Table 4-5 provides a recap of all of the mentioned summary tables, in addition to a summary of all the wall tests, in terms of instrumentation and ground motion records used.  Table 4-5: Outline of all the Result Summary Tables Specimen Number Run Number Table Number Instrumentation Channels Ground Motions Used Displacement Acceleration Strain Sensing Synced Video GoPro & VCR GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 Wall-1 1 – 25 Table 4-6 8 9 8 4 5 ●  ● ●   ● Wall-2 1 – 5 Table 4-7 8 9 - 4 5 ●   ●    Wall-3 1 – 13 Table 4-8 8 9 8 4 5 ● ● ● ● ●   14 – 21 Table 4-12 8 9 8 4 5 ● ● ● ● ●   Wall-4 1 – 4 Table 4-9 8 9 - 4 5    ●  ●  Wall-5 1 – 4 Table 4-10 8 9 - - 4     ● ●  Wall-6 1 – 4 Table 4-11 8 9 - 4 5   ●  ●   97  It must be noted that all of the test runs (Run-IDs) are labeled and sorted in a chronological order, in which the walls are tested. For example, on Wall-1 there has been a total number of 25 distinct ground motion runs, from Run-1 to Run-25, as listed in Table 4-6, in the order of testing sequence, one after each other over the course of three separate days for this specific specimen.  Table 4-6: Summary of the Shake Table Testing for Wall # 1 Specimen ID Ground Motion Run ID Scale factor (% of actual int.) Collapse (Yes / No) Comments on the damage state Wall-1 GM-1 Run-1 10 % No No Visible damage Run-2 20 % No No Visible damage Run-3 30 % No No Visible damage Run-4 40 % No No Visible damage Run-5 50 % No No Visible damage Run-6 80 % No No Visible damage Run-7 100 % No No Visible damage Run-8 120 % No No Visible damage Run-9 150 % No No Visible damage Run-10 180 % No No Visible damage Run-11 200 % No No Visible damage GM-4 Run-12 100 % No No Visible damage Run-13 150 % No No Visible damage Run-14 200 % (1st Run) No No Visible damage Run-15 200 % (2nd Run) No No Visible damage Run-16 200 % (3rd Run) No No Visible damage GM-3 Run-17 100 % No No Visible damage Run-18 150 % No No Visible damage Run-19 200 % (Interrupt) No No Visible damage Run-20 200 % No No Visible damage Run-21 250 % No No Visible damage Run-22 300 % No Minor cracks GM-7 Run-23 100 % No Minor cracks Run-24 150 % No One major crack Run-25 200 % Yes 1 localized crack @ lower 1/2 of height 98  The results of Wall-1 conclude that double-sided retrofit with the premium EDCC mix is performing beyond all of the requirements of SRG III for out-of-plane confinement, for all of the considered performance criteria. The double-sided retrofit can also be a very good solution for areas with extreme seismicity, when low overall drifts are required for such walls. Wall # 1 was tested up to 300% actual intensity of GM-3, the Chi-Chi Earthquake of Taiwan, which is a very aggressive natural ground motion, with high peak ground velocities, containing a high frequency spectral content, as listed in Table 4-6.   However finally, it had to be tested to failure with a 200% scale factor of a very aggressive UBC modified synthetized motion (GM-7). This waveform is called the “Verteqii Waveform”, formally listed as GM-7 in Table 4-3 and Table 4-4. The GM-7 waveform has a PGA of 1.2 g and contains a very high frequency content, which these short and stiff wall specimens are particularly sensitive to. This waveform is purposely selected, so the level of damage required to fail Wall-1 can be achieved during the shaking. The table accelerations exceeds 3 g during the last run (Run-25) of Wall-1 and accelerations recorded at the mid height of the wall during the last shakings are ranging from + 5.2 g to - 6.1 g, before the failure. This difference shows serious amplification effects, indicating that Wall-1 is actually flexing during the aggressive shakings of Run-25, before getting damaged and fail.  For discussion purposes, in addition to Wall-1, which is taken as a representative sample for double-sided retrofit case, Wall-2 is also discussed in further details throughout the thesis, as a representative specimen for the single-sided retrofitted URM walls. As indicated before, Wall-2 goes through very large cycles of deformation, experiences large peak accelerations at its mid 99  height, and takes multiple cycles of “impact-like” loads before it fails and collapses at Run-5. In Table 4-7, a summary for the ground motion runs on Wall-2 is presented along with some observatory comments from the post-inspections done on the wall in between the tests.  Table 4-7: Summary of the Shake Table Testing for Wall # 2 Specimen ID Ground Motion Run ID Scale factor  (% of actual int.) Collapse (Yes / No) Comments on the damage state Wall-2 GM-1 Run-1 100 % No No damage or visible cracks present anywhere GM-4 Run-2 100 % No No damage or visible cracks present anywhere GM-1 Run-3 120 % No Minor cracks at some joints Run-4 150 % No Cracks at all the joints Run-5 180 % Yes One localized crack at the mid-height of the wall  The results confirm that a single sided retrofit with premium mix EDCC can highly increase the global ductility of the system and potentially change the fundamental behaviour of the wall from a typical “Rocking Mechanism” to a “Beam Bending” type behaviour, with significant rotations at the hinge supports (will be discussed further). In this single-sided system, it is observed that all the joints on the non-retrofitted side get cracked all along the height of the wall, so plastic hinges are formed at all the wall joints and, consequently, the observed deformations are significant.   The perceived flexibility of the system results in a large amount of energy dissipation, and therefore, pushing the wall to the deformation limits beyond what is normally detected for non-retrofitted URM walls. It is consistently observed that during the shake table testing of all the single sided walls, the maximum mid-height deflections are more than double on the negative 100  side of the wall, when the EDCC layer is undergoing compression, compared to the positive deflections, when the EDCC layer is acting in tension. In order to provide a graphical representation of the displacement cycles of a single-sided wall during a typical ground motion, the displacement trace for one second, from Run-4 of Wall-2, is provided in Figure 4-11; this one-second trace is a cut out from the 133rd to 134th second of Run-4 (Tohuku @ 150%).   Figure 4-11: Displacement Trace of Wall-2 from 133rd to 134th Second of Run-4  Although the large deformations can dissipate a lot of energy, they can potentially cause problems or induce potential damage to the wall mounted accessories or furniture in some types Wall-2 | Run-4  Note: the EDCC layer is on the right-hand side of the wall shown  Mid-H Deflections Positive Side: 18 mm Negative Side: 72 mm  Wall Accelerations* Max = + 1.98 g Min = – 5.34 g *Maxima @ H = 2.3 m  Table Accelerations Pos. PGA = + 0.72 g Neg. PGA = – 0.58 g 101  of buildings (i.e. school or hospital) during an earthquake. However, for the cases where access to both sides of a masonry wall is not possible or economical, a single sided retrofit can be effective to prevent collapse, despite of the large displacements. On the other hand, the double-sided walls show minimum amounts of deflection, even during the most severe shakings. In order to provide a basis for comparison and discussion, Figure 4-12 shows a double-sided wall, Wall-1, undergoing the exact same ground motion, 150% of Tohuku (Run-9); and, the deflection values are plotted using the same scales for the axes, as in Figure 4-11, for ease of comparison between the two cases.   Figure 4-12: Displacement Trace of Wall-1 from 126th to 127th Second of Run-9 Wall-1 | Run-9  Note: the 20mm thick layer of EDCC exist on both sides of the wall  Mid-H Deflections Positive Side: 3.3 mm Negative Side: 3.5 mm  Mid-H Accelerations* Max = + 0.95 g Min = – 0.88 g *Maxima @ H = 2.3 m  Table Accelerations Pos. PGA = + 0.69 g Neg. PGA = – 0.64 g 102  Table 4-8 summarizes all the ground motion runs performed on Wall-3, which is another double-sided specimen but differs from Wall-1 in that it is retrofitted with the Regular EDCC mix instead of the Premium EDCC mix (i.e. it has 1% PVA + 1% PET as opposed to 2% PVA fibers). This wall was tested with all of the selected crustal and subduction records, tightly following the targeted spectra; and then tested with large magnitude records for data.  Table 4-8: Summary of the Shake Table Testing for Wall # 3 Specimen ID Ground Motion Run ID Scale factor  (% of actual int.) Collapse (Yes / No) Comments on the damage state Wall-3 GM-1 Run-1 100 % No No damage or visible cracks present anywhere GM-4 Run-2 100 % No No damage or visible cracks present anywhere GM-2 Run-3 100 % No No damage or visible cracks present anywhere GM-1 Run-4 150 % No No damage or visible cracks present anywhere Run-5 180 % No No damage or visible cracks present anywhere GM-4 Run-6 150 % No No damage or visible cracks present anywhere Run-7 180 % No No damage or visible cracks present anywhere GM-2 Run-8 150 % No No damage or visible cracks present anywhere GM-3 Run-9 100 % No Very minor cracks at some joints Run-10 150 % No Minor cracks at some joints at the mid-height of the wall GM-5 Run-11 150 % No Minor cracks at some joints at the mid-height of the wall GM-3 Run-12 200 % (Interrupt) No Due to a system error, test got interrupted, still the same minor cracks at some joints of the wall Run-13 200 % (Interrupt) No Due to a system error, an emergency shutdown happened causing a major crack at about the mid-height of the wall 103  As can be noted from the summarized results in Table 4-8 for Wall-3, during the 13 runs done on this double-sided wall, the specimen did not collapse. However, due to an unfortunate circumstance, an emergency hydraulic system shut down happened once during Run-12 and once again at Run-13, which severely damaged the specimen. Fortunately, all of the necessary ground motion runs to cover the targeted hazard spectra for the scheduled testing program were finished before the wall was damaged. Table 4-8 shows the accelerations (in units of g) imposed to the wall due to the sudden system shutdown at Run-13. The lowest bar set on the graph represents the table accelerations and the top most bar set is the channel for frame’s accelerations.   Figure 4-13: Acceleration profile at the impulse on Wall-3 at Run-13  Thus, it is decided to save this damaged specimen for a separate study on the effects of aftershocks on a damaged specimen. The post-damage assessment strategy and aftershock effect investigations are presented in following section of this chapter, after discussion of the results for -10 -5 0 5 10 15-3.5776-7.5722-7.4085-5.6828-5.942-6.1648-8.6634-6.7936-5.82231.96916.43065.67194.84497.10266.51515.6612.21914.2858IMPULSE ON WALL-3 | RUN-13Negative Accelerations (g) Positive Accelerations (g)Acceleration Channels 104  the main testing program. The next wall tested as part of the main program is Wall-4, for which the result summary is presented in Table 4-9. Wall-4 is a single-sided specimen, retrofitted with the Regular EDCC mix.  Table 4-9: Summary of the Shake Table Testing for Wall # 4 Specimen ID Ground Motion Run ID Scale factor  (% of actual int.) Collapse (Yes / No) Comments on the damage state Wall-4 GM-4 Run-1 100 % No No damage or visible cracks present anywhere GM-6 Run-2 100 % No No damage or visible cracks present anywhere GM-4 Run-3 120 % No Minor cracks at most joints Run-4 100 % Yes One localized crack at the upper half height of the wall  Wall-4 is one of the two walls tested with the selected sub-crustal ground motion record of this testing program, GM-6, which is the earthquake from 2001 in Nisqually of Washington, USA. This is a considerably weaker ground motion, compared to the rest of the ground motion records, with a PGA of 0.19 g. In fact, this was selected to complete the testing program, by having all three types of ground motions, which all can happen in BC.   This wall remained intact until the end of the third run, when it developed some minor cracks at about 40% point along the height, from the top. The cracks are barely visible at this stage, and the wall was judged to be fully stable and intact. Since the damage state is not fully clear, it is decided to scale down the motion, and re-test the specimen at the same intensity of the starting point, the same as the first run. This could give us an indication on the perceived damage state from visual inspection. Thus, in Run-4, the wall is again tested with 100% intensity of Kobe, the 105  same motion as Run-1. Surprisingly, the wall reacts to the same motion with much higher displacement amplitudes, develops a localized crack during the strong motion peak of Kobe, and is not able to recover at the second cycle of rocking; it hits the point of instability and comes down on the table. The radius of the debris are similar to Wall-2, which was measured to be around 1.5m all around the table. Compared to the tested bare walls, this radius for the debris thrown is about less than 1/3 of a bare wall, as observed from the previous wall test videos.  The results summary for Wall-5 is given in Table 4-10. This wall is not tested to failure, and the specimen is saved for further testing. Wall-5, as described in Table 4-1, has no lateral joint reinforcement and is hand-applied with 20mm thick layers of Regular Mix EDDC on both sides.  Table 4-10: Summary of the Shake Table Testing for Wall # 5 Specimen ID Ground Motion Run ID Scale factor  (% of actual int.) Collapse (Yes / No) Comments on the damage state Wall-5 GM-6 Run-1 100 % No No damage or visible cracks GM-5 Run-2 100 % No No damage or visible cracks GM-6 Run-3 150 % No No damage or visible cracks GM-5 Run-4 150 % No No damage or visible cracks  As visible in Table 4-10 for Wall-5, this specimen is left undamaged on purpose. In fact, this wall specimen was left until the end of the testing program because it was realized that braking the double-sided walls on the shake table, by using natural ground motions, is a challenge and sometime not even possible, unless GM-7 at extreme intensities is used. However, at this stage through the testing schedule, it was evident that the double-sided walls with 20mm thick layers 106  of hand-applied EDCC on both sides would perform beyond the targeted requirements for the considered spectra. Therefore, after a few low intensity records and absolutely no damage observed on the wall, it is decided to stop the runs, remove and save the specimen for possible future investigations, and conclude the testing program using the existing data, at this point.   Finally, Table 4-11 provides the summary for tested Wall-6, a single-sided specimen, retrofitted with a single 20mm thick layer of hand-applied Regular Mix of EDCC, as indicated in Table 4-1.  Table 4-11: Summary of the Shake Table Testing for Wall # 6 Specimen ID Ground Motion Run ID Scale factor  (% of actual int.) Collapse (Yes / No) Comments on the damage state Wall-6 GM-5 Run-1 100 % No No damage or visible cracks present anywhere Run-2 150 % No Minor cracks at some joints GM-3 Run-3 100 % No Minor cracks at most joints Run-4 150 % Yes One localized crack at about the mid-height of the wall  Testing of this specimen is started by GM-5, the only ground motion scaled for long period buildings (TC = 1.0 sec), based on Victoria’s high seismicity hazard spectrum for crustal events.  As indicated in Table 4-1, this is the only single sided wall with no joint reinforcement; thus, it might have a slightly lower initial cracking strength at its mortar joints compared to other single-sided specimens, and to complete the testing program, one long period crustal motion, GM-5, for a high seismicity area is selected for Wall-6. This is the Landers earthquake of 1992 in California, US, with a PGA of 0.73 g (see Table 4-4). This wall is tested in four runs, until collapse, and the radius of debris thrown are consistent with the other single-sided specimens. 107  4.3.1 Effects of Aftershocks on a Partially Damaged Wall As explained in the preceding sections of this chapter, while testing Wall-3 specimen, due to an unforeseen technical glitch within the control system at Run-12, the shake table went through an emergency hydraulic shut down, and came to an immediate stop. This induced a huge spike of accelerations, with a table PGA of 2.95 g and wall peak accelerations of + 5.1 g and – 6.3 g. No visible damage was observed on the specimen after the post-inspections. The same situation happened again, when Run-12 was being repeated on the same specimen, logged as Run-13, causing maximum excitations of -8.7 g and +12.2g on the wall, as shown in Figure 4-13. A horizontal large localized crack was formed across the wall, right through the layer of EDCC on one side of the wall, but the EDCC layer on the opposite side is still intact. Eight aftershocks where run on the damaged specimen, as listed in Table 4-12. The results indicate that a severely damaged, double-sided, heavy weight wall still takes large accelerations before it fully collapses.  Table 4-12: Effect of Aftershocks on Damaged Wall # 3 - Shake Table Testing Summary Specimen ID Ground Motion Run ID Scale factor  (% of actual int.) Collapse (Yes / No) Comments on the damage state Wall-3  (This wall is previously damaged and cracked) GM-1 Run-14 50 % (1st aftershock) No One major crack existing at about the mid-height of the wall already Run-15 100 % (2nd aftershock) No One major crack and some minor cracks at mid-height of the wall GM-2 Run-16 100 % (3rd aftershock) No One major crack and some minor cracks at about mid-height of wall GM-4 Run-17 100 % (4th aftershock) No One major crack and many cracks at about mid-height of the wall GM-5 Run-18 100 % (5th aftershock) No One major crack and many cracks at about mid-height of the wall GM-3 Run-19 50 % (6th aftershock) No One major crack and many minor cracks at mid-height of the wall Run-20 100 % (7th aftershock) No One major crack and many major cracks at about mid-height of wall GM-4 Run-21 100 % (8th aftershock) Yes One major localized crack (same crack) became unstable and fails 108  4.3.2 Force Distribution and Motion Amplification Factors The basis for all the force calculations in the following sections are the recorded accelerations across all the channels. Load-deflection curves, moment-curvature diagrams, and other global responses are also assembled based on the acceleration results. Thus, it is important to review the acceleration distribution over the height of a wall, during one of the ground motions. As an example, Figure 4-14 shows the variation of acceleration for all the channels, along the height of the wall, for the entire 249 sec duration of Run-4 of Wall-2, for which the deflection traces for one second of the run were presented in Figure 4-11.   Figure 4-14: Acceleration Traces for all Channels along the Height of Wall-2 at Run-4 109  It should be highlighted that, unlike the deflection profile, which has a patterned distribution along the height of the wall, with peak values at the mid-height, the accelerations are distributed more randomly, with peak accelerations seen toward the base and the top of the wall, for both positive and negative acceleration values. Similar to what was done for the 1 sec long deflection traces in Figure 4-11 and Figure 4-12, in order to provide comparison basis, Figure 4-15 shows the acceleration traces for a double-sided wall, Wall-1, going through the same ground motion, Tohuku at 150% (Run-9), drawn for the entire record on the same axes scales as Figure 4-14.   Figure 4-15: Acceleration Traces for all Channels along the Height of Wall-1 at Run-9 110  There are a few critical observations, which also explain the difficulty in assembling the hysteresis curves for the walls from the acceleration-displacement data. In a single-sided wall, there is a significant amplification factor between the table and the base of the wall. Initially, it was believed that base movements create the observed base amplifications; however, by looking at the double-sided response and other less flexible specimens, it is confirmed that Wall-2 is uniformly excited over its entire height, creating huge amplification factors. Figure 4-16 graphically presents the amplification factors for Wall-1 versus Wall-2, in percentage differences from the table, for both accelerations and displacements along the normalized height of the wall.   Figure 4-16: Acceleration and Displacement Amplification Factors for W-1 vs. Wall-2 -1000 -500 0 500 1000Normalized Wall HeightAmplification (%)Acceleration Amplification (Wall-1 | Wall-2)Wall-1 Accel. Envl.Wall-2 Accel. Envl.-20 -10 0 10 20Normalized Wall HeightAmplification (%)Displacement Amplification (Wall-1 | Wall-2)Wall-1 Displ. Envl.Wall-2 Displ. Envl.111  4.3.3 Displacement Pattern and Damage Model In order to come up with a logical model for the progressive damage for the specimens, a single sided wall, Wall-2, is discussed in further details. The same wall is also used and discussed for a different damage detection or quantification technique, using the operational modal analysis method, in the following sections. Figure 4-17 shows the time-history of the mid-height deflection for Wall-2 at its first run (Run-1); this deflection is calculated by subtracting the shake table displacements from wall’s mid-height point movements during Run-1. The graph also indicates the location of the upper and lower boundaries for the wall displacement, with respect to wall’s geometrical local vertical axes, and shows the mean deflection by a red dotted line. For discussion purposes, there is a linear trend line and a cubic fitted curve that indicate the overall trend of the deflections during the entire motion. The trend lines will be discussed and compared for all the runs on Wall-2.   Figure 4-17: Deflections of Wall-2 at its Mid-Height Point at Run 1 112  Having a closer look at Figure 4-17, a difference of - 14 mm is noticed between the “deflection-median” (dotted red line) and the last point on the “Mid-Height Deflection” curve. This indicates an irreversible or plastic type deflection for Wall-2 after Run-1, not letting the wall reposition to its zero start point, bowed toward the negative side at mid-height (i.e. the ‘positive side’ is where the EDCC layer is applied). Considering the maximum measured deflection on the negative side being - 41 mm, the irreversible portion is 35% of the maximum negative deflection. To put this in an overall drift perspective, the 14 mm deflection at midpoint of the wall is equal to - 1.0% drift, calculated by dividing the mid-point deflection by half of the wall’s height (½ × 2.8 m). The negatively sloped (- 6%) trend line also confirms the same. On the other hand, the best-fitted curve, which is a cubic function, indicates that the wall deflections stayed in the negative side at the middle of the motion, and then the deflection trend is coming back toward the positive side. Now, let us look at the deflections during the second run (Run-2) of the wall in Figure 4-18.   Figure 4-18: Deflections of Wall-2 at its Mid-Height Point at Run 2 113  Looking at the same parameters now, with respect to Figure 4-18 reveals interesting results. First, the trend line has changed slope from negative slope of - 6% to a positive slope of + 13% from Run-1 to Run2. Also, the wall has now developed a plastic deflection of +17mm after the second run, that is 55% of the maximum positive deflection of +31mm, exactly on the opposite side now, compared to the final position after the first run (Run-1). This is equal to + 1.2% drift. This change in direction and the irreversible deformations are likely coming from the EDCC layer, which is located on the positive deflection side. This makes it necessary to look at the same deflection values for the same wall during its next run (Run-3) in Figure 4-19 now.   Figure 4-19: Deflections of Wall-2 at its Mid-Height Point at Run 3  Investigation on the same factors again confirm that the EDCC layer is likely going through irreversible plastic deformations, but now passed its bend-over point of the material response, deforming in an elastoplastic manner, in the plastic response plateau of the material. 114  This nonlinearity in the EDCC is affecting the composite response of the wall, as evident by its global response. The trendline is still maintaining its positive slope, + 2.3% at this point, and the wall is sitting + 6mm more offset at the end of Run-3, compared to the end of its position after Run-2. Thus, the absolute position is + 9mm from the start point (-14mm + 17mm + 6mm). The cubic fitted curve also indicates an increasing rate of permanent deformations for this wall. Now, by looking at one more run (Run-4) of Wall-2 in Figure 4-20, and comparing the same parameters, the reasons for this observed behaviour can be further confirmed.   Figure 4-20: Deflections of Wall-2 at its Mid-Height Point at Run 4  As observed during Run-4 video recordings and by looking at the extreme deflection values during the fourth run, higher damage of the EDCC layer is expected. The trend line inclining more in the positive side, now having + 4.6% of slope, and the cubic fitted curve also indicating the positively rising trend for the deflections, the progressive damage is evident. 115  The wall is now leaning even more toward the positive side by additional +11 mm, making a total permanent deflection of + 20mm from the wall’s start point before the first run; equal to +1.43% overall permanent drift. This is 47% of the total positive deflection of + 24mm during the fourth run for this wall. Table 4-13 summarizes all the parametric values discussed.  Table 4-13: Parametric Study Values for Wall-2 from Run-1 to Run-4 Wall & Run IDs Mean Deflection Max Positive Deflection Max Negative Deflection Added Permanent Deflection Cumulative Permanent Deflection Cumulative Permanent Total Drift Wall-2 | Run-1 - 9.05 mm 3.31 mm 40.66 mm - 14 mm - 14 mm - 1.0 % Wall-2 | Run-2 + 3.56 mm 30.37 mm 59.65 mm + 17 mm + 3 mm + 0.2 % Wall-2 | Run-3 + 0.78 mm 21.70 mm 48.82 mm + 6 mm + 9 mm + 0.64 % Wall-2 | Run-4 + 1.55 mm 24.11 mm 67.90 mm + 11 mm + 20 mm + 1.43 %  It is worth referring back to the one-second long displacement trace presented in Figure 4-11, which shows the deflections that Wall-2 is going through at only one single cycle of impact-like load during Run-4 (Tohuku @ 150%). This large peak of impact load creating the one-second displacement trace (133rd – 134th second), can now be looked at more closely from the mid-height deflection curve presented in Figure 4-20, which is from the same wall at the same run.  The progressive damage shows that the EDCC layer, as the tension cord for the wall, which is undergoing bending rather than rocking now, has certainly progressed past the linear through to the non-linear portion of its stress-strain response curve, from the materials perspective; and, this is well beyond the bend-over point presented in the graph of  Figure 6-9. The reason for the wall 116  not being able to come back to its absolute zero displacement position after Run-2, with increasing cumulative permanent deflection values, is that the EDCC layer has developed some micro-cracks in a multiple cracking regime, as explained in the preceding chapter. Hence, the elastic portion of the strain is regained but the plastic portion of the strain is not recoverable. This, in fact, is also due to the damage at the crack openings and the debris, which are formed accordingly at the crack, filling up the crack and hence not allowing the crack opening to perfectly close. When the same cracks go through many cycles of opening and closing during the consecutive runs, the crack mouths will get larger, making a visible pattern of multiple cracking on the surface. The trendlines and the curves fitted to the deflection patterns, for successive runs, confirm the discussed progressive damage model. For reference, Table 4-14 lists all the equations of the trend lines and the fitted curves for the runs discussed all in this section.  Table 4-14: Equations of the Trend Lines and Fitted Curves for Deflections of Wall-2 Wall & Run IDs Linear Trend-line Equation Polynomial Fitted Curve Equation Wall-2 | Run-1 y = - 0.060 x - 2.1 y = 6.0e-06 x3 - 0.0012 x2 - 0.064 x + 1.70 Wall-2 | Run-2 y = + 0.130 x - 4.5 y = 1.6e-03 x2 - 0.076 x - 0.20 Wall-2 | Run-3 y = + 0.023 x – 2.0 y = 1.4e-06 x3 - 0.00013 x2 - 0.017 x + 0.55 Wall-2 | Run-4 y = + 0.046 x - 4.1 y = 2.2e-06 x3 - 7.6e-05 x2 - 0.057 x + 1.80  The existing mathematical model for the second mode of rocking for out-of-plane (OP) failure, which is formally referred to as the “OP-3 Rocking Model,” can numerically predict the location of the initial crack formation for URM walls (SRG III, 2017). The OP-3 rocking model for a bare wall indicates formation of one or a few discrete localized cracks, logically formed at 40% to 117  60% of the height from top or bottom of the wall, separating the wall into few rigid bodies during the rocking cycles. However, considering the elastoplastic and strain hardening type behaviour of EDCC in pure tension, there are now cracking zones formed throughout the wall’s height within the EDCC layer, instead of a few localized cracks; thus, the many cracks not coming to the absolute closed position would cause the noticed irreversible deflections.  4.3.4 Stability and Displacement Capacity Enhancements Based on the systematical evaluation using a simplified procedure by Griffith et al., the collapse of a non-retrofitted URM wall is mainly conditioned by its ultimate displacement capacity and not by its initial stiffness. The lateral static strength and the ultimate displacement of a bare URM wall subject to out-of-plane forces or excitations are mainly driven by wall’s geometry, the boundary conditions, and the applied vertical forces, including self-weight.  (Griffith, Magenes, Melis, & Picchi, 2003).  For Run-4 of Wall-2, some test photos are shown in Figure 4-9, the deflection traces are presented in Figure 4-11, and the peak values are tabulated in Table 4-13. In this run, there are a few stability observations, which are consistently seen in all the single-sided retrofitted walls. At the mentioned run, accelerations recorded slightly above the mid-height of Wall-2 at the strongest impact cycles are ranging from + 2.0 g to - 5.4 g, and the peak lateral deflections at mid-height are about + 24mm to - 68mm during the same run.   Considering Wall-2 is a 90mm thick URM wall, measured, with an additional 20mm thick layer of hand-applied EDCC, the wall is certainly pushed to the limits of its geometrical stability point, 118  calculated based the OP-3 rocking models provided by many researchers in the field. The failure criterion for an out-of-plane rocking wall is that if the displacement at the effective height of the wall exceeds the effective instability displacement, then the wall would collapse, based on the mathematical model. Looking at the wall in Figure 4-21, the instability displacement is 2T/3, when T is wall’s thickness, and there is a uniform distribution of weight and stiffness throughout the cross section of the wall. (Doherty, Griffith, Lam, & Wilson, 2002) However, having the EDCC layer on one side, would force the wall to hit instability in displacements less than 2T/3.   Figure 4-21: Idealization of Out-of-Plane Rocking by Doherty et al. (2002)  In fact, during Run-4 of Wall-2, there is about 65% difference between wall’s center of mass and geometrical center at peak deflections. This large mid-point deflection would create an additional 119  large lateral force due to the extra moment created through the p-delta effect over the overall height of the wall; this additional force is now pushing the wall further out of its own plane, toward the instability point, initiating the onset of collapse. However, what is still holding the blocks together at such large deflections, undoubtedly, is the existence of the EDCC layer behind the wall, creating a spring force to pull the wall back into its geometrically stable zone, preventing the collapse, despite of the unbalanced additional weight imposed by the EDCC layer.  In order to understand the behaviour of retrofitted walls after losing their EDCC layer(s) in full, during the test, it is helpful to look at a simplified trilinear force-displacement model by Doherty et al. (2002), shown in Figure 4-22, which is based on a “semi-rigid” force-displacement relationship defined by three displacement parameters. In this idealized model, ∆1 controls the initial stiffness reduction, ∆2 controls the strength reduction of the wall, and wall’s idealized rocking in rigid body motions happens when maximum forces stay within the rigid threshold resistance of F0 and the maximum stable displacement of ∆f (Ferreira, Costa, & Costa, 2014).   Figure 4-22: Trilinear Force-Displacement Rocking Model ( Ferreira et al., 2014) 120  4.3.5 Discussion on Performance Comparison The experimental models in this work reveal that the EDCC layer does not solely act as a pure membrane, unlike what preliminary was assumed during the numerical predictions. In fact, when the retrofitted URM walls are experiencing cycles of deformation on the shake table, the EDCC layer would constantly go through tensile and compressive stress cycles; this is true for both single-sided and double-sided walls. Indeed, when the EDCC layer is acting at the compression cord, the compressive forces developed in the EDCC layer during the negative cycles would prevent the wall from collapsing due to geometrical instability (i.e. the single sided wall deflecting or bending in the direction that the EDCC layer is not applied). Although the developed compressive stresses might be relatively low in magnitude, this minor stress, however, can act highly in favor of the deformed wall, when EDCC is applied as a single-sided retrofit.  In particular, in a single-sided retrofit configuration, the wall is lacking a tension cord on the negative side (i.e. on positive is the EDCC layer), so all the mortar joints would crack and then joints constantly open and close in loading and unloading cycles. However, the EDCC layer going to compression prevents the cracks from opening wide and stops the wall from hitting its instability point; this claim is clearly visible in the shake table testing videos of all the single-sided walls. This explains the effectiveness of single-sided EDCC layer in retrofit of URM walls.   Explicitly, the EDCC single-sided retrofit option, for out-of-plane restraining of URM walls, would result in performance enhancements of much higher degrees, compared to the alternative single-sided retrofit options. For instance, a URM wall retrofitted on one side with FRP strips collapsed at about 65% intensity of GM-4 record, previously tested on the same shake table at 121  the UBC EERF (unpublished data), using the same test setup as this study (SRG III, 2017). Whereas Wall-2 (single-sided with Premium EDCC) and Wall-4 (single-sided with Regular EDCC) were able to withstand 100% and 120% of the actual intensity of the exact same record (GM-4), respectively. Moreover, the same specimen (Wall-2), after taking the mentioned 100% intensity of GM-4, survived two more runs of GM-1 (at 120% and 150%), which is a considerably long duration record with significant velocity and acceleration components.  The single-sided FRP, contradictory to the EDCC layer, works purely in a membrane action, and cannot take any compressive forces during the negative cycles. It is worth mentioning that the strain gages installed on the EDCC layer, for some of the tested specimens, confirm that EDCC layer does take significant amount of compression at some points during the ground motions. In fact, the strain gage readings of up + 12,500 µƐ (tension) to - 15,800 µƐ (compression) were recorded at the face of Wall-3 during the few last impact cycles shown in Figure 4-13.  Furthermore, from the numerical comparison between the recorded signals for the shapes and values of the peak acceleration cycles, it is evident that significant amount of the velocity is being damped at each of the loading/unloading or acceleration/deceleration cycles. Considering the sensitivity of URM walls to the velocity content of ground motions, this attribute also explains the great enhancement of the overall performance of an EDCC retrofitted wall to a non-retrofitted URM wall. Experimental results from the previously tested bare wall specimens on the linear shake table at UBC EERF, using the exact same test setup as this study, indicate extremely lower resistances to some of the ground motions. For example, a non-retrofitted wall fails at about 60% intensity of GM-1, the Tohuku earthquake (SRG III, 2017). 122  4.4 Detailed Studies of the Shake Table Testing Results In this segment, a few detailed studies have been conducted to extract more in depth information from the shake table test data and compiled results. The objectives of these studies is to gain a better understanding of the global response of the tested specimens from the information within the data signals (Wang L.-J. , 1996); and, to provide rational comparisons on different damage states for the specimens after each run. Therefore, a deeper look into the data using advanced signal processing techniques has been done.  This section presents the load-deflection curves, moment-rotation plots, and moment-curvature diagrams for Wall-2, as a representative sample. All the curves are fitted with strength degradation trends as predictive damage models. Furthermore, in Chapter 5:, vibration based methods have been used to study the dynamics of the walls, and to extract their modal behaviour at different damage states. The full script of the MATLAB generated codes, scripts, and functions for the analyses and modeling are selectively presented in Appendix G  , for reference.  4.4.1 Shake Table Testing Results: Load-Deflection Curves A set of load-deflection curves for a representative wall is presented in this section. For ease of comparison, the forces are all presented in terms of “total lateral force” or “total shear force” for the wall; and, the displacements are presented in terms of mid-height drift. As previously discussed, and shown in Figure 4-8, there are seven independent accelerometers installed on each wall specimen, evenly spaced out throughout the height of the wall. On the opposite side of the wall, directly behind each of the accelerometers, there is a string pot (i.e. potentiometer) installed to directly measure displacement values at the same height as the acceleration measurements. 123  In order to calculate the total shear, each wall is modeled as a simple seven horizontal degrees of freedom (7DOF) system with lumped masses at each DOF (accelerometer locations). A mass vector of size 7×1 is assembled for each specimen, associating the calculated masses to the corresponding DOF, based on the tributary area principles used for mass and load allocations to structural systems. The total mass of each specimen is the linear summation of all the elements of its mass vector and is presented in Table 4-1 along with other specifications of the specimens. The shear force at the location of each DOF is calculated by linearly multiplying the absolute accelerations recorded at the DOF by its lumped mass. Subsequently, the total shear or the total lateral load is calculated as the linear summation of the entire shear forces at all the DOFs. The total lateral force for Wall-2 is plotted against its mid-height drift, for all the runs, in Figure 4-23.   Figure 4-23: Base Shear vs. Mid-Height Drift for all the Runs of Wall-2 124  The drift value at mid-height is achieved by dividing the relative displacements at the wall’s mid-point by half of wall’s height (½ × 2.8 m). The relative displacements of the wall are, in fact, ongoing deflections at each DOF location, calculated by subtracting the base (table) displacements, from measured translational movements recorded at each DOF on the wall.  In Figure 4-23, the linear trend lines are plotted for each curve, fitted such that they can be used as an estimation to the linear and non-linear portions of the behaviour. As expected, the slope of the data trend line is decreasing after each run, indicating stiffness degradations after each earthquake motion that wall goes through. For discussion purposes, the equations for trend lines corresponding to Run-1 and Run-5 are shown on the plot. The slope drop from + 2.86 in Run-1 to + 0.72 in Run-5 is equal to 75%, indicating a major strength degradation, as expected.  4.4.2 Shake Table Testing Results: Moment-Rotation Diagrams For a representative specimen (Wall-2), overturning moment at half-height is calculated and plotted against the average rotations at both supports. The same assumed horizontal degrees of freedom (DOF) and their associated shear forces are utilized to calculate the overturning moment values. The rotations at the supports, however, are obtained by calculating the cumulative rotations at the location of each DOF throughout the height of the wall.  As can be noted from Figure 4-11, deflection profile of the single sided walls are non-uniform and, therefore, rotations at the base of the wall have different values than the rotations at the top of it. To account for such difference, the rotation of the wall is incrementally integrated over the height, from the maximum point, and an average value is obtained by taking the linear average of 125  the wall rotations at the top and bottom supports. Figure 4-24 shows the curves for all the runs of Wall-2, for the change in overturning moment, calculated at the mid-height of the wall, versus the average rotations at wall supports.   Figure 4-24: Overturning Moment vs. Average Rotations at Supports for Wall-2  It is worth discussing that calculating the overturning moments mathematically, by simple mechanics formulations (wall’s shear forces acting at its mid-height), would give slightly lower values than by directly calculating it from the accelerations acting at the masses (obtaining the curvature by incremental integrations). This is due to the contribution of the p-delta effect, which in this case is not negligible due to high mid-point deflections. The trend lines, again, indicate cumulative strength degradations. The slope change for the trend line from Run-1 to Run-5, from 126  +7.6 to +2.5, indicates an overall drop of 68%, which demonstrates a major strength degradation, but slightly less than what was calculated from the force-drift curves previously.  4.4.3 Shake Table Testing Results: Multiple Curvature Bending Deflections It is noticed from looking at the synchronized video recordings that the walls undergo multiple curvatures during some of the deflection cycles. Therefore, before attempting to calculate wall curvature values, for the moment-curvature diagrams presented in the next section, it is useful to have a closer look at the actual deflected shapes of Wall-2 at Run-4, using the recorded displacement signals. Figure 4-25 shows Wall-2 undergoing a double curvature deflection scenario at the 180th second of Run-4, obtained from actual deflected shapes (a 0.025 sec trace).   Figure 4-25: Double-Curvature Bending Deflections for Wall-2 during Run-4 127  On a separate attempt, the deflected shapes are also calculated from double integration of the acceleration signals and it is noticed that Wall-2 undergoes vibrations that would make the wall deform with multiple curvatures during the motion, as shown in Figure 4-26.  In Figure 4-26 (plots from the measured data), the diagram on the left shows Wall-2 deflecting with in a double curvature shape at the 81st second of Run-2 and the deflected shape on the right shows the same wall experiencing resonance from the 82nd second to the 83rd second of Run-3.   Figure 4-26: Multiple Curvature Deflections for Wall-2  Calculating the curvatures for the walls from the different signals made it possible to assemble the moment-curvature diagrams presented in the next section.  128  4.4.4 Shake Table Testing Results: Moment-Curvature Diagrams The same moments calculated for the preceding section, and the curvatures calculated through investigations on the actual deflected shapes of Wall-2, all from the measured data, are used to assemble the moment-curvature diagram for all the runs of Wall-2, presented in Figure 4-27.   Figure 4-27: Moment-Curvature Diagram for all the runs of Wall-2  Unlike what is seen from the load-drift and moment-rotation diagrams, no clear trend is found showing any drop in the slope of the trend lines drawn for these curves. The trend line equations also indicate minor differences between the slopes of the curves in their linear ranges, except for Wall-5, for which the excessive curvatures are due to its unstable pre-collapse deflections. 129  4.5 Final Discussion on the Overall Shake Table Testing Results When it comes to ground shaking, the predominant outcome in out-of-plane motion for URM walls is known to be collapse after a number of “rocking” cycles. In fact, considering the week mortar joints, which hold the masonry units together, the wall becomes non-linear at the very first moments of the ground motion. The rocking mechanism for these walls is very easy to predict by mathematical models, as discussed in section 2.3.2 and section 4.3.4 of this thesis.  Indeed, due to the very weak nature of the masonry mortar joints in tension, the wall usually develops a major crack at about 40% of the wall height from the top of the wall, the crack passes through the mortar joint, and then rocking starts about the cracked joint. Although the mentioned localized crack is sometimes referred to as a “plastic hinge”, the formed hinge shows almost zero plastic type deformation, so having zero stress carrying capacity, it mostly acts as pivot point which lets the masonry blocks above and below the joint to rotate about it, creating a rocking mechanism for the wall. The rocking is driven entirely by the self-weight of the wall, in the case of this experimental work, where there is no surcharge on the URM wall.  Considering that the wall is now divided into two (or more) rigid bodies, the rocking motion is ongoing with a different momentum for each piece of the rigid body, creating differential forces. Depending on the degree of fixity at walls upper and lower boundary conditions, the wall may or may not develop a few other plastic hinges throughout the height of the wall, at different mortar joints. The additional joint cracks would usually happen between 30% to 70% points of the wall height from the top or bottom. The more plastic hinges formed the more energy dissipative rocking behaviour is obtained during the motion, leading the wall to stay upright, and not 130  collapse, for a longer duration of time on the shake table. This type of rocking manner is known to be the fundamental behaviour of URM walls undergoing an earthquake ground motion.   In addition, because of the EDCC retrofit, particularly the single-side retrofitted walls, the base rotation is much more evident during the ground motion. Not only does this decrease the out-of-plane base shear demand on the wall, which sometime causes sliding and collapse for such walls, it also keeps the deformations more uniform and the geometrical instability happens at much higher drift values for the wall.   When an URM wall undergoes rocking, the center of the weight goes back and forth with respect to the center of the geometry of the wall, out of its own plane, during the ground motion. Anytime that center of weight is pushed away from the center of geometry, beyond the 2/3 point (see Table 2-1) of the wall’s actual thickness, by the momentum of the wall rocking, there is a significant p-delta effect, which puts an extra overall bending demand on the wall. A typical URM wall has a very low bending capacity, due to its rocking type behaviour, whereas, now the wall will be able to withstand the bending forces, through some base rotations, and restore its position back to upright by the spring action of its overall bending stiffness.  This experimental work illustrated that fundamental rocking behaviour is changed to a bending-type behaviour for these walls, when a 20mm thick layer of EDCC is applied only on one side of the URM wall. This change in fundamental behaviour results in cracks to form at almost every mortar joint, generating a very high drift capacity for the wall due to the uniform, highly energy dissipative deformations during the entire stretch of the ground motion; keeping the wall longer. 131  Chapter 5: Vibration Based Characteristics Assessment of the Specimens For some representative specimens, the fundamental dynamic characteristics are investigated using vibration measurement based techniques, in order to understand their behaviour under vibrations. The studies include free vibration assessment, simple modal investigations, and system identification using advanced operational modal analysis.  5.1 Vibration Assessment of EDCC Retrofitted Walls Each wall goes through many small cycles of free and forced vibrations in every run, especially at the beginning or toward the end of the runs, when the strong motion part of the record is not running. As an example, Figure 5-1 shows one vibration cycle, in units of milli-g, for Wall-2.   Figure 5-1: Vibration Cycle at Mid-Height of Wall-2 for 30th to 36th Second of Run-4 132  However, during the strong motion part, the wall does not come to complete rest, and there are always cycles of resonant frequencies picked up by the data acquisition system, from the table, the loading frame, the hydraulic system, and even the wall specimen itself. The six-second long vibration shown in Figure 5-1 is truncated from the 30th to 36th second of the accelerations recorded at the mid-point of Wall-2, when no strong motion is happening. There are also instances when the wall undergoes damped cycles of small vibrations, like the one shown in Figure 5-2 for Wall-2, that it is captured from the 60th second of Run-4. Both of the vibrations are taken from the initial part of the record, when there is no strong motion occurring.   Figure 5-2: Damped Free Vibration at Mid-Height of Wall-2 at 60th Second of Run-4 133  From the damped vibration waves shown for Wall-2, measured at its mid-height, some fundamental properties can be estimated for its first natural mode of vibration. As can be measured directly from the graphs, the first natural period of vibration for this wall, measured from Figure 5-1 is about 0.189 Sec (equal to 5.29 Hz); and measured from Figure 5-2 is estimated to be about 0.18 Sec (equal to 5.56 Hz).  For a closer look, the 3-second long signal from Figure 5-1 is taken into the frequency domain, using Fourier transformation, and the power spectral density of signal is shown in Figure 5-3.   Figure 5-3: PSD for Six Seconds of Vibration of Wall-2 at 30th Second of Run-4 134  As a quick try, Half-Power Bandwidth theory, from Chopra A. K. (2012), is used to estimate the natural frequency and damping ratio from the frequency-response curve of Figure 5-3. By having a quick look at the curve, the density of the power spectral has a major amplitude at the frequency of 5.65 Hz, which should be corresponding to the first natural frequency of vibration for Wall-4 at this stage, just before going through the strong motion part of Run-4. The half-band theory formulation shown below (Chopra, 2012) is used to estimate the damping ratios, as graphically presented in Figure 5-4 (Carrillo, Alcocer, & Gonzalez, 2012).  𝜁 =  𝑓𝑏 − 𝑓𝑎2𝑓𝑛     𝑓𝑜𝑟 𝑏𝑎𝑛𝑑𝑤𝑖𝑡ℎ 𝑎𝑡 (1√2⁄ )  𝑜𝑓 𝑡ℎ𝑒 𝑅𝑒𝑠𝑜𝑛𝑎𝑛𝑡 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒   Figure 5-4: Damping Assessment using Bandwidth Theory (Carrillo et al., 2012)  From the mentioned peak of the curve, the damping ratio is estimated as 1.77%. In order to confirm the estimated damping ratio, different frequency response curves have been assembled 135  (with different record lengths) to recalculate the damping ratio. However, similar damping ratios are estimated for the first natural frequency for Wall-2 at the start of Run-4.  It is worth mentioning that the estimated damping for Wall-2 is from Run-4, when the wall is already damaged from the previous three runs. However, the damping ratio would have a different value, if calculated from records of earlier runs. Thus, the same technique is used to calculate the values presented in Table 5-1, listed for Wall-2. It should be noted that the “peaceful” portion of each signal, before the start of the strong motion parts, are used in this technique. This method needs the data from only one sensor, which is the accelerometer at the wall mid-height. This means that each assesment represents the damage state existing after the previous runs. For example, the frequencies and damping ratios shown for Run-4, indicate the damage that occurred on the wall by the end of Run-3.  Table 5-1: Natural Frequencies, Periods, and Damping Ratios from Short Vibration Cycles Wall & Run IDs fn (Hz) Tn (Sec) Damping Ratio (%) Wall-2 | Run-1 7.00 0.143 0.80 Wall-2 | Run-2 6.39 0.157 1.27 Wall-2 | Run-3 5.66 0.177 2.23 Wall-2 | Run-4 5.65 0.177 2.65 Wall-2 | Run-5 5.66 0.177 3.85  136  The frequencies tabluetd in Table 5-1 are plotted in Figure 5-5 with the associated linear trendline and a fitted curve, for discussion purposes. The linear trendline indicates the noticed degredation, but the 3rd order polynomial fitted curve would attain an upward slope after the last data point, so it can only be used to calculate the trend for the downward portion of the data.   Figure 5-5: Fundamental Frequencies and Fitted Curves for Wall-2  Although this is only a simple estimation of the first mode of vibration, monitored at each run, it can be used as a simple damage model for the specimens during the testing program, as only a short portion of the vibration is used in these estimations. The challenge, however, might be to find a cycle of free vibration within the acceleration signal manually, where the table acceleration is nearly zero and the specimen is undergoing a damped vibration. However, a MATLAB generated code can easily scan the entire signal for such free-vibration instances. 137  Figure 5-6 plots the damping ratios obtained for all the runs of Wall-2; a linear trendline and a second order polynomial curve have been fitted to the data.   Figure 5-6: Damping Ratios for Wall-2 after all the Runs, from Short Vibration Cycles  As expected, the fundamental frequencies drop as the wall is damaged through the testing program. Both the linear trendline and the third degree polynomial curve fit the data very well, and so they can be used as helpful predictive tools for rough damage estimations during a single shake table test. Although all the values are extracted from a six-second long data signal, still they provide the information needed for a simple damage estimation model. On a separate attempt, different six-second long data have been extracted from five different clean portions of the data, and different segments of each data signal are examined for extracting the same damage information; the results are reasonably consistent for assigning an approximate damage state. 138  Finally, for the same six-second long isolated vibration cycle, shown in Figure 5-1, the total force on the wall is calculated using all the acceleration channels, along the wall’s height, using the same technique elaborated in the preceding section. In Figure 5-7, the change in calculated total shear force (i.e. the base shear) is plotted against the measured deflections at the wall’s mid-height point, for the six-second long segment of the data (30th to 36th second of Run-4).   Figure 5-7: Damped Force-Displacement Cycle for Wall-2 at 30th Second of Run-4  The damped force shown in Figure 5-7, as the wall comes to a stop, indicates the observed damping during the damage assessment. In this graph, the wall is coming from a -1mm 139  deflection point on the negative side, passes through the zero displacement point and comes to a full stop at +0.5mm displacement point on the positive side. The wall changes direction and moves back toward the negative side again and after a few short amplitude resonance cycles stops vibrating. This pattern of displacement is observed frequently throughout the records, and the reaction force to the displacement pattern control the parameters discussed in the damage assessment model.  5.2 Multi-Degree-of-Freedom Modal Analysis for Retrofitted Walls Before continuing with more operational modal analysis, a simple static modal response analysis is performed, using the methodology given by Chopra A. K. (2012). For this modal analysis, as a sample, Wall-1 is modeled as a generalized lumped-mass seven degrees of freedom system, with 5% assumed damping ratio. Wall-1 matrices for mass (in kg) and stiffness (in kN/m) are:  𝑀 = [      2.0 0 0 0 0 0 00 1.6 0 0 0 0 00 0 1.6 0 0 0 00 0 0 1.6 0 0 00 0 0 0 1.6 0 00 0 0 0 0 1.6 00 0 0 0 0 0 1.2]      × 102  𝐾 = [      2.0 −1.0 0 0 0 0 0−1.0 2.0 −1.0 0 0 0 00 −1.0 2.0 −1.0 0 0 00 0 −1.0 2.0 −1.0 0 00 0 0 −1.0 2.0 −1.0 00 0 0 0 −1.0 2.0 −1.00 0 0 0 0 −1.0 2.8 ]      × 105 140  The mass matrix has been assembled using the mass model used for the double-sided walls. The same mass configuration has been used in all parts of this thesis. The stiffness matrix is also associated with the double-sided walls, calculated as the stiffness per unit-length, for a strip of Wall-1 between each two degrees of freedom.  The eigenvalues and eigenvectors are assembled, and the seven normalized mode shape vectors for Wall-1 are calculated, as presented in Figure 5-8; this is the same for all the double-sided walls. Please note that some small degree of flexibility (~ 20%) is assumed for the test frame on the table, and the flexibility has been incorporated as a coefficient within the stiffness matrix.  Figure 5-8: Normalized Mode Shapes for the Double Sided Walls  141  From the modal analysis, using MATLAB, the vector of the natural cyclic frequencies of vibration (fn) and the natural circular frequencies of vibration (ωn) for Wall-1 are:  𝑓𝑛 = [      9.618.827.134.340.043.946.0]       𝐻𝑧               𝑎𝑛𝑑             𝜔𝑛 = [      60.3118.0170.5215.6251.3276.0289.0]       𝑅𝑎𝑑/𝑠𝑒𝑐  The vector of the peak modal equivalent static forces are calculated and presented below for Wall-1, which would be similar to all the other double-sided walls. In this matrix, each column represents the static equivalent forces for one mode shape, Mode 1 to Mode 7, and each row represents one of the degrees of freedoms at each mode, from DOF 1 to DOF 7. A MATLAB code, listed in Appendix G  for reference, is generated and used to conduct the modal analysis.  𝑓 =[      741 −41 648 −143 385 −81 471356 −55 414 25 −369 126 −901740 −34 −384 139 −32 −118 1251827 10 −659 −50 400 58 −1501603 47 −36 −130 −350 27 1611106 53 636 73 −65 −100 −159427 25 442 117 412 130 143 ]       𝑘𝑁  The peak modal base shear (Vb) and the peak modal base overturning moment (Mb) are calculated for each mode and presented in Table 5-2. The values are presented in both units of kN and Kips, for convenience. 142  Table 5-2: Peak Modal Base Shear and Overturning Moment for all Modes of Wal1-1  Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Mode 7 Vb (kN) 8793 6 1060 31 381 43 78 Vb (kips) 1977 1 238 7 86 10 17 Mb (kN-m) 13645 211 1794 298 771 201 201 Mb (kip-ft) 10064 156 1323 220 568 148 149  The calculated peak modal shear forces and overturning moments of the previous table, which are calculated for all the modes of Wall-1, are combined using three different methods: the Absolute Sum (ABSSUM) method, the Square Root of Sum of Squares (SRSS) method, and the Complete Quadratic Combination (CQC) method. In addition to the base shear on the table (Vb), and the peak base overturning moment (Mb), the force combinations for the peak forces at the top of the blue frame (Vt) and the peak modal displacement for the top of the frame (ut) are all calculated during the modal analysis of Wall-1. Therefore, for reference, they are listed in Table 5-3, in both SI and imperial units for convenience.  Table 5-3: Modal Combination of Forces, Moments, and Displacements for Wall-1  ABSSUM SRSS CQC Peak Shear at Table Vb (kN) 10392 8866 8882 Vb (kips) 2336 1993 1997 Peak Frame Top Shear Vt (kN) 1689 771 900 Vt (kips) 380 173 202 Peak Base Overturning Moment Mb (kN-m) 17121 13792 13848 Mb (kip-ft) 12628 10173 10214 Peak Frame Top Displacement ut (cm) 3.16 2.54 2.55 ut (in) 1.24 1.00 1.01  143  The modal analysis of the 7DOF system of Wall-1, presented in this section, are done based on the techniques discussed by Chopra A. K. (2012). However, the MATLAB generated codes used to conduct the analyses are scripted by the author of the thesis. The full script library of the MATLAB codes and functions are presented in Appendix G  , for reference.  5.3 Possible Amplification Effects by the Test Setup Finally, considering the discussion on some possible flexibilities of the blue frame, which is part of the setup that holds the wall on the table during the shake table testing, it is helpful to look at some of the spectral content of the accelerations recorded directly on the blue frame, for reference. Even slight flexibilities from the frame can affect the mode shapes and natural frequencies of the system. Particularly, this becomes more important when the modal properties of the specimens are monitored and used for damage assessment. Figure 5-9 shows the pseudo spectral acceleration of the signal recorded on the blue frame during Run-7, when testing Wall-1.   Figure 5-9: Spectral Acceleration for the Blue Frame during Run-7 of Wall-1 144  Pseudo velocity of the same signal recorded at the same location on the blue frame by the accelerometer installed there is plotted in Figure 5-10.   Figure 5-10: Spectral Velocity for the Blue Frame during Run-7 of Wall-1  By only looking at the spectral content of the acceleration and velocity, presented in Figure 5-9 and Figure 5-10, it can be noted that signals contain significant amount of low period (high frequency) content. Considering the walls have natural frequencies in the same range, it should be noted that some of the mode shapes might have been coupled with the mode shapes of the blue frame, or might be of “closely-spaced-modes” with the natural frequencies of the wall. Therefore, judging the modal deflected shapes might become challenging in such case. For reference, the spectral content of blue frame’s displacement is shown in Figure 5-11. 145   Figure 5-11: Spectral Displacement for the Blue Frame during Run-7 of Wall-1  It is worth it to refer back to the spectral content of GM-1, shown in Figure 4-5, taken from the recorded signals on the shake table during the same run (Wall-1 | Run-7). In fact, the spectral contents discussed here, for the blue frame, are extracted from the same run purposely, so that it makes the basis for easier comparison between the peak spectral values. Looking at the shape of the acceleration, velocity, and displacement spectra it can be noted that same frequency content is recorded at the top of the frame, since there is no shift in any of the amplitudes. However, the peak spectral values for acceleration are amplified about 45% in average. The velocity spectral peaks, on the other hand, are de-amplified by about 15%, showing a damping component in the system, possibly induced by the wall damping itself. The spectral displacement peaks are consistent with the table spectral displacement, by only showing slight amplification of about 0.5% in average. Therefore, some minor flexibilities can be noticed from the testing frame. 146  5.4 Operational Modal Analysis using ARTeMIS Modal Pro After the simple vibration assessment and the modal analysis presented in the preceding sections, performed using MATLAB, estimations of the modal properties for a double-sided wall are discussed. In this section, operational modal analysis (OMA) is done by creating a simple model for the walls using a commercially available software, called ARTeMIS Modal Pro, which is one of the most advanced signal processing software programs for OPA, and is well recognized globally, in the field of structural vibrations. ARTeMIS Modal Pro is a software program from Structural Vibration Solutions A/S, Denmark. It is widely used for operational modal analysis using Frequency Domain Decomposition (FDD) and Singular Value Decomposition (SVD) techniques, as well as other frequency or time-history based methods. Figure 5-12 shows the wall model, a simple 7-DOF system, in ARTeMIS Modal Pro.    Figure 5-12: ARTeMIS Model Showing Wall-1 at Run-3 Vibrating at 1st and its 2nd Modes 147  For all the ARTeMIS analysis, the acceleration data is used from the seven accelerometers installed directly onto the wall, and the two channels recording accelerations at the shake table and the top of the blue frame have been turned off. For each run, the very first portion of the acceleration data are truncated, until the moment that strong motions start; this usually gives us ambient type vibration data for minimum of 30 seconds to a maximum of 100 seconds for each run. All the data channels are recorded at 200 Hz frequency, having a time step of 0.005 second. Figure 5-13 shows the spectral densities of all the data channels for Run-3 of Wall-1, with no filtering or decimation done, obtained by singular value decomposition (SVD) in ARTeMIS.   Figure 5-13: Singular Values of Spectral Densities of Wall-1 at Run-3 148  Figure 5-12 is Wall-1 with all the data channels of Run-3 analyzed, after modal estimation and modal validation, animated at its 1st and 2nd modes of vibration. As expected, there is always a component of frame flexibility, seen as a coupled mode, with wall’s 1st and 2nd mode shapes. For instance, Figure 5-14 shows the translational mode component, coupled with wall modes of vibration, coming from the difference in horizontal rigidity of the supports.   Figure 5-14: Coupled Modes with Frame Components for Wall-1 at Run-2 in ARTeMIS  This should not be of a surprise, since the horizontal rigidity at the top support and the bottom support are different due to multiple factors. Aside from blue frame’s possible flexibility, the wall is simply built on a base beam (laid and grouted on); the base beam is bolted on to the shake 149  table. The wall just sitting on the beam causes the frictional forces from walls’ self-weight to provide some translational rigidity, but not a laterally fixed connection. This condition is the same for any walls in reality as well, since the self-weight at the top and bottom of the wall would make a difference in supporting conditions, and accordingly, to the connection rigidity.  Data decimation is not recommended during the data processing, since the original data sampling rate of 200 Hz is not very high, and down sampling would result in loss of information within the signal. Also, most of the acceleration data are of a high quality, so no major filtering is usually needed. However, a low order of low-pass filter with cut-off frequencies not less than 60Hz can condition the data, if needed. As an example, Figure 5-15 shows the processed data for Run-6 of Wall-1, conditioned with a mild low-pass filter of order 3, plotted in 256Hz resolution window.   Figure 5-15: Singular Values of Spectral Densities of Filtered Data of Wall-1 at Run-6 150  The wall needs to be restrained more carefully at the top, since the wall should not be allowed to lose its grip and slide out of the blue frame during the aggressive motions, while maintaining the semi-pin connection criteria. Figure 5-16 shows the mode shapes for Wall-2 obtained by ARTeMIS using the vibration data from the first 70 seconds of Run-4.   Figure 5-16: Mode Shapes 1–6 for Wall-2 before Run-5 using ARTeMIS Modal Pro  In order for the wall to be able to rock freely, there is an approximately 50mm gap at the top of the wall. This is due to the fact that the URM wall increases in height when completing a rocking cycle. Therefore, this additional 50 mm reveal has to be accounted for when installing a retrofitted wall into the “blue frame” for testing. This gap likely reduces the connection rigidity at the top, which also contributes to the uneven deflected wall profiles and the modal shapes. 151  5.4.1 Damage Model by Monitoring Modal Parameters using ARTeMIS Modal Pro Since only the first three mode shapes could be clearly identified from the records for all the runs, using ARTeMIS, the first three mode shapes are monitored for Wall-1 and Wall-2, as representative specimens for the single-sided and double-sided walls, respectively.  By carefully identifying the mode shapes and monitoring the targeted natural frequencies in ARTeMIS for each mode shape, the graph in Figure 5-17 is assembled. It should be noted that there are 25 runs for Wall-1 and for each run the three natural frequencies, f1, f2, and f3, corresponding to each mode shape of the wall are all monitored.   Figure 5-17: Monitoring Natural Frequencies for all the Runs on Wall-1 152  The values plotted in Figure 5-17 are tabulated in Table 5-4 for reference and discussion purposes in the following sections.  Table 5-4: Wall-1 ARTeMIS Natural Frequencies and Modal Damping Ratios for all Runs   As very well expected, the double-sided wall, for which Figure 5-17 is assembled, does not drop stiffness until the very last runs. Breaking this wall was indeed a challenge during the testing 153  program. As documented from the three test days for this wall, until the last few runs, where high amplitude and synthetic motions are used, the wall stays completely undamaged. The best-fitted curves for the three frequencies are of polynomial curves of third order. In the curve fitting process, a clear linear trend with downward slope exists for all three modes, but the polynomial function of order 3 would fit the data almost perfectly.  Similar to Wall-1, the same graph and table are assembled for Wall-2, which is a representative specimen for the single-sided walls. Table 5-5 lists all the natural frequencies, as well as the modal damping ratios for the 1st and 2nd mode of all the runs for Wall-2.  Table 5-5: Wall-2 ARTeMIS Natural Frequencies and Modal Damping Ratios for all Runs   In addition, Figure 5-18 shows the plot of all the natural frequencies for the first three modes of vibrations for Wall-2 during all the runs for this wall, as listed in Table 5-5, with linear trendlines and fitted 3rd order polynomial curves for each mode. 154   Figure 5-18: Monitoring Natural Frequencies for all the Runs on Wall-2  5.4.2 Discussion on the Damage Assessment Results of Operational Modal Analysis Similar to the Wall-1 data, a 3rd order polynomial function is consistently a very good fit for the drop in the natural frequencies of Wall-2, for all the three modes. A very clear semi-linear trend, going downward, indicates successive strength degradations as the test program progresses.  One of the important conclusions, which can be drawn from the mentioned trends realized in all of the presented curves in Figure 5-17 and Figure 5-18 is that overall system flexibility has a significant role in the presented damage model. After the initial stiffness drop caused by the first run, the additional ductility of Wall-2, compared to Wall-1, is apparent from the calculated 155  natural frequencies. This ductility would certainly have an important role in the strength degradation regime of these walls during an earthquake. The initial stiffness drop in Wall-1 happens after Run-22, which confirms the visual crack observations listed in Table 4-6. However, for Wall-2, the initial stiffness drop happens after the first run and the wall keeps accumulating damage through the large displacement cycles. It should be noted that the initial large displacements would induce large rotations at the top and bottom boundary conditions of Wall-2, and therefore detaching the wall from its base, which creates a major initial stiffness drop as seen in Figure 5-18. However thereafter, the stiffness drop is happening at a milder slope, while the damping ratio keeps increasing, as seen in Table 5-5, due to the large deformations of the system, causing much higher imposed strains to the EDCC layer.  By looking only at the linear portion of Wall-1’s natural frequencies, from Run-1 to Run-21, still a low but constantly downward trendline could be easily fitted. A linear trendline with different slope can be fitted to the data for Run-22 to Run25. This shows a major stiffness drop, which is an indication that a major drift capacity threshold is passed.  The composite response of an EDCC retrofitted URM wall is a combination of two components: (i) the plain URM wall, referring back to Figure 4-21, and (ii) the EDCC pure dynamic material response, referring forward to Figure 6-9. Therefore, a sudden stiffness drop would indicate a damage in the composite system, which can be from the fracture in any of the composite components or the interfaces involved. For Wall-2 as well, this clearly shows the wall is passing the bend-over point of its load-deflection response. This perceived behaviour of Wall-2 is very consistent with the data presented in Figure 4-23, for the actual load-deflection of Wall-2. 156  Chapter 6: Effect of High Strain Rates on Constitutive Response of EDCC During the initial development phase of EDCC, the material is tested for its mechanical properties at slow rates of loading. However, many structures could be subjected to high strain rates of loading caused by earthquakes, impacts, or blasts. In fact, EDCC is targeted to be used for seismic retrofit applications for its ductility, great toughness, and high energy absorption capacity. Thus, studying the effects of high loading rates on EDCC and how to improve its performance under these circumstances has become an important topic (Cadoni, Meda, & Plizzari, 2009). This chapter elaborates on the experimental program where the effects of higher rates of loading on the tensile behaviour of EDCC are assessed, and then compared with the obtained static test data (Wang, Banthia, & Sun, 2013) and (Soleimani-Dashtaki, Soleimani, Wang, Banthia, & Ventura, 2017). This investigation discloses that the approximate static to dynamic ratio for the tensile strength of EDCC varies between 0.75 and 1.00 in magnitude, which indicates a dynamic increase factor (DIF) in the range of 1.00 to 1.33; and, the strain capacity ratio (static/dynamic) varies between 1.0 and 3.0 for this material. Results demonstrated that EDCCs are highly strain-rate sensitive materials and their performance during an earthquake should not be assessed from routine quasi-static tests.  6.1 Targeted Strain Rates Strain-rate ratios of the orders of 103 (dynamic to static) are investigated.  The rate of loading is chosen to coincide with strain-rates normally observed during earthquakes. The EDCCs tested are fiber reinforced concrete materials having a total fiber volume of 2%. Non-oiled Poly-Vinyl Alcohol (PVA) fibers and Poly-Ethylene Terephthalate (PET) fibers are used in the EDCC mixes in three different combinations: 2% PVA, 2% PET, a hybrid mix of 1% PVA + 1% PET fibers. 157  6.2 Experimental procedure In this study, four different sets of specimens are tested under high strain rate tensile loading (dynamic) and the results are then compared against the ones obtained by testing specimens with the same mix design going through quasi-static type tensile loading with very slow strain rates (quasi-static). For the quasi-static tests, a normal closed-loop test set-up is used. For the dynamic tests, a newly designed test setup using an air gun is utilized. Figure 6-1 shows the sample size.   Figure 6-1: Sample’s Dimensions (mm)  6.2.1 Preparing the specimens The specimens for both dynamic and static testing are taken from the same batch of concrete in order to minimize the effect of casting conditions on the properties of the samples, to reduce uncertainties. The ingredients, as listed in Table 3-1, are measured in small buckets and beakers using a scale with a precision of 0.1 grams. The dry ingredients including cement, fly ash, silica fume, and sand are mixed first and then a small portion of the solution of water and super plasticizer is added followed by the fibers, which are added very slowly, in order to achieve a 158  proper fiber dispersion. Finally, the remaining solution is added gradually. Figure 6-2 shows the equipment used (left photo) and the measured mixture of PVA and PET fibers (right photo).   Figure 6-2: Measuring & Mixing Equipment (left); Mixture of PVA + PET Fibers (right)  EDCC is poured and evenly distributed in the molds, which are pre-lubricated using light oil and consolidated using the vibrating table. The specimens are covered in plastic sheets for 24 hours in room temperature and then demolded and cured in moist room for 56 days before being tested. Figure 6-3 shows the casting process including molding, consolidation, labeling, respectively from left to right.   Figure 6-3: Casting, Consolidating, and Demolding EDCC Specimens (from left to right) 159  6.2.2 Dynamic Tensile Testing The tensile test is performed using a dynamic uniaxial tensile testing machine, which uses the air force in a pressurized chamber to apply sudden uniaxial tensile load on the specimen that is secured by a set of special grips. Displacement is measured using a high accuracy laser sensor mounted on the specimen, monitoring the proper gage length. Thus, the only variable to adjust on the machine is the air pressure. Figure 6-4 shows the dynamic tensile loading apparatus on the left photo, the grip mechanism at the top right picture, and the air pressure chamber along with its pressure control knobs for loading and unloading, at the bottom right corner.    Figure 6-4: Apparatus (left), grip mechanism (top right), and Air Chamber (bottom right) 160  Maintaining a constant high air pressure for all the specimens within a set ensures a consistent rate of loading for the specimens within that set of samples, which are expected to have similar strength values. Through various trial tests and looking at the numbers and accuracy of the recorded data, it is decided that setting the air pressure to about 100 psi gives a reasonable outcome for the targeted range of loading rates, stated in section 6.1 of this document.  The samples are held firmly in place by the two custom made grips during the loading. It has been also verified that the grips do not damage the specimens prior to loading, while they do minimize slippage of the specimens when loading is taking place.  As previously mentioned, each specimen is instrumented by a laser sensor at the time of loading for displacement measurements. The laser beam emitter is mounted at the upper neck, directly on the specimen, using a special bracket. In addition, a reflector plate is mounted at the bottom neck of the sample to reflect the laser rays. A digital data acquisition box precisely records the measured displacement at the gage length, based on the information from the laser sensor.  Figure 6-4 illustrates the test setup as well as the exact locations of the laser sensor and its reflector plate, in a typical test setup. The sampling rate is set such that the tensile load and the distance between the laser and its reflector plate are recorded every 0.003 sec, during the test.  In order to ensure that the displacement is measured within the 70mm targeted gage length, any specimen which fails by a localized crack outside of the specimen neck or even at the vicinity of the boundaries of the brackets is discarded. 161   Figure 6-5: Tested Specimens (right) and the Fiber Pull Out at the Crack Opening (left)  The samples usually failed as expected, at the middle of the neck, unless they are already defected or damaged at another location, caused during the demolding process or when mounting the specimens into the loading grips. Figure 6-5 shows some of the samples after the test and illustrates the orientation of the fibers being pulled out at the crack opening, in one specimen.  6.3 EDCC Dynamic Test Results This section presents the test results obtained from the dynamic testing of the EDCC specimens under uniaxial tension. In addition, the dynamic results are compared against the static results, from the previous tests. A full set of graphs are presented in the Appendix B  of this thesis, in a larger format for reference purposes.  Using the recorded data obtained from the dynamic tensile testing, the stress strain curves are drawn for all the tested samples. Figure 6-6 shows the graphs comparing the average load-time curves and the stress-strain curves are presented in Figure 6-7 for all of the four mix designs.  162  The average curves are developed after data decimation, normalization, and a light filtering of the noise coming from the high sampling rate and use of the laser system.  Moreover, the stress-strain and the load-time representative curves for each set of the samples, for the three mix designs (2% PVA, 2% PET, and 1% PVA + 1% PET), are all presented in Appendix B  , to show the typical graphs obtained from all the dynamic tests separately.   Figure 6-6: Average Curves for Load vs. Time  The coefficient of variations (CV) of loads corresponding to changes in displacement are also shown in Figure 6-8 for each set of the 12 specimens tested. These three graphs are also presented in the Appendix B  of this thesis, in a larger format for ease of comparison.  163   Figure 6-7: Average Curves for Stress vs. Stain   Figure 6-8: Coefficient of Variation (Load vs. Displacement) 164  6.3.1 Dynamic vs. Static Tensile Testing This section presents a series of comparative stress-strain curves in order to relate the dynamic response of the EDCC samples relative to their associated static behaviour. Figure 6-9 and Figure 6-10 show the average curves comparing the stress-strain responses obtained from both quasi-dynamic (referred to as “dynamic” hereafter) and quasi-static (referred to as “static” hereafter) uniaxial tensile tests for the two of the mix designs with single fibers, 2% PVA (called the “Premium EDCC” mix) and 2% PET, respectively.   Figure 6-9: Static vs. Dynamic Stress-Strain Response of Premium EDCC Mix  Figure 6-11 shows the same response for the hybridized fiber system of 1% PET + 1% PVA fibers (called the “Regular EDCC” mix). For these graphs, the specimens with an average outcome are chosen from each set of samples. The complete set is presented in Appendix B  . 165   Figure 6-10: Static vs. Dynamic Stress-Strain Response of EDCC Mix with 2% PET   Figure 6-11:  Static vs. Dynamic Stress-Strain Response of Regular EDCC Mix  Based on the recorded data obtained from both dynamic and static tensile tests, for each set of 12 specimens, six of the average samples are picked for further analysis (based on the results). The 166  data is then used to calculate parameters to make easier comparison between the different mix designs and the two series of the tests, quasi-dynamic and quasi-static. Table 6-1 provides an extensive summary of the aforementioned calculated values.  Table 6-1: Summary of the Calculated Parameters  The maximum stress and strain values are calculated for each set, along with the associated averaged values obtained from the selected samples. In addition, the average stress and strain rates are calculated for specimens from each mix design separately. In the static tests, the strain rate is kept constant during all of the tests at 0.2% per minute (0.0033% per second). However, the rate of loading is varied amongst the specimens for the dynamic loading. Thus, specimens loaded with similar rates of loading are picked and averaged for discussion purposes.  Mix Design Stress (MPa) Strain Avg. Stress Rate (MPa/sec) Avg. Strain Rate (/s) Max Avg. Max Max Avg. Max Up to Peak Plateau Dynamic Plain (No Fiber) 3.75 - 0.02% - 273.93 - 0.9374% 2% PVA 7.45 6.78 4.84% 2.91% 419.61 25.80 6.1177% 2% PET 1.61 1.50 1.73% 1.21% 81.300 24.37 5.1627% 1% PVA+1% PET 5.45 4.62 1.28% 0.94% 249.36 26.61 6.0954% Static Plain (No Fiber) 3.13 - 0.04% - 1.2781 - 0.0033% 2% PVA 5.68 5.19 4.97% 3.24% 0.87488 0.1633 0.0033% 2% PET 1.63 1.61 2.76% 2.41% 0.32573 0.1711 0.0033% 1% PVA+1% PET 4.06 3.88 3.49% 2.45% 0.75463 0.1943 0.0033% Ratio (Dynamic/Static or DIF*)  *DIF = Dynamic Increase Factor Plain (No Fiber) 1.20 - 0.53 - 214.13 - 280.90 2% PVA 1.31 1.31 0.97 0.90 480.77 157.98 1834.86 2% PET 0.99 0.93 0.63 0.50 249.38 142.45 1547.99 1% PVA+1% PET 1.34 1.19 0.37 0.39 330.03 136.99 1828.15 167  The values of the average strain rates for the dynamic tests and the average stress rates during the strain-hardening phase for both of the tests (dynamic and static) are similar for all of the EDCC mix designs. However, among all of the three tested mix designs, the samples with 2% PVA content show higher stress and strain capacities in general. The design containing the mixture of the two fibers gives a good outcome in terms of strength while showing relatively lower strain capacities compared to the samples with only 2% PVA fibers, as expected.  The mix design containing 2% PET also result in an acceptable strain capacity, but shows a very small tensile strength, compared to other specimen types. The low tensile strength, which sometimes can even be less than the samples with no fiber reinforcement, for both static and dynamic tests, can be an indication of a poor fiber dispersion in this set of samples. Some of the results, only from the 2% PET specimens, had to be discarded because of the possibility of poor fiber dispersion.  The last section of Table 6-1 provides the ratios between the values obtained from the static tests to those from the dynamic test results. The average dynamic strain rates fall within the range of 10-4 for the EDCC samples. This is consistent with the expected range for strain rates listed in Table 6-3, for the scope of earthquake loading (Zhou, Yang, Ci, & Chen, 2016). However, in terms of tensile strength, the ratio is within the range of 0.74 to 1.0, as calculated. The strain capacity varies from 1.0% to 3.5%, depending on the fiber mixes. Therefore, from the calculated ratios in Table 6-1, it can be concluded that the maximum tensile strength achieved is consistently higher during dynamic loading for all the mix designs, with the exception of the specimens with the 2% PET fibers, for which dynamic strength is slightly lower. 168  On the other hand, the strain capacity highly depends on the mix design. In all of the samples, this capacity is generally higher for the static loading, as predicted. However, for the samples with 2% PVA fibers only (the Premium EDCC mix), ultimate strain capacities slightly higher are observed from the dynamic loading, compared to static. That is while the samples containing only 2% PET fibers show a greater difference, in terms of strain capacity, between the two tests.  6.3.2 Discussion on the Dynamic Test Results For the purpose of this study, EDCC mixes containing high fly ash contents are chosen. This material, which shows some strain-hardening type behaviour, has a relatively high strain capacity under tensile loading, achieved through the well-known multiple cracking phenomenon. After various trial tests, the fiber volume fraction of 2% is chosen as the optimum fiber content for most of the EDCC mixes, since mixes with smaller or larger amounts of fiber failed to show enhanced outcomes (Wang, Banthia, & Sun, 2013) and (Soleimani-Dashtaki, et al., 2017).  As shown in Table 3-1, the exact same mix proportioning is utilized with three different combinations of fibers: 2% PVA (called the “Premium EDCC” mix in this thesis), 2% PET, and 1% PVA + 1% PET (called the “Regular EDCC” mix in this thesis). In addition, a control mix, containing no fiber reinforcement, is casted from the same mix design to be tested for developing the baselines for the experiment. The samples are then tested at different loading rates and the results are compared against each other to see the effects of fiber type and the rate of loading on the overall stress and strain capacities as well as the general composite strain-stress response.  169  For the cases of larger volume fractions, the observed poor performance is mainly caused due to the low workability of the concrete mix. In fact, by increasing the fiber content, the workability and fluidity of the mix generally decreases. This can result in poor distribution of fibers, and as a consequence, fiber dispersion related problems start to show up, causing the development of weak planes within the mortar body as well as negatively affecting the Interfacial Transition Zones (ITZ) within the cementitious matrix (Bentur & Mindess, 2007).   On the other hand, using lower fiber contents would also result in a weaker performance for the EDCC. There would be insufficient volume of fibers to support the load that is carried by the matrix as it cracks. Thus, multiple cracking does not occur as much and a tension-softening behaviour would replace the strain-hardening type performance consequently (Wang, Banthia, & Sun, 2013) and (Soleimani-Dashtaki, Soleimani, Wang, Banthia, & Ventura, 2017).  It is observed that when the strain rate goes from static to dynamic, the strain capacity of EDCC is more sensitive to the type of the fiber used compared to the corresponding tensile strength, which is more independent of the fiber type and content.   The outcome of this study showed that when PET fiber is used in the mix design, close attention should be given to the fiber dispersion. For small sample sizes similar to the one used for the purpose of this experiment, it is very difficult to control the uniform distribution of the PET fibers within the mix. That results in a poor fiber dispersion, and consequently, a drop in the strength of the EDCC. Moreover, the study shows that PVA fiber is a better choice of fiber when it comes to the dynamic type of loading, as it shows a better overall performance. 170  6.4 Actual Dynamic Loading Rates for EDCC from Shake Table Testing This section examines the actual loading rates and the stress strain demand the EDCC retrofit layer experiences during the shake table testing. Figure 6-12 shows the acceleration and displacement time histories for Wall-2 at Run-3, illustrating the multiple distinct peaks, which can easily be isolated for further calculations. The presented time histories are the wall’s actual unfiltered absolute accelerations and displacements, as directly measured at the mid-height of the wall by the sensors labeled as “ACCEL. 4” and “DISPL. 4” in Figure 4-8, respectively.   Figure 6-12: Acceleration and Displacement Peaks in Time-History of Wall-2 at Run-3  6.4.1 Isolating the Impact Cycles from the Data During the shake table testing program, some particular walls go through much higher loading rates and impact cycles than others. This depends on a few factors, including motion amplification, which is discussed in full in the previous chapter. Based on the observations and 171  screening the recorded signals, representative walls are selected, which seem to experience the highest loading rates on the shake table, based on the peak values. As shown in Figure 6-12, some of the peaks can be easily isolated and looked at closely. As an example, the six strongest load peaks that Wall-2 experiences are happening during Run-4 and Run-5, and are isolated and plotted together in Figure 6-13, with their time of occurrence labeled. Force is wall’s total shear force, as calculated in section 4.4.1, and displacement is wall’s actual mid-height deflection.   Figure 6-13: The Largest Six Impact-Like Load-Deflection Cycles for Wall-2  The six peaks are selected from Run-4 and Run-5 only based on the magnitude of the load, so they are the highest six impact forces on Wall-2 during the entire last two runs of the wall, before collapse. In Figure 6-14, the isolated force peaks (from the force time-history plots) are then 172  shifted on a time-normalized scale to coincide the force maxima at the same location on the x-axis, the arbitrary “1-Sec” point, for the ease of comparison. The impact cycles are labeled from Impact-1 to Impact-6, in order of occurrence. For instance, Impact-1 to Impact-4 have happened during Run-4 and Impact-5 and Impact-6 are taken from Run-5. It should be noted that there might be many other peaks between any of the two selected impacts, but at lower magnitudes.   The same discussed six strongest impact-like load peaks that Wall-2 experiences during Run-4 and Run-5 are isolated, time-shifted, and superimposed in Figure 6-14, in order of occurrence (Impact-1 to Impact-6). Note: the actual shapes of the load peaks are maintained (i.e. no scaling).   Figure 6-14: Force-Time Curves for the Six Highest Impact Loads for Wall-2 173  As discussed, it should be noted that the peaks are selected based on the six largest forces (or loads) imposed on the wall, within all the runs combined. The corresponding deflections for each of the selected impact-like load peaks are calculated (mid-height displacement minus the table/base displacement), as all explained in section 4.4.1. Figure 6-15 shows the deflections that Wall-2 takes at mid-height during each of the selected load peaks. It should be noted that the displacement curves are plotted on the same time scale as Figure 6-14. This means that not only the force peaks are not happening at the same time as the displacement peaks, but also deflection curves do not attain their maximums magnitudes when the force is at its maximum peak value. This lag between force and displacement is expected from tests with high dynamic rates.   Figure 6-15: Deflection-Time Curves Corresponding to the Selected Load Peaks for Wall-2 174  The curves presented in Figure 6-15 can be mathematically differentiated to obtain displacement rates or velocity. For discussion purposes, the displacement rates are calculated and plotted against time in Figure 6-16. The displacement rate curves are plotted on the same time scale as both Figure 6-14 and Figure 6-15, meaning that the displacement rate peaks are also not happening when force is at its peak value, but unlike deflections, displacement rate attains a maximum peak value during each of the impact cycles, as expected.   Figure 6-16: Displacement Rates for Wall-2 at six Major Peaks (Run-4 and Run-5)  In order to investigate load rates, curves in Figure 6-14 are mathematically differentiated to obtain the associated loading rates for the same six impact-like load peaks on Wall-2. It is expected that when load reaches its maximum peak value, a zero loading rate is observed.  175  The obtained loading rates are plotted against time in Figure 6-17, maintaining the same time scale used in Figure 6-14 and all the presented and discussed displacement plots.   Figure 6-17: Load Rates for Wall-2 at six Major Peaks (Run-4 and Run-5)  Looking at the loading rates presented in the curves, the wall reaches maximum load rates of about 1500 kN/Sec at some of the peaks. The forces used to calculate the loading rates for this graph are calculated based on the methodology explained in section 4.4.1 of this thesis. The forces, which create the indicated loading rates, are total shear forces acting along the height of the wall, presented in form of base shear. Converting this to overturning moment, as explained in section 4.4.2, and by using simple mechanics and geometric formulations, the loading rate on the EDCC layer can be estimated. For instance, the maximum rate of 1500 KN/Sec for the wall 176  would impose an average stress rate of about 50 MPa/Sec to the EDCC layer, for the case of Wall-2. This number can be compared to the loading rates summarized Table 6-1. The same table indicates that Premium Mix EDCC, which is also used in Wall-2, has been tested with the rates as high as 420 MPa/Sec for the pre-peak portion and 26 MPa/Sec for the post-peak Plateau section of the response.   Figure 6-18 shows the relationship between the changes in the loading rate with respect to the change in displacement rate, as a function of time, at the same impact cycles. The presented curves have the unit of kN/mm (stiffness unit), and are obtained by dividing the loading rate by the displacement rate, representing “instant stiffness” or the load-deflection variations as a function of time, at each impact cycle. The curves maintain the same time scale as before.   Figure 6-18: Load-Deflection Rate Variation Curves for the Six Load Peaks of Wall-2 177  6.4.2 Peak Strain Readings – Rates and Values from Shake Table Testing As described in section 4.2.1 and shown in Figure 4-8, the double-sided walls are instrumented with eight strain gages, four on the front and four on the back. Figure 6-19 shows one of the strain gages used for strain measurements on the specimens along with its specification sheet.   Figure 6-19: Strain Gages for Strain Sensing of EDCC on the Full-Scale Specimens  The strain gages, which can measure strains of up to 8%, are installed on the locations marked in Figure 4-8, based on the instructions provided by the strain gage manufacturer. The surface preparation was done by carefully grinding the surface down to a very smooth finish, in multiple steps. The ground surface was subsequently polished and cleaned, before gluing-on the gages using the ultra-ductile epoxy (12% strain capacity) provided by the gage manufacturer. 178  Figure 6-20 shows the time-history of average strain values from the front and back of Wall-11 during Run-22.   Figure 6-20: Average EDCC Strain Readings at Mid-Height of Wall-1 at Run-22  The average strains are calculated by linearly averaging Strain Gage No. 2 and 3 (front side) with Strain Gage No. 6 and 7 (rear side), as per labeling system provide in Figure 4-8. The trendlines indicate that the two records are drifting apart slowly, starting right after the strong motion part of the record. This indicates that EDCC layer is progressing into its elastoplastic range, after passing its bend over point; this is an irreversible strain. This progressive damage was also explained and discussed in section 4.3.3 and section 4.3.5, through a discussed damage model. In order to understand what magnitude of ultimate strain the EDCC layer is experiencing and what are the actual strain rates that EDCC layer sees at different ground motion runs, it is helpful 179  to look at some of the peak values Wall-1 goes through in Table 6-2. The table provides tensile and compressive peak strains (green rows) as well as strain rates (blue rows) at the eight different locations on Wall-1, from SG-1 to SG-8 (left side of the table), as well as the ultimate peak values for each run (the last two columns, on the right side of the table). The ultimate peak values are essentially the absolute largest (tension) or smallest (compression) value of each row.  Table 6-2: Table of Peak Strain Values for Wall-1 during Run-7 and Run-22 to 25  180  It should be notes that based on the damage assessments discussed in section 4.4 and 5.4, Wall-1 is assumed to be fully elastic up to the end of Run-21 and start getting non-linear from Run-22 onward. The strain values reported in the green rows of Table 6-2 are the measured values on the EDCC layer in tension and compression for each run. As an example, Figure 6-21 presents a mildly filtered two-second long strain-time trace for the strain gage labeled SG_6 from the 22nd to the 24th seconds of the last run (Run-25) of Wall-1. This wall develops a major localized crack at the 26th second of this run, goes through cycles of rocking, and collapses at the 31st second of this run. At the cracking moment, some strain gages are reporting unstable strain readings of up to 35,000 µƐ, which are considered unreal smeared (gage-length dependent) strain values. The signal is cut-off and degraded after the 25th second, when reporting peak values in Table 6-2.   Figure 6-21: Strain Trace for SG_6 from 22nd to 24th Second of Run-25 for Wall-1 181  The strain rates, presented in the blue color rows of Table 6-2 are obtained by calculating the slope of the filtered signal over the time steps of 0.005 sec in positive and negative parts of the signal, and reporting the maximum values for the tensile strains and minimum values for the compressive strains. As an example, Figure 6-22 illustrates a few cycles of up and down for the mentioned time steps of 0.005 sec. This is a 0.2-second long trace, which is a cutout from the signal shown in Figure 6-21, shows the highest recorded peak of 11.34 µƐ for Wall-1 at Run-25, as reported in Table 6-2.   Figure 6-22: A Short 0.2 Second Long Strain Trace with Trends for Wall-1 at Run-25  On two different attempts, and for discussion purposes, the strain rate for the smeared (gage-length dependent) strain values, like the one shown in Figure 6-22, can be calculated with two different approaches. The first three peaks in Figure 6-22 can be connected and an unloading strain rate can be calculated from the slope of the line, as shown by a red arrow in Figure 6-22, 182  Also, the linear trend of the signal can be calculated for shorter portions of the strain trace, representing an average smeared strain rate. For example, the maximum strain rate value for the peak shown in Figure 6-22 is reported as 158% per second in Table 6-2 (from direct calculation), which is much higher than expected for strain rates associated to earthquake generated loading rates (Zhou, Yang, Ci, & Chen, 2016); this is discussed over the next section. As an example, the directly calculated strain rates from Figure 6-21 are graphically presented in Figure 6-23. The highest strain rates reported by Table 6-2 for Run-25 are also covered in this figure.   Figure 6-23: Calculated Strain Rates for 2-Sec Trace of SG_6 Strains on Wall-1 at Run-25  As mentioned, the highest peak calculated in Figure 6-23 reports an extremely high rate of strain (1580 mƐ/sec), which does not have any physical meaning from the materials perspective. The strain rate associated to the same peak, calculated from the “average-peaks method” discussed before would be 800 mƐ/sec and is about 450 mƐ/sec from the discussed slope of the trendline taken over 20 time steps (0.1-second long trace). These values are discussed in the next section. 183  6.4.3 Discussion on Actual Strain Rates for EDCC from Shake Table Testing By looking at the peak values of Table 6-2, the peak values of Run-7 (Tohoku @ 100%) are provided for reference. With reference to all the damage assessments done on Wall-1 in previous chapters, the wall is considered undamaged at Run-7, and it should still be in its linear range of consecutive response. The peak values recorded for EDCC as 30 µƐ in tension and 40 µƐ in compression confirm that EDCC should still be in its elastic range, assuming a cracking strain of about 120 µƐ for the mortar matrix for EDCC.  Referring back to Table 4-6, the wall shows no sign of visible damage until after Run-22, and this is when the strain trends are drifting apart, as shown in Figure 6-20. Now, looking again at the peak values in Table 6-2, the peak values for the last four runs of Wall-1before collapse indicate that wall starts getting nonlinear after Run-22, and experiencing higher ultimate strains of 11,340 µƐ both in tension and compression before collapse. It must be mentioned that the strain gages show extremely high values just before the gage ruptures. Therefore, the records have been carefully cut off, after the 25th second point of Run-25, to avoid reporting unreal strain values in Table 6-2 for ultimate strains. Wall-1 developed major cracks at the 26th second of Run-25 and collapsed at the 31st second of the same run.  It should be discussed that strain rates presented in Table 6-2 for Run-7, which is during the linear elastic deformations of Wall-1 are confirmed to be valid. However, as proceeding to the non-linear portions of wall’s (and EDCC’s) behaviour, the strain rates are not completely associated with the actual strains that EDCC is going through. In fact, both the strain and the strain-rate values are based on “smeared” tensile or compressive stress-strain curves for EDCC. 184  The smeared values are gage-length dependent, and cannot be taken as the actual strains imposed to the material. In particular, these values should be reported as smeared strains and smeared strain rates. The reason is the existence of multiple cracks under the strain gage across its gage length, which causes relief of stresses at the micro-crack opening locations. Thus, the reported strains are indeed based on the 3” (7.62 cm) gage length, which the measurement are read as average smeared strain values. Figure 6-24 shows the schematic representation of the situation were reported strain values should be considered “smeared” strains.   Figure 6-24: Schematic Representation of Smeared Strain Readings over the Gage Length  Looking at the peak strain values up to Run-24, reported in Table 6-2, tensile strain rates of up to about 600,000 µƐ/sec in are indicated, which compared to the measured tensile static strain rate of 33 µƐ/sec in Table 6-1 is about 18,200 larger in magnitude. This rate is approximately within the expected range of the strain rates (10-4/s ~ 10-1/s) expected for ordinary concrete within the scope of the earthquake (Zhou, Yang, Ci, & Chen, 2016).  In particular, the domain of strain rates reported by Zhou et al. (2016) for ordinary concrete material under different loading cases are shown in Table 6-3. Looking at the highest calculated strain rates for Wall-1 during Run-25, 1.6 Ɛ/sec (tensile) and -1.7 Ɛ/sec (compressive), as 76.2 mm or 3” 185  presented in Table 6-2, it can be noticed that they fall within the “impact range” based on the review paper results shown in Table 6-3 (Zhou, Yang, Ci, & Chen, 2016).  Table 6-3: Domain of Strain Rates for Concrete Material under Different Loading Cases Creepage (1/sec) Static (1/sec) Earthquake (1/sec) Impact (1/sec) Explosion (1/sec) < 10−6 10−6 ~ 10−5 10−4 ~ 10−1 100 ~ 101 > 102  On the other hand, one can discuss that the peak strain rates of 1,576,000 µƐ/sec reported in Table 6-2 for Run-25 should not be taken as real, even though they are believed to be smeared values. In fact, Wall-1 is going through fast happening localized micro-cracks and deformations before the failure, so points of sudden peaks of strain rate raises and drops are noticed within the data, as shown in Figure 6-23, since the strain values are rapidly changing. Therefore, calculated such a high strain rate can be argued to be mathematically possible, but having no physical representation or real meaning.  Based on Table 6-1, dynamic strain rates of up to 6% /sec are tested for Premium Mix EDCC and ultimate strain capacity of 4.8% is reported for this material in pure tension dynamic tests. However, during the shake table testing of Wall-1, which is retrofitted with the same material, strain rates of up to 70 % /sec are repeatedly reported for EDCC during Run-24 and Run-25 and ultimate strain of about 0.49% to 1.13% is reported from the strain gages. Therefore, it can be concluded that EDCC experiences much higher strain rates but lower ultimate strain capacities during the shake testing program, compared to the dynamic loading of the pure material. 186  However, it must be noted that Wall-1 in Run-22 to Run-25 is being tested with extreme waveform and very aggressive motions, VERTEQ II waveform, which is from a standard used for testing not structural components; therefore, it has much higher peak accelerations compared to any natural earthquake. Indeed, this waveform contains higher peak accelerations than the design spectral values provided by the Appendix C of the NBCC 2015 document (NRC, 2015).   In fact, the extreme strain rates and values are reported from the last run of Wall-1 before collapse (Run-25). At this specific run, the base accelerations at the shake table reach to 3.0 g and accelerations recorded at the mid height of the wall during the last shakings are ranging from + 5.2 g to - 6.1 g, before the failure. These are very high PGA values and not true representative of natural earthquakes or hazard spectra values.  As discussed before, it is worth mentioning that significant compressive strains are noticed from the EDCC layer, when it is acting as the compression cord for the wall. This attribute makes single-sided EDCC retrofit solution a much more successful retrofit strategy, compared to single-sided applied FRP wraps previously tested at the EERF for URM walls, based on the unpublished data discussed at the end of section 4.3.5 (SRG III, 2017). 187  Chapter 7: Conclusions, Recommendations, and Future Work This chapter starts with a brief restatement of the problem plus the goals and objectives of the research work done. It also provides a brief summary of the experimental work performed and their associated results, contributions, and the overall significance of the work with respect to the problem statement and objectives outlined in section 1.1.1 and section 1.1.2, respectively. Conclusions are followed by recommendations for the future work needed for further investigations and development of the technology.   This chapter proudly highlights the successful transfer of the developed technology to the outside world, as it is now officially part of the seismic retrofit guidelines for the province of British Columbia (SRG III). Further, through a demonstration project in November 2017, the technology has already seen its first real-life application at a Vancouver public elementary school.   7.1 Scope of the Research Work and Related Contributions As also outlines at the introductory chapter, masonry blocks, due to their good sound and thermal insulation properties, are considered one of the most common types of wall systems, either as in-fill or stand-alone, widely used in partitioning of many of the commercial and residential buildings worldwide. These walls, in their unreinforced form, formally known as URM, are found in many of the mid-age, low-rise to mid-rise, school and hospital buildings in North America and across the globe.  URM partition walls are known to have very low displacement or drift capacities in seismic events, and the failure mechanisms are classified to be mostly brittle and catastrophic during an 188  earthquake shaking. Compared to any other partitioning systems, URM walls generally perform poorly during an earthquake, leaving behind many casualties, injuries, and fatalities.  Non-load bearing and non-grouted URM walls are very prone to failure when it comes to severe ground motions. As discussed in the first two chapters of this thesis, fully securing this type of walls during seismic upgrade work is currently very difficult, considering the high cost and complications with the currently available techniques. Therefore, in most cases, removal of such walls is the most often chosen solution at the moment, replacing them with a different partitioning system, such as metal studs and gypsum panels. This can be very difficult, costly, and significantly increases the construction time. Although this can sometimes be due to a change in space use, the main driving factor for such a decision by the building owner can be the negligible cost difference between the price of keeping and strengthening a URM partition wall, versus its replacement cost.  The research has developed a cost effective novel methodology for seismic strengthening of existing infrastructures using Sprayable Ecofriendly Ductile Cementitious Composite (EDCC), which is a form of fiber reinforced engineered cementitious-based composite material. In particular, this retrofit strategy primarily targets strengthening of URM partition walls, in order to provide restraint for the wall to prevent out-of-plane collapse in an earthquake ground motion.  7.1.1 The Overall Contributions of the Thesis This section provides the overall contributions of the thesis to the field, both scientific and industrial contributions, in a bullet-point format with reference to the appropriate thesis chapters. 189   The conducted work on Ecofriendly Ductile Cementitious Composite (EDCC), through material optimization, sprayability, hybridization, and strain-rate effect investigations, as discussed in Chapter 3: and Chapter 6: of this thesis.   Development of the retrofit methodology, the presented technology for strengthening of URM partition walls for prevention of out-of-plane failure and collapse, by providing out-of-plane restraint, as discussed in Chapter 4: and shown in Appendix A  .   Development of a simple vibration based assessment methodology, using the existing techniques, for specimen evaluation before, during, and after a shake table test, as discussed in Chapter 5:.   Technology deployment by getting the technology peer reviewed and approved by a committee of local structural engineers and the technical review board of the third edition of the Seismic Retrofit guidelines (SRG III), developed at UBC as part the province’s seismic upgrade program for British Columbia (BC) schools. The retrofit technology is now officially included in SRG III document (Vol. 6 and 7), as shown in Appendix A  .   Technology demonstration through a demo project by deploying the technology in November 2017 at a Vancouver public elementary school, owned by Vancouver School Board. The design and deployment of the retrofit was done based on the specifications provided by SRG III, with reference to section A.1 of Appendix A  . The highlights of the deployment process are in Appendix F  . 190  7.2 Significance of the Experimental Work and Notable Results Dynamic testing of full-scale specimens is one of the most effective experiments, which can be performed in order to fully understand the out-of-plane behaviour of brittle systems, like URM walls. The experimental results from the shake table testing revealed that EDCC retrofit technology is a very effective technique for seismic strengthening of such walls.   Shake table tests indicated that even a single-sided retrofit with appropriate EDCC can significantly enhance the overall ductility of the system and would change the fundamental behaviour of the wall from a typical “Rocking Mechanism” to a “Beam” type behaviour, with significant base rotations at the supports. The added flexibility to the system resulted in a substantial increase in energy dissipation, and thereby increasing the overall drift capacity before collapsing, causing the wall to withstand extensive levels of shaking under different types and intensities of earthquake generated ground motions.  The overall results of the experimental program also confirm that a single-sided EDCC retrofit of 20mm thickness would be sufficient for most of the low-rise school buildings across the province of British Columbia. The numerical estimations, based on the experimental results, can also approximate that even a 10mm thickness of the Premium Mix EDCC would be enough to keep the wall intact for a major earthquake in areas far away from the coast of BC, where the major North American coastline faults are located.   The thesis also concludes that a double-sided EDCC retrofit is also a great option for special cases where the ultimate drift needs to be limited for serviceability issues. Examples of such 191  cases include hospital buildings, where walls generally contain several mounted accessories, or libraries where heavy bookshelves need to be attached to the wall. Therefore, the wall movements need to be limited for safety and serviceability concerns. A double-sided retrofit can be applied in either 10mm or 20mm thickness and the Regular Mix EDCC would be enough, since there will not be any extensive strain demand on the EDCC layer during the course of the earthquake, as the overall wall deformations are now much limited in such case.   The Premium EDCC Mix, having a higher toughness, is ideal for single-sided applications, in which the wall is undergoing a number of large deformation cycles during the ground motion and, hence, the EDCC layer is required to take much larger tensile strains in order to dissipate the feed energy coming from the many repetitive large load-deformation cycles.  7.3 Technology Transfer through Demonstration Project Translation of this research to real-world applications has been a major goal from the beginning. In order to ensure the transfer of technology, it was decided to use the Eco-friendly Ductile Cementitious Composite (EDCC) for a seismic upgrade to a URM wall at a public school in British Columbia. This demonstrates the practicality of the technology as well as ensuring that the material and the structural design procedures are in place.  7.3.1 Inclusion of EDCC as a URM Retrofit Option in SRG III Currently, the BC Seismic Retrofit Guideline (SRG III), along with its web-based platform, is an approved toolbox commonly used in BC, developed for design engineers, to assess the current condition of school buildings, based on the local seismicity and seismic hazard, and to design 192  effective retrofit solutions for the schools across the province. As of July 2017, EDCC is an officially recognized retrofit option by the third edition of the BC Seismic Retrofit Guidelines (SRG III), for out-of-plane retrofit of URM walls. This retrofit technique, which is referred to as “URM # 11” in Volume 7 of SRG III, allows design engineers to use sprayed or troweled EDCC as a retrofit option for securing URM walls for out-of-plane failure, by providing out-of-plane restrain. The detailed designs and specification drawings for the EDCC retrofit option (URM#11) are provided in SRG III, as a convenient tool for structural engineers working on the current seismic upgrades in BC. Please refer to Appendix A  for the full information and design specs for EDCC (URM#11) option, as presented in Volume 7 of SRG III.  7.3.2 Retrofit of a URM Wall at Annie B. Jamieson Elementary School In order to demonstrate the implementation of the technology in a real-life application, as part of the research plan, Dr. Annie Jamieson Elementary School is selected, with the help from the structural engineers working on the project. This school is owned by the Vancouver School Board and it operates under the legislations of BC Ministry of Education. The school has been going through a seismic upgrade, for which Bush, Bohlman & Partners LLP is the structural design firm in charge and Heatherbrae Builders Co. LTD is the general contractor. The retrofit of the URM wall was completed on Nov 7, 2017, based on the retrofit details provided in SRG III for the EDCC retrofit option (URM#11); this document is provided in Appendix A  of this thesis, for reference. The actual retrofit work is done by Salman Soleimani-Dashtaki, the author of this thesis, and a sub-contractor was hired by UBC to provide help with material and equipment transportation, as well as providing labour work during the course of EDCC retrofitting of the URM wall at Jamieson School. The project highlights are in Appendix F  . 193  7.4 Recommendations for Future Investigations This section provides recommendations toward future research work, with reference to the conducted investigations by this thesis. For some of the recommended topics, this thesis provides experimental setup designs, specimen specifications, and possible testing guidelines.  7.4.1 Static Monotonic and Cyclic Testing of EDCC Retrofitted Wall Panels Along with the six full-scale wall specimens, which are built and strengthened with EDCC layers for the shake table testing of this thesis, there are another 20 half-scale wall panels (1.2m × 1.2m) built and retrofitted with EDCC layers. The inventory of these specimens are listed in Table 7-1.  Table 7-1: Inventory of the Half-Scale EDCC Strengthened Wall Panels URM Wall Building Units Retrofit Layer EDCC Application Method & Finish Single Sided Double Sided Concrete Masonry Units (CMUs)  10 Wallets 2 Controls 8 Retrofitted Premium Mix EDCC (20 mm) Hand-Applied ● ● Regular Mix EDCC (20 mm) Hand-Applied ● ● Regular Mix EDCC (20 mm) Sprayed – Rough Finish ● ● Regular Mix EDCC (20 mm) Sprayed – Smooth Finish ● ● Clay Bricks  10 Wallets 2 Controls 8 Retrofitted Premium Mix EDCC (20 mm) Hand-Applied ● ● Regular Mix EDCC (20 mm) Hand-Applied ● ● Regular Mix EDCC (20 mm) Sprayed – Rough Finish ● ● Regular Mix EDCC (20 mm) Sprayed – Smooth Finish ● ●  194  As listed in Table 7-1, there are 10 walls for each masonry type and all the panels are retrofitted with 20 mm thick layer(s) of different EDCC material. For each case, there are both single-sided and double-sided wallet specimen. The specifications for the clay bricks and CMUs are provided in Appendix C  of this thesis.  There are two different test setups designed, fabricated, and already assembled at the structural engineering research lab at UBC, to perform both monotonic and cyclic out-of-plane testing on these fabricated wall panels. It should be noted that the specimens are all cured and ready to be tested. There are quality control (QC) tensile and flexural specimens already existing to be tested in parallel with these walls. In addition, it must be mentioned that all the double-sided walls with smooth finish have already eight strain gages installed on them. The entire test setup, including the instrumentation (string pods and strain gages) plus the data acquisition system is in place, installed, and calibrated for the tests. All the drawings, instrumentation details, boundary condition specifications, and other relevant documents are provided in Appendix D  .  7.4.2 Effect of Bi-Directional Motions on Full-Scale EDCC Retrofitted Walls As mentioned in section 4.1, one of the specimens, Wall-5, is saved for further testing and investigations. This full-scale wall, which is a double-sided specimen, retrofitted with Regular Mix EDCC, is not damaged at all, based on the post shake table testing inspection. It is recommended that this specimen be used on the Multi-Linear Shake Table (MAST) to be tested with a few bi-directional motions (both out-of-plane and vertical or z-axis components). In particular, it is encouraged that GM-3 of Table 4-3 and Table 4-4 be used, with its associated 195  existing vertical component record. Alternatively, this specimen can also be used for in-plane behaviour investigations, as explained over the next section.  7.4.3 Investigation on In-Plane Capacity of Full-Scale EDCC Retrofitted Walls Even though the primarily focus of this research has been enhancing the out-of-plane performance of these walls, the in-plane strengthening, is an unavoidable but appreciated outcome and should be investigated enough to provide appropriate design guidelines for the engineers and industry players using the technique. This has already been requested by the structural engineers and other researchers in the field, who know about the technology.  Therefore, this retrofit technique can be extended further in order to address these specific requirements for improving both out-of-plane and in-plane performance of URM walls. It should be noted that the intent of the retrofit would remain the out-of-plane strengthening of the partition walls, which typically are of non-load bearing type and would not usually have proper foundations to support additional base shear, or shear force dragline. Thus, they should not be looked at as the main Lateral Load Resisting System (LLRS) for the mentioned buildings. However, application of a thin (10 mm to 20 mm) layer of EDCC over a large surface area (i.e. all the corridor walls in a building) can incrementally increase the overall in-plane capacity. Therefore, it can help the Lateral Drift Resisting System (LDRS) for these buildings to potential drop down to a lower risk level (e.g. from high risk down to medium or low risk) in the overall building assessment.  196  7.4.4 Spray Process Characterization and Testing As discussed in section 3.4, it would be useful to spray complete sets of tensile specimens, cut out from various thickness panels sprayed onto a bond breaker surface. The specimens should be tested in tensile loading, possibly both static and dynamic, in order to officially characterize and quantify the attributes of “sprayed EDCC”.  In addition, it is recommended that the spray system itself would be more useful if is properly characterized, for adaptability to different EDCC mix designs and applications. It is recommended that typical shotcrete quantifications are performed on the developed EDCC spray process. These may include, but not limited to, rebound values, penetration resistances, particle counts, particle velocity distribution, and various methods to characterize fiber distribution and void inclusion problems. With the existing SIERA spray chamber, this is well possible.  7.4.5 Tensile and Flexural Testing of EDCC in High Dynamic Rates of Loading Based on the results presented in section 6.4.2 of this thesis, it would be useful to test more EDCC specimens in tension at much higher rates of loading. In fact, the EDCC layer has experienced extreme rates of loading on the shake table, as discussed.   Considering that EDCC is a load-rate and strain-rate sensitive material, it would be useful to collect and analyze some data for its stress-strain response under high dynamic strain rates, rather than quasi-dynamic tests, like what was initially done in this thesis for preliminary material development, as discussed in section 6.2.2.  197  7.4.6 Recommended Numerical and Analytical Modeling It would be useful to come up with a scientific finite element model for the EDCC retrofitted walls. ABAQUS or similar software are recommended to be used for this purpose. The model should include material nonlinearity with appropriate rate effects. In addition, a consecutive or numerical model should be assembled to model the strain rate effect on different mixes of EDCC. 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The appendices are mentioned and discussed within the thesis, when appropriate.  Appendix A  - Retrofit Details as Presented in Volume 7 of SRG III This section shows the summary of the retrofit options, the factors affecting the cost, and the details of the design. This document, as presented here, is in Volume 7 of the 3rd Edition of the Seismic Retrofit Guidelines (SRG III, 2017).  A.1 SRG III – URM partition walls (# 11) – Restraint of Wall using Sprayed EDCC Description of Retrofit: This retrofit can be used to brace URM walls out-of-plane.  Mechanically restrain the UR masonry wall throughout the full height, by spraying 0.5” to 0.75” thick layer of the EDCC (Ecofriendly Ductile Cementitious Composite) material on one side of existing wall.  Typical Existing Building Conditions  Partition walls are typically of 4” or 6” concrete masonry units or 4” clay bricks.  Example Factors Affecting Cost of Retrofit  Re/re existing finishes and services.  Interior or exterior walls.  Story height and Ease of access.  Remediate vermiculite void fill.  Application options: Sprayed or Hand Applied.   Finish options: Smooth Finish (troweled) or Rough Finish 209   Figure 7-1: SRG III – Retrofit Details for URM Partition # 11 – EDCC Technique 210  Appendix B  - Additional Graphs and Data for Chapter 6: This appendix belongs to the data and discussions of Chapter 6: Effect of High Strain Rates on Constitutive Response of EDCC. Some of the graphs presented in this appendix have already been presented within the body of the chapter, in different layouts, but they are presented again here, in larger formats, for more readability of their contents.  B.1 EDCC Premium Mix - 2% PVA Fibers   Figure 7-2: Dynamic Load-Time Representative Curves for EDCC Premium Mix  211   Figure 7-3: Dynamic Stress-Strain Representative Curves for EDCC Premium Mix  B.2 EDCC Mix with 2% PET Fibers  Figure 7-4: Dynamic Load-Time Representative Curves for EDCC Mix with 2% PET 212   Figure 7-5: Dynamic Stress-Strain Representative Curves for EDCC Mix with 2% PET  B.3 Regular EDCC Mix – Hybrid of 1% PVA + 1% PET Fibers  Figure 7-6: Dynamic Load-Time Representative Curves for EDCC Regular Mix 213   Figure 7-7: Dynamic Stress-Strain Representative Curves for EDCC Regular Mix  B.4 Additional Detailed Combined Graphs for all EDCC Mixes  Figure 7-8: Dynamic Load-Time Average Curves for EDCC Mixes 214   Figure 7-9: Dynamic Stress-Strain Average Curves for EDCC Mixes   Figure 7-10: Coefficient of Variation for Dynamic Load-Displacement for EDCC Mixes 215   Figure 7-11: Dynamic vs. Static Stress-Strain Response for EDCC Premium Mix   Figure 7-12: Dynamic vs. Static Stress-Strain Response for EDCC Mix with 2% PET 216   Figure 7-13: Dynamic vs. Static Stress-Strain Response for EDCC Regular Mix            217  Appendix C  - Raw Materials’ Specifications of the Masonry Specimens Information for the clay bricks, cinder blocks, and the mortar used for the specimens, targeted for the retrofit program, are all provided here. This appendix does not include details about EDCC.  C.1 Concrete Masonry Unit (CMU) Specifications and Details The building blocks of some of the specimens are Concrete Masonry Units (CMU). Regular weight 10cm Standard CMUs are chosen. This CMU has the nominal dimensions of 400 x 100 x 200mm (L x W x H). The exact dimensions and sections are shown in Figure 7-14 below.    Figure 7-14: Concrete Masonry Products - 10cm Standard CMU Dimensions 218  Some of the technical specifications and mechanical properties of the used regular weight 10cm Standard CMU are listed in Table 7-1.  Table 7-1: Unit Data for 10cm Standard CMU from Concrete Masonry Products Unit weight (Heavy Weight “A” type) 12.1 Kg Percent Solid 76.0% Void Volume 0.00161 m3 Net Area 0.0245 m2  The CMU are order directly by an industrial partner and are delivered to space shared by at the structural lab and Earthquake Engineering Research Facility (EERF). Figure 7-15 shows the specimens as delivered to UBC.   Figure 7-15: CMU delivered for building the specimens 219  C.2 Clay Bricks Specifications and Details The building blocks of some of the specimens are regular Clay Bricks. Normal weight standard clay brick is chosen for this project. The bricks are delivered to UBC for construction of these specimens, as shown in Figure 7-16.   Figure 7-16: Standard Clay Brick for Half-Scale Wall Panels           220  C.3 The mortar used for the Specimens The mortar used in the construction of all the specimens is of standard mortar Type S, and the mortar joints are all 10mm thick, as regular practice. The specification sheets are provided here.   221   222  Appendix D  - Out-of-Plane Panel Tests: Specimens, Setup, and Instrumentation This appendix provides details for the half-scale wall panel specimens built and retrofitted at UBC for the static monotonic and cyclic out-of-plane testing.  D.1 Concrete Masonry Unit (CMU) Wall Panel (wallet) Specimens Each specimen is 1.2m x 1.2m x 0.1m (length x height x depth), built of 6 rows of blocks with each row having 3 blocks in different configurations. The overall shape and dimensions of the specimens are illustrated in Figure 7-17. The mortar used in the construction of these specimens is of standard mortar Type S, as finalized before and the mortar joints are 10mm wide.   Figure 7-17: The overall shape and dimensions of the CMU wall panels  There are 10 wall specimens of this type constructed. The building blocks of this type of specimen are Concrete Masonry Units (CMU). Regular weight 10cm Standard CMU is chosen 223  for this specimen type. This CMU has the nominal dimensions of 400 x 100 x 200mm (L x W x H). The exact dimensions and sections are provided in the previous appendix. The constructed wall specimens are framed and wrapped in plywood sheets in order to prevent any possible damage to the specimens during the transportation process. It is worth mentioning that the wall specimens are transported in the standing position and each two walls are placed on one pallet for transportation. Figure 7-18 shows the mentioned framed specimens.   Figure 7-18: Framed up CMU wall specimens at UBC  Eight of the specimens are retrofitted using Regular Mix or Premium Mix EDCC, in three methods of hand-applied, hopper sprayed, and pumped sprayed as discussed in the thesis. Some of the wallets are already tested using a monotonic loading protocol, but some are in line of being cyclic tested, as part of a future testing program. 224  D.2 Clay Brick Wall Panel Specimens There are 10 wall specimens of this type constructed. Each specimen is 1.2m x 1.2m x 0.1m (length x height x depth), built of 18 rows of clay bricks with each row having 6 bricks in different configurations, using standard mortar Type S. The overall shape and dimensions of the specimens are illustrated in Figure 7-17. The specifications for the clay bricks and the mortar type and its specifications are all provided in detail in the previous appendix of this thesis.   Figure 7-19: The Overall Shape and Dimensions of the Clay Brick Wallet Specimens 225  The constructed wall specimens are framed and wrapped in plywood sheets in order to prevent any possible damage to the specimens during the transportation process. The specimens are wrapped and transported similar to the concrete cinder block specimens, described in the last section of this appendix. Figure 7-20 shows the framed clay brick wall specimens.   Figure 7-20: Secured Clay Brick Wallet Specimens at UBC  The building blocks of this type of specimens are regular Clay Bricks. Normal weight standard clay brick is chosen with dimensions 194 x 92 x 57mm (L x W x H), constructed with mortar joints of 10mm, as described in the previous appendix.  226  Appendix E  Monotonic and Cyclic Testing of EDCC Strengthened URM Wallets This appendix provides details for the half-scale wall panel specimens built and retrofitted at UBC for the static monotonic and cyclic out-of-plane testing.   E.1 Overall Specimen Dimensions and Mounting Configuration This section provides the sketches for the overall dimensions of these specimens, number of CMU units, and the configuration that the CMUs are assembled to build the wallets. Figure 7-21 also shows the wallets on the loading beams, which are fabricated at UBC, to secure the wallets in position during the testing.   Figure 7-21: Half-Scale Wall Specimens for Static OP Tests  227  E.2 Instrumentation Details and Data Collection The schematic sketch presented here shows the location and number of data acquisition channels, which are be incorporated for this test, plus the support details, in Figure 7-22 and Figure 7-23.   Figure 7-22: Instrumentation Details for the Half-Scale Specimens for Static OP Tests   Figure 7-23: Static Tests Top Frame Supporting Condition Details 228  E.3 Monotonic Testing of Half-Scale EDCC Strengthened URM Walls This section presents the details for the actuator setup and configuration details for the monotonic tests. Figure 7-24 also provides a sketch of the monotonic test setup.   Figure 7-24: The Test Setup for the Static-Monotonic OP Testing of Half-Scale Walls 229  E.4 Cyclic Testing of Half-Scale EDCC Strengthened URM Walls This section presents the details for the actuator setup and configuration details for the cyclic tests. Figure 7-25 also provides a sketch of the monotonic test setup.   Figure 7-25: The Test Setup for the Static-Cyclic OP Testing of Half-Scale Walls  230  Appendix F  - Selected Photos from the Demo Project at Jamieson Elementary School This appendix highlights a few photos and snapshots taken during the retrofit process of a URM wall at Dr. Annie B. Jamieson Elementary School in Vancouver, BC. This demonstration retrofit project took place during the course of three days, from November 6th to November 8th, 2017.   Figure 7-26: The UBC Crew Setting Up and Getting Ready to Start at Jamieson School  231   Figure 7-27: Design Specifications Being Reviewed and EDCC Getting Prepared        232   Figure 7-28: Mixing EDCC with a Typical 60L Mortar Mixer at Jamieson School        233  Appendix G  - Library of Generated MATLAB Codes, Scripts, and Functions This appendix provides the full script of all the MATLAB codes generated for this thesis work. This includes scripts developed for data import, pre-processing, processing, and post-processing. The signal conditioning, plotting, and data import functions are also included, for reference.   G.1 Import Functions and Scripts for Data Import from ASCII Files This code looks up the original ASCII file with the raw data in it, loads it, reads the data, organizes them, and then saves them in the form of MATLAB data clusters, one cluster file per wall per run (i.e. Wall-1_Run-2_...), to be used for the pre-processing codes next.  clc clear close all; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Reading file heather information here %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Original_Data_Worksheet_Name = 'Wall_test_June9_2016_v8_without_StrainGauges' Recording_Date = '09/06/2016, 10:44:56 AM' ID_Wall = 2 ID_Run = 2 ID_GM = 4 ID_GM_Intensity = '100%' Block_Lenght = 100 Time_Step_Sec = 0.005  No_of_Channels = {'Accelerometer', 'Strain Gage', 'String Pod'; 'Acceleration', 'Strain', 'Displacement' ;9,8,8}; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Input_File_Name_User = input ('Enter file name here: ', 's') Input_File_Name = [Input_File_Name_User '.ASC'] Input_Acceleration_Data_File_Name = '2016 June9 Wall Test Acc Data_Kobe_100%.ASC' Input_Strain_Gage_Data_File_Name = 'xxx.ASC' Input_String_Pods_Data_File_Name = '2016 June9 Wall Test SP Data_Kobe_100%.ASC' Data_ACC_All = importfile_ACC(Input_Acceleration_Data_File_Name); Data_SG_All = importfile_SG(Input_Strain_Gage_Data_File_Name); Data_SP_All = importfile_SP(Input_String_Pods_Data_File_Name); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 234  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Reorganizing and renaming the data columns %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  Data_ACC_All.Properties.VariableNames{1} = 'Time_hhmmss'; Data_ACC_All = Data_ACC_All(:,[1 10 2:9]); Data_ACC_All.Properties.VariableNames{2} = 'Accel_0_Table_g'; Data_ACC_All = Data_ACC_All(:,[1:2 5 3:4 6:end]); Data_ACC_All.Properties.VariableNames{3} = 'Accel_1_g'; Data_ACC_All = Data_ACC_All(:,[1:3 10 4:9]); Data_ACC_All.Properties.VariableNames{4} = 'Accel_2_g'; Data_ACC_All = Data_ACC_All(:,[1:4 7 5:6 8:end]); Data_ACC_All.Properties.VariableNames{5} = 'Accel_3_g'; Data_ACC_All = Data_ACC_All(:,[1:5 7 6 8:end]); Data_ACC_All.Properties.VariableNames{6} = 'Accel_4_g'; Data_ACC_All = Data_ACC_All(:,[1:6 8 7 9:end]); Data_ACC_All.Properties.VariableNames{7} = 'Accel_5_g'; Data_ACC_All.Properties.VariableNames{8} = 'Accel_6_g'; Data_ACC_All = Data_ACC_All(:,[1:8 10 9]); Data_ACC_All.Properties.VariableNames{9} = 'Accel_7_g'; Data_ACC_All.Properties.VariableNames{10} = 'Accel_8_Frame_g';  Data_SG_All.Properties.VariableNames{1} = 'Time_hhmmss'; Data_SG_All.Properties.VariableNames{2} = 'STRN_1_mStrain'; Data_SG_All = Data_SG_All(:,[1:2 4 3 5:end]); Data_SG_All.Properties.VariableNames{3} = 'STRN_2_mStrain'; Data_SG_All.Properties.VariableNames{4} = 'STRN_3_mStrain'; Data_SG_All.Properties.VariableNames{5} = 'STRN_4_mStrain'; Data_SG_All.Properties.VariableNames{6} = 'STRN_5_mStrain'; Data_SG_All = Data_SG_All(:,[1:6 8 7 end]); Data_SG_All.Properties.VariableNames{7} = 'STRN_6_mStrain'; Data_SG_All.Properties.VariableNames{8} = 'STRN_7_mStrain'; Data_SG_All.Properties.VariableNames{9} = 'STRN_8_mStrain';  Data_SP_All.Properties.VariableNames{1} = 'Time_hhmmss'; Data_SP_All = Data_SP_All(:,[1 8 2:7 end]); Data_SP_All.Properties.VariableNames{2} = 'DISPL_0_Table_mm'; Data_SP_All.Properties.VariableNames{3} = 'DISPL_1_mm'; Data_SP_All.Properties.VariableNames{4} = 'DISPL_2_mm'; Data_SP_All = Data_SP_All(:,[1:4 8 5:7 end]); Data_SP_All.Properties.VariableNames{5} = 'DISPL_3_mm'; Data_SP_All.Properties.VariableNames{6} = 'DISPL_4_mm'; Data_SP_All.Properties.VariableNames{7} = 'DISPL_5_mm'; Data_SP_All = Data_SP_All(:,[1:7 9 8]); Data_SP_All.Properties.VariableNames{8} = 'DISPL_6_mm'; Data_SP_All.Properties.VariableNames{9} = 'DISPL_7_mm';   235  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Import using scripts, instead of function %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% delimiter = ';' startRow = 8 formatSpec = '%{hh:mm:ss.SSS}D%f%f%f%f%f%f%f%f%f%[^\n\r]'  fileID = fopen(Input_Acceleration_Data_File_Name,'r'); dataArray = textscan(fileID, formatSpec, 'Delimiter', delimiter, 'TextType', 'string', 'HeaderLines' ,startRow-1, 'ReturnOnError', false, 'EndOfLine', '\r\n'); fclose(fileID);  Data_ACC_All = table(dataArray{1:end-1}, 'VariableNames', {'Measurementtimehhmmss','A1D1g','A1D2g','A1D_3g','A1D4g','A1D5g','A1D8g','A1D7g','A1D6g','TableAccg'}); clearvars fileID dataArray ans;  fileID = fopen(Input_Strain_Gage_Data_File_Name,'r'); dataArray = textscan(fileID, formatSpec, 'Delimiter', delimiter, 'TextType', 'string', 'HeaderLines' ,startRow-1, 'ReturnOnError', false, 'EndOfLine', '\r\n'); fclose(fileID);  Data_SG_All = table(dataArray{1:end-1}, 'VariableNames', {'Measurementtimehhmmss','SG0mStrain','SG1mStrain','SG2mStrain','SG3mStrain','SG4mStrain','SG5mStrain','SG6mStrain','SG7mStrain'}); May25WallTestSGData = table(dataArray{1:end-1}, 'VariableNames', {'Measurementtimehhmmss','SG0mStrain','SG1mStrain','SG2mStrain','SG3mStrain','SG4mStrain','SG5mStrain','SG6mStrain','SG7mStrain'}); clearvars fileID dataArray ans;  fileID = fopen(Input_String_Pods_Data_File_Name,'r'); dataArray = textscan(fileID, formatSpec, 'Delimiter', delimiter, 'TextType', 'string', 'HeaderLines' ,startRow-1, 'ReturnOnError', false, 'EndOfLine', '\r\n'); fclose(fileID);  Data_SP_All = table(dataArray{1:end-1}, 'VariableNames', {'Measurementtimehhmmss','SP17mm','SP15mm','SP18mm','SP13mm','SP20mm','SP19mm','TableDispmm','SP51mm'}); clearvars delimiter startRow formatSpec fileID dataArray ans;  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Output_File_Name = ['Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' ID_GM_Intensity] save (Output_File_Name); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 236  G.2 Pre-Processing and Data Conditioning Scripts and Functions This code loads up the previously saved MATLAB data cluster for each specific run, goes through the file, looks up peak values, plots the raw data indicating the peak values, so that the data can be checked for quality assurance, before proceeding to the processing section.  close all; clear; clc;  File_Name = 'Wall-1_Run-22_GM-3@300%.mat' load (File_Name)  clearvars Input_Acceleration_Data_File_Name Input_Strain_Gage_Data_File_Name Input_String_Pods_Data_File_Name Output_File_Name  No_of_Channels = {'Accelerometer', 'String Pod', 'Strain Gage'; 'Acceleration', 'Displacement', 'Strain';9,8,8}  data = Data_ACC_All;  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Calculating the duration & Frequency range of the record %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% [Row, Col] = size(data); Data_freq = 1/Time_Step_Sec Duration_of_Rec = Row * Time_Step_Sec Freq_Step = 1/Duration_of_Rec Freq_Domain = Freq_Step * Row  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Raw_Time (:,1) = table2array(data (:,1)); GM_Duration = max(Raw_Time(:,1)) - min(Raw_Time(:,1)) Time (:,1) = Raw_Time (:,1) - min(Raw_Time(:,1)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  Raw_Accel_All = zeros(Row,Col-1);  for i=1:table2array (No_of_Channels(3,1))          Raw_Accel (:,1) = table2array(data (:,i+1));     Raw_Accel_All (:,i) = table2array(data (:,i+1));       237      figure(1)     plot(Time, Raw_Accel)     xlabel('Time (Sec)','Color', 'b');     ylabel('Acceleration (g)','Color', 'b');     title ({['\fontsize{10} \bf \color{magenta} Time History for Accelerometer No. ' num2str(i-1) ' - Raw Data'] ; ['\fontsize{9} \rm \color{black} (Max Accel. = ' num2str(max(Raw_Accel(:,1))) ' g | Min Accel. = ' num2str(min(Raw_Accel(:,1))) ' g | Median = ' num2str(median((Raw_Accel(:,1)))) ' g)']});     legend({['\rm \color{red} Peak Acceleration = ' num2str(max(abs(max(Raw_Accel(:,1))), abs(min(Raw_Accel(:,1))))) ' g']}, 'Location','northeast', 'FontSize', 8);     set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '--');     grid(gca,'minor');     saveas (figure(1), ['Figures\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-' num2str(i-1)]);     saveas (figure(1), ['Figures\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-' num2str(i-1)], 'svg');     saveas (figure(1), ['Figures\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-' num2str(i-1)], 'pdf');     saveas (figure(1), ['Figures\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-' num2str(i-1)], 'png');     close(figure(1));      end    238  figure(2) plot(Time, Raw_Accel_All) xlabel('Time (Sec)','Color', 'b'); ylabel('Acceleration (g)','Color', 'b'); title('{\bf Time History of All the Acceleration Channels}','Color', 'r') legend({'Table-Accel', 'Wall Accel-1', 'Wall Accel-2', 'Wall Accel-3', 'Wall Accel-4', 'Wall Accel-5', 'Wall Accel-6', 'Wall Accel-7', 'Frame-Accel'}, 'FontSize', 6) legend('boxoff') set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '-.'); grid(gca,'minor'); saveas (figure(2), ['Figures\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-All']); saveas (figure(2), ['Figures\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-All'], 'svg'); saveas (figure(2), ['Figures\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-All'], 'pdf'); saveas (figure(2), ['Figures\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-All'], 'png'); close(figure(2));        239  figure(3) Ax1 = subplot(3,1,1); plot (Ax1, Time, Raw_Accel_All(:,9)); title (Ax1, {['\fontsize{8} \bf \color{magenta} Frame Acceleration vs. Time\fontsize{7} \rm \color{black}(Max = ' num2str(max(Raw_Accel_All(:,9))) ' g | Min = ' num2str(min(Raw_Accel_All(:,9))) ' g | Median = ' num2str(median(Raw_Accel_All(:,9))) ' g)']}); ylabel (Ax1, 'Acceleration (g)', 'Color', 'b', 'FontSize', 8) xlabel (Ax1, 'Time (Sec)', 'Color', 'b', 'FontSize', 8) Ax2 = subplot(3,1,2); plot (Ax2, Time, Raw_Accel_All(:,5)); title (Ax2, {['\fontsize{8} \bf \color{magenta} Wall Mid-Height Acceleration vs. Time\fontsize{7} \rm \color{black}(Max = ' num2str(max(Raw_Accel_All(:,5))) ' g | Min = ' num2str(min(Raw_Accel_All(:,5))) ' g | Median = ' num2str(median(Raw_Accel_All(:,5))) ' g)']}); ylabel (Ax2, 'Acceleration (g)', 'Color', 'b', 'FontSize', 8) xlabel (Ax2, 'Time (Sec)', 'Color', 'b', 'FontSize', 8) Ax3 = subplot(3,1,3); plot (Ax3, Time, Raw_Accel_All(:,1)); title (Ax3, {['\fontsize{8} \bf \color{magenta} Table Acceleration vs. Time\fontsize{7} \rm \color{black}(Max = ' num2str(max(Raw_Accel_All(:,1))) ' g | Min = ' num2str(min(Raw_Accel_All(:,1))) ' g | Median = ' num2str(median(Raw_Accel_All(:,1))) ' g)']}); ylabel (Ax3, 'Acceleration (g)', 'Color', 'b', 'FontSize', 8) xlabel (Ax3, 'Time (Sec)', 'Color', 'b', 'FontSize', 8) saveas (figure(3), ['Figures\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-Combo_Table-Wall-Frame']); saveas (figure(3), ['Figures\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-Combo_Table-Wall-Frame'], 'svg'); saveas (figure(3), ['Figures\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-Combo_Table-Wall-Frame'], 'pdf'); saveas (figure(3), ['Figures\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-Combo_Table-Wall-Frame'], 'png'); clearvars Ax1 Ax2 Ax3 close(figure(3));          240        figure(4) Ax1 = subplot(2,2,1); plot (Ax1, Time, Raw_Accel_All(:,2)); title (Ax1, {['\fontsize{8} \bf \color{magenta} Wall Base Acceleration vs. Time'] ; ['\fontsize{5} \rm \color{black} (Max = ' num2str(max(Raw_Accel_All(:,2))) ' g | Min = ' num2str(min(Raw_Accel_All(:,2))) ' g | Median = ' num2str(median(Raw_Accel_All(:,2))) ' g)']}); legend(Ax1, {['\rm \color{red} Peak Acceleration = ' num2str(max(abs(max(Raw_Accel_All(:,2))), abs(min(Raw_Accel_All(:,2))))) ' g']}, 'Location','northeast', 'FontSize', 4); ylabel (Ax1, 'Acceleration (g)', 'Color', 'b', 'FontSize', 7) xlabel (Ax1, 'Time (Sec)', 'Color', 'b', 'FontSize', 7) Ax2 = subplot(2,2,2); plot (Ax2, Time, Raw_Accel_All(:,8)); title (Ax2, {['\fontsize{8} \bf \color{magenta} Wall Top Acceleration vs. Time'] ; ['\fontsize{5} \rm \color{black} (Max = ' num2str(max(Raw_Accel_All(:,8))) ' g | Min = ' num2str(min(Raw_Accel_All(:,8))) ' g | Median = ' num2str(median(Raw_Accel_All(:,8))) ' g)']}); 241  legend(Ax2, {['\rm \color{red} Peak Acceleration = ' num2str(max(abs(max(Raw_Accel_All(:,8))), abs(min(Raw_Accel_All(:,8))))) ' g']}, 'Location','northeast', 'FontSize', 4); ylabel (Ax2, 'Acceleration (g)', 'Color', 'b', 'FontSize', 7) xlabel (Ax2, 'Time (Sec)', 'Color', 'b', 'FontSize', 7) Ax3 = subplot(2,2,3); plot (Ax3, Time, Raw_Accel_All(:,1)); title (Ax3, {['\fontsize{8} \bf \color{magenta} Table Acceleration vs. Time'] ; ['\fontsize{5} \rm \color{black} (Max = ' num2str(max(Raw_Accel_All(:,1))) ' g | Min = ' num2str(min(Raw_Accel_All(:,1))) ' g | Median = ' num2str(median(Raw_Accel_All(:,1))) ' g)']}); legend(Ax3, {['\rm \color{red} Peak Acceleration = ' num2str(max(abs(max(Raw_Accel_All(:,1))), abs(min(Raw_Accel_All(:,1))))) ' g']}, 'Location','northeast', 'FontSize', 4); ylabel (Ax3, 'Acceleration (g)', 'Color', 'b', 'FontSize', 7) xlabel (Ax3, 'Time (Sec)', 'Color', 'b', 'FontSize', 7) Ax4 = subplot(2,2,4); plot (Ax4, Time, Raw_Accel_All(:,9)); title (Ax4, {['\fontsize{8} \bf \color{magenta} Frame Acceleration vs. Time'] ; ['\fontsize{5} \rm \color{black} (Max = ' num2str(max(Raw_Accel_All(:,9))) ' g | Min = ' num2str(min(Raw_Accel_All(:,9))) ' g | Median = ' num2str(median(Raw_Accel_All(:,9))) ' g)']}); legend(Ax4, {['\rm \color{red} Peak Acceleration = ' num2str(max(abs(max(Raw_Accel_All(:,9))), abs(min(Raw_Accel_All(:,9))))) ' g']}, 'Location','northeast', 'FontSize', 4); ylabel (Ax4, 'Acceleration (g)', 'Color', 'b', 'FontSize', 7) xlabel (Ax4, 'Time (Sec)', 'Color', 'b', 'FontSize', 7) saveas (figure(4), ['Figures\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-Combo_Boundaries']); saveas (figure(4), ['Figures\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-Combo_Boundaries'], 'svg'); saveas (figure(4), ['Figures\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-Combo_Boundaries'], 'pdf'); saveas (figure(4), ['Figures\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-Combo_Boundaries'], 'png'); clearvars Ax1 Ax2 Ax3 Ax4 close(figure(4));        242       figure(5) Ax1 = subplot(3,1,1); plot (Ax1, Time, Raw_Accel_All(:,8)); title (Ax1, {['\fontsize{8} \bf \color{magenta} Wall Top Acceleration vs. Time\fontsize{7} \rm \color{black}(Max = ' num2str(max(Raw_Accel_All(:,8))) ' g | Min = ' num2str(min(Raw_Accel_All(:,8))) ' g | Median = ' num2str(median(Raw_Accel_All(:,8))) ' g)']}); ylabel (Ax1, 'Acceleration (g)', 'Color', 'b', 'FontSize', 8) xlabel (Ax1, 'Time (Sec)', 'Color', 'b', 'FontSize', 8) Ax2 = subplot(3,1,2); plot (Ax2, Time, Raw_Accel_All(:,5)); title (Ax2, {['\fontsize{8} \bf \color{magenta} Wall Mid-Height Acceleration vs. Time\fontsize{7} \rm \color{black}(Max = ' num2str(max(Raw_Accel_All(:,5))) ' g | Min = ' num2str(min(Raw_Accel_All(:,5))) ' g | Median = ' num2str(median(Raw_Accel_All(:,5))) ' g)']}); ylabel (Ax2, 'Acceleration (g)', 'Color', 'b', 'FontSize', 8) xlabel (Ax2, 'Time (Sec)', 'Color', 'b', 'FontSize', 8) Ax3 = subplot(3,1,3); plot (Ax3, Time, Raw_Accel_All(:,2)); 243  title (Ax3, {['\fontsize{8} \bf \color{magenta} Wall Base Acceleration vs. Time\fontsize{7} \rm \color{black}(Max = ' num2str(max(Raw_Accel_All(:,2))) ' g | Min = ' num2str(min(Raw_Accel_All(:,2))) ' g | Median = ' num2str(median(Raw_Accel_All(:,2))) ' g)']}); ylabel (Ax3, 'Acceleration (g)', 'Color', 'b', 'FontSize', 8) xlabel (Ax3, 'Time (Sec)', 'Color', 'b', 'FontSize', 8) saveas (figure(5), ['Figures\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-Combo_Wall-Base-Mid-Top']); saveas (figure(5), ['Figures\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-Combo_Wall-Base-Mid-Top'], 'svg'); saveas (figure(5), ['Figures\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-Combo_Wall-Base-Mid-Top'], 'pdf'); saveas (figure(5), ['Figures\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Accel-Combo_Wall-Base-Mid-Top'], 'png'); clearvars Ax1 Ax2 Ax3 close(figure(5));    244  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Calculating and Plotting the String Pod (Displacement) Data %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clearvars data Row Col Time Raw_Time data = Data_SP_All;  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Raw_Time (:,1) = table2array(data (:,1)); Time (:,1) = Raw_Time (:,1) - min(Raw_Time(:,1)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% [Row, Col] = size(data); Raw_SP_All = zeros(Row,Col-1); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  for i=1:table2array (No_of_Channels(3,2))          Raw_SP (:,1) = table2array(data (:,i+1));     Raw_SP_All (:,i) = table2array(data (:,i+1));          figure(6)     plot(Time, Raw_SP)     xlabel('Time (Sec)','Color', 'b');     ylabel('Displacement (mm)','Color', 'b');     title ({['\fontsize{10} \bf \color{magenta} Time History for String Pod No. ' num2str(i-1) ' (DISPL. ' num2str(i-1) ') - Raw Data'] ; ['\fontsize{9} \rm \color{black} (Max Displ. = ' num2str(max(Raw_SP(:,1))) ' mm | Min Displ. = ' num2str(min(Raw_SP(:,1))) ' mm | Median = ' num2str(median((Raw_SP(:,1)))) ' mm)']});     legend({['\rm \color{red} Peak Displacement = ' num2str(max(abs(max(Raw_SP(:,1))), abs(min(Raw_SP(:,1))))) ' mm']}, 'Location','northeast', 'FontSize', 8);     set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '--');     grid(gca,'minor');     saveas (figure(6), ['Figures\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-' num2str(i-1)]);     saveas (figure(6), ['Figures\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-' num2str(i-1)], 'svg');     saveas (figure(6), ['Figures\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-' num2str(i-1)], 'pdf');     saveas (figure(6), ['Figures\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-' num2str(i-1)], 'png');     close(figure(6));      end 245       figure(7) plot(Time, Raw_SP_All) xlabel('Time (Sec)','Color', 'b'); ylabel('Displacement (mm)','Color', 'b'); title('{\bf Time History of All the Displacement Channels}','Color', 'r') legend({'Table-Displ', 'Wall Displ-1', 'Wall Displ-2', 'Wall Displ-3', 'Wall Displ-4', 'Wall Displ-5', 'Wall Displ-6', 'Wall Displ-7'}, 'FontSize', 6) legend('boxoff') set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '-.'); grid(gca,'minor'); saveas (figure(7), ['Figures\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-All']); saveas (figure(7), ['Figures\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-All'], 'svg'); saveas (figure(7), ['Figures\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-All'], 'pdf'); saveas (figure(7), ['Figures\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-All'], 'png'); close(figure(7));  246        figure(8) Ax1 = subplot(3,1,1); plot (Ax1, Time, Raw_SP_All(:,8)); title (Ax1, {['\fontsize{7} \bf \color{magenta} Wall Top Displacement vs. Time\fontsize{6} \rm \color{black}(Max = ' num2str(max(Raw_SP_All(:,8))) ' mm | Min = ' num2str(min(Raw_SP_All(:,8))) ' mm | Median = ' num2str(median(Raw_SP_All(:,8))) ' mm)']}); ylabel (Ax1, 'Displacement (mm)', 'Color', 'b', 'FontSize', 8) xlabel (Ax1, 'Time (Sec)', 'Color', 'b', 'FontSize', 8) Ax2 = subplot(3,1,2); plot (Ax2, Time, Raw_SP_All(:,5)); title (Ax2, {['\fontsize{7} \bf \color{magenta} Wall Mid-Point Displacement vs. Time\fontsize{6} \rm \color{black}(Max = ' num2str(max(Raw_SP_All(:,5))) ' mm | Min = ' num2str(min(Raw_SP_All(:,5))) ' mm | Median = ' num2str(median(Raw_SP_All(:,5))) ' mm)']}); ylabel (Ax2, 'Displacement (mm)', 'Color', 'b', 'FontSize', 8) xlabel (Ax2, 'Time (Sec)', 'Color', 'b', 'FontSize', 8) Ax3 = subplot(3,1,3); plot (Ax3, Time, Raw_SP_All(:,2)); 247  title (Ax3, {['\fontsize{7} \bf \color{magenta} Wall Base Displacement vs. Time\fontsize{6} \rm \color{black}(Max = ' num2str(max(Raw_SP_All(:,2))) ' mm | Min = ' num2str(min(Raw_SP_All(:,2))) ' mm | Median = ' num2str(median(Raw_SP_All(:,2))) ' mm)']}); ylabel (Ax3, 'Displacement (mm)', 'Color', 'b', 'FontSize', 8) xlabel (Ax3, 'Time (Sec)', 'Color', 'b', 'FontSize', 8) saveas (figure(8), ['Figures\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-Combo_Wall-Base-Mid-Top']); saveas (figure(8), ['Figures\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-Combo_Wall-Base-Mid-Top'], 'svg'); saveas (figure(8), ['Figures\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-Combo_Wall-Base-Mid-Top'], 'pdf'); saveas (figure(8), ['Figures\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-Combo_Wall-Base-Mid-Top'], 'png'); clearvars Ax1 Ax2 Ax3 close(figure(8));     248  figure(9) Ax1 = subplot(2,2,1); plot (Ax1, Time, Raw_SP_All(:,5)); title (Ax1, {['\fontsize{8} \bf \color{magenta} Wall Mid-Point Displacement vs. Time'] ; ['\fontsize{5} \rm \color{black} (Max = ' num2str(max(Raw_SP_All(:,5))) ' mm | Min = ' num2str(min(Raw_SP_All(:,5))) ' mm | Median = ' num2str(median(Raw_SP_All(:,5))) ' mm)']}); legend(Ax1, {['\rm \color{red} Peak Displacement = ' num2str(max(abs(max(Raw_SP_All(:,5))), abs(min(Raw_SP_All(:,5))))) ' mm']}, 'Location','northeast', 'FontSize', 4); ylabel (Ax1, 'Displacement (mm)', 'Color', 'b', 'FontSize', 7) xlabel (Ax1, 'Time (Sec)', 'Color', 'b', 'FontSize', 7) Ax2 = subplot(2,2,2); plot (Ax2, Time, Raw_SP_All(:,8)); title (Ax2, {['\fontsize{8} \bf \color{magenta} Wall Top Displacement vs. Time'] ; ['\fontsize{5} \rm \color{black} (Max = ' num2str(max(Raw_SP_All(:,8))) ' mm | Min = ' num2str(min(Raw_SP_All(:,8))) ' mm | Median = ' num2str(median(Raw_SP_All(:,8))) ' mm)']}); legend(Ax2, {['\rm \color{red} Peak Displacement = ' num2str(max(abs(max(Raw_SP_All(:,8))), abs(min(Raw_SP_All(:,8))))) ' mm']}, 'Location','northeast', 'FontSize', 4); ylabel (Ax2, 'Displacement (mm)', 'Color', 'b', 'FontSize', 7) xlabel (Ax2, 'Time (Sec)', 'Color', 'b', 'FontSize', 7) Ax3 = subplot(2,2,3); plot (Ax3, Time, Raw_SP_All(:,1)); title (Ax3, {['\fontsize{8} \bf \color{magenta} Table Displacement vs. Time'] ; ['\fontsize{5} \rm \color{black} (Max = ' num2str(max(Raw_SP_All(:,1))) ' mm | Min = ' num2str(min(Raw_SP_All(:,1))) ' mm | Median = ' num2str(median(Raw_SP_All(:,1))) ' mm)']}); legend(Ax3, {['\rm \color{red} Peak Displacement = ' num2str(max(abs(max(Raw_SP_All(:,1))), abs(min(Raw_SP_All(:,1))))) ' mm']}, 'Location','northeast', 'FontSize', 4); ylabel (Ax3, 'Displacement (mm)', 'Color', 'b', 'FontSize', 7) xlabel (Ax3, 'Time (Sec)', 'Color', 'b', 'FontSize', 7) Ax4 = subplot(2,2,4); plot (Ax4, Time, Raw_SP_All(:,2)); title (Ax4, {['\fontsize{8} \bf \color{magenta} Wall Base Displacement vs. Time'] ; ['\fontsize{5} \rm \color{black} (Max = ' num2str(max(Raw_SP_All(:,2))) ' mm | Min = ' num2str(min(Raw_SP_All(:,2))) ' mm | Median = ' num2str(median(Raw_SP_All(:,2))) ' mm)']}); legend(Ax4, {['\rm \color{red} Peak Displacement = ' num2str(max(abs(max(Raw_SP_All(:,2))), abs(min(Raw_SP_All(:,2))))) ' mm']}, 'Location','northeast', 'FontSize', 4); ylabel (Ax4, 'Displacement (mm)', 'Color', 'b', 'FontSize', 7) xlabel (Ax4, 'Time (Sec)', 'Color', 'b', 'FontSize', 7) saveas (figure(9), ['Figures\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-Combo_Wall-Heights']); 249  saveas (figure(9), ['Figures\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-Combo_Wall-Heights'], 'svg'); saveas (figure(9), ['Figures\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-Combo_Wall-Heights'], 'pdf'); saveas (figure(9), ['Figures\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-Combo_Wall-Heights'], 'png'); clearvars Ax1 Ax2 Ax3 Ax4 close(figure(9));     figure(10) Ax1 = subplot(2,1,1); plot (Ax1, Time, Raw_SP_All(:,2)); title (Ax1, {['\fontsize{8} \bf \color{magenta} Wall Base Displacement vs. Time\fontsize{7} \rm \color{black}(Max = ' num2str(max(Raw_SP_All(:,2))) ' mm | Min = ' num2str(min(Raw_SP_All(:,2))) ' mm | Median = ' num2str(median(Raw_SP_All(:,2))) ' mm)']}); ylabel (Ax1, 'Displacement (mm)', 'Color', 'b', 'FontSize', 8) 250  xlabel (Ax1, 'Time (Sec)', 'Color', 'b', 'FontSize', 8) Ax2 = subplot(2,1,2); plot (Ax2, Time, Raw_SP_All(:,1)); title (Ax2, {['\fontsize{8} \bf \color{magenta} Table Displacement vs. Time\fontsize{7} \rm \color{black}(Max = ' num2str(max(Raw_SP_All(:,1))) ' mm | Min = ' num2str(min(Raw_SP_All(:,1))) ' mm | Median = ' num2str(median(Raw_SP_All(:,1))) ' mm)']}); ylabel (Ax2, 'Displacement (mm)', 'Color', 'b', 'FontSize', 8) xlabel (Ax2, 'Time (Sec)', 'Color', 'b', 'FontSize', 8) saveas (figure(10), ['Figures\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-Combo_Boundary']); saveas (figure(10), ['Figures\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-Combo_Boundary'], 'svg'); saveas (figure(10), ['Figures\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-Combo_Boundary'], 'pdf'); saveas (figure(10), ['Figures\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-Combo_Boundary'], 'png'); clearvars Ax1 Ax2 Ax3 close(figure(10));    251  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Calculating and Plotting the Strain Gage Data %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clearvars data Row Col Time Raw_Time data = Data_SG_All;  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Raw_Time (:,1) = table2array(data (:,1)); Time (:,1) = Raw_Time (:,1) - min(Raw_Time(:,1)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% [Row, Col] = size(data); Raw_SG_All = zeros(Row,Col-1); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%% Changing milli-Strain to Micro-Strain %%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  for i=1:table2array (No_of_Channels(3,3))          Raw_SG (:,1) = table2array(data (:,i+1))*1000;     Raw_SG_All (:,i) = table2array(data (:,i+1))*1000;           figure(11)     plot(Time, Raw_SG)     xlabel('Time (Sec)','Color', 'b');     ylabel('Strain (\mu\epsilon)','Color', 'b');     title ({['\fontsize{10} \bf \color{magenta} Time History for Strain Gage No. ' num2str(i) ' (STRN. ' num2str(i) ') - Raw Data'] ; ['\fontsize{9} \rm \color{black} (Max Strain. = ' num2str(max(Raw_SG(:,1))) ' \mu\epsilon | Min Strain. = ' num2str(min(Raw_SG(:,1))) ' \mu\epsilon | Median = ' num2str(median((Raw_SG(:,1)))) ' \mu\epsilon)']});      legend({['\rm \color{red} Peak Strain = ' num2str(max(abs(max(Raw_SG(:,1))), abs(min(Raw_SG(:,1))))) ' \mu\epsilon']}, 'Location','northeast', 'FontSize', 8);     set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '--');     grid(gca,'minor');      saveas (figure(11), ['Figures\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-' num2str(i)]);      saveas (figure(11), ['Figures\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-' num2str(i)], 'svg'); 252      saveas (figure(11), ['Figures\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-' num2str(i)], 'pdf');      saveas (figure(11), ['Figures\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-' num2str(i)], 'png');      close(figure(11));  end               253  figure(12) plot(Time, Raw_SG_All) xlabel('Time (Sec)','Color', 'b'); ylabel('Strain (\mu\epsilon)','Color', 'b'); title('{\bf Time History of All the Strain Gage Readings}','Color', 'r') legend({'STRN-1', 'STRN-2', 'STRN-3', 'STRN-4', 'STRN-5', 'STRN-6', 'STRN-7', 'STRN-8'}, 'FontSize', 5, 'Orientation', 'vertical', 'location', 'northeast') legend('boxoff') set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '-.'); grid(gca,'minor'); saveas (figure(12), ['Figures\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-All']); saveas (figure(12), ['Figures\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-All'], 'svg'); saveas (figure(12), ['Figures\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-All'], 'pdf'); saveas (figure(12), ['Figures\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-All'], 'png'); close(figure(12));     254  figure(13)  Ax1 = subplot(2,2,3); plot (Ax1, Time, Raw_SG_All(:,1)); title (Ax1, {['\fontsize{6} \bf \color{magenta} Front-Bottom Strain Gage (STRN.1) vs. Time'];['\fontsize{5} \rm \color{black}(Max = ' num2str(max(Raw_SG_All(:,1))) ' \mu\epsilon | Min = ' num2str(min(Raw_SG_All(:,1))) ' \mu\epsilon | Median = ' num2str(median(Raw_SG_All(:,1))) ' \mu\epsilon)'];[];[]}); ylabel (Ax1, 'Strain (\mu\epsilon)', 'Color', 'b', 'FontSize', 8) xlabel (Ax1, 'Time (Sec)', 'Color', 'b', 'FontSize', 8)   Ax2 = subplot(2,2,4); plot (Ax2, Time, Raw_SG_All(:,4)); title (Ax2, {['\fontsize{6} \bf \color{magenta} Front-Top Strain Gage (STRN.4) vs. Time'] ; ['\fontsize{5} \rm \color{black}(Max = ' num2str(max(Raw_SG_All(:,4))) ' \mu\epsilon | Min = ' num2str(min(Raw_SG_All(:,4))) ' \mu\epsilon | Median = ' num2str(median(Raw_SG_All(:,4))) ' \mu\epsilon)'];[];[]}); ylabel (Ax2, 'Strain (\mu\epsilon)', 'Color', 'b', 'FontSize', 8) xlabel (Ax2, 'Time (Sec)', 'Color', 'b', 'FontSize', 8)   Ax3 = subplot(2,2,1); plot (Ax3, Time, Raw_SG_All(:,2)); title (Ax3, {['\fontsize{6} \bf \color{magenta} Front-Left Strain Gage (STRN.2) vs. Time'] ; ['\fontsize{5} \rm \color{black} (Max = ' num2str(max(Raw_SG_All(:,2))) ' \mu\epsilon | Min = ' num2str(min(Raw_SG_All(:,2))) ' \mu\epsilon | Median = ' num2str(median(Raw_SG_All(:,2))) ' \mu\epsilon)'];[];[]}); ylabel (Ax3, 'Strain (\mu\epsilon)', 'Color', 'b', 'FontSize', 8) xlabel (Ax3, 'Time (Sec)', 'Color', 'b', 'FontSize', 8)   Ax4 = subplot(2,2,2); plot (Ax4, Time, Raw_SG_All(:,3)); title (Ax4, {['\fontsize{6} \bf \color{magenta} Front-Right Strain Gage (STRN.3) vs. Time'] ; ['\fontsize{5} \rm \color{black} (Max = ' num2str(max(Raw_SG_All(:,3))) ' \mu\epsilon | Min = ' num2str(min(Raw_SG_All(:,3))) ' \mu\epsilon | Median = ' num2str(median(Raw_SG_All(:,3))) ' \mu\epsilon)'];[];[]}); ylabel (Ax4, 'Strain (\mu\epsilon)', 'Color', 'b', 'FontSize', 8) xlabel (Ax4, 'Time (Sec)', 'Color', 'b', 'FontSize', 8) saveas (figure(13), ['Figures\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-Combo_Front-Gages']);   255  saveas (figure(13), ['Figures\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-Combo_Front-Gages'], 'svg');  saveas (figure(13), ['Figures\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-Combo_Front-Gages'], 'pdf');  saveas (figure(13), ['Figures\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-Combo_Front-Gages'], 'png');  clearvars Ax1 Ax2 Ax3 Ax4  close(figure(13));          256  figure(14)   Ax1 = subplot(2,2,3); plot (Ax1, Time, Raw_SG_All(:,5)); title (Ax1, {['\fontsize{6} \bf \color{magenta} Rear-Bottom Strain Gage (STRN.5) vs. Time'] ; ['\fontsize{5} \rm \color{black}(Max = ' num2str(max(Raw_SG_All(:,5))) ' \mu\epsilon | Min = ' num2str(min(Raw_SG_All(:,5))) ' \mu\epsilon | Median = ' num2str(median(Raw_SG_All(:,5))) ' \mu\epsilon)'];[];[]}); ylabel (Ax1, 'Strain (\mu\epsilon)', 'Color', 'b', 'FontSize', 8) xlabel (Ax1, 'Time (Sec)', 'Color', 'b', 'FontSize', 8)   Ax2 = subplot(2,2,4); plot (Ax2, Time, Raw_SG_All(:,8)); title (Ax2, {['\fontsize{6} \bf \color{magenta} Rear-Top Strain Gage (STRN.8) vs. Time'] ; ['\fontsize{5} \rm \color{black}(Max = ' num2str(max(Raw_SG_All(:,8))) ' \mu\epsilon | Min = ' num2str(min(Raw_SG_All(:,8))) ' \mu\epsilon | Median = ' num2str(median(Raw_SG_All(:,8))) ' \mu\epsilon)'];[];[]}); ylabel (Ax2, 'Strain (\mu\epsilon)', 'Color', 'b', 'FontSize', 8) xlabel (Ax2, 'Time (Sec)', 'Color', 'b', 'FontSize', 8)   Ax3 = subplot(2,2,1); plot (Ax3, Time, Raw_SG_All(:,6)); title (Ax3, {['\fontsize{6} \bf \color{magenta} Rear-Left Strain Gage (STRN.6) vs. Time'] ; ['\fontsize{5} \rm \color{black} (Max = ' num2str(max(Raw_SG_All(:,6))) ' \mu\epsilon | Min = ' num2str(min(Raw_SG_All(:,6))) ' \mu\epsilon | Median = ' num2str(median(Raw_SG_All(:,6))) ' \mu\epsilon)'];[];[]}); ylabel (Ax3, 'Strain (\mu\epsilon)', 'Color', 'b', 'FontSize', 8) xlabel (Ax3, 'Time (Sec)', 'Color', 'b', 'FontSize', 8)   Ax4 = subplot(2,2,2); plot (Ax4, Time, Raw_SG_All(:,7)); title (Ax4, {['\fontsize{6} \bf \color{magenta} Rear-Right Strain Gage (STRN.7) vs. Time'] ; ['\fontsize{5} \rm \color{black} (Max = ' num2str(max(Raw_SG_All(:,7))) ' \mu\epsilon | Min = ' num2str(min(Raw_SG_All(:,7))) ' \mu\epsilon | Median = ' num2str(median(Raw_SG_All(:,7))) ' \mu\epsilon)'];[];[]}); ylabel (Ax4, 'Strain (\mu\epsilon)', 'Color', 'b', 'FontSize', 8) xlabel (Ax4, 'Time (Sec)', 'Color', 'b', 'FontSize', 8)     257  saveas (figure(14), ['Figures\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-Combo_Rear-Gages']);  saveas (figure(14), ['Figures\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-Combo_Rear-Gages'], 'svg');  saveas (figure(14), ['Figures\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-Combo_Rear-Gages'], 'pdf'); saveas (figure(14), ['Figures\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-Combo_Rear-Gages'], 'png');  clearvars Ax1 Ax2 Ax3 Ax4  close(figure(14));      258  figure(15) Ax1 = subplot(2,2,1); plot (Ax1, Time, Raw_SG_All(:,4)); title (Ax1, {['\fontsize{6} \bf \color{magenta} Front-Top Strain Gage (STRN.4) vs. Time'] ; ['\fontsize{5} \rm \color{black}(Max = ' num2str(max(Raw_SG_All(:,4))) ' \mu\epsilon | Min = ' num2str(min(Raw_SG_All(:,4))) ' \mu\epsilon | Median = ' num2str(median(Raw_SG_All(:,4))) ' \mu\epsilon)'];[];[]}); ylabel (Ax1, 'Strain (\mu\epsilon)', 'Color', 'b', 'FontSize', 8) xlabel (Ax1, 'Time (Sec)', 'Color', 'b', 'FontSize', 8)   Ax2 = subplot(2,2,2); plot (Ax2, Time, Raw_SG_All(:,8)); title (Ax2, {['\fontsize{6} \bf \color{magenta} Rear-Top Strain Gage (STRN.8) vs. Time'] ; ['\fontsize{5} \rm \color{black}(Max = ' num2str(max(Raw_SG_All(:,8))) ' \mu\epsilon | Min = ' num2str(min(Raw_SG_All(:,8))) ' \mu\epsilon | Median = ' num2str(median(Raw_SG_All(:,8))) ' \mu\epsilon)'];[];[]}); ylabel (Ax2, 'Strain (\mu\epsilon)', 'Color', 'b', 'FontSize', 8) xlabel (Ax2, 'Time (Sec)', 'Color', 'b', 'FontSize', 8)   Ax3 = subplot(2,2,3); plot (Ax3, Time, Raw_SG_All(:,1)); title (Ax3, {['\fontsize{6} \bf \color{magenta} Front-Bottom Strain Gage (STRN.1) vs. Time'] ; ['\fontsize{5} \rm \color{black} (Max = ' num2str(max(Raw_SG_All(:,1))) ' \mu\epsilon | Min = ' num2str(min(Raw_SG_All(:,1))) ' \mu\epsilon | Median = ' num2str(median(Raw_SG_All(:,1))) ' \mu\epsilon)'];[];[]}); ylabel (Ax3, 'Strain (\mu\epsilon)', 'Color', 'b', 'FontSize', 8) xlabel (Ax3, 'Time (Sec)', 'Color', 'b', 'FontSize', 8)   Ax4 = subplot(2,2,4); plot (Ax4, Time, Raw_SG_All(:,5)); title (Ax4, {['\fontsize{6} \bf \color{magenta} Rear-Bottom Strain Gage (STRN.5) vs. Time'] ; ['\fontsize{5} \rm \color{black} (Max = ' num2str(max(Raw_SG_All(:,5))) ' \mu\epsilon | Min = ' num2str(min(Raw_SG_All(:,5))) ' \mu\epsilon | Median = ' num2str(median(Raw_SG_All(:,5))) ' \mu\epsilon)'];[];[]}); ylabel (Ax4, 'Strain (\mu\epsilon)', 'Color', 'b', 'FontSize', 8) xlabel (Ax4, 'Time (Sec)', 'Color', 'b', 'FontSize', 8)  saveas (figure(15), ['Figures\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-Combo_Vertical']); 259  saveas (figure(15), ['Figures\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-Combo_Vertical'], 'svg');  saveas (figure(15), ['Figures\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-Combo_Vertical'], 'pdf');  saveas (figure(15), ['Figures\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-Combo_Vertical'], 'png');  clearvars Ax1 Ax2 Ax3 Ax4  close(figure(15));         260  figure(16)  Ax1 = subplot(2,2,2); plot (Ax1, Time, Raw_SG_All(:,3)); title (Ax1, {['\fontsize{6} \bf \color{magenta} Front-Right Strain Gage (STRN.3) vs. Time'] ; ['\fontsize{5} \rm \color{black}(Max = ' num2str(max(Raw_SG_All(:,3))) ' \mu\epsilon | Min = ' num2str(min(Raw_SG_All(:,3))) ' \mu\epsilon | Median = ' num2str(median(Raw_SG_All(:,3))) ' \mu\epsilon)'];[];[]}); ylabel (Ax1, 'Strain (\mu\epsilon)', 'Color', 'b', 'FontSize', 8) xlabel (Ax1, 'Time (Sec)', 'Color', 'b', 'FontSize', 8)   Ax2 = subplot(2,2,4); plot (Ax2, Time, Raw_SG_All(:,7)); title (Ax2, {['\fontsize{6} \bf \color{magenta} Rear-Right Strain Gage (STRN.7) vs. Time'] ; ['\fontsize{5} \rm \color{black}(Max = ' num2str(max(Raw_SG_All(:,7))) ' \mu\epsilon | Min = ' num2str(min(Raw_SG_All(:,7))) ' \mu\epsilon | Median = ' num2str(median(Raw_SG_All(:,7))) ' \mu\epsilon)'];[];[]}); ylabel (Ax2, 'Strain (\mu\epsilon)', 'Color', 'b', 'FontSize', 8) xlabel (Ax2, 'Time (Sec)', 'Color', 'b', 'FontSize', 8)   Ax3 = subplot(2,2,1); plot (Ax3, Time, Raw_SG_All(:,2)); title (Ax3, {['\fontsize{6} \bf \color{magenta} Front-Left Strain Gage (STRN.2) vs. Time'] ; ['\fontsize{5} \rm \color{black} (Max = ' num2str(max(Raw_SG_All(:,2))) ' \mu\epsilon | Min = ' num2str(min(Raw_SG_All(:,2))) ' \mu\epsilon | Median = ' num2str(median(Raw_SG_All(:,2))) ' \mu\epsilon)'];[];[]}); ylabel (Ax3, 'Strain (\mu\epsilon)', 'Color', 'b', 'FontSize', 8) xlabel (Ax3, 'Time (Sec)', 'Color', 'b', 'FontSize', 8)   Ax4 = subplot(2,2,3); plot (Ax4, Time, Raw_SG_All(:,6)); title (Ax4, {['\fontsize{6} \bf \color{magenta} Rear-Left Strain Gage (STRN.6) vs. Time'] ; ['\fontsize{5} \rm \color{black} (Max = ' num2str(max(Raw_SG_All(:,6))) ' \mu\epsilon | Min = ' num2str(min(Raw_SG_All(:,6))) ' \mu\epsilon | Median = ' num2str(median(Raw_SG_All(:,6))) ' \mu\epsilon)'];[];[]}); ylabel (Ax4, 'Strain (\mu\epsilon)', 'Color', 'b', 'FontSize', 8) xlabel (Ax4, 'Time (Sec)', 'Color', 'b', 'FontSize', 8)  saveas (figure(16), ['Figures\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-Combo_Horizontal']); 261  saveas (figure(16), ['Figures\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-Combo_Horizontal'], 'svg');  saveas (figure(16), ['Figures\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-Combo_Horizontal'], 'pdf');  saveas (figure(16), ['Figures\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Strain-Combo_Horizontal'], 'png');  clearvars Ax1 Ax2 Ax3 Ax4  close(figure(16));        262  G.3 Post-Processing and Plotting Scripts and Functions This codes starts by loading up the data clusters again, and produces meaningful data out of the raw data. It calculates spectral contents of the motions (Wickramarachi, 2003), forces, moments, displacements, plot curves, examines the polarities, performs modal analysis, and generates necessary plots.  close all clear clc  File_Name = 'Wall-2_Run-4_GM-1@150%'; load (File_Name) clearvars Input_Acceleration_Data_File_Name Input_Strain_Gage_Data_File_Name Input_String_Pods_Data_File_Name Output_File_Name No_of_Channels = {'Accelerometer', 'String Pod', 'Strain Gage'; 'Acceleration', 'Displacement', 'Strain';9,8,8};  data = Data_SP_All;  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Calculating the duration & Frequency range of the record %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% [Row, Col] = size(data); Data_freq = 1/Time_Step_Sec; Duration_of_Rec = Row * Time_Step_Sec; Freq_Step = 1/Duration_of_Rec; Freq_Domain = Freq_Step * Row; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Raw_Time (:,1) = table2array(data (:,1)); GM_Duration = max(Raw_Time(:,1)) - min(Raw_Time(:,1)); Time_Temp = datevec (Raw_Time); Time = zeros(Row,1); for i=1:Row     Time(i,1)=(Time_Temp(i,4)*60*60)+(Time_Temp(i,5)*60)+(Time_Temp(i,6)); end Time (:,1) = Time (:,1) - min(Time(:,1)); Time = zeros(Row,1); for i=1:Row      Time (i,1) = (i-1)*Time_Step_Sec;  end clearvars Time_Temp i 263  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Cleaning up and plotting the String Pod (Displacement) Data %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  SP_CN = 5;  %% Set the decimation and filering orders here: %%% PreFilt_Decimation_Order = 1; PostFilt_Decimation_Order = 2; Smoothing_Step = 12;  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Best result is when Pre_Dec is 2, Post_Dec is 4, & Smoothing step is 12 %% Also, Filter_Order 9 and Cut_Off_Freq is 1.5 Hz, best results %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% If designing a "moving average filter" use: %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  Filter_WindowSize = 12; bb = (1/Filter_WindowSize)*ones(1,Filter_WindowSize); aa = 1; freqz (bb,aa)                                                 264  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% If designing a "Low Pass Butterworth Filter" use: %%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  Filter_Order = 9; Cut_Off_Freq = 2.5; Filter_Type = 'low' Filter_Type = 'high' Wn = Cut_Off_Freq/(Freq_Domain/2); [b,a] = butter (Filter_Order, Wn, Filter_Type); freqz (b,a)          %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%  d = fdesign.lowpass; %%%  Lowpass = design(d,'butter','matchexactly','stopband','SystemObject',true); %%%  fvtool(Lowpass); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 265  Raw_SP_All = zeros(Row,Col-1); Dec_SP_All = zeros(Row/PreFilt_Decimation_Order,Col-1); Filt_Dec_SP_All = zeros(Row/PreFilt_Decimation_Order,Col-1); Dec_Filt_Dec_SP_All = zeros(Row/PreFilt_Decimation_Order/PostFilt_Decimation_Order,Col-1); Smth_Dec_Filt_Dec_SP_All = zeros(Row/PreFilt_Decimation_Order/PostFilt_Decimation_Order,Col-1);  for i=1:table2array (No_of_Channels(3,2))          Raw_SP_All (:,i) = table2array(data (:,i+1));     Dec_SP_All (:,i) = decimate (Raw_SP_All(:,i), PreFilt_Decimation_Order);     Filt_Dec_SP_All (:,i) = filter (b, a, Dec_SP_All(:,i));     Dec_Filt_Dec_SP_All (:,i) = decimate (Filt_Dec_SP_All(:,i), PostFilt_Decimation_Order);     Smth_Dec_Filt_Dec_SP_All (:,i) = smooth (Dec_Filt_Dec_SP_All (:,i), Smoothing_Step);      End  PreFilt_Dec_Time = decimate(Time, PreFilt_Decimation_Order); PostFilt_Dec_Time = decimate(PreFilt_Dec_Time, PostFilt_Decimation_Order); Max_SP_Before = max (Raw_SP_All(:,SP_CN)) Max_SP_After = max  (Smth_Dec_Filt_Dec_SP_All(:,SP_CN)) Min_SP_Before = min (Raw_SP_All(:,SP_CN)) Min_SP_After = min  (Smth_Dec_Filt_Dec_SP_All(:,SP_CN)) plot (Time, Raw_SP_All(:,SP_CN)) plot (PreFilt_Dec_Time, Dec_SP_All(:,SP_CN)) plot (PreFilt_Dec_Time, Filt_Dec_SP_All(:,SP_CN)) plot (PostFilt_Dec_Time, Dec_Filt_Dec_SP_All(:,SP_CN)) plot (PostFilt_Dec_Time, Smth_Dec_Filt_Dec_SP_All(:,SP_CN)) Displ1 = Raw_SP_All(:,6) - Raw_SP_All (:,1); Displ2 = Dec_SP_All(:,6) - Dec_SP_All (:,1); Displ3 = Filt_Dec_SP_All(:,6) - Filt_Dec_SP_All (:,1); Displ4 = Dec_Filt_Dec_SP_All(:,6) - Dec_Filt_Dec_SP_All (:,1); Displ5 = Smth_Dec_Filt_Dec_SP_All(:,6) - Smth_Dec_Filt_Dec_SP_All (:,1); Max_Displ_Before = max (Displ1(:,1)) Max_Displ_After = max  (Displ5(:,1)) Min_Displ_Before = min (Displ1(:,1)) Min_Displ_After = min  (Displ5(:,1)) plot (Time,Displ1) plot (PreFilt_Dec_Time, Displ2) plot (PreFilt_Dec_Time, Displ3) plot (PostFilt_Dec_Time, Displ4) plot (PostFilt_Dec_Time, Displ5) plot (Displ2, Displ3); plot (Displ4, Displ5);  266          267     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Raw_SP_All(:,1) = fft(Raw_SP_All(:,SP_CN)); AMPL_FFT_Raw_SP_All(:,1) = abs(FFT_Raw_SP_All(:,1)); PSD_Raw_SP_All(:,1) = pwelch(Raw_SP_All(:,SP_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Dec_SP_All(:,1) = fft(Dec_SP_All(:,SP_CN)); AMPL_FFT_Dec_SP_All(:,1) = abs(FFT_Dec_SP_All(:,1)); PSD_Dec_SP_All(:,1) = pwelch(Dec_SP_All(:,SP_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Filt_Dec_SP_All(:,1) = fft(Filt_Dec_SP_All(:,SP_CN)); AMPL_FFT_Filt_Dec_SP_All(:,1) = abs(FFT_Filt_Dec_SP_All(:,1)); PSD_Filt_Dec_SP_All(:,1) = pwelch(Filt_Dec_SP_All(:,SP_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Dec_Filt_Dec_SP_All(:,1) = fft(Dec_Filt_Dec_SP_All(:,SP_CN)); AMPL_FFT_Dec_Filt_Dec_SP_All(:,1) = abs(FFT_Dec_Filt_Dec_SP_All(:,1)); PSD_Dec_Filt_Dec_SP_All(:,1) = pwelch(Dec_Filt_Dec_SP_All(:,SP_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Smth_Filt_Dec_SP_All(:,1) = fft(Smth_Dec_Filt_Dec_SP_All(:,SP_CN)); AMPL_FFT_Smth_Dec_Filt_Dec_SP_All(:,1) = abs(FFT_Smth_Filt_Dec_SP_All(:,1)); PSD_Smth_Dec_Filt_Dec_SP_All(:,1) = pwelch(Smth_Dec_Filt_Dec_SP_All(:,SP_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  268  for k = 1:Row/PreFilt_Decimation_Order/PostFilt_Decimation_Order/10          X (k, 1) = k * Freq_Step;     Y1 (k, 1) = AMPL_FFT_Dec_SP_All(k,1);     Y2 (k, 1) = AMPL_FFT_Filt_Dec_SP_All(k,1);     Y3 (k, 1) = AMPL_FFT_Dec_Filt_Dec_SP_All(k,1);     Y4 (k, 1) = AMPL_FFT_Smth_Dec_Filt_Dec_SP_All(k,1);      end plot (X, Y1) plot (X, Y2) plot (X, Y3) plot (X, Y4) clearvars X k; [Row_Temp, ~] = size(PSD_Dec_SP_All); for k = 1:Row_Temp/PostFilt_Decimation_Order/6          X (k, 1) = k * Freq_Step;     Y5 (k, 1) = PSD_Dec_SP_All (k,1);     Y6 (k, 1) = PSD_Filt_Dec_SP_All (k,1);     Y7 (k, 1) = PSD_Dec_Filt_Dec_SP_All (k,1);     Y8 (k, 1) = PSD_Smth_Dec_Filt_Dec_SP_All (k,1);      end plot (X, Y5) plot (X, Y6) plot (X, Y7) plot (X, Y8) clearvars data k Row_Temp Col_Temp X Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8;                    269  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Cleaning up, filtering, and Plotting the Acceleration Data %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clearvars data Smoothing_Step PostFilt_Decimation_Order PreFilt_Decimation_Order clearvars FFT_Dec_Accel_All FFT_Dec_Filt_Dec_Accel_All FFT_Filt_Dec_Accel_All FFT_Raw_Accel_All clearvars AMPL_FFT_Dec_Accel_All AMPL_FFT_Dec_Filt_Dec_Accel_All AMPL_FFT_Filt_Dec_Accel_All  clearvars PSD_Dec_Accel_All PSD_Dec_Filt_Dec_Accel_All PSD_Filt_Dec_Accel_All PSD_Raw_Accel_All clearvars AMPL_FFT_Raw_Accel_All Filter_Order Cut_Off_Freq b a aa bb X Y i clearvars Dec_Displ5 A_up A_lo D_up D_lo Filter_Order Cut_Off_Freq close all data = Data_ACC_All; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Designing a "Low Pass Butterworth Filter": %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Filter_Order = 9; Cut_Off_Freq = 55; [b, a] = butter (Filter_Order, Cut_Off_Freq/(Freq_Domain/2),'low');  freqz (b,a) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% If designing a "moving average filter," use: %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Filter_WindowSize = 5; aa = (1/Filter_WindowSize)*ones(1,Filter_WindowSize);  bb = 1; freqz (bb,aa) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Accel_CN = 1; %% Set the decimation and filering orders here: PreFilt_Decimation_Order = 1; PostFilt_Decimation_Order = 2; Smoothing_Step = 1; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Raw_Accel_All = zeros(Row,Col-1); Dec_Accel_All = zeros(Row/PreFilt_Decimation_Order,Col-1); Filt_Dec_Accel_All = zeros(Row/PreFilt_Decimation_Order,Col-1); Dec_Filt_Dec_Accel_All = zeros(Row/PreFilt_Decimation_Order/PostFilt_Decimation_Order,Col-1); Smth_Dec_Filt_Dec_Accel_All = zeros(Row/PreFilt_Decimation_Order/PostFilt_Decimation_Order,Col-1); for i=1:table2array (No_of_Channels(3,1))          Raw_Accel_All (:,i) = table2array(data (:,i+1));     Dec_Accel_All (:,i) = decimate (Raw_Accel_All(:,i), PreFilt_Decimation_Order);     Filt_Dec_Accel_All (:,i) = filter (b, a, Dec_Accel_All(:,i)); 270      Dec_Filt_Dec_Accel_All (:,i) = decimate (Filt_Dec_Accel_All(:,i), PostFilt_Decimation_Order);     Smth_Dec_Filt_Dec_Accel_All (:,i) = smooth (Dec_Filt_Dec_Accel_All (:,i), Smoothing_Step);      end PreFilt_Dec_Time = decimate(Time, PreFilt_Decimation_Order); PostFilt_Dec_Time = decimate(PreFilt_Dec_Time, PostFilt_Decimation_Order); Max_ACC_Before = max (Raw_Accel_All(:,Accel_CN)) Max_ACC_After = max  (Filt_Dec_Accel_All(:,Accel_CN)) Min_ACC_Before = min (Raw_Accel_All(:,Accel_CN)) Min_ACC_After = min  (Filt_Dec_Accel_All(:,Accel_CN)) plot (Time, Raw_Accel_All(:,Accel_CN)) plot (PreFilt_Dec_Time, Dec_Accel_All(:,Accel_CN)) plot (PreFilt_Dec_Time, Filt_Dec_Accel_All(:,Accel_CN)) plot (PostFilt_Dec_Time, Dec_Filt_Dec_Accel_All(:,Accel_CN)) plot (PostFilt_Dec_Time, Smth_Dec_Filt_Dec_Accel_All(:,Accel_CN))     d = fdesign.lowpass;     Lowpass = design(d,'butter','matchexactly','stopband','SystemObject',true);     fvtool(Lowpass);    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Raw_Accel_All(:,1) = fft(Raw_Accel_All(:,Accel_CN)); AMPL_FFT_Raw_Accel_All(:,1) = abs(FFT_Raw_Accel_All(:,1)); PSD_Raw_Accel_All(:,1) = pwelch(Raw_Accel_All(:,Accel_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Dec_Accel_All(:,1) = fft(Dec_Accel_All(:,Accel_CN)); AMPL_FFT_Dec_Accel_All(:,1) = abs(FFT_Dec_Accel_All(:,1)); PSD_Dec_Accel_All(:,1) = pwelch(Dec_Accel_All(:,Accel_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Filt_Dec_Accel_All(:,1) = fft(Filt_Dec_Accel_All(:,Accel_CN)); AMPL_FFT_Filt_Dec_Accel_All(:,1) = abs(FFT_Filt_Dec_Accel_All(:,1)); PSD_Filt_Dec_Accel_All(:,1) = pwelch(Filt_Dec_Accel_All(:,Accel_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Dec_Filt_Dec_Accel_All(:,1) = fft(Dec_Filt_Dec_Accel_All(:,Accel_CN)); AMPL_FFT_Dec_Filt_Dec_Accel_All(:,1) = abs(FFT_Dec_Filt_Dec_Accel_All(:,1)); PSD_Dec_Filt_Dec_Accel_All(:,1) = pwelch(Dec_Filt_Dec_Accel_All(:,Accel_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Smth_Filt_Dec_Accel_All(:,1) = fft(Smth_Dec_Filt_Dec_Accel_All(:,Accel_CN)); AMPL_FFT_Smth_Dec_Filt_Dec_Accel_All(:,1) = abs(FFT_Smth_Filt_Dec_Accel_All(:,1)); PSD_Smth_Dec_Filt_Dec_Accel_All(:,1) = pwelch(Smth_Dec_Filt_Dec_Accel_All(:,Accel_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   271  for k = 1:Row/PreFilt_Decimation_Order/PostFilt_Decimation_Order          X (k, 1) = k * Freq_Step;     Y1 (k, 1) = AMPL_FFT_Dec_Accel_All(k,1);     Y2 (k, 1) = AMPL_FFT_Filt_Dec_Accel_All(k,1);     Y3 (k, 1) = AMPL_FFT_Dec_Filt_Dec_Accel_All(k,1);     Y4 (k, 1) = AMPL_FFT_Smth_Dec_Filt_Dec_Accel_All(k,1);      end plot (X, Y1) plot (X, Y2) plot (X, Y3) plot (X, Y4) clearvars X k; [Row_Temp, ~] = size(PSD_Dec_Accel_All); for k = 1:Row_Temp/PostFilt_Decimation_Order          X (k, 1) = k * Freq_Step;     Y5 (k, 1) = PSD_Dec_Accel_All (k,1);     Y6 (k, 1) = PSD_Filt_Dec_Accel_All (k,1);     Y7 (k, 1) = PSD_Dec_Filt_Dec_Accel_All (k,1);     Y8 (k, 1) = PSD_Smth_Dec_Filt_Dec_Accel_All (k,1);      end plot (X, Y5) plot (X, Y6) plot (X, Y7) plot (X, Y8) clearvars k Row_Temp Col_Temp X Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8;      272  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% close all plot (Displ1, Raw_Accel_All (:,5)) plot (Displ4, Dec_Filt_Dec_Accel_All (:,5)) plot (Displ5, Smth_Dec_Filt_Dec_Accel_All (:,5)) plot(Displ5) plot(Smth_Dec_Filt_Dec_Accel_All(:,6)) %%% Look at i = 1500:2500 in W2-R4 record for damped motion for i = 1500:2500     X (i,1) = Displ5 (i+40,1);     Y (i,1) = Smth_Dec_Filt_Dec_Accel_All (i,5); end plot (X,Y, 'color','red'); hold on clearvars X Y i TEMP_Excel_Data                273  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%% Calculating the envelope of the values: %%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% envelope (Smth_Dec_Filt_Dec_Accel_All (:,Accel_CN), 100, 'peak') hold off [D_up,D_lo] = envelope (Smth_Dec_Filt_Dec_SP_All (:,SP_CN), 500, 'peak'); [A_up,A_lo] = envelope (Smth_Dec_Filt_Dec_Accel_All (:,Accel_CN), 80, 'peak');        plot (PostFilt_Dec_Time, A_up, PostFilt_Dec_Time,A_lo, 'color', [1,0.5,0.5]) xlabel('Time (Sec)','Color', 'b', 'FontSize', 12); ylabel('Acceleration (g)','Color', 'b', 'FontSize', 12); title (['\fontsize{12} \bf \color{magenta} Acceleration Time-History Signal with Envelopes, Recorded on LST for GM-1 @ 100%']); legend({['\rm \color{black} Max = ' num2str(Max_ACC_Before) ' g'] ; ['\rm \color{black} Min = ' num2str(Min_ACC_Before) ' g']}, 'Location','northwest', 'FontSize', 10); hold on plot (PostFilt_Dec_Time, Smth_Dec_Filt_Dec_Accel_All (:,Accel_CN),'DisplayName',' Time-History', 'LineWidth',0.5,'Color',[0,0.6,1]) set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '-'); grid(gca,'minor'); hold off plot (PostFilt_Dec_Time,D_up,PostFilt_Dec_Time,D_lo, 'color', [1,0.5,0.5]) xlabel('Time (Sec)','Color', 'b', 'FontSize', 12); ylabel('Displacement (mm)','Color', 'b', 'FontSize', 12); 274  title (['\fontsize{12} \bf \color{magenta} Displacement Time-History Signal with Envelopes, Reocrded on LST for GM-1 @ 100%']); legend({['\rm \color{black} Max = ' num2str(Max_SP_Before) ' mm'] ; ['\rm \color{black} Min = ' num2str(Min_SP_Before) ' mm']}, 'Location','northwest', 'FontSize', 10); hold on plot (PostFilt_Dec_Time, Smth_Dec_Filt_Dec_SP_All (:,SP_CN),'DisplayName',' Time-History', 'LineWidth',0.5,'Color',[0,0.6,1]) set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '-'); grid(gca,'minor'); hold off plot (D_up, A_up) plot (D_lo, A_lo)    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     275  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% Calculation of the actual wall's recorded base shear %%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clearvars i Height_Vector Mass_Vector %% Generating the walls' height (in m) and mass (in kg) vetors Height_Vector = [0.3;0.7;1.1;1.5;1.9;2.3;2.7]; %%% from table to accelerometers if ID_Wall == 1 || ID_Wall == 3 || ID_Wall == 5          Mass_Vector = [200;160;160;160;160;160;120]; %%% 20mm Double-Sided      elseif ID_Wall == 2 || ID_Wall == 4 || ID_Wall == 6          Mass_Vector = [182;146;146;146;146;146;110]; %%% 20mm Single-Sided      else          'Unable to create mass vector; please assign manually ...'      end %% Calculating forces and moments at the location of each of the 7 accelerometers [Col_Temp,~] = size (Mass_Vector); [Row_Temp,~] = size (Smth_Dec_Filt_Dec_Accel_All(:,1)); Floor_Shears_TH = zeros(Row_Temp,Col_Temp); Floor_OTM_TH = zeros(Row_Temp,Col_Temp); Base_Shear_TH = zeros(Row_Temp,1); %% Time History (TH) of the floor shears TH and the overall base shear force TH (in KN) for i=1:Col_Temp          Floor_Shears_TH (:,i) = Mass_Vector (i,1)*9.80665*Smth_Dec_Filt_Dec_Accel_All (:,i+1)/1000;     Base_Shear_TH (:,1) = Base_Shear_TH (:,1) + Floor_Shears_TH (:,i);        end plot (PostFilt_Dec_Time, Floor_Shears_TH) plot (PostFilt_Dec_Time, Base_Shear_TH) %% Overturning Moment (OTM) at each accelerometer and the overal OTM (in KN.m) Floor_OTM_TH (:,1) = Height_Vector (1,1) * Floor_Shears_TH (:,1); for i=2:Col_Temp          Floor_OTM_TH(:,i)=Floor_OTM_TH(:,i-1)+(Height_Vector(i,1)*Floor_Shears_TH(:,i));      end Base_OTM_TH = 2.8/2 * Base_Shear_TH; plot (PostFilt_Dec_Time, Floor_OTM_TH) plot (PostFilt_Dec_Time, Floor_OTM_TH(:,7)) plot (PostFilt_Dec_Time, Base_OTM_TH) 276  plot (Base_OTM_TH,Floor_OTM_TH(:,7)) clearvars i Row_Temp Col_Temp          277  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% Calculation of hystoresis loops from the base shear %%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clearvars Moment_Rotation i Force_Displ Force Moment Hyst_Data Hyst_Data_Sorted Force_Drift Dec_Fact = 1; Rel_Displ_All = decimate((Smth_Dec_Filt_Dec_SP_All - Smth_Dec_Filt_Dec_SP_All(:,1)), Dec_Fact); Rel_Displ_Mid = Rel_Displ_All(:,5); Force = decimate(Base_Shear_TH(:,1),Dec_Fact); Moment = decimate(Floor_OTM_TH(:,7),Dec_Fact); Time_Vector = decimate (PostFilt_Dec_Time(:,1),Dec_Fact); Hyst_Data (:,1) = Time_Vector(:,1); Hyst_Data (:,2) = Rel_Displ_Mid(:,1); Hyst_Data (:,3) = Force(:,1); Hyst_Data_Sorted = sortrows(Hyst_Data,1,'descend'); Hyst_Data_Sorted = sortrows(Hyst_Data,1); plot (Hyst_Data_Sorted(:,2), Hyst_Data_Sorted(:,3)) scatter(Hyst_Data_Sorted(:,2),Hyst_Data_Sorted(:,3))          278  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% force-displacement and force-drift calculations %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Force_Displ (:,1) = sortrows(Rel_Displ_Mid,1); Force_Displ (:,2) = sortrows(Force,1); figure(1) plot(Force_Displ(:,1),Force_Displ (:,2)) xlabel('Displacement (mm)','Color', 'b'); xlim([0.02,50]); axis 'on' ylabel('Base Shear (KN)','Color', 'b'); ylim([0.02,50]); title('Force-Displacement Diagram','FontSize',12,'Color', 'r'); legend({['\rm \color{red} Peak Displacement = ' num2str(max(abs(max(Raw_SP(:,1))), abs(min(Raw_SP(:,1))))) ' mm']}, 'Location','northeast', 'FontSize', 8); set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '--'); grid(gca,'minor'); saveas (figure(1), ['Figures_Tez\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-' num2str(i-1)]); saveas (figure(1), ['Figures_Tez\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-' num2str(i-1)], 'svg'); saveas (figure(1), ['Figures_Tez\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-' num2str(i-1)], 'pdf'); saveas (figure(1), ['Figures_Tez\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-' num2str(i-1)], 'png'); close(figure(1)); Force_Drift (:,1) = sortrows(Rel_Displ_Mid,1)*100/1400; Force_Drift (:,2) = sortrows(Force,1); figure(2) plot(Force_Displ(:,1),Force_Displ (:,2)) xlabel('Drift (%)','Color', 'b'); ylabel('Base Shear (KN)','Color', 'b'); title('Base Shear vs. Drift','FontSize',12,'Color', 'r'); set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '--'); grid(gca,'minor'); saveas (figure(2), ['Figures_Tez\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-' num2str(i-1)]); saveas (figure(2), ['Figures_Tez\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-' num2str(i-1)], 'svg'); 279  saveas (figure(2), ['Figures_Tez\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-' num2str(i-1)], 'pdf'); saveas (figure(2), ['Figures_Tez\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-' num2str(i-1)], 'png'); close(figure(2)) figure(3) plot(Moment,Force) xlabel('Overturning Moment (KN.m)','Color', 'b'); ylabel('Base Shear (KN)','Color', 'b'); title('Base Shear (KN) vs. Overturning Moment (KN.m)','FontSize',12,'Color', 'r'); set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '--'); grid(gca,'minor');               280        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Moment-Base Rotation and Moment-Curvature calculations %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Moment_Rotation (:,1) = atan (sortrows(Rel_Displ_Mid,1)/1400) * (180/pi()); Moment_Rotation (:,2) = sortrows(Moment,1); figure(4) plot(Moment_Rotation(:,1),Moment_Rotation(:,2)) xlabel('Base Rotation (degrees)','Color', 'b'); ylabel('Overturning Moment (KN.m)','Color', 'b'); title('Overturning Moment (KN.m) vs. Base Rotation (degrees)','FontSize',12,'Color', 'r'); set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '--'); grid(gca,'minor'); %% Mathematically calculating the curvature in units of 1/m %%% Curvature (:,1) = (asin ((Rel_Displ_All(:,2) - Rel_Displ_All(:,1))/300))/0.3; for i=2:7     Curvature (:,i) = (asin ((Rel_Displ_All(:,i+1) - Rel_Displ_All(:,i))/400))/0.4; end Curvature (:,8) = (asin ((0 - Rel_Displ_All(:,1))/100))/0.1; %% Calculating the weighted average of the wall curvature in units of 1/m %%% Curvature_Average (:,1) = Rel_Displ_All(:,1); %%% Since the first column is all zeros Curvature_Average (:,1) = Curvature_Average (:,1) + (Curvature (:,1)*3/28); for i=2:7     Curvature_Average (:,1) = Curvature_Average (:,1) + (Curvature (:,i)*4/28); end Curvature_Average (:,1) = Curvature_Average (:,1) + (Curvature (:,8)*1/28); 281  %% Ploting moment-curvature hystoresis loops %%% plot (Curvature_Average,Moment) xlabel('Curvature (1/m)','Color', 'b'); ylabel('Moment (KN.m)','Color', 'b'); title('Moment-Curvature Hytoresis Loop','FontSize',12,'Color', 'r'); set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '--'); grid(gca,'minor'); Moment_Curvature (:,1) = sortrows(Curvature_Average,1); Moment_Curvature (:,2) = sortrows(Moment,1); figure(6) plot(Moment_Curvature(:,1),Moment_Curvature(:,2)) xlabel('Curvature (1/m)','Color', 'b'); ylabel('Moment (KN.m)','Color', 'b'); title('Moment-Curvature Diagram','FontSize',12,'Color', 'r'); set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '--'); grid(gca,'minor');             282  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Calculations and ploting the displacement traces along the wall height %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% close all [Row_Temp, Col_Temp] = size(Rel_Displ_All); Wall_Height = [0, 0.3, 0.7, 1.1, 1.5, 1.9, 2.3, 2.7, 2.8]; figure(6) %% i = 13300:13400 for W2-R4 gives max %% i = 18083:18086 for Double Curvature Bending Senario at W2-R4 %% i = 8096:8103 for Double Curvature Bending Senario at W2-R2 %% i = 8130:8135 for Multiple Curvatures Senario for W2-R3 for i = 13300:13400       Wall_Displ =  [Rel_Displ_All(i,1), Rel_Displ_All(i,2), Rel_Displ_All(i,3), Rel_Displ_All(i,4), Rel_Displ_All(i,5), Rel_Displ_All(i,6), Rel_Displ_All(i,7), Rel_Displ_All(i,8), 0];     Wall_Accel =  [Smth_Dec_Filt_Dec_Accel_All(i,1), Smth_Dec_Filt_Dec_Accel_All(i,2), Smth_Dec_Filt_Dec_Accel_All(i,3), Smth_Dec_Filt_Dec_Accel_All(i,4), Smth_Dec_Filt_Dec_Accel_All(i,5), Smth_Dec_Filt_Dec_Accel_All(i,6), Smth_Dec_Filt_Dec_Accel_All(i,7), Smth_Dec_Filt_Dec_Accel_All(i,8), 0];     hold on     plot(Wall_Displ, Wall_Height, '-s')     plot(Wall_Accel, Wall_Height, '-s')     hold off end xlabel('Absolute Acceleration (g)','Color', 'b','FontSize',12); ylabel('Wall Height (m)','Color', 'b','FontSize',12); title('Acceleration Trace Over the Height for Wall-2 at Run-4','FontSize',14,'Color', 'm'); legend('\rm \color{red} Wall-2 at Run-4', 'Location','northeast'); set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '--'); grid(gca,'minor'); axis([-80 80 0 3.0], 'vis3d'); clearvars Row_Temp Col_Temp               283  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Quick check for curvature change throughout the height of the wall %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% [Row_Temp,~]=size(Curvature) Pol_Check = zeros(Row_Temp,1); Indicator = zeros (Row_Temp,1); Counter_Pos = 0; Counter_Neg = 0; for i=1:Row_Temp     Pol_Check (i,1) = Curvature(i,2)*Curvature(i,3)*Curvature(i,4)*Curvature(i,5)*Curvature(i,6)*Curvature(i,7);     if Pol_Check (i,1)>0         Indicator (i,1) = 11;         Counter_Pos = Counter_Pos + 1;     elseif Pol_Check (i,1)<0         Indicator (i,1) = 99;         Counter_Neg = Counter_Neg + 1;     end end Counter_Pos Counter_Neg plot (Indicator) clearvars Row_Temp Pol_Check Indicator Counter_Neg Counter_Pos  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Free-Vibration Assesment to find Wall's Fundamental Dynamic Properties %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clearvars X Y Y_mg TEMP_Excel_Data AMPL_FFT_Y FFT_Y PSD_Y TEMP_Freq_Vector clearvars TEMP_FDD FFT_Y TEMP_Freq_Vector AMPL_FFT_Y close all %% find an issolated free vibration cycle %% NOTE: for W2-R4 range 3000:3500 is good for force-displ %% NOTE: for W2-R4 range 3000:3600 is good for free vibration %% NOTE: for W2-R4 range 5843:6197 is good for forced vibration Range_L = 5843; Range_H = 6197; for i = Range_L:Range_H     X (i+1-Range_L,1) = Displ5 (i,1);     Y (i+1-Range_L,1) = Smth_Dec_Filt_Dec_Accel_All (i,5); end X (Range_H-Range_L+1,1) = 0; Y (Range_H-Range_L+1,1) = 0; [Row_Temp,~] = size(X); TEMP_Time_Vector = zeros(Row_Temp, 1); for i=1:Row_Temp     TEMP_Time_Vector (i,1) = (i-1)*Time_Step_Sec*2; %(Duration_of_Rec/Row_Temp);  end 284  TEMP_Time_Vector = flip (TEMP_Time_Vector); Y_mg = Y*1000; %%% Accelerations in mili g Y_mg = flip(Y*1000); %%% changing units from g to mili g and order reversed TEMP_Excel_Data(:,1) = TEMP_Time_Vector(:,1); TEMP_Excel_Data(:,2) = X(:,1); TEMP_Excel_Data(:,3) = Y_mg(:,1); plot (TEMP_Time_Vector,X); figure(6) plot (TEMP_Time_Vector,Y_mg); xlabel('\fontsize{12} \bf Time (Sec)','Color', 'b'); ylabel('\fontsize{12} \bf Acceleration (mg)','Color', 'b'); title ({['\fontsize{14} \bf \color{magenta} Mid-Height Free Vibration for Wall-2 | Run-4'] ; ['\fontsize{10} \rm \color{black} (Max Accel. = ' num2str(max(Y_mg(:,1))) ' mg | Min Accel. = ' num2str(min(Y_mg(:,1))) ' mg | Median = ' num2str(median((Y_mg(:,1)))) ' mg)']}); legend({['\rm \color{red} Acceleration Trace from 30th to 36th Second of Run-4']}, 'Location','northeast', 'FontSize', 9); set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '--'); grid(gca,'minor'); %% plot (X,Y); figure(7) plot (X,Y_mg); xlabel('\fontsize{12} \bf Time (Sec)','Color', 'b'); ylabel('\fontsize{12} \bf Acceleration (mg)','Color', 'b'); title ({['\fontsize{13} \bf \color{magenta} One Isolated Free Vibration Cycle for Wall-2 from Run-4'] ; ['\fontsize{10} \rm \color{black} (Max Accel. = ' num2str(max(Y_mg(:,1))) ' mg | Min Accel. = ' num2str(min(Y_mg(:,1))) ' mg | Median = ' num2str(median((Y_mg(:,1)))) ' mg)']}); legend({['\rm \color{red} Acceleration Trace in mg']}, 'Location','northeast', 'FontSize', 9); set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '--'); grid(gca,'minor'); createfigure (TEMP_Time_Vector,Y) createfigure (X,Y_mg)               285  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Plotting FFT and PSD for the Free Vibration Records%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Y = fft(Y); AMPL_FFT_Y = abs(FFT_Y); for i=1:Row_Temp/2     TEMP_Freq_Vector (i,1) = (i-1)*(Freq_Domain/2/Row_Temp); %%Decimation     TEMP_FDD (i,1) = AMPL_FFT_Y (i,1); end plot(TEMP_Freq_Vector, TEMP_FDD, 'color',[1 0.5 0.3],'LineWidth',1) xlabel('\fontsize{12} \bf Frequency (Hz)','Color', 'b'); ylabel('\fontsize{12} \bf Power Spectural Density Amplitue (RMS)','Color', 'b'); title ({['\fontsize{14} \bf \color{magenta} Frequency Domain Decomposition from Wall-2 | Run-4']}); legend({['\rm \color{red} PSD for 30th to 36th Sec of Run-4']}, 'Location','northeast', 'FontSize', 9); set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '--'); xlim([0,50]); grid(gca,'minor'); clearvars X Y Y_mg i           286  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Ploting Force-Displ in Free Vibration %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for i = Range_L:Range_H          X (i+1-Range_L,1) = Rel_Displ_Mid (i,1);     Y (i+1-Range_L,1) = Force (i,1);      end Y = Y*1000; %%% changing units from KN to N Y = flip(Y*1000); %%% changing units from KN to N and recerse order figure(8) plot (X,Y); xlabel('\fontsize{12} \bf Displacement (mm)','Color', 'b'); ylabel('\fontsize{12} \bf Force (N)','Color', 'b'); title ({['\fontsize{13} \bf \color{magenta} Damped Force-Displacement Cycle for Wall-2 at Run-4'] ; ['\fontsize{10} \rm \color{black} (Max F = ' num2str(max(Y(:,1))) ' N | Min F = ' num2str(min(Y(:,1))) ' N | Median = ' num2str(median((Y(:,1)))) ' N)']}); legend({['\rm \color{red} Trace from 30th to 36th Sec of Run-4']}, 'Location','northeast', 'FontSize', 9); set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '--'); grid(gca,'minor'); clearvars X Y i Range_L Range_H TEMP_Time_Vector %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     287  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% Calculation Spectural Content of the ground motion %%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  Data_CH_Spect = 9; Ground_Motion_Record (:,1) = Raw_Accel_All(:,Data_CH_Spect); Ground_Displacement_Record (:,1) = Raw_SP_All(:,8);  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Calculation Spectural Content of the ground motion for Simple SDF %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Set the time step of the input acceleration time history dt=Time_Step_Sec; %% Set the input acceleration time history in units of g xgtt = Ground_Motion_Record (:,1); %% Set the eigenperiod of an ideally zero-stiffness SDOF oscillator,  %% -> in order to calculate the maximum velocity of the earthquake Tsoft=1000; %% Set the eigenperiod range for which the response spectra will be calculated Tspectra=logspace(log10(0.02),log10(50),1000)'; %% Set three distinct values for the critical damping ratio of the  %% response spectra to be calculated -> i.e. 0, 0.05, 0.1 (or 0%, 5%, 10%) ksi1=0; ksi2=0.05; ksi3=0.1; %% Set the minimum absolute value of the eigenvalues of the amplification matrix rinf=1; %% Set the algorithm to be used for the integration AlgID='U0-V0-Opt'; %% Set the initial displacement of all SDOF oscillators analysed u0=0; %% Set the initial velocity of all SDOF oscillators analysed ut0=0;  %%%%%%%%%%%%%%%%% %% Processing %%% %%%%%%%%%%%%%%%%% %% Take the maximum ground acceleration maxxgtt=max(abs(xgtt));  %% Calculation of the maximum velocity of the earthquake [~,~,~,maxxgt,~]=LERS(dt,xgtt,Tsoft,0); %% Find maximum ground displacemeent directly from signal (in units of m) maxxg = max(abs(Ground_Displacement_Record))/1000; %% Extraction of the elastic response spectra and pseudospectra  %% -> for the three values of the critical damping ratio [PSa1,PSv1,Sd1,Sv1,Sa1]=LERS(dt,xgtt,Tspectra,ksi1); [PSa2,PSv2,Sd2,Sv2,Sa2]=LERS(dt,xgtt,Tspectra,ksi2); [PSa3,PSv3,Sd3,Sv3,Sa3]=LERS(dt,xgtt,Tspectra,ksi3); 288  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Plot acceleration and pseudo acceleration spectra for critical damping of 5%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure('Name','Accel. & Pseudo Accel. Spectra','NumberTitle','off') semilogx(Tspectra,Sa2/maxxgtt,'-b','LineWidth',1.) hold on semilogx(Tspectra,PSa2/maxxgtt,'-r','LineWidth',1.) hold off grid on xlabel('T_n (Sec)','FontSize',14); ylabel('S_A/max_a  or  PS_A/max_a','FontSize',14); title('\bf Accel. & Pseudo Accel. Spectra for \xi = 5%','color','m','FontSize',14) xlim([0.02,50]); legend('S_A/maxa','PS_A/maxa') lgd.FontSize = 12; lgd.FontWeight = 'bold'; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Plot relative velocity and pseudo velocity spectra for critical damping of 5%         %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure('Name','Relative Velocity & Pseudo Velocity Spectra','NumberTitle','off') semilogx(Tspectra,Sv2/maxxgt,'-b','LineWidth',1.) hold on semilogx(Tspectra,PSv2/maxxgt,'-r','LineWidth',1.) hold off grid on xlabel('T_n (Sec)','FontSize',14); ylabel('S_V/max_v  or  PS_V/max_v','FontSize',14); title('\bf Relative & Pseudo Velocity Spectra for \xi = 5%','color','m','FontSize',14) xlim([0.02,50]); legend('S_V/maxv','PS_V/maxv') lgd.FontSize = 12; lgd.FontWeight = 'bold'; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Plot Deormation Responce Spectrum for critical damping of 5% %%%                  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure('Name','Deformation Responce Spectrum','NumberTitle','off') semilogx(Tspectra,Sd2*10/maxxg,'-b','LineWidth',1.) grid on xlabel('T_n (Sec)','FontSize',14); ylabel('S_D/max_d','FontSize',14); title('\bf Deformation Responce Spectrum for \xi = 5%','color','m','FontSize',14) xlim([0.02,50]); legend('S_D/maxd','location','northwest') lgd.FontSize = 12; lgd.FontWeight = 'bold';  289  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Plot pseudo-acceleration/acceleration ratio for three critical damping ratios  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure('Name','Pseudo-Accel./Accel. Ratios','NumberTitle','off') semilogx(Tspectra,PSa1./Sa1,'-b','LineWidth',1.) hold on semilogx(Tspectra,PSa2./Sa2,'-r','LineWidth',1.) semilogx(Tspectra,PSa3./Sa3,'-g','LineWidth',1.) hold off grid on xlabel('T_n (Sec)','FontSize',12); ylabel('PS_A/S_A','FontSize',12); title('\bf Pseudo-Accel./Accel. Ratios for \xi = 0%, 5%, 10%','color','m','FontSize',14) xlim([0.02,50]); legend(' \xi = 0.00',' \xi = 0.05',' \xi = 0.10','Location','SouthWest')  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Plot pseudo-velocity/relative velocity ratios for three values of critical damping ratios %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure('Name','Pseudo-Vel./Relative Vel. Ratios','NumberTitle','off') semilogx(Tspectra,PSv1./Sv1,'-b','LineWidth',1.) hold on semilogx(Tspectra,PSv2./Sv2,'-r','LineWidth',1.) semilogx(Tspectra,PSv3./Sv3,'-g','LineWidth',1.) hold off grid on xlabel('T_n (Sec)','FontSize',14); ylabel('PS_V/S_V','FontSize',14); title('\bf Pseudo-Vel./Relative Vel. Ratios for \xi = 0%, 5%, 10%','color','m','FontSize',14) xlim([0.02,50]); legend(' \xi = 0.00',' \xi = 0.05',' \xi = 0.10') lgd.FontSize = 12; lgd.FontWeight = 'bold';  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Plot Deormation Responce Spectra for three values of critical damping ratios  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure('Name','Deformation Responce Spectra','NumberTitle','off') semilogx(Tspectra,Sd1*10/maxxg,'-b','LineWidth',1.) hold on semilogx(Tspectra,Sd2*10/maxxg,'-r','LineWidth',1.) semilogx(Tspectra,Sd3*10/maxxg,'-g','LineWidth',1.) hold off grid on xlabel('T_n (Sec)','FontSize',14); 290  ylabel('S_D/max_d','FontSize',14); title('\bf Def. Responce Spectra for \xi = 0%, 5%, 10%','color','m','FontSize',14) xlim([0.02,50]); legend(' \xi = 0.00',' \xi = 0.05',' \xi = 0.10', 'location','northwest') lgd.FontSize = 12; lgd.FontWeight = 'bold'; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Calculation Spectural Responces for the tested Retrofitted URM Wall %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Set the storey height of the structure in ft. h=16/12; h=2.8; %%% in metric (m) %% Set the number of eigenmodes of the structure, which is equal to the number of its storeys. neig=7; %% Set the lateral stiffness between each two DOFs in kips/inch. k=560; k=40/0.4*1000  %%% in metric (kN/m) %% Set the lumped mass at each DOF in lbs/g (g=386.4 inch/sec^2). m=400/9.81*0.0254; %%% 2300lb/7 for single sided or 2750lb/7 for double-sided m=150; %%% in metric (N/g or kg) - 1050/7 for Single-Side or 1250/7 Double Side %% Calculate the stiffness matrix of the structure in kips/inch. K=k*(diag([2*ones(neig-1,1);1])+diag(-ones(neig-1,1),1)+diag(-ones(neig-1,1),-1)); K(neig,neig)=2.8*k; %%% to adjust for the testing frame's flexibility %% Calculate the mass matrix of the structure. M=m*eye(neig); %% Set the spatial distribution of the effective earthquake forces. Earthquake forces are applied at all dofs of the structure. R=ones(neig,1); %% Set parameters dt=Time_Step_Sec; %% Set the input acceleration time history in inch/sec^2. xgtt=9.81/0.0254*Ground_Motion_Record(:,1); xgtt=9.81*Ground_Motion_Record(:,1); %%% in metric (m/sec^2) %% Set the critical damping ratio of the response spectra to be calculated ($$\mathrm{\xi}=0.05$) ksi=0.05; %% Dynamic Response Spectrum Analysis [U,~,~,f,omega,Eigvec] = DRSA(K,M,R,dt,xgtt,ksi);    291  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Ploting the natural modes of vibration of the EDCC retrofitted URM Wall %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FigHandle=figure('Name','Natural Modes','NumberTitle','off'); set(FigHandle,'Position',[50, 50, 1000, 500]); for i=1:neig     subplot(1,neig,i)     plot([0;Eigvec(:,i)],(0:h:h*neig)','LineWidth',2.,'Marker','.',...         'MarkerSize',20,'Color',[0 0 1],'markeredgecolor','k')     grid on     xlabel('Displacement','FontSize',12);     ylabel('Height','FontSize',12);     title(['Mode ',num2str(i)],'FontSize',12) end  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Ploting the peak modal displacement response %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FigHandle=figure('Name','Displacements','NumberTitle','off'); set(FigHandle, 'Position', [50, 50, 1000, 500]); for i=1:neig     subplot(1,neig,i)     plot([0;U(:,i)],(0:h:h*neig)','LineWidth',2.,'Marker','.',...         'MarkerSize',20,'Color',[0 1 0],'markeredgecolor','k')     xlim([-max(abs(U(:,i))) max(abs(U(:,i)))])     grid on     xlabel('Displacement','FontSize',12);     ylabel('Height','FontSize',12);     title(['Mode ',num2str(i)],'FontSize',12) end  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Ploting the peak modal equivalent static force response %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FigHandle=figure('Name','Equivalent static forces','NumberTitle','off'); set(FigHandle, 'Position', [50, 50, 1000, 500]); for i=1:neig     subplot(1,neig,i)     plot([0;f(:,i)],(0:h:h*neig)','LineWidth',2.,'Marker','.',...         'MarkerSize',20,'Color',[1 0 0],'markeredgecolor','k')     xlim([-max(abs(f(:,i))) max(abs(f(:,i)))])     grid on     xlabel('Static force','FontSize',12);     ylabel('Height','FontSize',12);     title(['Mode ',num2str(i)],'FontSize',12) end   292  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Calculating the peak modal base shear in kips %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Vb=zeros(1,neig); for i=1:neig     Vb(i)=sum(f(:,i)); end Vb  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Calculating the peak modal base overturning moment in kips-ft %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Mb=zeros(1,neig); for i=1:neig     Mb(i)=sum(f(:,i).*(h:h:neig*h)'); end Mb  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Modal combination with the AbSolute SUM (ABSSUM) method %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Peak base shear VbAbsSum=ABSSUM(Vb); %% Peak top-story shear VtAbsSum=ABSSUM(f(neig,:)); %% Peak base overturning moment MbAbsSum=ABSSUM(Mb); %% Peak top-story displacement utAbsSum=ABSSUM(U(neig,:));  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Modal combination with the Square Root of Sum of Squares (SRSS) method %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Peak base shear VbSRSS=SRSS(Vb); %% Peak top-story shear VtSRSS=SRSS(f(neig,:)); %% Peak base overturning moment MbSRSS=SRSS(Mb); %% Peak top-story displacement utSRSS=SRSS(U(neig,:));  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Modal combination with the Complete Quadratic Combination (CQC) method %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Peak base shear VbCQC=CQC(Vb,omega,ksi); %% Peak top-story shear 293  VtCQC=CQC(f(neig,:),omega,ksi); %% Peak base overturning moment MbCQC=CQC(Mb,omega,ksi); %% Peak top-story displacement utCQC=CQC(U(neig,:),omega,ksi);  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Assemble values of peak response in a table %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Assemble values of peak response in a cell C{1,2}='Vb (kips)'; C{1,3}='Vt (kips)'; C{1,4}='Mb (kip-ft)'; C{1,5}='ut (in)'; C{2,1}='ABSSUM'; C{2,2}=VbAbsSum; C{2,3}=VtAbsSum; C{2,4}=MbAbsSum; C{2,5}=utAbsSum; C{3,1}='SRSS'; C{3,2}=VbSRSS; C{3,3}=VtSRSS; C{3,4}=MbSRSS; C{3,5}=utSRSS; C{4,1}='CQC'; C{4,2}=VbCQC; C{4,3}=VtCQC; C{4,4}=MbCQC; C{4,5}=utCQC; C  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Calculating pseudo spectral acceleration, velocity and displacement spectra  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Input for main characters -> acceleration in cm/s2 gacc (:,1) = 9.80665*100*Ground_Motion_Record (:,1); dt = Time_Step_Sec; %% xi = ratio of critical damping xi = 0.05;   %% sPeriod = spectral period vector sPeriod = [0.01,0.02,0.022,0.025,0.029,0.03,0.032,0.035,0.036,...     0.04,0.042,0.044,0.045,0.046,0.048,0.05,0.055,0.06,0.065,0.067,0.07,...     0.075,0.08,0.085,0.09,0.095,0.1,0.11,0.12,0.125,0.13,0.133,0.14,0.15,...     0.16,0.17,0.18,0.19,0.2,0.22,0.24,0.25,0.26,0.28,0.29,0.3,0.32,0.34,...     0.35,0.36,0.38,0.4,0.42,0.44,0.45,0.46,0.48,0.5,0.55,0.6,0.65,0.667,...     0.7,0.75,0.8,0.85,0.9,0.95,1,1.1,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,...     2,2.2,2.4,2.5,2.6,2.8,3,3.2,3.4,3.5,3.6,3.8,4,4.2,4.4,4.6,4.8,5,7.5,10]; [PSA, PSV, SD] = responseSpectra(xi, sPeriod, gacc, dt); 294  figure('Name','Pseudo Spectral Acceleration','NumberTitle','off') plot(sPeriod,PSA/100,'LineWidth',2, 'Color','[0.5 0.7 1]') grid(gca,'minor'); set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '-'); xlabel('T_n (Sec)','FontSize',12); xlim([0,3]); ylabel('Pseudo Acceleration (m/s^2)','FontSize',12); title('Pseudo Spectral Acceleration','FontSize',12) legend('PSA') figure('Name','Pseudo Spectral Velocity','NumberTitle','off') plot(sPeriod,PSV/100,'LineWidth',2, 'Color','[0.5 0.7 1]') grid(gca,'minor'); set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '-'); xlabel('T_n (Sec)','FontSize',12); xlim([0,3]); ylabel('Pseudo Velocity (m/s)','FontSize',12); title('Pseudo Spectral Velocity','FontSize',12) legend('PSV') figure('Name','Spectral Displacement','NumberTitle','off') plot(sPeriod,SD,'LineWidth',2, 'Color','[0.5 0.7 1]') grid(gca,'minor'); set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '-'); xlabel('T_n (Sec)','FontSize',12); xlim([0,3]); ylabel('Displacement (cm)','FontSize',12); title('Spectral Displacement','FontSize',12) legend('SD') %% plot PSA, PSV and SD spectrum  plotSpectra(1,sPeriod,PSA,PSV,SD,'./plots/','responseSpectra'); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Calculating pseudo spectral acceleration, velocity and displacement spectra  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Time Interval (Sampling Time) of Record dt = Time_Step_Sec; %% Gravitational Constant; e.g. 9.81 m/s/s g = 9.80665; %% Ground Motion Acceleration in g  Ag (:,1) = g * Ground_Motion_Record (:,1); %% Damping Ratio in percent (%); e.g. 5 zet = 5;   %% End Period of Spectra; e.g. 4 sec endp = 10; %% OUTPUTS: %% T:   Period of Structures (sec) %% Spa: Elastic Pseudo Acceleration Spectrum %% Spv: Elastic Pseudo Velocity Spectrum %% Sd:  Elastic Displacement Spectrum [T, Spa, Spv, Sd] = SPEC(dt,Ag,zet,g,endp); 295  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Calculating and saving the peak values %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clearvars Maxima_Table Temp_Maxima Maxima_Table (1,:) = {'CH No.','Max Accel','Min Accel','Max Displ','Min Displ','Max Strain','Min Strain'}; Maxima_Table (2,:) = {'Units','g','g','mm','mm','milistrain','milistrain'}; for i = 1:8          Maxima_Table (i+2,1) = {i};          Maxima_Table (i+2,2) = {max(Raw_Accel_All (:,i))};     Maxima_Table (i+2,3) = {min(Raw_Accel_All (:,i))};          Maxima_Table (i+2,4) = {max(Raw_SP_All (:,i))};     Maxima_Table (i+2,5) = {min(Raw_SP_All (:,i))};          Maxima_Table (i+2,6) = {max(Raw_SG_All (:,i))};     Maxima_Table (i+2,7) = {min(Raw_SG_All (:,i))};      end Maxima_Table (11,1) = {9}; Maxima_Table (11,2) = {max(Raw_Accel_All (:,i))}; Maxima_Table (11,3) = {min(Raw_Accel_All (:,i))}; for i=4:7     Maxima_Table (11,i) = {'N/A'}; end for i=1:7     Maxima_Table (12,i) = {'-----'}; end Maxima_Table (13,1) = {'Run-Peak -->'}; for i=2:5 %%% change this to 2:7 for Wall-1,3,5 for Strain Gages          for j=3:10                  Temp_Maxima (j-2,1) = table2array(Maxima_Table (j,i));         Maxima_Table (13,i) = {max(abs(Temp_Maxima(:,1)))};         clearvars Temp_Maxima              end      end % Saving Data Files --> Maxiam and Peak value tables clearvars Output_File_Name Output_File_Name = ['ARTeMIS_Data\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' ID_GM_Intensity ' - ARTeMIS Raw Data']; save ([Output_File_Name '.mat'], 'Raw_Accel_All', 'Raw_SP_All', '-mat'); clearvars Output_File_Name 296  Output_File_Name = ['Peak_Value_Tables\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' ID_GM_Intensity '- Peak Values Table']; save ([Output_File_Name '.mat'], 'Maxima_Table', '-mat'); %% Saving Data Files as input for Modal Analysis using ARTeMIS Modal Pro clearvars Output_File_Name Output_File_Name = ['ARTeMIS Data\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' ID_GM_Intensity ' - ARTeMIS Raw Data']; save ([Output_File_Name '.mat'], 'Raw_Accel_All', 'Raw_SP_All', '-mat'); clearvars Output_File_Name Output_File_Name = ['ARTeMIS Data\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' ID_GM_Intensity '- ARTeMIS Raw Accel Data']; save ([Output_File_Name '.txt'], 'Raw_Accel_All', '-ascii', '-tabs'); clearvars Output_File_Name Output_File_Name = ['ARTeMIS Data\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' ID_GM_Intensity '- ARTeMIS Raw Displ Data']; save ([Output_File_Name '.txt'], 'Raw_SP_All', '-ascii', '-tabs');     figure(6)     plot(Time, Raw_SP)     xlabel('Time (Sec)','Color', 'b');     ylabel('Displacement (mm)','Color', 'b');     title ({['\fontsize{10} \bf \color{magenta} Time History for String Pod No. ' num2str(i-1) ' (DISPL. ' num2str(i-1) ') - Raw Data'] ; ['\fontsize{9} \rm \color{black} (Max Displ. = ' num2str(max(Raw_SP(:,1))) ' mm | Min Displ. = ' num2str(min(Raw_SP(:,1))) ' mm | Median = ' num2str(median((Raw_SP(:,1)))) ' mm)']});     legend({['\rm \color{red} Peak Displacement = ' num2str(max(abs(max(Raw_SP(:,1))), abs(min(Raw_SP(:,1))))) ' mm']}, 'Location','northeast', 'FontSize', 8);     set(gca, 'XGrid','on','YGrid','on', 'GridLineStyle', '--');     grid(gca,'minor');     saveas (figure(6), ['Figures\MatFig\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-' num2str(i-1)]);     saveas (figure(6), ['Figures\SVG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-' num2str(i-1)], 'svg');     saveas (figure(6), ['Figures\PDF\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-' num2str(i-1)], 'pdf');     saveas (figure(6), ['Figures\PNG\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' num2str(ID_GM_Intensity) '_Displ-' num2str(i-1)], 'png');     close(figure(6));    297  G.4 Peak Value Extraction and Data Input Creator for ARTeMIS Modal Pro This set of codes creates plots for maxima analysis, scales the plots, normalizes them, and saves them for comparison. Table of peak values are generated and saved.  close all clear clc File_Name = 'Wall-1_Run-9_GM-1@150%'; load (File_Name) clearvars Input_Acceleration_Data_File_Name Input_Strain_Gage_Data_File_Name Input_String_Pods_Data_File_Name Output_File_Name No_of_Channels = {'Accelerometer', 'String Pod', 'Strain Gage'; 'Acceleration', 'Displacement', 'Strain';9,8,8}; data = Data_SP_All;  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Calculating the duration & Frequency range of the record %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  [Row, Col] = size(data); Data_freq = 1/Time_Step_Sec; Duration_of_Rec = Row * Time_Step_Sec; Freq_Step = 1/Duration_of_Rec; Freq_Domain = Freq_Step * Row;  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  Raw_Time (:,1) = table2array(data (:,1)); GM_Duration = max(Raw_Time(:,1)) - min(Raw_Time(:,1)); Time_Temp = datevec (Raw_Time); Time = zeros(Row,1);  for i=1:Row     Time(i,1)=(Time_Temp(i,4)*60*60)+(Time_Temp(i,5)*60)+(Time_Temp(i,6)); end  Time (:,1) = Time (:,1) - min(Time(:,1)); Time = zeros(Row,1);  for i=1:Row     Time (i,1) = (i-1)*Time_Step_Sec; end clearvars Time_Temp i %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 298  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Cleaning up and Plotting the String Pod (Displacement) Data %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% SP_CN = 1; %% Set the decimation and filering orders here: %%% PreFilt_Decimation_Order = 1; PostFilt_Decimation_Order = 2; Smoothing_Step = 12; %% Best result is when Pre_Dec is 2, Post_Dec is 4, & Smoothing step is 12 %% Also, Filter_Order 9 and Cut_Off_Freq is 1.5 Hz, best results %%%% If designing a "moving average filter" use: %%%%%%%%%%%%%%%%%%%% Filter_WindowSize = 15; bb = (1/Filter_WindowSize)*ones(1,Filter_WindowSize); aa = 1; freqz (bb,aa) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% If designing a "Low Pass Butterworth Filter" use: %%%%%%%%%%%%%% Filter_Order = 9; Cut_Off_Freq = 2.5; Filter_Type = 'low' Filter_Type = 'high' Wn = Cut_Off_Freq/(Freq_Domain/2); [b,a] = butter (Filter_Order, Wn, Filter_Type); freqz (b,a) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Raw_SP_All = zeros(Row,Col-1); Dec_SP_All = zeros(Row/PreFilt_Decimation_Order,Col-1); Filt_Dec_SP_All = zeros(Row/PreFilt_Decimation_Order,Col-1); Dec_Filt_Dec_SP_All = zeros(Row/PreFilt_Decimation_Order/PostFilt_Decimation_Order,Col-1); Smth_Dec_Filt_Dec_SP_All = zeros(Row/PreFilt_Decimation_Order/PostFilt_Decimation_Order,Col-1); for i=1:table2array (No_of_Channels(3,2))          Raw_SP_All (:,i) = table2array(data (:,i+1));     Dec_SP_All (:,i) = decimate (Raw_SP_All(:,i), PreFilt_Decimation_Order);     Filt_Dec_SP_All (:,i) = filter (b, a, Dec_SP_All(:,i));     Dec_Filt_Dec_SP_All (:,i) = decimate (Filt_Dec_SP_All(:,i), PostFilt_Decimation_Order);     Smth_Dec_Filt_Dec_SP_All (:,i) = smooth (Dec_Filt_Dec_SP_All (:,i), Smoothing_Step);      end PreFilt_Dec_Time = decimate(Time, PreFilt_Decimation_Order); PostFilt_Dec_Time = decimate(PreFilt_Dec_Time, PostFilt_Decimation_Order); Max_SP_Before = max (Raw_SP_All(:,SP_CN)) Max_SP_After = max  (Smth_Dec_Filt_Dec_SP_All(:,SP_CN)) Min_SP_Before = min (Raw_SP_All(:,SP_CN)) 299  Min_SP_After = min  (Smth_Dec_Filt_Dec_SP_All(:,SP_CN)) plot (Time, Raw_SP_All(:,SP_CN)) plot (PreFilt_Dec_Time, Dec_SP_All(:,SP_CN)) plot (PreFilt_Dec_Time, Filt_Dec_SP_All(:,SP_CN)) plot (PostFilt_Dec_Time, Dec_Filt_Dec_SP_All(:,SP_CN)) plot (PostFilt_Dec_Time, Smth_Dec_Filt_Dec_SP_All(:,SP_CN)) Displ1 = Raw_SP_All(:,6) - Raw_SP_All (:,1); Displ2 = Dec_SP_All(:,6) - Dec_SP_All (:,1); Displ3 = Filt_Dec_SP_All(:,6) - Filt_Dec_SP_All (:,1); Displ4 = Dec_Filt_Dec_SP_All(:,6) - Dec_Filt_Dec_SP_All (:,1); Displ5 = Smth_Dec_Filt_Dec_SP_All(:,6) - Smth_Dec_Filt_Dec_SP_All (:,1); Max_Displ_Before = max (Displ1(:,1)) Max_Displ_After = max  (Displ5(:,1)) Min_Displ_Before = min (Displ1(:,1)) Min_Displ_After = min  (Displ5(:,1)) plot (Time,Displ1) plot (PreFilt_Dec_Time, Displ2) plot (PreFilt_Dec_Time, Displ3) plot (PostFilt_Dec_Time, Displ4) plot (PostFilt_Dec_Time, Displ5) plot (Displ2, Displ3); plot (Displ4, Displ5);     d = fdesign.lowpass;     Lowpass = design(d,'butter','matchexactly','stopband','SystemObject',true);     fvtool(Lowpass);  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Raw_SP_All(:,1) = fft(Raw_SP_All(:,SP_CN)); AMPL_FFT_Raw_SP_All(:,1) = abs(FFT_Raw_SP_All(:,1)); PSD_Raw_SP_All(:,1) = pwelch(Raw_SP_All(:,SP_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Dec_SP_All(:,1) = fft(Dec_SP_All(:,SP_CN)); AMPL_FFT_Dec_SP_All(:,1) = abs(FFT_Dec_SP_All(:,1)); PSD_Dec_SP_All(:,1) = pwelch(Dec_SP_All(:,SP_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Filt_Dec_SP_All(:,1) = fft(Filt_Dec_SP_All(:,SP_CN)); AMPL_FFT_Filt_Dec_SP_All(:,1) = abs(FFT_Filt_Dec_SP_All(:,1)); PSD_Filt_Dec_SP_All(:,1) = pwelch(Filt_Dec_SP_All(:,SP_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Dec_Filt_Dec_SP_All(:,1) = fft(Dec_Filt_Dec_SP_All(:,SP_CN)); AMPL_FFT_Dec_Filt_Dec_SP_All(:,1) = abs(FFT_Dec_Filt_Dec_SP_All(:,1)); PSD_Dec_Filt_Dec_SP_All(:,1) = pwelch(Dec_Filt_Dec_SP_All(:,SP_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Smth_Filt_Dec_SP_All(:,1) = fft(Smth_Dec_Filt_Dec_SP_All(:,SP_CN)); AMPL_FFT_Smth_Dec_Filt_Dec_SP_All(:,1) = abs(FFT_Smth_Filt_Dec_SP_All(:,1)); PSD_Smth_Dec_Filt_Dec_SP_All(:,1) = pwelch(Smth_Dec_Filt_Dec_SP_All(:,SP_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  300  for k = 1:Row/PreFilt_Decimation_Order/PostFilt_Decimation_Order/10          X (k, 1) = k * Freq_Step;     Y1 (k, 1) = AMPL_FFT_Dec_SP_All(k,1);     Y2 (k, 1) = AMPL_FFT_Filt_Dec_SP_All(k,1);     Y3 (k, 1) = AMPL_FFT_Dec_Filt_Dec_SP_All(k,1);     Y4 (k, 1) = AMPL_FFT_Smth_Dec_Filt_Dec_SP_All(k,1);      end plot (X, Y1) plot (X, Y2) plot (X, Y3) plot (X, Y4) clearvars X k; [Row_Temp, ~] = size(PSD_Dec_SP_All); for k = 1:Row_Temp/PostFilt_Decimation_Order/6          X (k, 1) = k * Freq_Step;     Y5 (k, 1) = PSD_Dec_SP_All (k,1);     Y6 (k, 1) = PSD_Filt_Dec_SP_All (k,1);     Y7 (k, 1) = PSD_Dec_Filt_Dec_SP_All (k,1);     Y8 (k, 1) = PSD_Smth_Dec_Filt_Dec_SP_All (k,1);      end plot (X, Y5) plot (X, Y6) plot (X, Y7) plot (X, Y8) clearvars data k Row_Temp Col_Temp X Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%                  301  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Cleaning up, filtering, and Plotting the Acceleration Data %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clearvars data Smoothing_Step PostFilt_Decimation_Order PreFilt_Decimation_Order clearvars FFT_Dec_Accel_All FFT_Dec_Filt_Dec_Accel_All FFT_Filt_Dec_Accel_All FFT_Raw_Accel_All clearvars AMPL_FFT_Dec_Accel_All AMPL_FFT_Dec_Filt_Dec_Accel_All AMPL_FFT_Filt_Dec_Accel_All clearvars PSD_Dec_Accel_All PSD_Dec_Filt_Dec_Accel_All PSD_Filt_Dec_Accel_All PSD_Raw_Accel_All clearvars AMPL_FFT_Raw_Accel_All Filter_Order Cut_Off_Freq b a aa bb X Y i clearvars Dec_Displ5 A_up A_lo D_up D_lo Filter_Order Cut_Off_Freq close all data = Data_ACC_All;  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Designing a "Low Pass Butterworth Filter": %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Filter_Order = 9; Cut_Off_Freq = 55; [b, a] = butter (Filter_Order, Cut_Off_Freq/(Freq_Domain/2),'low'); freqz (b,a)  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% If designing a "moving average filter," use: %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Filter_WindowSize = 5; aa = (1/Filter_WindowSize)*ones(1,Filter_WindowSize); bb = 1; freqz (bb,aa)  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Accel_CN = 1; %% Set the decimation and filering orders here: PreFilt_Decimation_Order = 1; PostFilt_Decimation_Order = 2; Smoothing_Step = 1; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Raw_Accel_All = zeros(Row,Col-1); Dec_Accel_All = zeros(Row/PreFilt_Decimation_Order,Col-1); Filt_Dec_Accel_All = zeros(Row/PreFilt_Decimation_Order,Col-1); Dec_Filt_Dec_Accel_All = zeros(Row/PreFilt_Decimation_Order/PostFilt_Decimation_Order,Col-1); Smth_Dec_Filt_Dec_Accel_All = zeros(Row/PreFilt_Decimation_Order/PostFilt_Decimation_Order,Col-1);  for i=1:table2array (No_of_Channels(3,1))      302      Raw_Accel_All (:,i) = table2array(data (:,i+1));     Dec_Accel_All (:,i) = decimate (Raw_Accel_All(:,i), PreFilt_Decimation_Order);     Filt_Dec_Accel_All (:,i) = filter (b, a, Dec_Accel_All(:,i));     Dec_Filt_Dec_Accel_All (:,i) = decimate (Filt_Dec_Accel_All(:,i), PostFilt_Decimation_Order);     Smth_Dec_Filt_Dec_Accel_All (:,i) = smooth (Dec_Filt_Dec_Accel_All (:,i), Smoothing_Step);    End  PreFilt_Dec_Time = decimate(Time, PreFilt_Decimation_Order); PostFilt_Dec_Time = decimate(PreFilt_Dec_Time, PostFilt_Decimation_Order); Max_ACC_Before = max (Raw_Accel_All(:,Accel_CN)) Max_ACC_After = max  (Filt_Dec_Accel_All(:,Accel_CN)) Min_ACC_Before = min (Raw_Accel_All(:,Accel_CN)) Min_ACC_After = min  (Filt_Dec_Accel_All(:,Accel_CN)) plot (Time, Raw_Accel_All(:,Accel_CN)) plot (PreFilt_Dec_Time, Dec_Accel_All(:,Accel_CN)) plot (PreFilt_Dec_Time, Filt_Dec_Accel_All(:,Accel_CN)) plot (PostFilt_Dec_Time, Dec_Filt_Dec_Accel_All(:,Accel_CN)) plot (PostFilt_Dec_Time, Smth_Dec_Filt_Dec_Accel_All(:,Accel_CN))     d = fdesign.lowpass;     Lowpass = design(d,'butter','matchexactly','stopband','SystemObject',true);     fvtool(Lowpass);  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Raw_Accel_All(:,1) = fft(Raw_Accel_All(:,Accel_CN)); AMPL_FFT_Raw_Accel_All(:,1) = abs(FFT_Raw_Accel_All(:,1)); PSD_Raw_Accel_All(:,1) = pwelch(Raw_Accel_All(:,Accel_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Dec_Accel_All(:,1) = fft(Dec_Accel_All(:,Accel_CN)); AMPL_FFT_Dec_Accel_All(:,1) = abs(FFT_Dec_Accel_All(:,1)); PSD_Dec_Accel_All(:,1) = pwelch(Dec_Accel_All(:,Accel_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Filt_Dec_Accel_All(:,1) = fft(Filt_Dec_Accel_All(:,Accel_CN)); AMPL_FFT_Filt_Dec_Accel_All(:,1) = abs(FFT_Filt_Dec_Accel_All(:,1)); PSD_Filt_Dec_Accel_All(:,1) = pwelch(Filt_Dec_Accel_All(:,Accel_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Dec_Filt_Dec_Accel_All(:,1) = fft(Dec_Filt_Dec_Accel_All(:,Accel_CN)); AMPL_FFT_Dec_Filt_Dec_Accel_All(:,1) = abs(FFT_Dec_Filt_Dec_Accel_All(:,1)); PSD_Dec_Filt_Dec_Accel_All(:,1) = pwelch(Dec_Filt_Dec_Accel_All(:,Accel_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Smth_Filt_Dec_Accel_All(:,1) = fft(Smth_Dec_Filt_Dec_Accel_All(:,Accel_CN)); AMPL_FFT_Smth_Dec_Filt_Dec_Accel_All(:,1) = abs(FFT_Smth_Filt_Dec_Accel_All(:,1)); PSD_Smth_Dec_Filt_Dec_Accel_All(:,1) = pwelch(Smth_Dec_Filt_Dec_Accel_All(:,Accel_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 303  for k = 1:Row/PreFilt_Decimation_Order/PostFilt_Decimation_Order          X (k, 1) = k * Freq_Step;     Y1 (k, 1) = AMPL_FFT_Dec_Accel_All(k,1);     Y2 (k, 1) = AMPL_FFT_Filt_Dec_Accel_All(k,1);     Y3 (k, 1) = AMPL_FFT_Dec_Filt_Dec_Accel_All(k,1);     Y4 (k, 1) = AMPL_FFT_Smth_Dec_Filt_Dec_Accel_All(k,1);      End  plot (X, Y1) plot (X, Y2) plot (X, Y3) plot (X, Y4)  clearvars X k;  [Row_Temp, ~] = size(PSD_Dec_Accel_All); for k = 1:Row_Temp/PostFilt_Decimation_Order          X (k, 1) = k * Freq_Step;     Y5 (k, 1) = PSD_Dec_Accel_All (k,1);     Y6 (k, 1) = PSD_Filt_Dec_Accel_All (k,1);     Y7 (k, 1) = PSD_Dec_Filt_Dec_Accel_All (k,1);     Y8 (k, 1) = PSD_Smth_Dec_Filt_Dec_Accel_All (k,1);      End  plot (X, Y5) plot (X, Y6) plot (X, Y7) plot (X, Y8) clearvars k Row_Temp Col_Temp X Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%              304  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Cleaning up, filtering, and Plotting the Strain Gage Data %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clearvars data Smoothing_Step PostFilt_Decimation_Order PreFilt_Decimation_Order clearvars FFT_Dec_Accel_All FFT_Dec_Filt_Dec_Accel_All FFT_Filt_Dec_Accel_All FFT_Raw_Accel_All clearvars AMPL_FFT_Dec_Accel_All AMPL_FFT_Dec_Filt_Dec_Accel_All AMPL_FFT_Filt_Dec_Accel_All clearvars PSD_Dec_Accel_All PSD_Dec_Filt_Dec_Accel_All PSD_Filt_Dec_Accel_All PSD_Raw_Accel_All clearvars AMPL_FFT_Raw_Accel_All Filter_Order Cut_Off_Freq b a aa bb X Y i clearvars Dec_Displ5 A_up A_lo D_up D_lo Filter_Order Cut_Off_Freq close all data = Data_SG_All;  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Designing a "Low Pass Butterworth Filter": %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Filter_Order = 5; Cut_Off_Freq = 50; Filter_Type = 'low' Filter_Type = 'high' Wn = Cut_Off_Freq/(Freq_Domain/2); [b,a] = butter (Filter_Order, Wn, Filter_Type); freqz (b,a)  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% If designing a "moving average filter," use: %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Filter_WindowSize = 15; bb = (1/Filter_WindowSize)*ones(1,Filter_WindowSize); aa = 1; freqz (bb,aa) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% SG_CN = 1; %% Set the decimation and filering orders here: PreFilt_Decimation_Order = 1; PostFilt_Decimation_Order = 2; Smoothing_Step = 1; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Raw_SG_All = zeros(Row,Col-1); Dec_SG_All = zeros(Row/PreFilt_Decimation_Order,Col-1); Filt_Dec_SG_All = zeros(Row/PreFilt_Decimation_Order,Col-1); Dec_Filt_Dec_SG_All = zeros(Row/PreFilt_Decimation_Order/PostFilt_Decimation_Order,Col-1); Smth_Dec_Filt_Dec_SG_All = zeros(Row/PreFilt_Decimation_Order/PostFilt_Decimation_Order,Col-1);  305  for i=1:table2array (No_of_Channels(3,3))          Raw_SG_All (:,i) = table2array(data (:,i+1));     Dec_SG_All (:,i) = decimate (Raw_SG_All(:,i), PreFilt_Decimation_Order);     Filt_Dec_SG_All (:,i) = filter (b, a, Dec_SG_All(:,i));     Dec_Filt_Dec_SG_All (:,i) = decimate (Filt_Dec_SG_All(:,i), PostFilt_Decimation_Order);     Smth_Dec_Filt_Dec_SG_All (:,i) = smooth (Dec_Filt_Dec_SG_All (:,i), Smoothing_Step);      End  PreFilt_Dec_Time = decimate(Time, PreFilt_Decimation_Order); PostFilt_Dec_Time = decimate(PreFilt_Dec_Time, PostFilt_Decimation_Order); Max_STRN_Before = max (Raw_SG_All(:,SG_CN)) Max_STRN_After = max  (Filt_Dec_SG_All(:,SG_CN)) Min_STRN_Before = min (Raw_SG_All(:,SG_CN)) Min_STRN_After = min  (Filt_Dec_SG_All(:,SG_CN)) plot (Time, Raw_SG_All(:,SG_CN)) plot (PreFilt_Dec_Time, Dec_SG_All(:,SG_CN)) plot (PreFilt_Dec_Time, Filt_Dec_SG_All(:,SG_CN)) plot (PostFilt_Dec_Time, Dec_Filt_Dec_SG_All(:,SG_CN)) plot (PostFilt_Dec_Time, Smth_Dec_Filt_Dec_SG_All(:,SG_CN))     d = fdesign.lowpass;     Lowpass = design(d,'butter','matchexactly','stopband','SystemObject',true);     fvtool(Lowpass);  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Raw_SG_All(:,1) = fft(Raw_SG_All(:,SG_CN)); AMPL_FFT_Raw_SG_All(:,1) = abs(FFT_Raw_SG_All(:,1)); PSD_Raw_SG_All(:,1) = pwelch(Raw_SG_All(:,SG_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Dec_SG_All(:,1) = fft(Dec_SG_All(:,SG_CN)); AMPL_FFT_Dec_SG_All(:,1) = abs(FFT_Dec_SG_All(:,1)); PSD_Dec_SG_All(:,1) = pwelch(Dec_SG_All(:,SG_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Filt_Dec_SG_All(:,1) = fft(Filt_Dec_SG_All(:,SG_CN)); AMPL_FFT_Filt_Dec_SG_All(:,1) = abs(FFT_Filt_Dec_SG_All(:,1)); PSD_Filt_Dec_SG_All(:,1) = pwelch(Filt_Dec_SG_All(:,SG_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Dec_Filt_Dec_SG_All(:,1) = fft(Dec_Filt_Dec_SG_All(:,SG_CN)); AMPL_FFT_Dec_Filt_Dec_SG_All(:,1) = abs(FFT_Dec_Filt_Dec_SG_All(:,1)); PSD_Dec_Filt_Dec_SG_All(:,1) = pwelch(Dec_Filt_Dec_SG_All(:,SG_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT_Smth_Filt_Dec_SG_All(:,1) = fft(Smth_Dec_Filt_Dec_SG_All(:,SG_CN)); AMPL_FFT_Smth_Dec_Filt_Dec_SG_All(:,1) = abs(FFT_Smth_Filt_Dec_SG_All(:,1)); PSD_Smth_Dec_Filt_Dec_SG_All(:,1) = pwelch(Smth_Dec_Filt_Dec_SG_All(:,SG_CN)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 306  for k = 1:Row/PreFilt_Decimation_Order/PostFilt_Decimation_Order          X (k, 1) = k * Freq_Step;     Y1 (k, 1) = AMPL_FFT_Dec_SG_All(k,1);     Y2 (k, 1) = AMPL_FFT_Filt_Dec_SG_All(k,1);     Y3 (k, 1) = AMPL_FFT_Dec_Filt_Dec_SG_All(k,1);     Y4 (k, 1) = AMPL_FFT_Smth_Dec_Filt_Dec_SG_All(k,1);      end plot (X, Y1) plot (X, Y2) plot (X, Y3) plot (X, Y4) clearvars X k; [Row_Temp, ~] = size(PSD_Dec_SG_All); for k = 1:Row_Temp/PostFilt_Decimation_Order          X (k, 1) = k * Freq_Step;     Y5 (k, 1) = PSD_Dec_SG_All (k,1);     Y6 (k, 1) = PSD_Filt_Dec_SG_All (k,1);     Y7 (k, 1) = PSD_Dec_Filt_Dec_SG_All (k,1);     Y8 (k, 1) = PSD_Smth_Dec_Filt_Dec_SG_All (k,1);      end plot (X, Y5) plot (X, Y6) plot (X, Y7) plot (X, Y8) clearvars k Row_Temp Col_Temp X Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%                  307  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Calculating and saving the peak values %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clearvars Maxima_Table Temp_Maxima Maxima_Table (1,:) = {'CH No.','Max Accel','Min Accel','Max Displ','Min Displ','Max Strain','Min Strain'}; Maxima_Table (2,:) = {'Units','g','g','mm','mm','milistrain','milistrain'}; for i = 1:8          Maxima_Table (i+2,1) = {i};          Maxima_Table (i+2,2) = {max(Raw_Accel_All (:,i))};     Maxima_Table (i+2,3) = {min(Raw_Accel_All (:,i))};          Maxima_Table (i+2,4) = {max(Raw_SP_All (:,i))};     Maxima_Table (i+2,5) = {min(Raw_SP_All (:,i))};          Maxima_Table (i+2,6) = {max(Raw_SG_All (:,i))};     Maxima_Table (i+2,7) = {min(Raw_SG_All (:,i))};      end Maxima_Table (11,1) = {9}; Maxima_Table (11,2) = {max(Raw_Accel_All (:,i))}; Maxima_Table (11,3) = {min(Raw_Accel_All (:,i))}; for i=4:7     Maxima_Table (11,i) = {'N/A'}; end for i=1:7     Maxima_Table (12,i) = {'-----'}; end Maxima_Table (13,1) = {'Run-Peak -->'}; for i=2:7 %%% change this from 2:5 to 2:7 for Wall-1,3,5 for Strain Gages          for j=3:10                  Temp_Maxima (j-2,1) = table2array(Maxima_Table (j,i));         Maxima_Table (13,i) = {max(abs(Temp_Maxima(:,1)))};         clearvars Temp_Maxima              end      end       308  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Saving Data Files as input for Modal Analysis using ARTeMIS Modal Pro %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  clearvars Output_File_Name  Output_File_Name = ['ARTeMIS_Data\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' ID_GM_Intensity ' - ARTeMIS Raw Data'];  save ([Output_File_Name '.mat'], 'Raw_Accel_All', 'Raw_SP_All', '-mat');  clearvars Output_File_Name  Output_File_Name = ['Peak_Value_Tables\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' ID_GM_Intensity '- Peak Values Table'];  save ([Output_File_Name '.mat'], 'Maxima_Table', '-mat');  clearvars Output_File_Name  Output_File_Name = ['ARTeMIS_Data\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' ID_GM_Intensity '- ARTeMIS Raw Accel Data'];  save ([Output_File_Name '.txt'], 'Raw_Accel_All', '-ascii', '-tabs');  clearvars Output_File_Name  Output_File_Name = ['ARTeMIS_Data\Wall-' num2str(ID_Wall) '_Run-' num2str(ID_Run) '_GM-' num2str(ID_GM) '@' ID_GM_Intensity '- ARTeMIS Raw Displ Data'];  save ([Output_File_Name '.txt'], 'Raw_SP_All', '-ascii', '-tabs');  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% THE END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  

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