Applied Science, Faculty of
Civil Engineering, Department of
DSpace
UBCV
Iliouchetchev, Anthony
Master of Applied Science - MASc
University of British Columbia
In Canada, reinforced masonry shear walls (RMSWs) can be used as the primary seismic force resisting system (SFRS) in mid to high-rise buildings. In moderate to high seismic regions, the performance of a SFRS is primarily defined by its ability to maintain its strength capacity at large drift demands. Research completed over the last two decades in Canada has shown that boundary elements (BEs) can be used to improve the seismic performance of RMSWs, which has led to their adoption in Canada’s masonry design standard CSA S304 (Canadian Standards Association, 2024). The BEs consist of specially reinforced sections provided at both wall ends which can either be thickened or embedded within the wall. However, research on RMSWs with embedded BEs is limited. The motivation for this thesis was to fill this research gap and explore the potential of embedded BEs to improve the seismic performance of RMSWs. The experimental study in this thesis evaluated the seismic performance of two full-scale, 240 mm RMSW specimens subjected to in-plane reversed cyclic loading without axial compression. The specimens were designed to be identical, except that one of them was built with embedded BEs, whereas the other was not. The influence of the embedded BEs was evaluated by comparing the response of the specimens. Also, a separate analytical study was conducted, which focused on presenting approaches for developing generalized force-displacement curves for RMSWs with and without boundary elements for potential applications in numerical modelling. The primary finding of the experimental study was that, without applied axial compression, the seismic performance of RMSWs with and without embedded boundary elements was comparable. The hysteretic force-displacement responses, wall capacities, progressions and extents of damage, energy dissipation properties, and ductility ratios were compared amongst the specimens to support this statement. The primary finding of the analytical study was that the proposed approaches provided reasonably accurate results, based on their implementation and validation against selected experimental results from other Canadian researchers.
EXPERIMENTAL AND ANALYTICAL STUDIES OF REINFORCED MASONRY SHEAR WALLS WITH AND WITHOUT BOUNDARY ELEMENTS SUBJECTED TO IN-PLANE CYCLIC LOADING by Anthony Iliouchetchev B.Sc., University of Manitoba, 2021 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Civil Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) August 2025 © Anthony Iliouchetchev, 2025ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled: Experimental and analytical studies of reinforced masonry shear walls with and withoutboundary elements subjected to in-plane cyclic loading submitted by Anthony Iliouchetchev in partial fulfilment of the requirements for the degree of Master of Applied Science in Civil Engineering Examining Committee: Tony T. Y. Yang, Professor, Department of Civil Engineering, UBC Supervisor Svetlana Nikolic-Brzev, Adjunct Professor, Department of Civil Engineering, UBC Supervisory Committee Member iii ABSTRACT In Canada, reinforced masonry shear walls (RMSWs) can be used as the primary seismic force resisting system (SFRS) in mid to high-rise buildings. In moderate to high seismic regions, the performance of a SFRS is primarily defined by its ability to maintain its strength capacity at large drift demands. Research completed over the last two decades in Canada has shown that boundary elements (BEs) can be used to improve the seismic performance of RMSWs, which has led to their adoption in Canada’s masonry design standard CSA S304 (Canadian Standards Association, 2024). The BEs consist of specially reinforced sections provided at both wall ends which can either be thickened or embedded within the wall. However, research on RMSWs with embedded BEs is limited. The motivation for this thesis was to fill this research gap and explore the potential of embedded BEs to improve the seismic performance of RMSWs. The experimental study in this thesis evaluated the seismic performance of two full-scale, 240 mm RMSW specimens subjected to in-plane reversed cyclic loading without axial compression. The specimens were designed to be identical, except that one of them was built with embedded BEs, whereas the other was not. The influence of the embedded BEs was evaluated by comparing the response of the specimens. Also, a separate analytical study was conducted, which focused on presenting approaches for developing generalized force-displacement curves for RMSWs with and without boundary elements for potential applications in numerical modelling. The primary finding of the experimental study was that, without applied axial compression, the seismic performance of RMSWs with and without embedded boundary elements was comparable. The hysteretic force-displacement responses, wall capacities, progressions and extents of damage, energy dissipation properties, and ductility ratios were compared amongst the specimens to support this statement. The primary finding of the analytical study was that the iv proposed approaches provided reasonably accurate results, based on their implementation and validation against selected experimental results from other Canadian researchers. v LAY SUMMARY This thesis describes experimental and analytical studies of reinforced masonry shear walls (RMSWs) subjected to in-plane reversed cyclic loading. Experimental results from cyclic loading tests of RMSWs provide insight towards their potential behaviour during earthquakes. This experimental study focused on evaluating the effect of embedded boundary elements (BEs) in RMSWs. BEs are typically thickened and specially reinforced sections provided at both ends of a RMSW to enhance its seismic performance. If the BE is not thickened, it is considered to be embedded within the wall. RMSWs with embedded BEs are advantageous to RMSWs with thickened (external) BEs as they can satisfy architectural constraints with greater ease, since their exterior appearance is identical to RMSWs without BEs. Finally, the analytical study described methods for developing generalized force-displacement curves for RMSWs with and without BEs, which are used by engineers in numerical analyses of reinforced masonry buildings. vi PREFACE Portions of the experimental program described in Chapter 4 were performed jointly with Yu-Cheng Hsu. Experimental testing and data acquisition used to prepare the contents of Chapter 5 were also performed jointly with Yu-Cheng Hsu. This thesis is the original and unpublished work by the author, Anthony Iliouchetchev. Generative artificial intelligence (AI) was not used for any aspects of the work in this thesis. vii TABLE OF CONTENTS ABSTRACT ............................................................................................................................... iii LAY SUMMARY .......................................................................................................................... v PREFACE .................................................................................................................................. vi TABLE OF CONTENTS ............................................................................................................ vii LIST OF TABLES ..................................................................................................................... xii LIST OF FIGURES .................................................................................................................. xiv LIST OF SYMBOLS................................................................................................................ xxv ACKNOWLEDGEMENTS ...................................................................................................... xxix 1. INTRODUCTION ................................................................................................................ 1 1.1 Introduction ....................................................................................................................... 1 1.2 Objectives and Scope ....................................................................................................... 5 1.3 Thesis Organization .......................................................................................................... 5 2. BACKGROUND .................................................................................................................. 7 2.1 Introduction ....................................................................................................................... 7 2.2 Nonlinear Properties of RMSWs ....................................................................................... 7 2.3 Behaviour of RMSWs Subjected to In-Plane Lateral Cyclic Loading ................................17 2.3.1 Failure Mechanisms of RMSWs ................................................................................21 2.4 Ductility ............................................................................................................................23 2.5 Summary .........................................................................................................................24 viii 3. LITERATURE REVIEW OF EXPERIMENTAL STUDIES ...................................................25 3.1 Introduction ......................................................................................................................25 3.2 Experimental Studies on Regular RMSWs Subjected to In-Plane Lateral Cyclic Loading 25 3.3 Experimental Studies on RMSWs with External Boundary Elements Subjected to In-Plane Lateral Cyclic Loading ...........................................................................................................35 3.4 Review of Seismic Design Provisions for RMSWs with Boundary Elements ....................53 3.5 Summary .........................................................................................................................59 4. EXPERIMENTAL PROGRAM ............................................................................................60 4.1 Introduction ......................................................................................................................60 4.2 Specimen Design & Construction ....................................................................................60 4.2.1 Specimen Design & Detailing ....................................................................................60 4.2.2 Specimen Construction .............................................................................................66 4.2.2.1 Construction of Footing Beams ...........................................................................67 4.2.2.2 Construction of Masonry Walls ...........................................................................73 4.2.2.3 Construction of Loading Beams ..........................................................................83 4.3 Material Testing ...............................................................................................................89 4.3.1 Masonry Prisms ........................................................................................................89 4.3.2 Concrete Masonry Units ............................................................................................93 4.3.3 Grout .........................................................................................................................95 4.3.3.1 Grout Cylinders ...................................................................................................95 4.3.3.2 Grout Prisms.......................................................................................................98 4.3.4 Mortar Cubes .......................................................................................................... 101 ix 4.3.5 Steel Reinforcement ................................................................................................ 103 4.3.6 Footing and Loading Beams Concrete .................................................................... 106 4.4 Test Setup ..................................................................................................................... 107 4.4.1 Strong Floor and Wall .............................................................................................. 110 4.4.2 Horizontal Actuator & Supports ............................................................................... 110 4.4.3 Box Beams .............................................................................................................. 112 4.4.4 Loading Beam-to-Actuator Connection .................................................................... 115 4.4.5 Out-of-Plane Support Frames ................................................................................. 116 4.4.6 Miscellaneous Modifications of the Test Setup ........................................................ 118 4.5 Instrumentation and Controls ......................................................................................... 119 4.5.1 Strain Gauges ......................................................................................................... 119 4.5.2 Potentiometers ........................................................................................................ 122 4.6 Testing Procedure and Loading Protocol ....................................................................... 127 4.6.1 Specimen W-1......................................................................................................... 128 4.6.2 Specimen W-2......................................................................................................... 130 4.7 Summary ....................................................................................................................... 130 5. EXPERIMENTAL RESULTS & DISCUSSION ................................................................. 132 5.1 Introduction .................................................................................................................... 132 5.2 Experimental Results for Specimen W-1 ........................................................................ 132 5.2.1 Hysteretic Force-Displacement Plot ........................................................................ 132 5.2.2 Experimental Observations ..................................................................................... 133 x 5.2.3 Drift Profiles ............................................................................................................ 141 5.2.4 Average Curvature Profiles ..................................................................................... 142 5.2.5 Strain Readings ...................................................................................................... 143 5.2.6 Sliding Shear, Rocking, & Shear Displacements ..................................................... 145 5.3 Experimental Results for Specimen W-2 ........................................................................ 148 5.3.1 Hysteretic Force-Displacement Plot ........................................................................ 148 5.3.2 Experimental Observations ..................................................................................... 150 5.3.3 Drift Profiles ............................................................................................................ 161 5.3.4 Average Curvature Profiles ..................................................................................... 162 5.3.5 Strain Readings ...................................................................................................... 164 5.3.6 Sliding Shear, Rocking, & Shear Displacements ..................................................... 165 5.4 Analysis of Results and Comparison in Specimen Response ........................................ 167 5.4.1 Force-Displacement Envelopes ............................................................................... 167 5.4.2 Wall Capacities ....................................................................................................... 169 5.4.3 Displacements ........................................................................................................ 170 5.4.4 Extent of Damage & Failure Mechanisms ............................................................... 172 5.4.5 Energy Dissipation .................................................................................................. 177 5.4.6 Ductility Ratios ........................................................................................................ 179 5.4.7 Key Takeaways & Conclusions ................................................................................ 180 5.5 Summary ....................................................................................................................... 181 6. PROPOSED BACKBONE MODELS FOR REINFORCED MASONRY SHEAR WALLS . 182 xi 6.1 Introduction .................................................................................................................... 182 6.2 Backbone Model for Regular RMSWs ........................................................................... 187 6.3 Backbone Model for RMSWs with Boundary Elements .................................................. 205 6.4 Summary ....................................................................................................................... 218 7. CONCLUSIONS .............................................................................................................. 219 7.1 Summary ....................................................................................................................... 219 7.2 Key Findings .................................................................................................................. 219 7.3 Future Research Needs ................................................................................................. 222 BIBLIOGRAPHY .................................................................................................................... 224 xii LIST OF TABLES Table 3-1: Selected Experimental Studies for Regular RMSWs (Adapted from Hsu et al., 2022) .................................................................................................................................................27 Table 3-2: Selected Experimental Studies for RMSWs with External Boundary Elements (BEs) (Adapted from Hsu et al., 2022) ................................................................................................36 Table 4-1: Test Matrix ................................................................................................................66 Table 4-2: Construction Schedule for the Masonry Walls ...........................................................74 Table 4-3: Slump Test Results for Grout ....................................................................................79 Table 4-4: Test Samples Prepared during Masonry Construction ..............................................82 Table 4-5: Masonry Prism Compressive Strength: Testing Results (Specimens W-1 & W-4) .....91 Table 4-6: Masonry Prism Compressive Strength: Testing Results (Specimens W-2 & W-3) .....92 Table 4-7: Concrete Masonry Units Compressive Test Results .................................................94 Table 4-9: Grout Prism Compressive Test Results .................................................................. 100 Table 4-10: Mortar Cubes Compressive Test Results .............................................................. 103 Table 4-11: Steel Reinforcement Tensile Testing Results ......................................................... 105 Table 4-12: Compressive Testing Results for Concrete Cylinders ............................................ 106 Table 5-1: Summary of Strain Observations for Vertical Bars in Wall Ends for Specimen W-1 . 144 Table 5-2: Summary of Strain Observations for Vertical Bars in Boundary Elements for Specimen W-2 ........................................................................................................................ 164 Table 5-3: Summary of Strain Observations for Ties in Boundary Elements for Specimen W-2 ............................................................................................................................................... 165 Table 5-4: Wall Capacities for Specimens W-1 & W-2 ............................................................. 169 xiii Table 5-5: Ductility Ratios for Specimens W-1 & W-2 .............................................................. 179 Table 6-1: Summary of Parameters from Strain Profiles from Referenced Studies .................. 200 Table 6-2: Design Approach for Developing Backbone Curves for Regular RMSWs ............... 204 Table 6-3: Summary of Parameters from Strain Profiles from Referenced Studies .................. 215 Table 6-4: Design Approach for Developing Backbone Curves for RMSWs with BEs .............. 217 xiv LIST OF FIGURES Figure 1-1: Cross Sections: a) Regular RMSW; b) RMSW with Embedded Boundary Elements; c) RMSW with 2-Block Boundary Elements; d) RMSW with Pilaster Boundary Elements ........... 3 Figure 1-2: 3-D View of 2-Block Boundary Element (Adapted from Banting & El-Dakhakhni, 2014) ......................................................................................................................................... 3 Figure 2-1: Typical Strain Distribution in a RMSW ...................................................................... 8 Figure 2-2: RMSW Idealization as a Cantilever .......................................................................... 9 Figure 2-3: Elastic Curvature, Rotation, and Displacement in a Cantilever RMSW ....................10 Figure 2-4: a) Schematic of Inelastic Curvature Distribution in a RMSW (Brzev & Anderson, 2018); b) Experimentally Obtained Curvature Distribution (Banting & El-Dakhakhni, 2014)....... 11 Figure 2-5: Idealized Inelastic Curvature, Rotation, and Displacement Profiles in a Cantilever RMSW ......................................................................................................................................12 Figure 2-6: Inelastic Curvature, Rotation, and Displacement in a Cantilever RMSW .................13 Figure 2-7: Idealized Nonlinear Models: a) Plastic Hinge; b) Nonlinear Spring Hinge; c) Finite Length Hinge Zone; d) Fiber Section; e) Finite Element (Deierlein et al., 2010) ........................14 Figure 2-8: Strain Profile Used for Computing Average Curvatures (Adapted from Shedid, 2009) .................................................................................................................................................16 Figure 2-9: Average Curvature Profile of a RMSW (Adapted from Shedid, 2009) ......................16 Figure 2-10: Internal Forces in a Tall RMSW .............................................................................18 Figure 2-11: Example of a Hysteretic Force-Displacement Diagram and a Backbone Curve .....20 Figure 2-12: Failure Mechanisms of RMSWs (Adapted from Robazza et al., 2020) ..................22 xv Figure 3-1: Wall 1 Force vs. Displacement Hysteresis Curves (ρv = 0.29%) (Shedid et al., 2008) .................................................................................................................................................29 Figure 3-2: Wall 4 Force vs. Displacement Hysteresis Curves (ρv = 1.31%) (Shedid et al., 2008) .................................................................................................................................................29 Figure 3-3: Progression of Failure in Regular RMSW Specimens: a) Horizontal Bed Joint Cracks; b) Stepped Cracks; c) Diagonal Cracks; d) Masonry Splitting; e) Spalling of End Face Shell and f) Splitting of Grout (Shedid et al., 2008) ....................................................................32 Figure 3-4: Specimen W2 at 1.84% Drift (Robazza et al., 2018) ...............................................34 Figure 3-5: Cross Sections of RMSW Specimens (Shedid et al., 2010) ....................................38 Figure 3-6: RMSW Specimen W5 with Flanged Boundary Elements, Force vs. Displacement Hysteresis Curves (Shedid et al., 2010) ....................................................................................40 Figure 3-7: RMSW Specimen W6 with 2-Block Boundary Elements, Force vs. Displacement Hysteresis Curves (Shedid et al., 2010) ....................................................................................40 Figure 3-8: RMSW Specimen W4 with 2-Block Boundary Elements, Force vs. Displacement Hysteresis Curves (P/Agf’m = 10%) (Banting and El-Dakhakhni, 2012) ......................................43 Figure 3-9: Regular RMSW Specimen W1 Force vs. Displacement Hysteresis Curves (P/Agf’m = 7%) (Shedid et al., 2010) ..........................................................................................................43 Figure 3-10: Wall 3 Failure Patterns: a) Loss of Face Shell and b) Final Failed State (Banting and El-Dakhakhni, 2012) ...........................................................................................................45 Figure 3-11: Specimen 1 Force vs. Displacement Hysteresis Curves (2lBE / lw = 0.07) (Banting and El-Dakhakhni, 2014) ...........................................................................................................47 Figure 3-12: Specimen 5 Force vs. Displacement Hysteresis Curves (2lBE / lw = 0.15) (Banting and El-Dakhakhni, 2014) ...........................................................................................................47 xvi Figure 3-13: Curvature Profiles for Walls 1 to 3 (Adapted from Banting & El-Dakhakhni, 2014) 48 Figure 3-14: Seismic Force Distribution in an Actual RMSW Versus Test Specimen (Aly & Galal, 2020a) ......................................................................................................................................49 Figure 3-15: Cross Section of Specimen W7 (Aly & Galal, 2020a) ............................................50 Figure 3-16: Wall 7 Force vs. Displacement Hysteresis Curve (Aly & Galal, 2020a) ..................51 Figure 3-17: Detailing Requirements for Ductile RMSWs (Adapted from Brzev & Anderson, 2018) ........................................................................................................................................55 Figure 3-18: Summary of Detailing Requirements for RMSWs with Boundary Elements ...........58 Figure 4-1: Cross Sections: a) Specimen W-1 and b) Specimen W-2 ........................................61 Figure 4-2: Elevation of Specimen W-2 .....................................................................................62 Figure 4-3: Cross Section of Concrete Footing Beam ...............................................................63 Figure 4-4: Close-Up of Typical Confinement Tie Used in Specimen W-2 .................................65 Figure 4-5: Temporary Formwork for Footing Beam: a) Elevation View; b) Side View; c) Plan View ..........................................................................................................................................68 Figure 4-6: Completed Temporary Formwork for Footing Beams ..............................................69 Figure 4-7: Reinforcement Cage for Footing and Loading Beams .............................................70 Figure 4-8: a) Conventional Stirrup Assembly; b) Stirrup Assembly for Footing Beam Reinforcement...........................................................................................................................71 Figure 4-9: Footing Beam Reinforcement Cage Assembly ........................................................71 Figure 4-10: Footing Beam Construction: a) During Curing and b) After Formwork Removal ....73 Figure 4-11: Masonry Wall Construction: a) Day 2; b) Day 4; c) Day 8 ......................................75 Figure 4-12: Assembly of Confinement Ties in the Boundary Elements .....................................77 xvii Figure 4-13: a) Foreman Placing Mortar; b) Foreman Placing Blocks; c) Labourer Pointing a Head Joint .................................................................................................................................78 Figure 4-14: Mixing Grout with Smaller Concrete Mixer Prior to Transportation via a Wheelbarrow .............................................................................................................................79 Figure 4-15: a) Grout Placement with Pails and b) Grout Tub Attached to Crane ......................80 Figure 4-16: Typical Masonry Shear Key ...................................................................................81 Figure 4-17: a) Grout Consolidation and b) Water Seepage Following Grout Consolidation ......81 Figure 4-18: Front View of Temporary Formwork Support Frame, Section “A” of Figure 4-20 ....84 Figure 4-19: Elevation View of Temporary Formwork Support Frame, Section “C” of Figure 4-20 .................................................................................................................................................84 Figure 4-20: Plan View of Temporary Formwork Support Frame ...............................................85 Figure 4-21: Wall Specimens Prior to Concrete Pouring for the Loading Beams .......................86 Figure 4-22: Completed Wall Specimens with the Steel Frame Assembly .................................87 Figure 4-23: Construction of Loading Beams: a) Formwork Detail and b) View of Formwork for All Loading Beams ....................................................................................................................88 Figure 4-24: Loading Beams Upon Completion .........................................................................88 Figure 4-25: Wrapped Prisms for Specimens W-1 and W-4 (Topmost Row) and Freshly Cast Prisms for Specimens W-2 and W-3 (Bottommost Rows) ..........................................................90 Figure 4-26: Capping the Masonry Prisms ................................................................................91 Figure 4-27: Typical Masonry Prism Subjected to Compression ................................................93 Figure 4-28: a) Stretcher CMU During Testing; b) Half CMU During Testing ..............................94 Figure 4-31: Grout Prisms After Casting ....................................................................................99 xviii Figure 4-32: Grout Prism Before the Compression Testing ........................................................99 Figure 4-33: Mortar Cubes in Molds Following Preparation ..................................................... 101 Figure 4-34: Mortar Cube Subjected to Compression in the Testing Machine .......................... 102 Figure 4-35: Reinforcement Bar Subjected to Tension ............................................................ 104 Figure 4-36: Elevation View of Test Setup, Facing West ......................................................... 108 Figure 4-37: Elevation View of Test Setup, Facing South ........................................................ 108 Figure 4-38: Test Setup for Specimen W-2 .............................................................................. 109 Figure 4-39: Actuator Connection to Strong Wall ..................................................................... 111 Figure 4-40: Actuator Support Frame ...................................................................................... 112 Figure 4-41: A 3-D View of Steel Box Beam ............................................................................ 114 Figure 4-42: Front View and Welding Details of Box Beam ..................................................... 114 Figure 4-43: Post-Tensioning of Horizontal Box Beam Rods ................................................... 115 Figure 4-44: Out-of-Plane Support at the Loading Beam Elevation ......................................... 117 Figure 4-45: Method of Affixing PTFE Sheets to the Loading Beam ........................................ 117 Figure 4-46: Minor Modifications and Touch-Ups to the Test Setup ......................................... 118 Figure 4-47: Strain Gauge Locations for Specimen W-2 as seen from a) Top of Wall and b) Front of Wall, Facing East ................................................................................................................ 120 Figure 4-48: Strain Gauge Installation Sequence: a) Strain Gauge Attached to Reinforcement Bar; b) Strain Gauge Wrapped with Tape; c) Strain Gauges Expelled Through Head Joints ... 122 Figure 4-49: Potentiometer Layout for Specimen W-1, Facing East ........................................ 123 Figure 4-50: Potentiometer Layout for Specimen W-2, Facing East ........................................ 124 Figure 4-51: Typical Arrangement of Potentiometers Affixed to a) Specimen; b) Bracing ......... 126 xix Figure 4-52: a) Potentiometers P13 and P14; b) Potentiometer P21; c) Potentiometer P6 ...... 127 Figure 4-53: Loading Protocol for Specimen W-1 .................................................................... 129 Figure 4-54: Loading Protocol for Specimen W-2 .................................................................... 130 Figure 5-1: Hysteretic Force-Displacement Plot for Specimen W-1 ......................................... 133 Figure 5-2: Cracking and Spalling Recorded in Specimen W-1 at Drifts a) 0.2%; b) 0.4%; c) 0.6%; d) 0.8%; e) 1.0%; f) 1.4% .............................................................................................. 134 Figure 5-3: North Toe of Specimen W-1 During the Negative Loading Cycle at 0.6% Drift (Facing East) ....................................................................................................................................... 136 Figure 5-4: Specimen W-1 at 0.8% Drift (Facing East): a) South Toe; b) North Toe ................. 137 Figure 5-5: South Toe of Specimen W-1 (Facing West) at 1.2% Drift During a) First Loading Cycle; b) Second Loading Cycle ............................................................................................. 138 Figure 5-6: North Toe of Specimen W-1 at 1.2% Drift During a) First Loading Cycle (Facing East); b) Second Loading Cycle (Facing South) ...................................................................... 139 Figure 5-7: Specimen W-1 at 1.4% Drift: a) South Toe (Facing West); b) North Toe (Facing West) ...................................................................................................................................... 140 Figure 5-8: Specimen W-1 at 2.0% Drift: a) North Toe (Facing South); b) South Toe (Facing West) ...................................................................................................................................... 141 Figure 5-9:Lateral Wall Drift Profiles for Specimen W-1 in a) Negative Loading Direction and b) Positive Loading Direction ....................................................................................................... 142 Figure 5-10: Average Curvature Profiles for Specimen W-1 .................................................... 143 Figure 5-11: Sliding Displacements at Masonry Wall and Foundation Interface for Specimen W-1 ............................................................................................................................................... 145 xx Figure 5-12: Method for Decoupling Shear Displacements from Diagonal Potentiometer Readings (Adapted from Thomsen & Wallace, 1995) .............................................................. 147 Figure 5-13: Combined Shear & Sliding Shear Displacements Between Masonry Courses, Specimen W-1 ........................................................................................................................ 148 Figure 5-14: Hysteretic Force-Displacement Plot for Specimen W-2 ....................................... 149 Figure 5-15: Cracking and Spalling Recorded in Specimen W-2 at Drifts a) 0.2%; b) 0.4%; c) 0.6%; d) 0.8%; e) 1.0%; f) 1.6% .............................................................................................. 151 Figure 5-16: South Toe of Specimen W-2 During the Positive Loading Cycle at 0.6% Drift (Facing East) .......................................................................................................................... 154 Figure 5-17: North Toe of Specimen W-2 During the Negative Loading Cycle at 0.6% Drift (Facing East) .......................................................................................................................... 154 Figure 5-18: Bottom Five Courses of Specimen W-2 During the Negative Loading Cycle at 0.8% Drift (Facing East) ................................................................................................................... 155 Figure 5-19: Extent of Damage in South Toe of Specimen W-2 During a) 1.2% Drift and b) 1.4% Drift (Facing West) .................................................................................................................. 156 Figure 5-20: Face Shell Spalling in North Toe at 1.6% Drift: a) Closest to North Edge (Facing South); b) Furthest from North Edge (Facing East) ................................................................. 157 Figure 5-21: Bottom Two Courses of Specimen W-2 During Negative Loading Cycle at 1.6% Drift (Facing East) ................................................................................................................... 158 Figure 5-22: Progression of Face Shell Spalling at 1.8% Drift in a) South Toe (Facing West); b) South Toe (Facing East); c) North Toe (Facing South) ............................................................ 159 Figure 5-23: a) Specimen W-2 North Toe at 2.0% Drift (Facing West); b) Close-up of Outermost Buckled Bar in North Toe......................................................................................................... 160 xxi Figure 5-24: Specimen W-2 South Toe at 2.0% Drift (Facing West) ........................................ 161 Figure 5-25: Lateral Wall Drift Profiles for Specimen W-2 in a) Negative Loading Direction and b) Positive Loading Direction ....................................................................................................... 162 Figure 5-26: Average Curvature Profiles for Specimen W-2 .................................................... 163 Figure 5-27: Sliding Displacements at Masonry Wall and Foundation Interface for Specimen W-2 ............................................................................................................................................. 166 Figure 5-28: Combined Shear & Sliding Shear Displacements Between Masonry Courses, Specimen W-2 ........................................................................................................................ 167 Figure 5-29: Force-Displacement Envelopes for Specimens W-1 & W-2 ................................. 168 Figure 5-30: Flexural and Shear Displacements, Specimen W-1............................................. 171 Figure 5-31: Flexural and Shear Displacements, Specimen W-2............................................. 171 Figure 5-32: Flexural Displacements, Specimens W-1 & W-2 ................................................. 172 Figure 5-33: Specimens at 1.0% Drift: a) W-1; b) W-2 ............................................................. 174 Figure 5-34: Specimens at 1.8% Drift: a) W-1; b) W-2 ............................................................. 176 Figure 5-35: Bottom Four Courses of Specimen W-2 at 1.8% Drift (Facing East) .................... 177 Figure 5-36: Energy Dissipation of Specimens W-1 & W-2 ...................................................... 178 Figure 6-1: Moment-Curvature Relation and Force-Displacement Relation in a Nonlinear Model ............................................................................................................................................... 183 Figure 6-2: Backbone Curve: a) General Model; b) Backbone Curve Corresponding to a RMSW (Adapted from Shedid et al., 2010) .......................................................................................... 184 Figure 6-3: Moment-Curvature Relation for Regular RMSWs per NIST GCR 17-917-45 (Applied Technology Council, 2017) ...................................................................................................... 186 xxii Figure 6-4: Force-Displacement (Backbone) Curve for Flexure-Dominated Regular RMSWs per NIST GCR 17-917-45 (Applied Technology Council, 2017) ..................................................... 187 Figure 6-5: Force-Displacement (Backbone) Curve for Flexure-Dominated Fully Grouted Regular RMSWs ..................................................................................................................... 188 Figure 6-6: Conceptual Strain Profiles for a Regular RMSW Corresponding to Points 1-4 on the Backbone Curve ..................................................................................................................... 189 Figure 6-7: Sample RMSW Cross Section, Strain Profile, and Internal Force Distribution for a) Point 1 (Onset of Yielding) and b) Point 2 (Ultimate Moment Capacity) in a Regular RMSW Backbone Curve ..................................................................................................................... 190 Figure 6-8: Summary of Analytical Procedure to Determine Points 1 & 2 on a Regular RMSW Backbone Curve ..................................................................................................................... 192 Figure 6-9: Stress-Strain Relation for Steel Considering Bar Buckling and Fracture in Regular RMSWs (adapted from Applied Technology Council, 2017) ..................................................... 193 Figure 6-10: Sample RMSW Cross Section, Strain Profile, and Internal Force Distribution used in Section Analysis for Points 3 and 4 in a Regular RMSW Backbone Curve .......................... 195 Figure 6-11: Summary of Analytical Procedure to Determine Points 3 & 4 on a Regular RMSW Backbone Curve ..................................................................................................................... 196 Figure 6-12: Cross Section of Specimen 1 (Adapted from Shedid et al., 2008) ....................... 197 Figure 6-13: Cross Section of Specimen W1 (Adapted from Shedid et al., 2010) .................... 197 Figure 6-14: Fitted Backbone Curve to the Hysteretic Force-Displacement Plot of Specimen 1 (Adapted from Shedid et al., 2008) .......................................................................................... 198 Figure 6-15: Fitted Backbone Curve to the Hysteretic Force-Displacement Plot of Specimen W1 (Adapted from Shedid et al., 2010) .......................................................................................... 198 xxiii Figure 6-16: Compressive Strains vs. Lateral Loads in Courses 1 and 2 of Specimen W-1 (Shedid, 2009) ........................................................................................................................ 201 Figure 6-17: Fitted Backbone Curves to the Hysteretic Force-Displacement Plot of Specimen 1 using Varying Approaches (Adapted from Shedid et al., 2008) ................................................ 202 Figure 6-18: Internal Force Diagram and Distances for Computation of Probable Moment Resistance of a RMSW ........................................................................................................... 204 Figure 6-19: Backbone Curve for Fully Grouted Regular RMSWs with External Boundary Elements ................................................................................................................................. 206 Figure 6-20: Sample RMSW Cross Section, Strain Profile, & Internal Force Distribution used in Section Analysis for a) Point 1 and b) Point 2 in a Backbone Curve for RMSWs with BEs ...... 207 Figure 6-21: Conceptual Evolution (Progression) of Damage and the Corresponding Strain Profiles for Points 1 Through 4 on a Backbone Curve for RMSWs with BEs: a) Points 1 & 2; b) Point 3; c) Point 4 .................................................................................................................... 209 Figure 6-22: Stress-Strain Relationship for Steel Considering a Delayed Bar Buckling Due to Confinement Ties & Bar Fracture, RMSWs with External Boundary Elements (Adapted from Applied Technology Council, 2017) ......................................................................................... 210 Figure 6-23: Summary of Analytical Procedure to Determine Points 3 & 4 on a Backbone Curve for RMSWs with BEs ............................................................................................................... 211 Figure 6-24: Cross-Section of Specimen W3 (Adapted from Shedid et al., 2010) .................... 212 Figure 6-25: Cross-Section of Specimen W6 (Adapted from Aly & Galal, 2020a) .................... 212 Figure 6-26: Fitted Backbone Curve to the Hysteretic Force-Displacement Plot of Specimen W6 (Adapted from Shedid et al., 2010) .......................................................................................... 213 xxiv Figure 6-27: Fitted Backbone Curve to the Hysteretic Force-Displacement Plot of Specimen W7 (Adapted from Aly & Galal, 2020a) .......................................................................................... 213 xxv LIST OF SYMBOLS Ag = gross area of cross-section, mm2 ABE = area of boundary element, mm2 c = distance from extreme compression fibre to the neutral axis, mm E = elastic modulus, MPa f’g = compressive strength of grout, MPa f’m = compressive strength of masonry, MPa fy = yield strength of reinforcement steel, MPa fyBE = yield strength of reinforcement steel in the boundary elements, MPa fyv = yield strength of vertical reinforcement steel, MPa fyh = yield strength of horizontal reinforcement steel, MPa h = height, mm hgauge = height of a gauge instrument, defined by its relative distance to other gauges, mm hgauge(i) = height of a gauge instrument at point i, mm hp = idealized plastic hinge height, mm hpe = experimentally measured plastic hinge height, mm hpe(c) = experimentally measured plastic hinge height based on curvature profiles, mm hpe(d) = experimentally measured plastic hinge height based on displacement profiles, mm hw = height of wall, m, cm, or mm I = moment of inertia, mm4 Ie = elastic moment of inertia, mm4 k = effective elastic stiffness, kN/m xxvi lBE = length of boundary element, mm, cm, or m lw = length of wall, m, cm, or mm M = bending moment resistance of a RMSW, kN*m M80 = bending moment resistance of a RMSW when subjected to lateral load Q80, kN*m Mf = bending moment resistance of a RMSW when subjected to lateral load Qf, kN*m Mu = bending moment resistance of a RMSW when subjected to lateral load Qu, kN*m M’u = bending moment resistance of a RMSW when subjected to lateral load Q’u, kN*m My = bending moment resistance of a RMSW when subjected to lateral load Qy, kN*m P = axial load, kN Q = lateral load applied at the top of a reinforced masonry shear wall, kN Q80 = 80% of Qu defined below, corresponding to 20% strength degradation, kN Qf = lateral load capacity of a RMSW specimen at failure, kN Qu = ultimate (maximum) lateral load capacity of a RMSW, kN Q’u = lateral load capacity of a RMSW specimen with boundary elements at the onset of strength degradation, kN Qy = yield lateral load capacity of a RMSW specimen, kN Rd = ductility modification factor, unitless tBE = thickness of boundary element, m, cm, or mm tw = thickness of regular RMSW, and web thickness of a RMSW with boundary elements, m, cm, or mm β1 = ratio of the depth of rectangular compression block to depth of the neutral axis, unitless Δ = lateral displacement at the top of a reinforced masonry shear wall, mm or drift % xxvii Δ80 = lateral displacement at the top of a reinforced masonry shear wall when it is subjected to lateral load Q80, mm or drift % Δf = lateral displacement at the top of a reinforced masonry shear wall when it is subjected to lateral load Qf, mm or drift % Δp = lateral displacement at the top of a reinforced masonry shear wall corresponding to the total plastic, or inelastic, displacement, mm or drift % ΔQu = lateral displacement at the top of a reinforced masonry shear wall when it is subjected to lateral load Qu, mm or drift % ΔQ’u = lateral displacement at the top of a reinforced masonry shear wall when it is subjected to lateral load Q’u, mm or drift % Δu = ultimate (maximum) lateral displacement at the top of a reinforced masonry shear wall, mm or drift % Δy = lateral displacement at the top of a reinforced masonry shear wall when it is subjected to Qy, mm or drift % ε = strain, unitless εm = strain in masonry, unitless εm80 = strain in masonry when a reinforced masonry shear wall is subjected to lateral load Q80, unitless εmf = strain in masonry when a reinforced masonry shear wall is subjected to lateral load Qf, unitless εmu = strain in masonry when a reinforced masonry shear wall is subjected to lateral load Qu, unitless εm’u = strain in masonry when a reinforced masonry shear wall is subjected tolateral load Q’u, unitless εs = tensile strain in reinforcement steel, unitless xxviii ε's = compressive strain in reinforcement steel, unitlessθ = rotation, radiansθic = inelastic rotational capacity, radiansθid = inelastic rotational demand, radiansθp = plastic rotation, radiansθy = yield rotation, radiansμ = ductility ratio, unitlessρ = reinforcement ratio, unitlessρBE = vertical reinforcement ratio in boundary elements, unitlessρh = horizontal reinforcement ratio, unitlessρv = vertical reinforcement ratio, unitlessφ = curvature, rad/mmφ80 = extreme curvature in a reinforced masonry shear wall when subjected to lateralload Q80, rad/mmφavg = average curvature, measured experimentally, rad/mmφavg(i) = average curvature at point i, measured experimentally, rad/mmφf = extreme curvature in a reinforced masonry shear wall when subjected to lateralload Qf, rad/mmφp = total plastic curvature, rad/mmφQu = extreme curvature in a reinforced masonry shear wall when subjected to lateralload Qu, rad/mmφu’ = extreme curvature in a reinforced masonry shear wall when subjected to lateralload Q’u, rad/mmφy = extreme curvature in a reinforced masonry shear wall when subjected to lateralload Qy, rad/mm xxix ACKNOWLEDGEMENTS I would like to acknowledge my supervisory team of Dr. Tony Yang and Dr. Svetlana Brzev for their valuable technical input and guidance throughout the duration of this research study. I am also deeply grateful to PhD candidate Yu-Cheng Hsu for his daily support and invaluable contributions to the experimental work in this study. UBC’s Civil Engineering Laboratory Staff including Doug Hudniuk, Scott Jackson, Mehrtash Motamedi, Shota Inoda, Jun Sang Song, Corey Strain, Arthur Mak, Simon Lee, and Darian Tichler are thanked extensively for their efforts in helping me carry out the experimental portion of this thesis. The importance of their contributions cannot be emphasized enough. The industry partners involved in this research study included the Canada Masonry Design Centre (CMDC), Scorpio Masonry BC Inc., and the Canadian Concrete Masonry Producers Association (CCMPA). All partners are acknowledged for their respective contributions. Furthermore, the time and materials donations by Basalite Concrete Products, ULC Concrete, NUCOR, DYWIDAG, and George Third and Son (GTS) are acknowledged. The involvement of these parties was vital to the successful completion of this thesis. Finally, sponsorship received from the NSERC Alliance Grant is acknowledged. A personal thank you is extended to my employer, AECOM Canada ULC, for supporting my decision to pursue graduate studies, for the flexible work arrangements throughout my time in the program, and for the financial assistance provided to subsidize a portion of my tuition. A heartfelt thank you is extended to my loving family, namely my mother and sister, for their unwavering support during my time in this program. Our family friend residing in Vancouver is also acknowledged for inviting me to stay with them as I temporarily moved from Winnipeg to pursue my graduate studies at UBC. Finally, I am grateful to my friends in Winnipeg and Vancouver for their companionship and moral support during my time in this program. 1 1. INTRODUCTION 1.1 Introduction In Canada, structural engineers predominantly employ steel, wood, concrete and masonry to design buildings in accordance with the National Building Code of Canada (NBC). From those four materials, masonry is the focus of this thesis, and the type of masonry that is of most interest to structural engineers is reinforced masonry (RM) as it is the most common type of loadbearing masonry used in Canada. RM walls are one of the main forms of RM construction. A RM wall consists of hollow concrete masonry units (CMUs) laid in a mortar bed that are reinforced with steel bars which run both vertically and horizontally within the block cells as well as the bed joints. CMUs in Canada have a nominal depth of 200 mm and a nominal length of 400 mm, but the nominal thickness varies from 100 mm – 300 mm in increments of 50 mm. RM loadbearing walls are most commonly constructed in a running bond pattern, and upon completion of laying blocks with mortar joints and reinforcement placement, the cores (i.e., openings) of the blocks are filled with grout, either at a specified core spacing or within each core. Once this assembly is constructed, and is subjected to axial load, it becomes a loadbearing RM wall. As a structural member in a building, a RM wall must be designed to support gravity loads (dead, live, and snow/rain) and lateral loads (due to wind and earthquake actions). RM walls that are designed to support both gravity and lateral loads are called loadbearing reinforced masonry shear walls (RMSWs), which resist lateral loads primarily via their in-plane stiffness. The loading requirements for structural design purposes are based on NBC 2020 (Canadian Commission on Building and Fire Codes, 2022). RMSWs are designed for these loading requirements per the Canadian masonry design standard CSA S304-24 (Canadian Standards Association, 2024). 2 RM buildings constructed in regular and high seismic zones in Canada are designed to behave inelastically in the event that they endure the effects of a significant earthquake. Inelastic behaviour means that during the design earthquake, or an earthquake of comparable magnitude, the yield strength and elastic capacity of the building’s structural materials will be exceeded such that a large portion of the total deformation will occur following yielding. The anticipated magnitude of inelastic deformation provides insight towards the building’s ductility capacity and ability to dissipate energy. For RMSWs, Canadian designers can select from three types of RMSW classifications per NBC 2020: Conventional Construction, Moderately Ductile, and Ductile (Canadian Commission on Building and Fire Codes, 2022). The ductility factors Rd of these wall classifications are 1.5, 2.0, and 3.0, respectively; a higher ductility factor corresponds to greater potential for energy dissipation. Per NBC 2020, high importance buildings (such as schools and community centres) located in high seismic zones and post-disaster buildings (such as public safety facilities and hospitals) located in regular and high seismic zones constructed using RM must employ either Moderately Ductile or Ductile RMSWs. Ductile RMSWs can be constructed either as regular walls or walls with boundary elements. A cross section of a regular RMSW, with a rectangular cross-section and uniformly distributed vertical reinforcement, is shown in Figure 1-1 (a). Figure 1-1 (b) shows a RMSW cross section with embedded boundary elements, whereas cross sections of RMSWs with external boundary elements are shown in Figure 1-1 (c) and (d). Boundary elements are typically thickened and specially reinforced sections provided at both wall ends, which consist of additional vertical reinforcement bars enclosed by transverse reinforcement (ties). The 2-block boundary element shown in Figure 1-1 (c) and pilaster boundary element shown in Figure 1-1 (d) are similar, except that the former consists of two stretcher blocks per course of the boundary element, whereas the latter consists of two special C-shaped masonry blocks per course. A 3-D view of the configuration shown in Figure 1-1 (c) is provided in Figure 1-2. 3 Figure 1-1: Cross Sections: a) Regular RMSW; b) RMSW with Embedded Boundary Elements; c) RMSW with 2-Block Boundary Elements; d) RMSW with Pilaster Boundary Elements Figure 1-2: 3-D View of 2-Block Boundary Element (Adapted from Banting & El-Dakhakhni, 2014) 4 Boundary elements are provided in RMSWs primarily to increase their ductility potential. Ties in the boundary elements play a critical role in confining these elements and maintaining the structural integrity of the vertical concentrated reinforcement and grout within the boundary elements. This allows for greater energy dissipation in RMSWs with boundary elements at higher drift demands. The application of RMSWs with boundary elements can be considered in RM buildings in high seismic hazard zones, RM buildings requiring enhanced seismic performance, and tall RM buildings (10-20 storeys). RMSWs with boundary elements are particularly feasible for application in tall RM buildings, since RMSWs in such buildings experience greater seismic demand (in terms of the forces at the base of the walls) and drift demands compared to low and mid-rise buildings. These greater drift demands are better accommodated by more ductile systems which have greater capacity for inelastic deformations, such as RMSWs with boundary elements. The experimental portion of this thesis focused on studying the seismic behaviour of RMSWswith embedded boundary elements, as shown in Figure 1-1 (b). The reason for studyingRMSWs with embedded boundary elements is that in practice, it is often not possible toconstruct RMSWs with external boundary elements due to architectural constraints. RMSWswith embedded boundary elements have potential to overcome this issue while allowingengineers to design buildings with enhanced seismic performance compared to those withregular RMSWs. Experimental research studies on RMSWs with embedded boundary elementsare very limited, while experimental research studies on regular RMSWs and RMSWs withexternal boundary elements have been previously performed in Canada. The motivation for thisthesis is to provide experimental evidence related to structural behaviour of RMSWs withembedded boundary elements and explore their potential for field applications in Canada. 5 1.2 Objectives and Scope The objectives of this research study are to: 1. Provide experimental evidence related to the structural response of regular RMSWs and RMSWs with embedded boundary elements. This experimental evidence was obtained from experimental testing of two full-size 240 mm thick RMSW specimens subjected to reversed cyclic loading without axial compression. The specimens were designed to be identical, except that one of the specimens was a regular RMSW, and the other specimen was a RMSW with embedded boundary elements. This experimental evidence may be used to assess if the current provisions in CSA S304-24 for RMSWs with boundary elements are suitable for RMSWs with embedded boundary elements. The experimental evidence may also be used to propose revisions to the current CSA S304 provisions for the seismic design of regular RMSWs and RMSWs with boundary elements. 2. Employ the gathered experimental evidence to compare the performance of the specimens. The potential of embedded boundary elements in RMSWs to improve their seismic performance is assessed as part of this objective. 3. Present an analytical approach for developing generalized force-displacement curves for regular RMSWs and RMSWs with boundary elements. Force-displacement curves are less formally and more commonly known as “backbone curves”, which are frequently used in applications involving nonlinear static analysis (i.e., pushover analysis). 1.3 Thesis Organization In addition to this chapter, this thesis has been split into several chapters. Chapter 2: Background provides an overview of several fundamental concepts that are important in the context of this thesis. Namely, the analytical theory of nonlinear behaviour of RMSWs is presented, and a discussion is provided regarding how the various critical 6 parameters in this theory are measured experimentally. This chapter also includes discussions regarding in-plane reversed cyclic loading testing for RMSWs, and the chapter concludes with a discussion on ductility and the ductility ratio. Chapter 3: Literature Review of Experimental Studies provides an overview of previous experimental research studies for RMSWs subjected to in-plane reversed cyclic loading done in Canada. Summaries of selected research studies for regular RMSWs and RMSWs with external boundary elements are presented. The chapter concludes by summarizing the seismic design provisions for Ductile RMSWs with boundary elements based on CSA S304-24 (Canadian Standards Association, 2024). Chapter 4: Experimental Program provides an overview of the two specimens that were tested as part of this thesis. The scope of this chapter is to provide details regarding their design, construction, and material properties. The test setup and loading protocols for the specimens are discussed as well. Chapter 5: Experimental Results & Discussion provides selected experimental results from the testing of both specimens. Analysis of these results and comparison in the performance of the specimens is also provided in this chapter. Chapter 6: Proposed Backbone Models for Reinforced Masonry Shear Walls focuses on providing details for the analytical study performed in this thesis. Analytical methods for developing force-displacement curves for regular RMSWs and RMSWs with boundary elements are presented. Chapter 7: Conclusion summarizes the work done in this thesis, provides an overview of the key findings, and offers suggestions for future research. 7 2. BACKGROUND 2.1 Introduction The intent of this chapter is to provide a brief overview of several relevant topics related to key parameters influencing the seismic response of RMSWs. Section 2.2 covers the analytical theory of nonlinear behaviour of RMSWs; concepts from elastic beam theory are presented in this section on a very high-level. Section 2.3 provides a high-level review of what experimental in-plane reversed cyclic loading is, how results from this type of testing relate to earthquake loading, and key parameters of interest from these types of experiments. Finally, Section 2.4 focuses on ductility. The primary focus of this section is to explain the ductility ratio and how it is computed. 2.2 Nonlinear Properties of RMSWs In an analytical setting, elastic beam theory is useful to predict the behaviour of RMSWs. Figure 2-1 shows the typical strain distribution for a RMSW subjected to in-plane loading, where P is the axial load, M is the bending moment, εm is the masonry strain, εs is the strain in the outermost reinforcement steel bar, c is the depth of the neutral axis, and d is the effective depth. Section axes (i.e., x-x, y-y) are also shown. 8 Figure 2-1: Typical Strain Distribution in a RMSW Per Figure 2-1, a portion of the wall is in compression (i.e., within the range of c, shown with a hatch in Figure 2-1), whereas the remaining portion is in tension. Assuming small strains and therefore small angles, curvature φ is equal to εm / c, or εs / (d – c), which effectively represents the slope gradient of the strain diagram. From elastic beam theory it is known that curvature can also be computed using the following equation: 𝜑 =𝑀𝐸𝐼𝑒 (2-1) where M is the internal bending moment, E is the elastic modulus, and Ie is the elastic moment of inertia about the strong axis (x-x). As shown in Figure 2-2, a single-storey RMSW without openings can generally be treated as a cantilever subjected to a point load, for which: 𝑀(𝑧) = 𝑄(ℎ𝑤 − 𝑧) (2-2) where M(z) is the internal bending moment developed in a RMSW section at height z, Q is the applied lateral force, and hw is the wall height. Substituting Equation (2-2) into Equation (2-1) to obtain curvature at height z yields: 9 𝜑(𝑧) =𝑄(ℎ𝑤 − 𝑧)𝐸𝐼𝑒 (2-3) Figure 2-2: RMSW Idealization as a Cantilever Single integration of Equation (2-3) yields to the equation for rotation θ(z), and double integration of Equation (2-3) yields to the equation for deflection Δ(z). These derivations are not shown for brevity. However, knowing that the maximum internal bending moment and curvature occur at the base of the RMSW (i.e., z = 0) and the maximum rotation and displacement occur at the top of the RMSW (i.e., z = hw), it is possible to derive formulas for the maximum values of M, φ, θ, and Δ. These formulas are provided in Equations (2-4) through (2-7), respectively, where the subscript y has been added to denote yield, or elastic. In a RMSW, yielding occurs when the wall is subjected to yield moment My, during which the outermost reinforcement bar yields such that εs is equal to εy. This is illustrated in Figure 2-3 alongside sketches of φy, θy, and Δy. 10 Figure 2-3: Elastic Curvature, Rotation, and Displacement in a Cantilever RMSW 𝑀𝑦 = 𝑄𝑦ℎ𝑤 (2-4) 𝜑𝑦 =𝑀𝑦𝐸𝐼𝑒=𝜀𝑦𝑑 − 𝑐 (2-5) 𝜃𝑦 = 𝜑𝑦ℎ𝑤2=𝑀𝑦ℎ𝑤2𝐸𝐼𝑒 (2-6) 𝛥𝑦 = 𝜑𝑦ℎ𝑤23=𝑀𝑦ℎ𝑤23𝐸𝐼𝑒 (2-7) 11 If buildings constructed using RMSWs were designed to behave elastically during earthquakes, then these equations would be sufficient to predict and study the response of RMSWs subjected to either reversed cyclic or earthquake loading. As mentioned in Chapter 1, this is not the case, such that derivation for inelastic deformations, rotations, and curvatures is necessary. Generally, experimental results from studies such as those presented in Chapter 3 show that the distribution of inelastic curvature in RMSWs is complex, as shown in Figure 2-4. Figure 2-4 (a) shows an illustration of the actual distribution of inelastic curvature, adjacent to Figure 2-4 (b) which shows an experimental result sample from the study by Banting and El-Dakhakhni (2014) presented in greater detail in Chapter 3. In Figure 2-4, lw is the wall length, φu is the ultimate curvature, and hp is defined shortly. a) b) Figure 2-4: a) Schematic of Inelastic Curvature Distribution in a RMSW (Brzev & Anderson, 2018); b) Experimentally Obtained Curvature Distribution (Banting & El-Dakhakhni, 2014) Instead of using the actual distribution shown in Figure 2-4 (a), it is most practical to use an approximate distribution. This allows us to define the idealized plastic hinge height, hp, which is equal to the length over which the actual plastic curvature develops (shown hatched with a 12 stripe pattern in Figure 2-4 (a)). This implies that plastic curvature as a function of height (i.e., φp(z)) is equal to: 𝜑𝑝(𝑧) = {𝜑𝑝, 0 ≤ 𝑧 ≤ ℎ𝑝0, ℎ𝑝 < 𝑧 ≤ ℎ𝑤 (2-8) Similar to the elastic case, integration of Equation (2-8) yields to θp(z), and double integration of Equation (2-8) yields to Δp(z). These derived equations are listed in Equations (2-9) and (2-10), respectively. 𝜃𝑝(𝑧) = {𝜑𝑝𝑧, 0 ≤ 𝑧 ≤ ℎ𝑝𝜑𝑝ℎ𝑝, ℎ𝑝 < 𝑧 ≤ ℎ𝑤 (2-9) 𝛥𝑝(𝑧) ={ 𝜑𝑝𝑧22, 0 ≤ 𝑧 ≤ ℎ𝑝𝜑𝑝ℎ𝑝(𝑧 −ℎ𝑝2), ℎ𝑝 < 𝑧 ≤ ℎ𝑤 (2-10) Profiles of φp(z), θp(z), and Δp(z) are illustrated in Figure 2-5. Figure 2-5: Idealized Inelastic Curvature, Rotation, and Displacement Profiles in a Cantilever RMSW Similar to the elastic case, knowing that the maximum value of curvature occurs at the base of the RMSW (i.e., z = 0), and that the maximum values of rotation and displacement occur at the 13 top of the RMSW (i.e., z = hw) it is possible to obtain maximum values for φp, θp, and Δp. This is computed in Equations (2-11) through (2-13), respectively. It is also noted that the maximum value of φp is obtained when the compressive strain in the masonry at failure, εmf, is reached. This is shown in Figure 2-6, where Mf is defined as the internal bending moment at failure. 𝜑𝑝 =𝜀𝑚𝑓𝑐 (2-11) 𝜃𝑝 = 𝜑𝑝ℎ𝑝 =𝜀𝑚𝑓ℎ𝑝𝑐 (2-12) 𝛥𝑝 = 𝜃𝑝(ℎ𝑤 − 0.5ℎ𝑝) =𝜀𝑚𝑓ℎ𝑝𝑐(ℎ𝑤 − 0.5ℎ𝑝) (2-13) Figure 2-6: Inelastic Curvature, Rotation, and Displacement in a Cantilever RMSW 14 Since the ultimate displacement Δu of a RMSW is equal to the sum of the elastic and plastic displacements, it is possible to derive the following equation based on Equations (2-7) and (2-13): 𝛥𝑢 = 𝛥𝑦 + 𝛥𝑝 = 𝛥𝑦 + (𝜑𝑢 − 𝜑𝑦)ℎ𝑝(ℎ𝑤 − 0.5ℎ𝑝) (2-14) where φu - φy is equal to φp. Equation (2-14) is important because it is used to relate post-yield displacements to curvature, which becomes important in applications involving nonlinear structural analysis. It is also important to note that the derivation of this equation assumes the idealized nonlinear model referred to as the finite length hinge zone, which is shown in Figure 2-7 (c) amongst other material models used in nonlinear structural analysis (Deierlein et al., 2010). These models are briefly discussed later in Chapter 6. Figure 2-7: Idealized Nonlinear Models: a) Plastic Hinge; b) Nonlinear Spring Hinge; c) Finite Length Hinge Zone; d) Fiber Section; e) Finite Element (Deierlein et al., 2010) Studying the extent of the plastic hinge height is of much interest in experimental research studies involving RMSWs. Design codes, such as CSA S304-24, set hp to be equal to half the length of the RMSW, such that hp = lw / 2 (Canadian Standards Association, 2024). Also, studying the extent of plastic curvature is useful for developing force-deformation (backbone) curves, more of which is covered in Chapter 6. 15 The final concept that is discussed in this section is related to how the plastic hinge height hpe is measured experimentally. There are two ways to do this: 1. Studying the lateral displacement profile of the wall and estimating at which height the profile transitions from being linear to nonlinear. This aligns with the theoretical approach shown in Figure 2-5 and Figure 2-6: notice that the displacement profile Δp is nonlinear from the base of the wall to a height of hp and linear afterwards until a height of hw. Plastic hinge heights estimated using this approach are denoted as hpe(d) for the remainder of the thesis. 2. Studying the “average curvature” profiles of the wall and estimating at which height the average curvatures, φavg, are equal to or less than the yield curvature, φy. It was previously noted that curvature is the ratio of the masonry strain to the neutral axis depth. While strains are measurable in an experimental setting, the depth of the neutral axis is not, and the way to overcome this challenge is to measure the strains at both ends of the wall. As shown in Figure 2-8, knowing the compressive and tensile strains allows one to obtain the curvature profile without explicitly measuring the neutral axis depth (Shedid, 2009). Note that “average curvature” refers to the curvature measured over a given gauge height hgauge(i), which is determined by the on-centre distances between the instruments (gauges) used for recording vertical displacements. The formula for obtaining φavg(i) is based on simple trigonometry and is shown in Equation (2-15). Also, Figure 2-9 shows an illustration of an “average” curvature profile of a wall, adjacent to a wall showing the corresponding locations of the gauges. Plastic hinge heights estimating using this approach are denoted as hpe(c) for the remainder of the thesis. 𝜑avg(𝑖) =𝛥𝑇𝑖ℎ𝑔𝑎𝑢𝑔𝑒(𝑖)+𝛥𝐶𝑖ℎ𝑔𝑎𝑢𝑔𝑒(𝑖)𝑙𝑤 (2-15) In Equation (2-15), ΔTi is the vertical displacement due to tension (T), ΔCi is the vertical displacement due to compression (C), and lw is the wall length. 16 Figure 2-8: Strain Profile Used for Computing Average Curvatures (Adapted from Shedid, 2009) Figure 2-9: Average Curvature Profile of a RMSW (Adapted from Shedid, 2009) In general, some researchers report the experimental plastic hinge height by using either of these methods, and some researchers report results using both methods. Both methods are useful in their own ways, and results from both can be compared amongst one another to verify their accuracy. 17 2.3 Behaviour of RMSWs Subjected to In-Plane Lateral Cyclic Loading This section provides a general overview of the behaviour of RMSWs subjected to in-plane reversed lateral cyclic loading. Prior to commencing this discussion, a brief overview is provided regarding how earthquake loading is distributed to a RMSW, in order to be able to relate this concept to cyclic testing. Subsequently, some high-level details are provided for RMSW cyclic loading tests that are deemed to be of most interest in the context of this thesis. Chapter 1 mentioned that RMSWs are designed to resist earthquake forces via their in-plane stiffness. These forces induce in-plane shear forces and bending moments within the walls. Accordingly, RMSWs must be designed with factored resistances that exceed the calculated shear forces and bending moments resulting from seismic loading. For most design applications, NBC 2020 states that a building containing shear walls must be able to handle 100% of the computed earthquake load in each orthogonal direction independently (Canadian Commission on Building and Fire Codes, 2022). Also, the distribution of the computed earthquake base shear (per Clause 4.1.8.11 of NBC 2020) to each wall in each orthogonal direction depends on the assumptions for diaphragm stiffnesses employed during modelling. Masonry buildings commonly employ concrete floors and roofs, be it either cast in place or precast (such as hollow core), which allows designers to assume rigid diaphragms and distribute the storey shear forces to the walls depending on their relative stiffness. Furthermore, most shear walls are designed to be load-bearing and thus support an axial load depending on the wall’s tributary area. Based on this, shear walls are ultimately subjected to axial forces, shear forces, and bending moments. Idealized axial, shear, and bending moment diagrams for a multi-story masonry shear wall are shown in Figure 2-10; note that the hatched portion of the wall denotes an approximate visualization of the plastic hinge zone. It is noted that the way the computed base shear is distributed along the wall height is shown to be reasonably realistic, 18 based on Clause 4.1.8.11.7 of NBC 2020 (Canadian Commission on Building and Fire Codes, 2022). Figure 2-10: Internal Forces in a Tall RMSW There are several ways to evaluate the performance of structural systems, including RMSWs, to earthquake loading in an experimental setting. A common testing approach consists of subjecting RMSW specimens to lateral loads in a reversed cyclic manner. Lateral forces are typically applied via actuators in cycles of push and pull. RMSW specimens can be multi-storey, where the storeys are separated by slab interfaces and lateral loads are applied at the heights of these interfaces, resembling the base shear distribution shown in Figure 2-10. RMSW specimens can also be single storey (as is the case for the tested specimens in this thesis), such that lateral loading is only applied at the top of the wall. Depending on the test, axial compression may also be applied via simply loading the wall specimen with heavy weight or through forces applied via vertical actuators. While the presence of axial force more closely resembles RMSWs in real buildings, test setups that incorporate this become more complex. Consequently, many studies, including this one, perform testing in the absence of axial load. 19 Furthermore, the magnitude of applied lateral displacements are usually designated to varyduring the test, such that the maximum magnitude of lateral displacement applied during eachcycle is greater than the previous cycle. The way that this is defined for a given test is referred toas a loading protocol. Cyclic loading is typically classified as a quasi-static loading, meaning thatit is intended to simulate the effects of dynamic loads (such as from an earthquake) by means ofslow and controlled movements that are “almost static”. Cyclic loading is considered to bereasonably representative of wall behaviour subjected to in-plane seismic effects, and manyresults from experimental studies performed in Canada that involved cyclic loading contributedto the development of Canadian design standards such as CSA S304.Several results and documented items that are of interest when studying the in-plane cyclic behaviour of RMSWs include, but are not limited to: • Force-displacement diagrams capturing the hysteretic behaviour of the RMSW specimen. A conceptual example of this type of diagram for a RMSW is shown in Figure 2-11. Note the convention of positive and negative displacements that are shown in the sketch, which is consistent with how experimental results are presented in this thesis. The force-displacement (backbone) curve shown in red color is discussed shortly. • Photographs and descriptions of failure mechanisms. Further information regarding types of failure mechanisms in RMSWs is provided shortly. • Readings from strain and displacement sensors (gauges). These can be used for calculating certain properties of RMSWs (for example, average curvatures, as discussed previously). • Quantifying the extent of plastic behaviour, including the plastic hinge height, if a sufficient number of gauge readings are available along the height of the specimen. The parameters mentioned above will be discussed in this thesis, namely when presenting results from past research studies in Chapter 3 and results from this study in Chapter 5. 20 The final point of discussion, prior to discussing the types of failure mechanisms in RMSWs, is related to the example force-displacement (backbone) curve illustrated in red in Figure 2-11. A force-displacement curve, in essence, is an envelope of hysteresis curves obtained through experimental testing of a structural element. Typically, three to four points are defined on the backbone curve. Point 1 is the yield point (i.e., when a reinforced concrete or reinforced masonry specimen starts to yield), point 2 corresponds to the ultimate load (capacity) that a structural element can attain, point 3 corresponds to 80% of the ultimate load, and point 4 corresponds to the displacement at failure. These points are shown in Figure 2-11. Figure 2-11: Example of a Hysteretic Force-Displacement Diagram and a Backbone Curve It is noted that Figure 2-11 shows an idealized symmetrical response in both the positive and negative directions. In experimental settings, this is rarely the case, such that fitting backbone curves is a challenging task. The important takeaway is that in this thesis, when any parameters from a hysteretic diagram are reported (such as ultimate loads, ductility ratios, etc.) they are computed by taking the absolute averages of the results in both axes (unless noted otherwise). For example, if an experimental result showed ultimate loads of 190 kN and -180 kN in the positive and negative directions, respectively, 185 kN would be the reported value in this thesis. 21 2.3.1 Failure Mechanisms of RMSWs The following classification of failure mechanisms of RMSWs that will be used in this thesis is proposed by Robazza et al. (2020): • Ductile Flexure (DF) refers to a desirable failure mechanism that occurs when the wall’s structural integrity is maintained despite it undergoing significant masonry damage (cracking and crushing) and yielding of reinforcement due to inelastic deformations. • Diagonal Shear Failure (S), common in squat shear walls, typically occurs due to low axial loads and high shear forces. It is identifiable through the development of inclined cracks within the specimen. • Shear-Flexure Failure (SF), essentially when DF and S occur simultaneously. • Sliding Shear Failure (SL), a shear failure mechanism which initiates when either a single bed joint or multiple bed joints crack, allowing the specimen to slide along the cracked interface(s). Sliding at the base (wall-foundation interface) can occur if axial loads are low and shear forces are high. • Toe-crushing (TC), a flexural failure mechanism characterized by localized crushing and spalling of masonry units and grout in the toe area at the base of the wall, resulting from vertical compression stresses exceeding the masonry compressive strength. • Bar-buckling (BB) is characterized by localized buckling of longitudinal reinforcement bars at the wall end zones. • Bar-Fracture Failure (BF) is characterized by fracture of longitudinal reinforcement bars (usually at the wall end zones). • Rocking (RO) typically occurs in masonry piers with large aspect ratios (hw / lw) under low compressive stress, where the RMSW rotates about its base, typically at its toe. • Lateral Instability (LI) occurs when excessive out-of-plane lateral displacements contribute to the wall’s instability and failure. 22 Illustrations of these failure mechanisms, except for Diagonal Shear Failure, are shown in Figure 2-12. Figure 2-12: Failure Mechanisms of RMSWs (Adapted from Robazza et al., 2020) Robazza et al. (2020) further specified that two types of failure mechanisms can be defined for a given RMSW subjected to cyclic loading: a primary failure mechanism and a secondary failure mechanism. The primary failure mechanism is observed at the instance when the wall’s ultimate lateral load resistance is reached, and the secondary failure mechanism refers to the type of failure mechanism recorded afterwards (e.g., at 80% of the ultimate resistance) (Hsu et al., 2022). Identifying primary and secondary failure mechanisms in RMSWs is complex, as it is common for multiple failure mechanisms to occur either sequentially or simultaneously during experimental testing. For example, the toe-crushing (TC) failure mechanism is commonly observed in reversed cyclic tests on RMSWs following onset of the primary failure mechanism, although it is not always deemed to be the governing cause of the secondary failure 23 mechanism. A good analogy is that when a car breaks down, the mechanic may diagnose engine failure as the primary issue, although other problems such as issues with the ignition system or a faulty cooling system could have occurred earlier and contributed to the final breakdown. 2.4 Ductility In Chapter 1, it was mentioned that during an earthquake, the anticipated magnitude of inelastic deformation of a structural member provides insight towards its ductility capacity. As mentioned previously, inelastic deformations can be computed by subtracting yield displacements from the total displacements. Another parameter that also provides insight towards ductility capacity is the ductility ratio μ, which is the ratio of the ultimate displacement to the yield displacement as shown in the following equation: 𝜇 =∆𝑢∆𝑦 (2-16) where Δu is the ultimate displacement, and Δy is the yield displacement. For the purposes of this thesis, Δu is the ultimate displacement of a wall taken at load equal to 80% of peak strength, or 20% strength degradation. If a specimen does not attain at least 20% strength degradation, Δu corresponds to the displacement at which the test was terminated. The ductility ratio can be sensitive to the value used for Δy. Δy can either be computed using elastic beam theory or measured experimentally. Equation (2-7) is used in the theoretical approach, which requires computation of at least φy through the section analysis. Although the section analysis is generally accurate for computing a RMSW’s elastic properties, the analysis is sensitive to input of the material strengths which can significantly affect the value of Δy. Experimentally, Δy can be computed by analyzing strain gauge (sensor) recordings and hysteretic force-displacement plots in order to determine at which displacement the outermost vertical reinforcement bar yields. The drawback of this method is that the obtained experimental 24 value of Δy is sensitive to the researcher’s judgement and quality and calibration of the sensors. As a result, it is occasionally more advantageous to consider the ultimate lateral drift percentage (Δu) directly as a measure of inelastic deformation capacity, in order to eliminate the sensitivity related to Δy (since the magnitude of Δy is usually relatively small compared to Δu). Nevertheless, the ductility ratio remains a commonly reported parameter in studies for RMSWs. 2.5 Summary The purpose of this chapter was to provide a review of some fundamental concepts related to this thesis, which are important for understanding discussions in future chapters. This chapter provided a review of the analytical theory of the nonlinear behaviour of RMSWs, followed by a discussion of how some of the properties used in this theory were measured experimentally. Following, a review of cyclic loading testing was provided, its relationship to earthquake loading, and some of the parameters of interest from these tests. Finally, a discussion related to ductility was provided, which included defining the ductility ratio. 25 3. LITERATURE REVIEW OF EXPERIMENTAL STUDIES 3.1 Introduction Several experimental studies on RMSWs subjected to in-plane reversed cyclic loading have previously been performed in Canada, primarily at McMaster University, Concordia University, and the University of British Columbia. The goal of this chapter is to provide a summary of selected past Canadian experimental research studies on RMSWs both with and without boundary elements. The selected studies include those with RMSW specimens subjected to in-plane reversed cyclic loading with shear span ratios (M/Vlw) of at least 1.5, had ductile flexure (DF) as the primary failure mechanism, and were fully grouted. Hsu et al. (2022) conducted a comprehensive review of previous experimental studies on RMSWs, which is relevant for this chapter. This chapter is divided into several sections. Section 3.2 provides an overview of experimental research done in Canada on regular RMSWs subjected to in-plane reversed cyclic loading, while Section 3.3 focuses on RMSWs with external boundary elements. Finally, Section 3.4 provides an overview of design provisions for Ductile RMSWs with boundary elements per the Canadian masonry design standard CSA S304-24. 3.2 Experimental Studies on Regular RMSWs Subjected to In-Plane Lateral Cyclic Loading Regular RMSWs are the most commonly employed type of RM seismic force resisting system (SFRS) in present-day Canada. Until 2014, engineers and designers were restricted to the use of Conventional Construction and Moderately Ductile RMSWs. A new class, Ductile RMSWs, was introduced in the 2014 version of CSA S304 (Canadian Standards Association, 2014) based on results from several experimental studies performed in Canada, USA, and New Zealand. In this section, the experimental results for 13 specimens tested in Canada are 26 presented. 8 specimens were tested by Shedid et al. (2008, 2010) and 5 specimens were tested by Robazza et al. (2018). The focus of the studies by Shedid et al. (2008, 2010) was on the general behaviour, hysteretic responses, and failure mechanisms of the RMSW specimens. The focus of the study by Robazza et al. (2018) was to study out-of-plane instability of RMSWs, in addition to studying their general seismic behaviour. Table 3-1 summarizes the studies referenced in this section and shows the relevant parameters of the wall specimens. The symbols used in this table are defined in the List of Symbols. Finally, the ductility ratios (μ) listed in the table were computed using Equation (2-16). 27 Table 3-1: Selected Experimental Studies for Regular RMSWs (Adapted from Hsu et al., 2022) Wall ID Geometry Material Detailing Experimental Results hw (cm) lw (cm) tw (cm) hw / lw (-) f’m (MPa) fyv (MPa) fyh (MPa) ρv (%) ρh (%) P/Agf’m (%) Qu (kN) Δy (%) Δu (%) μ (-) SF Shedid et al. (2008)1 360 180 19 2.0 14.8 502 491 0.29 0.08 0 133 0.19 2.18 11.2 TC2 360 180 19 2.0 14.8 502 491 0.78 0.13 0 256 0.31 1.80 5.8 TC3 360 180 19 2.0 14.8 502 491 0.73 0.13 0 236 0.31 1.27 4.0 TC4 360 180 19 2.0 14.8 502 491 1.31 0.26 0 370 0.41 1.61 3.9 TC5 360 180 19 2.0 14.8 502 491 1.31 0.26 5 392 0.45 1.28 2.9 TC6 360 180 19 2.0 14.8 624 491 1.31 0.26 10 550 0.47 1.58 3.4 TCShedid et al. (2010)W1 399 180 9 2.22 16.4 495 534 1.17 0.30 7 179 0.20 1.11 5.5 TCW4 266 180 9 1.48 16.4 495 534 1.17 0.60 6 266 0.14 1.07 7.9 TCRobazza et al. (2018)W1 380 260 14 1.46 23.4 484 484 0.33 0.36 8 250 0.22 0.60 2.7 SFW2 380 260 14 1.46 23.4 512 512 0.33 0.36 0 208 0.29 1.48 5.1 LIW3 400 260 19 1.54 27.1 508 508 0.24 0.26 0 195 0.15 2.30 15.3 ROW4 400 140 19 2.86 27.1 465 465 0.15 0.26 0 39 0.10 1.43 14.3 BFW5 400 260 14 1.54 27.1 506 506 0.33 0.36 0 185 0.27 0.86 3.2 TC Note: SF = Secondary Failure mechanism28 The study by Shedid et al. (2008) involved the testing of six specimens; from these, Walls 1 to 4 had different amounts and distributions of vertical reinforcement, while Walls 4 to 6 were subjected to varying magnitudes of applied axial stress. The relationship between the vertical reinforcement ratio and ductility was found to be inversely proportional, and was primarily influenced by the RMSW’s yield displacements (Δy) rather than the displacements at ultimate load (ΔQu) or 80% of the ultimate load (Δ80). In other words, the magnitudes of the latter two displacements were comparable amongst the specimens, whilst the yield displacements varied heavily which influenced the ductility ratios. Figure 3-1 and Figure 3-2 highlight this phenomenon for Walls 1 and 4, which were both tested without axial compression and were characterized by minimum and maximum vertical reinforcement ratios of 0.29% and 1.31%, respectively. As shown in these figures, Wall 4’s yield displacement was 15 mm, which is 2.15 times greater than Wall 1’s yield displacement of 7 mm, whereas the ratio of Δu between Wall 4 and Wall 1 is only 1.35 (per Table 3-1). The difference in displacements is consistent with elastic beam theory, particularly in the context of Equation (2-7). Addition of vertical reinforcement increases both moment capacity My and stiffness EIe, however My is typically observed to increase at a higher rate than EIe, which results in a larger Δy value. 29 Figure 3-1: Wall 1 Force vs. Displacement Hysteresis Curves (ρv = 0.29%) (Shedid et al., 2008) Figure 3-2: Wall 4 Force vs. Displacement Hysteresis Curves (ρv = 1.31%) (Shedid et al., 2008) The same research study showed that the relationship between the magnitude of axial stress and ductility was inversely proportional, although the effect was not as significant as the effect of 30 vertical reinforcement. For example, Wall 4’s ductility ratio of 3.9 (tested without axial stress) is 1.34 times greater than Wall 5’s ductility ratio of 2.9 (tested with axial stress corresponding to 5% of axial capacity), while Wall 4’s ductility ratio is 1.15 times greater than Wall 6’s ductility ratio of 3.4 (tested with axial stress corresponding to 10% of axial capacity). On the contrary, Wall 1’s (least reinforced, ρv = 0.29%) ductility ratio of 11.2 is 2.87 times greater than Wall 4’s (most heavily reinforced, ρv = 1.31%) ductility ratio of 3.9. An interesting observation is that Wall 5 had a lower ductility ratio (2.9) than Wall 6 (3.4), despite being subjected to less axial stress. The researchers concluded that the “displacement ductility tends to decrease slightly with increases in axial compressive stress”. The relationship between ultimate load Qu and vertical reinforcement ratio ρv tends to be directly proportional. For example, specimens W1, W3, W2, and W4 with reinforcement ratios of 0.29%, 0.73%, 0.78%, and 1.31%, respectively had Qu values of 133 kN, 236 kN, 256 kN, and 370 kN, respectively. Therefore, an increase in reinforcement ratio from 0.29% to 1.31% (by more than 4 times) resulted in a similar increase in the value for Qu. The relationship between Qu and magnitude of axial stress is also apparent to be proportional, as specimens W4, W5, and W6 (tested with axial stress corresponding to 0%, 5%, and 10%, respectively) had Qu values of 370 kN, 392 kN, and 550 kN, respectively. These observations imply that the relationship between Qu and ductility should also be inversely proportional, theoretically meaning that ductility ratios between specimens should decrease in the order of W1, W3, W2, W4, W5, and W6. This can be seen from Table 3-1, however specimen W2’s ductility ratio is greater than specimen W3’s, and specimen W6’s ductility ratio is greater than specimen W5’s. However, specimens W2 and W3 have similar vertical reinforcement ratios, and both have ductility ratios less than specimen W1’s and greater than specimen W4’s. The overall observation by Shedid et al. was that despite the “perception that masonry structures do not have much ductility and are particularly vulnerable to seismic loading”, the test 31 specimens showed significant energy dissipation “with little strength degradation up to and beyond usable drift levels”. This is justified by recorded ductility ratios ranging from 2.80 – 11.2 at drifts less than or equal to 2.18%, all of which are less than the maximum code-permitted value of 2.5% for normal importance buildings per NBC 2020 (Canadian Commission on Building and Fire Codes, 2022). Shedid et al. recorded ductile flexure (DF) as the primary failure mechanism for all walls, and it was observed by others that toe crushing (TC) was the secondary failure mechanism (Hsu et al., 2022). The ductile flexure mechanism was characterized by stepped cracks extending to the top and bottom of the wall, along with diagonal cracking crossing through the grout filled blocks, as shown in Figure 3-3 (c). This behaviour was preceded by horizontal cracking along the bed joints, which eventually progressed to stepped cracks in the head joints, as shown in Figure 3-3 (a) and (b), respectively. The toe crushing (TC) failure mechanism was characterized by cracking in the masonry units due to vertical splitting, followed by spalling of the face shells of the masonry units allowing exposure of the lightly cracked grout column near the toes. Ultimately, splitting of the grout column allowed the buckled vertical reinforcement to be exposed. These stages are shown in Figure 3-3 (d), (e), and (f), respectively. It should be noted that the failure sequence shown in Figure 3-3 was typical for all six specimens, although the researchers mentioned that the behaviour was slightly different amongst specimens beyond the point of 50% strength degradation. 32 a) b) c) d) e) f) Figure 3-3: Progression of Failure in Regular RMSW Specimens: a) Horizontal Bed Joint Cracks; b) Stepped Cracks; c) Diagonal Cracks; d) Masonry Splitting; e) Spalling of End Face Shell and f) Splitting of Grout (Shedid et al., 2008) A final important note related to this study is concerned with the plastic hinge height. Based on their findings, hpe(c) varied between 700 and 1,100 mm (i.e., 0.38lw and 0.61lw, or 0.19hw and 0.31hw) with the larger values corresponding to walls with smaller bar sizes (i.e., Walls 1 and 2). The next study discussed is by Shedid et al. (2010). In this study, the researchers tested two regular RMSW specimens (W1 and W4) with different overall height and horizontal reinforcement ratios, while the remaining characteristics were the same. Specimen W1 was a three-storey high wall, while specimen W4 was a two-storey high wall. Ultimately, the progression of failure described by the researchers for both specimens was similar to the progression of failure described in the previous study (Shedid et al., 2008). The ductility ratios of 5.5 and 7.9, corresponding to test specimens W1 and W4, respectively, were greater than the 33 values obtained for the test specimens with similar vertical reinforcement ratios (i.e., W4, W5, and W6) by Shedid et al. (2008). Finally, the plastic hinge heights estimated from the experimental deflection measurements for both test specimens were found to be 1,300 mm (i.e., 0.72lw or 0.33hw for W1 and 0.72lw or 0.49hw for W4) (Shedid, 2009). Based on this, the researchers stated that the plastic hinge height may less likely be a function of the total wall height and instead be more closely related to the wall length. This is an important finding that they were unable to confirm in their previous study published in 2008, because the specimen heights in that study were equal. The final study reviewed in this section is by Robazza et al. (2018). The findings of this study are useful to study the ductile behaviour of RMSWs and make some observations relevant in the context of this thesis. Five RMSW specimens (W1 to W5) were subjected to in-plane reversed cyclic loading (see Table 3-1). Specimen W1 was the only one tested in the presence of axial stress. Specimen W2 was the reference case. Specimen W3 had the same area of vertical steel as W2 but made use of a larger bar size, which allowed for greater rebar spacing. Also, the wall thickness of W3 was greater than W2 (190 mm versus 140 mm, respectively), resulting in differing values of ρv between these two specimens. Specimen W4 had the highest aspect ratio (hw/lw) of 2.9 compared to the remaining walls, which had values of 1.5. Finally, specimen W5 utilized an out-of-plane support system capable of accommodating larger in-plane displacements compared to the other specimens. The researchers found that axial stress reduces ductility of RMSWs based on the results of specimen W1. W1 was the only specimen tested with axial stress (corresponding to 8% of axial capacity) and had the lowest ductility ratio of 2.9. The relationship between ρv and ductility was observed to be inversely proportional, as specimens W1, W2, and W5 (all with ρv = 0.33%) had significantly lower ductility ratios (2.9, 5.6, and 3.4, respectively) compared to specimens W3 (μ = 14.4, ρv = 0.24%) and W4 (μ = 15.4, ρv = 0.15%). Relatively high ductility ratios of W3 and W4 34 were attributed to the increased thickness of these specimens, which allowed for larger internal grout columns at the wall ends. Finally, the relatively low ductility ratio of specimen W5 was attributed to premature toe crushing, which occurred due to poorly consolidated grout at the wall’s toes observed after face shell spalling took place. Based on the results by Robazza et al., Hsu et al. (2022) observed that toe crushing (TC) was the secondary failure mechanism for only specimen W5. Although it was not observed to be the secondary failure mechanism for the remaining specimens, toe crushing (TC) and bar buckling (BB) were prevalent and contributed to the failure of all specimens. An example of this is shown in Figure 3-4, which portrays a photo of specimen W2 taken at 1.84% drift. The presence of toe crushing (TC) and bar buckling (BB) is evident, despite lateral instability (LI) observed as the secondary failure mechanism by Hsu et al. (2022). Figure 3-4: Specimen W2 at 1.84% Drift (Robazza et al., 2018) Based on the reviewed studies by Shedid et al. (2008, 2010) and Robazza et al. (2018), the following points are considered to be important related to ductile behaviour of RMSWs: 1. Ductility in regular RMSWs is heavily influenced by the vertical reinforcement ratio (ρv) as well as distribution of vertical reinforcement along the wall length. The relationship between 35 ρv and ductility is inversely proportional, mostly due to the influence that ρv has on the yield displacement rather than its influence on the ultimate displacement Δu. The presence of axial stress also has an influence on ductility, and the relationship between the two is also inversely proportional. Finally, the relationship between maximum lateral force Qu and ductility was also observed to be inversely proportional. 2. Regular RMSWs designed to fail in flexure are typically observed to have ductile flexure (DF) as the primary failure mechanism. In terms of the secondary failure mechanism, toe crushing (TC) either defines this failure mechanism entirely as was demonstrated by Shedid et al. (2008, 2010) or provides significant contribution to failure per the results from Robazza et al. (2018). Bar buckling (BB) of vertical reinforcement is also a common companion mechanism to toe crushing (TC). 3. Shedid et al. (2010) preliminary suggested that the plastic hinge height of regular RMSWs may be more closely related to the wall length rather than the wall height. 3.3 Experimental Studies on RMSWs with External Boundary Elements Subjected to In-Plane Lateral Cyclic Loading RMSWs with boundary elements are considered to be a relatively new solution for increasing ductility in RMSWs as they were first introduced in the 2014 version of CSA S304, alongside the Ductile RMSW class (Canadian Standards Association, 2014). Numerous experimental tests on RMSW specimens with boundary elements have been performed in Canada and the results for 20 specimens are presented in this section. Out of these, 5 specimens were tested by Shedid et al. (2010), 9 specimens were tested by Banting and El-Dakhakhni (2012, 2014), while the remaining 6 specimens were tested by Aly and Galal (2020a, b). Table 3-2 summarizes the studies referenced in this section and shows the relevant parameters of the wall specimens. The symbols used in this table are defined in the List of Symbols. Finally, the ductility ratios (μ) listed in the table were computed using Equation (2-16).36 Table 3-2: Selected Experimental Studies for RMSWs with External Boundary Elements (BEs) (Adapted from Hsu et al., 2022) Wall ID Geometry Material Detailing Experimental Results hw (cm) lw (cm) tw (cm) hw lw (-) lBE (cm) 2lBE lw (-) f’m (MPa) fyv & fyBE (MPa) fyh (MPa) ρv (%) ρh (%) ρBE (%) P Agf’m (%) Qu (kN) Δy (%) Δu (%) μ (-) SF Shedid et al. (2010) W2 399 180 9 2.2 9 0.1 16.4 495 534 0.6 0.3 1.2 5 153 0.26 1.73 6.6 BF W3 399 180 9 2.2 18.5 0.21 16.4 495 534 0.6 0.3 1.2 5 150 0.23 2.36 10.2 TC W5 266 180 9 1.5 9 0.1 16.4 495 534 0.6 0.6 1.2 5 242 0.19 1.64 8.6 BF W6 266 180 9 1.5 18.5 0.21 16.4 495 534 0.6 0.6 1.2 5 238 0.15 2.05 13.7 TC W7 266 180 9 1.5 18.5 0.21 16.4 495 534 0.6 0.6 1.2 5 241 0.19 2.42 12.7 TC Banting & El-Dakhakhni (2012) W1 399 180 9 2.2 18.5 0.21 13.7 496 583 0.6 0.3 1.2 3 143 0.25 3.0 12.0 BF W2 399 180 9 2.2 18.5 0.21 13.7 496 583 0.6 0.3 1.2 3 126 0.33 2.67 8.1 TC W3 399 180 9 2.2 18.5 0.21 13.7 496 583 0.6 0.3 1.2 3 141 0.25 3.80 15.2 TC W4 399 180 9 2.2 18.5 0.21 13.7 496 583 0.6 0.3 1.2 10 203 0.28 1.85 6.6 TC Banting & El-Dakhakhni (2014) 1 399 266 9 1.5 18.5 0.07 14.9 496 583 0.5 0.3 1.2 6 308 0.22 1.55 7.0 TC 2 399 124 9 3.2 18.5 0.15 14.9 496 583 0.7 0.3 1.2 6 93 0.40 3.40 8.5 BF 3 266 124 9 2.1 18.5 0.15 14.9 496 583 0.7 0.6 1.2 6 129 0.29 1.74 6.0 TC 4 266 124 9 2.1 18.5 0.15 14.9 496 583 1.2 0.6 1.2 6 177 0.36 1.98 5.5 TC 5 190 124 9 1.5 18.5 0.15 14.9 496 583 0.7 0.6 1.2 6 179 0.32 2.27 6.6 TC 37 Wall ID Geometry Material Detailing Experimental Results hw (cm) lw (cm) tw (cm) hw lw (-) lBE (cm) 2lBE lw (-) f’m (MPa) fyv & fyBE (MPa) fyh (MPa) ρv (%) ρh (%) ρBE (%) P Agf’m (%) Qu (kN) Δy (%) Δu (%) μ (-) SF Aly & Galal (2020a, b) W7 238 172 9 1.4 19.0 0.22 8.7 460 535 0.2 0.2 0.8 15 62 0.24 2.42 10.1 TC W8 238 172 9 1.4 19.0 0.22 8.7 460 535 0.2 0.2 1.6 15 83 0.27 2.70 10.0 TC W9 238 172 9 1.4 29.0 0.34 8.7 460 535 0.2 0.2 1.0 14 87 0.28 3.02 10.8 TC W10 238 172 9 1.4 19.0 0.22 14.2 460 535 0.2 0.2 0.8 16 113 0.25 2.02 8.1 TC W11 238 172 9 1.4 18.5 0.22 14.2 460 535 0.2 0.2 0.8 16 57 0.23 1.82 7.9 TC W12 238 172 9 1.4 19.0 0.22 14.2 460 535 0.2 0.2 0.8 16 62 0.17 1.70 10.0 TC W7 238 172 9 1.4 19.0 0.22 8.7 460 535 0.2 0.2 0.8 15 62 0.24 2.42 10.1 TC Note: SF = Secondary Failure Mechanism 38 The study by Shedid et al. (2010) focused on studying the behaviour of seven wall specimens (W1 – W7) subjected to reversed cyclic loading. Five specimens contained boundary elements (W2, W3, W5, W6, and W7), while specimens W1 and W4 had different overall heights and horizontal reinforcement ratios; the remaining characteristics were the same as other specimens. Specimens W2 and W5 had flanged boundary elements, while specimens W3 and W6 had 2-block boundary elements. Finally, specimen W7 had pilaster-like boundary elements that employed spiral reinforcement for ties. Cross sections and reinforcement details of the walls employed in this study are shown in Figure 3-5. Figure 3-5: Cross Sections of RMSW Specimens (Shedid et al., 2010) The researchers found that Walls 2 and 5 had ductility ratios 1.5 times greater than their rectangular wall counterparts (i.e., Walls 1 and 4), whereas Walls 3 and 5 had ductility ratios 2 times greater than Walls 1 and 4. This was computed by considering various definitions of ductility rather than just the definition per Equation (2-16). The increases in ductility for the specimens with boundary elements are greatly attributed to the effect of the ties, which delayed 39 the onset of toe crushing (TC) and bar buckling (BB). This is apparent based on the comparison of specimens W2 and W5, which had ductility ratios of 6.6 and 8.6, respectively. Specimen W2 had only the middle vertical bar in the boundary element confined by the 90-degree hook from the horizontal reinforcement, and that bar experienced a delayed onset of bar buckling (BB) compared to the other bars in the boundary element. However, in specimen W5 all bars in the boundary elements were confined via 180-degree hooks, which resulted in a higher ductility ratio compared to W2. This implies that the effect of confinement is more prevalent if more vertical reinforcement bars in the boundary elements are confined. This statement is justified as specimens W3 and W6, in which all vertical reinforcement bars in the boundary elements were confined, displayed greater ductility ratios than W2 and W5. The ductility ratios values for specimens W3 and W6 were 10.2 and 13.7, respectively. Higher ductility ratios in W3 and W6 could also be attributed to the increased size of the boundary elements, and possibly the presence of a confined grout column which specimens W2 and W5 did not have. Figure 3-6 and Figure 3-7 show the force vs displacement plots for specimens W5 and W6, respectively, highlighting the differences in ductility. An important observation is that not only the ductility ratio of specimen W6 is greater than the ratio of specimen W5, but the ultimate displacement (Δu) is also greater (2.05% drift versus 1.64% drift, respectively). 40 Figure 3-6: RMSW Specimen W5 with Flanged Boundary Elements, Force vs. Displacement Hysteresis Curves (Shedid et al., 2010) Figure 3-7: RMSW Specimen W6 with 2-Block Boundary Elements, Force vs. Displacement Hysteresis Curves (Shedid et al., 2010) Failure mechanisms for RMSW specimens with flanged boundary elements (W2 and W5) and 2-block boundary elements (W3 and W6) were similar to regular RMSW specimens W1 and W4. All specimens experienced ductile flexure (DF) as the primary failure mechanism, while toe 41 crushing (TC) and bar buckling (BB) were prevalent secondary failure mechanisms reported following the primary failure mechanism. As described previously, toe crushing (TC) and bar buckling (BB) were concentrated in the boundary elements at the base of the wall for all specimens, similar to the toe zones in regular RMSWs. Specimens W2 and W5 experienced toe crushing (TC) similarly to regular RMSWs, however specimens W3 and W6 experienced toe crushing (TC) in a slightly different way due to the presence of the confined grout column. Essentially, the confined grout column remained fully intact even after spalling of the face shell of masonry as well as the unconfined portion of grout in the boundary elements, which had a major influence on the higher ductility ratios reported in these specimens. The length of the plastic hinge region hpe(d) reported in this study was 1,200 mm for W2 and W3 (0.67lw or 0.3hw) and 1,300 mm for W5, W6, and W7 (0.72lw or 0.49hw) (Shedid, 2009). These values are comparable to the regular RMSW specimens W1 and W4, for which the values were 1,300 mm (i.e., 0.72lw or 0.33hw for W1 and 0.72lw or 0.49hw for W4) (Shedid, 2009). The next study discussed is the one by Banting and El-Dakhakhni (2012). This study is a direct successor to the previous study by Shedid et al. (2010), because all 4 specimens had characteristics nearly identical to specimen W3 by Shedid et al. Specimen W1 was subjected to an axial stress corresponding to 3% of axial capacity, versus specimen W3 by Shedid et al. which was subjected to an axial stress corresponding to 5% of axial capacity. Specimen W2 was subjected to the same magnitude of axial stress as specimen W1 but discontinued the boundary elements at the interface of the first and second stories. Specimen W3 was also subjected to an axial stress corresponding to 3% of axial capacity but was constructed without slabs at the interfaces of the three stories, which all other specimens had. Finally, Specimen W4 was similar to specimen W1, but was subjected to a higher magnitude of axial stress corresponding to 10% of axial capacity. 42 The researchers showed that the presence of boundary elements positively influences ductility, irrespective of varying characteristics between the specimens. Specimens W1, W2, W3, and W4 with boundary elements had ductility ratios of 12.0, 8.1, 15.2, and 6.6, respectively, which are greater than or equal to their rectangular RMSW counterparts (e.g., specimen W1 from the study by Shedid et al. (2010) which had a ductility ratio of 5.5). Most importantly, the larger ductility ratio of 6.6 for specimen W4 with boundary elements compared to the ductility ratio of 5.5 for regular RMSW specimen W1 by Shedid et al. (2010) suggest that boundary elements have a positive effect on ductility when RMSWs are subjected to increasing magnitudes of axial stress. This is because specimen W4 was subjected to an axial stress level corresponding to 10% of its axial load-resisting capacity, whereas this value was 7% for specimen W1 by Shedid et al. The force vs displacement plots for these specimens are shown in Figure 3-8 and Figure 3-9, respectively. Per these figures, an interesting observation is that strength degradation for specimen W4 occurs more rapidly compared to specimen W1 by Shedid et al.; in the former specimen, strength degradation is observed in the last cycle only, whereas in the latter specimen, it is observed in the last four cycles. 43 Figure 3-8: RMSW Specimen W4 with 2-Block Boundary Elements, Force vs. Displacement Hysteresis Curves (P/Agf’m = 10%) (Banting and El-Dakhakhni, 2012) Figure 3-9: Regular RMSW Specimen W1 Force vs. Displacement Hysteresis Curves (P/Agf’m = 7%) (Shedid et al., 2010) 44 The inversely proportional relationship between magnitude of axial stress and ductility determined for regular RMSWs is evident in RMSWs with external boundary elements based on the results from the study by Banting and El-Dakhakhni. This is because specimen W1 by Banting and El-Dakhakhni (P/Agf’m = 3%), specimen W3 by Shedid et al. (2010) (P/Agf’m = 5%), and specimen W4 by Banting and El-Dakhakhni (P/Agf’m = 10%), demonstrated a decrease in ductility ratios (the corresponding values were 12.0, 10.2, and 6.6, respectively). Finally, the inversely proportional relationship between Qu and ductility was also apparent based on the results from the same specimens, which had Qu values of 143 kN, 150 kN, and 203 kN, respectively. Banting and El-Dakhakhni had similar findings like Shedid et al. regarding the failure mechanisms of RMSWs with external boundary elements, as well as the influence of confinement in boundary elements. Their observations indicate that as long as the confined grout column remains intact throughout testing, and the surrounding grout and masonry spall or fall off entirely, there is generally no effect on the strength degradation of RMSWs with boundary elements. Figure 3-10 (a) shows specimen W3 immediately after the spalling of the face shell in the boundary elements, while Figure 3-10 (b) shows the same specimen at the end of the test; note that the grouted column remained nearly full intact. 45 a) b) Figure 3-10: Wall 3 Failure Patterns: a) Loss of Face Shell and b) Final Failed State(Banting and El-Dakhakhni, 2012)Banting and El-Dakhakhni (2014) tested five RMSW specimens with boundary elements, whichwere generally similar to the specimens from Banting and El-Dakhakhni (2012). Specimen 1from this study was similar to specimen W1 from Banting and El-Dakhakhni (2012), except for aslightly reduced vertical reinforcement ratio (ρv = 0.5% versus 0.6%) and increased length (2660mm versus 1800 mm), corresponding to an aspect ratio (hw / lw) of 1.5. Specimen 2 was similarto specimen 1, except for a slightly higher vertical reinforcement ratio (ρv = 0.7% versus 0.5%)and a significantly higher aspect ratio of 3.2. Specimen 3 was similar to specimen 2 except itsaspect ratio was 2.1. Specimen 4 was identical to specimen 3, except for an increased verticalreinforcement ratio (ρv = 1.2% versus 0.7%). Finally, specimen 5 was mostly similar to specimen2, except the aspect ratio was 1.5. All specimens were tested under the same level of axialstress, corresponding to 6% of their axial load-resisting capacity.The study showed that the presence of boundary elements has a positive influence on ductility of RMSWs. The ductility ratios varied between 4.9 and 8.0 amongst the specimens. The 46 observed failure mechanisms of the specimens were similar to those in the studies presented previously by Shedid et al. (2010) and Banting & El-Dakhakhni (2012). The effect of confinement ties on ductility in RMSWs with boundary elements was apparent in this study. The inversely proportional relationship between the vertical reinforcement ratio and ductility was observed based on the behaviour of specimens 3 (ρv = 0.7%) and 4 (ρv = 1.2%), which had ductility ratios of 6.0 and 5.5, respectively. The equal aspect ratios of specimens 1 and 5 (hw / lw = 1.5) allowed Banting and El-Dakhakhni (2014) to study the effect of the specimen height and length on their behaviour. The findings indicate that the ratio of the length of the boundary elements to wall length (2lBE / lw) appeared to have had an impact on the force-based responses of the specimens. Per Table 3-2, these ratios (2lBE / lw) were 0.07 for specimen 1 and 0.15 for specimen 5. Banting and El-Dakhakhni noted that while both specimens had comparable ductility ratios, which were 7.0 and 6.6 for specimens 1 and 5, respectively, the “manner by which each wall achieved this (ductility ratio) differed significantly”. Specimen 5 displayed greater ultimate curvature, ultimate drift and hpe(c) compared to specimen 1; this implies that Specimen 5 experienced a greater extent of inelastic response compared to Specimen 1. The researchers ultimately noted that specimen 5 “had an improved post peak performance attributed to the relatively large boundary element it possessed”. Figure 3-11 shows the force vs displacement plot for specimen 1, and Figure 3-12 shows this plot for specimen 5. In these figures, an important observation is that specimen 5 is able to maintain Qu for approximately five cycles following initial attainment, whereas specimen 1 maintains Qu for only approximately three cycles following initial attainment. Another important observation is that while specimen 1’s ductility ratio is higher than specimen 5’s, the ultimate drift (Δu) of the latter is significantly greater than the former (2.27% versus 1.55%, respectively). 47 Figure 3-11: Specimen 1 Force vs. Displacement Hysteresis Curves (2lBE / lw = 0.07) (Banting and El-Dakhakhni, 2014) Figure 3-12: Specimen 5 Force vs. Displacement Hysteresis Curves (2lBE / lw = 0.15) (Banting and El-Dakhakhni, 2014) 48 One of the most important findings by Banting and El-Dakhakhni is concerned with therelationship between the specimen’s aspect ratio and plastic hinge height. The findings of thestudy showed that the effect of changing the aspect ratio between specimens 2, 3, and 1 (hw / lwof 3.23, 2.15, and 1.5, respectively) had a “direct effect” on the plastic hinge height. The hpe(c)values for specimens 2, 3, and 1 were found to be 1235 mm (1.0lw or 0.31hw), 1085 mm (0.88lwor 0.41hw), and 1410 mm (0.53lw or 0.35hw), respectively, and the corresponding curvatureprofiles are shown in Figure 3-13. Also, specimen 5 with an aspect ratio of 1.5 (same asspecimen 1) had a comparable hpe(c) value to specimen 1 (if normalized with respect to lw). Thehpe(c) value for specimen 5 was equal to 0.6lw (742 mm, 0.39hw). While the researcherscompared the extent of the plastic hinge height for these specimens based on their normalizedvalues with respect to lw, they believed that its extent is “more strongly related to aspect ratiorather than wall length, because Wall 2 achieved a lpe nearly double that of Walls 1 and 5”. Notethat lpe is equivalent to hpe(c). Figure 3-13: Curvature Profiles for Walls 1 to 3 (Adapted from Banting & El-Dakhakhni, 2014) Aly and Galal (2020a, b) performed testing of 6 RMSW specimens with 2-block boundary elements. All specimens were 2.38 m high and were intended to simulate the bottom portion of 49 an 18.1 m tall RMSW, as shown in Figure 3-14, corresponding to an aspect ratio (hw/lw) of 10.5. Achieving this required subjecting the specimens to additional bending moment developed by two vertical actuators, to simulate the seismic demand due to multiple storeys. Figure 3-14: Seismic Force Distribution in an Actual RMSW Versus Test Specimen (Aly & Galal, 2020a) Aly and Galal (2020a) tested specimens W7, W8, and W9, which were similar except for the vertical reinforcement ratio in the boundary elements, equaling to 0.8%, 1.6%, and 1.0%, respectively. Also, the ratio of the length of the boundary elements to the wall length (2lBE/lw) of specimen W9 was greater than the ratio for both specimens W7 and W8 (0.34 versus 0.22). The cross section of specimen W7 is shown in Figure 3-15. Aly & Galal (2020b) tested 3 specimens: W10, W11, and W12. Specimen W10 was similar to specimen W7, but the former had half the shear span-to depth ratio (M / 0.8Vlw). Specimen W11 was similar to specimen W7, but the former was constructed using stretcher blocks in the boundary elements rather than C-shaped 50 blocks. Finally, specimen W12 was similar to specimen W7 but included lap-splicing of vertical reinforcement: the distributed bars were spliced at the wall-foundation interface, whereas the bars in the boundary elements were spliced at the interface of the first and second storeys. Figure 3-15: Cross Section of Specimen W7 (Aly & Galal, 2020a) In general, high ductility ratios were observed for all specimens, ranging from 7.9 to 10.9. On average, these values are greater than values reported in the previously presented studies; this can be attributed to the relatively low vertical reinforcement ratio of 0.2% used in the specimens by Aly & Galal (2020a, b), compared to the ratios used by Shedid et al. (2010) and Banting & El-Dakhakhni (2014) (see Table 3-2). High ductility ratios were achieved despite significantly higher magnitudes of axial stress compared to specimens from the previous studies, which ranged from 14% to 16% of the specimens’ axial load-resisting capacities. Out of all the presented studies, only Aly & Galal (2020 a, b) reported force vs displacement responses without strength degradation. The force-displacement hysteretic curves of specimen W7 are shown in Figure 3-16, clearly portraying this phenomenon. 51 Figure 3-16: Wall 7 Force vs. Displacement Hysteresis Curve (Aly & Galal, 2020a) The studies by Aly & Galal (2020a, b) provide several important findings regarding the effect of varying the size of boundary elements and quantity of vertical reinforcement within them. Increasing the size of the boundary elements contributed to an enhanced ductility ratio, justified based on the comparison of specimens W7, W8, and W9. Specimens W7 and W8, both with 2lBE/lw ratios of 0.22, had respective ductility ratios of 9.8 and 10.0 compared to W9, which had a 2lBE/lw ratio of 0.34 and a ductility ratio of 10.9. This increase in ductility is attributed to the increased size of the confined grout column in the boundary elements. Furthermore, increasing the quantity of vertical reinforcement within the boundary elements appeared to have resulted in an increase the lateral capacities and ductility ratios in the walls. This is justified as specimen W7 which contained 4 bars in the boundary elements had Qu of 62 kN and μ of 9.8, whereas specimens W8 and W9 which contained 8 bars in the boundary elements had Qu of 83 kN and 87 kN, respectively, and μ of 10.0 and 10.9, respectively. The curvature profiles produced by Aly & Galal (2020a, b) are useful to make observations regarding the extent of the plastic hinge height. Curvature profiles are available to a height 52 extending to the first storey (i.e., approximately 1900 mm, which is equal to 0.8hw or 1.1lw). It was observed that, except for specimen W10, the values of curvature at the height of the first storey are significantly greater than the yield curvature; this supports Banting & El-Dakhakhni’s (2014) observation that the plastic hinge height is more likely a function of the aspect ratio rather than wall length. This is justified as specimens W1, W2, W3, and W4 in the study by Banting & El-Dakhakhni (2012) with similar wall lengths of 1800 mm to the specimens in the current study (i.e., 1720 mm) had hpe(c) values of 1782 mm (0.99lw or 0.45hw), 2160 mm (1.2lw or 0.54hw), 1980 mm (1.1lw or 0.49hw), and 1404 mm (0.78lw or 0.35hw), respectively. If plastic hinge height was a function of wall length, the plastic hinge heights of the specimens in the studies by Aly & Galal (2020a, b) would be similar to those from the study by Banting & El-Dakhakhni (2012), but that was not true. Furthermore, the specimens tested by Aly & Galal (2020a, b) were intended to simulate a RMSW with an aspect ratio of 10.5, which supports this statement. Based on the studies by Shedid et al. (2010), Banting & El-Dakhakhni (2012, 2014), and Aly & Galal (2020a, b) reviewed in this section, the following points are considered to be important related to ductile behaviour of RMSWs with external boundary elements: 1. RMSWs with external boundary elements are generally able to display enhanced ductility compared to regular RMSWS; this is mostly attributed to the effect of ties on both the confined grout and vertical reinforcement in the boundary elements. The ties play a crucial role in delaying the onset of vertical bar buckling (BB) and toe crushing (TC) of the masonry. Otherwise, the failure mechanisms in RMSWs with external boundary elements are similar to regular RMSWs. 2. Increasing the size of the boundary elements, and subsequently the cross-sectional area of the confined grout column, increases the ductility of RMSWs. The larger size of the 53 boundary elements relative to the wall length also improves the post-peak performance of RMSWs. 3. The previously observed relationships for regular RMSWs, e.g., between ductility and the vertical reinforcement ratio, ductility and the magnitude of axial stress, and ductility and ultimate load capacity, are also evident in RMSWs with boundary elements. Generally, boundary elements are effective in reducing the rate of strength degradation with increased levels of axial stress. 4. The plastic hinge height in RMSWs with external boundary elements is likely dependent on the wall’s aspect ratio. The relationship between the plastic hinge height (when normalized to the RMSW’s length) appears to be proportional to the wall’s aspect ratio. 3.4 Review of Seismic Design Provisions for RMSWs with Boundary Elements The design process of RMSWs with boundary elements in accordance with CSA S304-24 (Canadian Standards Association, 2024) requires compliance with the provisions of Ductile shear walls as well as the provisions for boundary elements. This section will focus on reviewing the provisions for Ductile shear walls with boundary elements. The design provisions for Ductile shear walls include evaluating its axial resistance, shear resistances (diagonal and sliding) and moment resistance against the factored force demands. This is consistent with the design process of Conventional Construction and Moderately Ductile RMSWs. However, Clause 17.9 of CSA S304-24 (Canadian Standards Association, 2024) is specific to Ductile RMSWs and is concerned with specifying a minimum aspect ratio (hw/lw) ratio of 1, a limit on the unsupported height-to-thickness ratio, detailing requirements in the plastic hinge region, and verifying the inelastic rotational capacity against the inelastic rotational demand. The purpose of specifying a minimum aspect ratio of 1 is to ensure that the RMSW behaves as a slender versus squat shear wall, and the purpose of specifying a limit on the 54 unsupported height-to-thickness ratio is to ensure lateral stability of the RMSW. Finally, the Capacity Design approach is covered in this clause, and is intended to ensure a Ductile Flexure (DF) failure mechanism. The detailing requirements for Ductile shear walls are shown in Figure 3-17. 55 Figure 3-17: Detailing Requirements for Ductile RMSWs (Adapted from Brzev & Anderson, 2018) 56 Clause 17.8.7 of CSA S304-24 requires designers to verify that a Ductile RMSW can handle the necessary magnitude of inelastic deformation during the design earthquake. This is verified by ensuring that the inelastic rotational capacity of the wall, θic, is greater than the inelastic rotational demand, θid (Canadian Standards Association, 2024). The equation for θid is: 𝜃௜ௗ =൫∆௙ଵ𝑅ௗ𝑅௢ − ∆௙ଵ𝛾௪൯ℎ௪ − 0.5𝑙௪,௠௔௫ ≥ 𝜃௠௜௡ (3-1) where Δf1 is the elastic design displacement, γw is the ratio of the wall’s nominal wall resistance to that of its factored moment resistance (but need not be taken as less than 1.3), hw is the wall height, lw,max is the length of the longest wall of the primary SFRS in the direction being considered, and θmin is equal to 0.004 for Ductile RMSWs. The equation for θic is: 𝜃௜௖ = ൬𝜀௠௨𝑙௪2𝑐− 0.002൰ ≤ 0.025 (3-2) where εmu is the masonry’s ultimate strain taken as 0.003, lw is the wall length, and c is the distance from the extreme compression fibre to the neutral axis. The first term in Equation (3-2) can be obtained by substituting the value of hp assumed in CSA S304-24 (i.e., 0.5lw) into Equation (2-12) which gives the ultimate plastic rotation θp. The inelastic rotation is obtained by subtracting the elastic rotation θe from θp; the former can be computed using Equation (2-6) but is taken as 0.002 for simplicity (Brzev & Anderson, 2018). The design provisions for Ductile shear walls with boundary elements include the provisions for Ductile shear walls mentioned previously, as well as additional provisions related to boundary elements per Clauses 17.10 and 17.11 of CSA S304-24 (Canadian Standards Association, 2024). The design provisions consist of the maximum compression strain limit, the length of the boundary elements, and a design calculation check. These are summarized below: 57 1. The maximum compression strain limit εmu is permitted a maximum value of 0.008, versus 0.003 for regular RMSWs. 2. The length of a boundary element (lBE) is governed by the neutral axis depth c. It is taken as the maximum of c (εmu – 0.003) / εmu, (c – 0.1lw), and c / 2. 3. Besides the conventional design, an additional check is required to verify the shear resistance between the boundary element and the web. The detailing requirements for RMSWs with boundary elements are shown in Figure 3-18. Note that the detailing requirements shown in this figure must be followed in addition to the detailing requirements for Ductile shear walls shown in Figure 3-17. 58 Figure 3-18: Summary of Detailing Requirements for RMSWs with Boundary Elements 59 3.5 Summary The purpose of this chapter was to provide an overview of selected past Canadian experimental research studies on regular RMSWs and RMSWs with external boundary elements subjected to in-plane reversed cyclic loading. The goal of reviewing these studies was to gain an overall understanding of their behaviour and summarize some of the relevant bits of information that are most important in the context of this thesis. The chapter concluded with a brief overview of design provisions for Ductile RMSWs with boundary elements based on the Canadian masonry design standard CSA S304-24 (Canadian Standards Association, 2024). 60 4. EXPERIMENTAL PROGRAM 4.1 Introduction The influence of embedded boundary elements in RMSWs was studied by testing two specimens (W-1 and W-2) that were subjected to in-plane reversed cyclic loading without applied axial compression. Specimen W-1 was a regular RMSW, while specimen W-2 was a RMSW with embedded boundary elements. The specimens were designed to be identical except for the presence of embedded boundary elements. This chapter focuses on discussing the experimental program for these specimens and includes discussing their design and construction (Section 4.2), their material properties obtained through material testing (Section 4.3), the test setup (Section 4.4), instrumentation and controls (Section 4.5) and the testing procedure (Section 4.6). Construction and testing of the specimens were done in the University of British Columbia’s (UBC) Structures Laboratory. The results from this experimental program are provided in Chapter 5. 4.2 Specimen Design & Construction 4.2.1 Specimen Design & Detailing Specimens W-1 and W-2 each consisted of three components: a reinforced concrete footing beam, a reinforced masonry wall, and a reinforced concrete loading beam. The reinforced concrete footing beam was 450 mm deep, 500 mm wide, and 3300 mm long. The footing beam was perforated by eight 2-inch (51 mm) diameter openings, with embedded PVC pipes spaced at varying intervals along the beam length. The openings were provided to facilitate fastening of the specimen to the laboratory’s strong floor, as discussed later in this chapter. The masonry wall consisted of 17 courses of blocks, measuring 2590 mm in length, 3400 mm in height, and 240 mm in thickness. The loading beam was identical to the footing beam in terms of dimensions and reinforcement. Cross sections of the specimens are shown in Figure 4-1, and 61 an elevation of specimen W-2 is shown in Figure 4-2. It can be seen that specimens W-1 and W-2 were identical, except for the 10M ties spaced at 100 mm on-center at the boundary elements of specimen W-2. Figure 4-1: Cross Sections: a) Specimen W-1 and b) Specimen W-2 62 Figure 4-2: Elevation of Specimen W-2 Per Figure 4-2, the loading and footing beams were reinforced with 12-15M longitudinal bars and 10M stirrups at 80 mm spacing. A cross section of the footing beam is shown in Figure 4-3, showing the orientation of the reinforcement. The 2-inch (51 mm) diameter PVC pipes which 63 protruded horizontally through the footing beam in the transverse direction are shown in this figure as well. Figure 4-3: Cross Section of Concrete Footing Beam The purpose of the footing beam was to serve as a base (foundation of the specimen) and attach the specimen to the laboratory’s strong floor. The purpose of the loading beam was to facilitate the connection of the top of the specimen to the actuator. The details of these connections are discussed in Section 4.4. The footing and loading beams were intended to be significantly more rigid than the masonry wall; hence, both members were heavily reinforced. The target strength of the concrete used for the beams was 40 MPa, and the concrete conformed to the material requirements of CSA A23.1-24 (Canadian Standards Association, 2024). The reinforcement used in the beams was of Grade 400W which conformed to CSA G30.18-21 (Canadian Standards Association, 2021). The masonry walls of the specimens were constructed using 240 mm thick concrete blocks (250 nominal) arranged in a running bond pattern with 10 mm mortar joints using Type S mortar. These design features are representative of typical RM construction in Canada, except that 200 mm thick blocks are most often used in loadbearing masonry (Brzev & Anderson, 2018). The reason for using a thicker block size is discussed shortly. Design features of these specimens that are atypical include using masonry blocks with cut webs (as shown in Figure 4-1, and 64 discussed shortly) and placement of more than one vertical bar per block cell. As shown in Figure 4-1, four bars were placed in each block in the boundary elements of specimen W-2, and a similar arrangement was utilized in specimen W-1. The wall end zones of specimen W-1 are not considered as boundary elements; hence, specimen W-1 was simply a regular RMSW. Finally, both specimens were fully grouted along their entire heights. For specimen W-2, a 250 mm block size was selected to increase the spacing between the vertical reinforcement in the boundary elements as much as practically possible, which also increased the size of the confined grout column and allowed for easier grout consolidation during construction. Generally, while a 300 mm block (i.e., the largest available thickness in Canada) would have satisfied these requirements more adequately, the weight of a specimen constructed with these blocks would have exceeded the hoisting capacity of the 10-ton overhead crane in the UBC Structures Laboratory, which was used for transporting the specimens. Specimen W-1 was constructed with 250 mm blocks to maintain design consistency with specimen W-2. The blocks in specimens W-1 and W-2 conformed to CSA A165-14 (Canadian Standards Association, 2014) and were classified as H/15/A/M. The reinforcement used in the masonry walls of specimens W-1 and W-2 was Grade 400W and conformed to CSA G30.18-21 (Canadian Standards Association, 2021). The reinforcement used in the boundary elements of specimen W-2 consisted of 4-15M vertical bars within each element and 10M confinement ties spaced at 100 mm on-center. The 4-15M vertical bars had straight ends protruding into the loading beam and 90-degree hooks at the base of the footing beam. Confinement ties in the boundary elements had a 90-degree hook at one corner, as shown in Figure 4-4. Although a 90-degree hook differs from a conventional 135-degree “seismic hook”, it still conforms to Clause 13.2.6 of CSA S304-24 which currently does not enforce lateral ties to have 135-degree hooks (Canadian Standards Association, 2024). The remaining vertical wall reinforcement consisted of 4-15M distributed reinforcing bars (with 180-degree hooks at both 65 ends), and 15M dowels spaced at 400 mm on-center connecting the masonry wall to the loading beam (with 180-degree hooks into the beam). Also, 20M distributed horizontal reinforcement was provided at 400 mm on-center in bond beam blocks and had 90-degree hooks at each end. Finally, all reinforcement was continuous (without splicing) to prevent anchorage failures at high drift demands. Figure 4-4: Close-Up of Typical Confinement Tie Used in Specimen W-2 It can be seen from Figure 4-1 that all blocks in both specimens were missing their webs. This is because prior to construction of the masonry walls, the webs of these blocks were sawcut. At a minimum, it was required to cut the webs of the blocks used in the boundary elements of specimen W-2 in order to be able to place the confinement ties, however the webs of all remaining blocks were sawcut as well. This was done to facilitate easier block installation around the distributed vertical reinforcement, although only one web per block was cut since the reinforcement was spaced at alternating cores. If the webs in these blocks were not cut, each block would have to be lifted atop the continuous 3.8 m long reinforcement bar and lowered into place, which was deemed impractical. As mentioned previously, the practice of cutting all blocks for constructing a RMSW is not representative of typical masonry construction in Canada. 66 In general, specimens W-1 and W-2 conformed to the design and detailing requirements forDuctile RMSWs per CSA S304-14 (Canadian Standards Association, 2014). The design anddetailing of the specimens was performed by others (Hsu et al., 2023). Hsu et al. describedpreliminary ideas for the design of the specimens, although as noted in this section, the finaldesign differed (also performed by Hsu). The key activities performed related to design anddetailing involved evaluating the probable lateral resistances of specimens W-1 and W-2, whichwere computed and verified against the maximum capacity of the hydraulic actuator used fortesting. Also, a high horizontal reinforcement ratio of 0.33% was provided to minimize chancesof shear failure. Finally, an aspect ratio of 1.31 was utilized for all specimens to encourage aDuctile Flexure (DF) primarily failure mechanism.A test matrix summarizing the information presented in this section is provided in Table 4-1. The symbols used in this table are defined in the List of Symbols. Table 4-1: Test Matrix Wall ID Geometry Detailing hw (cm) lw (cm) tw & tBE (cm) hw lw (-) lBE (cm) 2lBE lw (-) Ag (cm2) ABE (cm2) 2ABE Ag (-) ρv (%) ρh (%) ρBE (%) W-1 340 259 24 1.3 - - 6216 - - 0.39 0.33 - W-2 340 259 24 1.3 39 0.30 6216 936 0.3 0.13 0.33 0.85 4.2.2 Specimen Construction The construction of specimens W-1 and W-2 was accomplished in the following sequential order: i) footing beams (Section 4.2.2.1), ii) masonry walls (Section 4.2.2.2), and iii) loading beams (Section 4.2.2.3). It is noted that specimens W-1 and W-2 were constructed alongside two additional specimens: W-3 and W-4. These specimens are identical to specimens W-1 and W-2, except for varying tie configurations in the boundary elements. Hence, they are not part of 67 this thesis but are part of the same research project. Therefore, intricacies of these additional specimens are not discussed in this thesis, but construction details are provided for all four specimens. 4.2.2.1 Construction of Footing Beams The first step in the construction of the footing beams was to build their formwork. Each footing beam’s formwork consisted of a box into which the reinforcement was placed, and concrete was poured. Also, each formwork assembly included an upright frame that held the specimen’s vertical reinforcement in place until the footing’s concrete was sufficiently hardened after casting. A drawing of an individual formwork assembly is shown Figure 4-5, and a photo of the completed formwork for all four footing beams is shown in Figure 4-6. Three materials made up the bulk of the formwork: plywood, lumber, and PVC pipes. The plywood used was 17.5 mm Crown 43 Douglas Fir sheets by Westlam Industries, shown lightly hatched in Figure 4-5. This material was used for the sheathing of the side, end, and bottom panels of the formwork boxes and is specifically intended for concrete formwork applications, allowing for easier formwork removal following concrete hardening. The lumber consisted of numerous segments of 2x4 SPF dimensional lumber, cut to suit the specific dimensions of the formwork design. It was used for the framing of the side, end, and bottom panels of the formwork boxes, as well as for the upright vertical frame. The lumber used in the assembly is shown without a hatch in Figure 4-5. Finally, the 2-inch (51 mm) PVC pipes are shown hatched darkest in Figure 4-5. The purpose of these pipes was to connect the footing beam to the strong floor during testing, as discussed previously. 68 Figure 4-5: Temporary Formwork for Footing Beam: a) Elevation View; b) Side View; c) Plan View 69 Figure 4-6: Completed Temporary Formwork for Footing Beams The sequence of formwork construction was as follows: 1. The side and end panels were constructed first, by fastening the Crown 43 sheets to the lumber framing via screws. Subsequently, the locations of holes for the PVC piping were measured and drilled. 2. The bottom panel was constructed and connected (via screws) to underlying 2x4 lumber members, which were used to strengthen the connection between the side and bottom panels. 3. Finally, the side and end panels were erected and connected to the bottom panel via screws. The side and end panels were also screwed to one another at the corners of the box for further strengthening. Any gaps identified between the side sheading and bottom sheathing (or other locations) were filled by caulking. 4. Next, the completed reinforcement assembly (“reinforcement cage”) of the footing beam was placed into the box. Details of reinforcement assembly are discussed shortly. 70 5. Following placement of the reinforcement cage, the upright lumber frame was constructed and erected. It was fastened to the end panels of the box with many screws. This allowed for erection of the vertical wall reinforcement, which was tied to the lumber beam of the upright frame that contained holes. 6. The final step was to install horizontal lumber members on top of the box and align the vertical reinforcement. A gap between the bottom of the lumber members and top of concrete was purposefully left to ensure a trowel can fit to produce a smooth concrete finish. The assembly of the reinforcement cage was accomplished by using rebar loop ties to connect the reinforcement bars together. A reasonable quantity of rebar loop ties was employed to ensure that the reinforcement cage was sturdy. A photo of a reinforcement cage is shown in Figure 4-7. Figure 4-7: Reinforcement Cage for Footing and Loading Beams 71 The assembly of the reinforcement cage was generally straightforward and conformed to conventional construction methods, except for the method for assembling the stirrups. In the construction industry, it is common for each stirrup to consist of one continuous reinforcement segment, as shown in Figure 4-8 (a). However, to facilitate easier reinforcement assembly, two separate reinforcement pieces were tied together to produce one stirrup, as shown in Figure 4-8 (b). A photo depicting the assembly process is shown in Figure 4-9. Finally, once the reinforcement cage was placed into the formwork box, 1.5-inch (38 mm) rebar chairs were installed between the cage and the formwork to maintain concrete cover. Figure 4-8: a) Conventional Stirrup Assembly; b) Stirrup Assembly for Footing Beam Reinforcement Figure 4-9: Footing Beam Reinforcement Cage Assembly 72 After the formwork was constructed and the reinforcement was in place, it was possible to pour the concrete in the footing beams. Concrete was provided by a local ready-mix supplier via a volumetric concrete mixer. The method of transporting the concrete from the mixer to the formwork consisted of wheelbarrowing it for two specimens, a combination of placing it directly from the mixer’s chute and wheelbarrowing for one of the specimens and placing it directly from the mixer’s chute for the remaining specimen. This was required as not all the formwork boxes were accessible for direct pour from the mixer’s chute. During the pour, the concrete was vibrated sufficiently to ensure adequate consolidation, but also not extensively to minimize the potential for segregation. Slump testing was not performed as the concrete mix contained superplasticizer, and air testing was not performed as the concrete mix did not contain air entrainment. However, several concrete cylinders were cast to verify that the concrete target compressive strength was met, and the test results are provided in Section 4.3. Finally, concrete finishing took place immediately after the pour was finished, which was done by smoothening the surface with a hand trowel. An adequate amount of concrete bleeding was observed following the completion of the pour. Concrete curing initiated shortly after the pour. This consisted of watering the concrete surface with a garden hose and covering the formwork box with polyethylene sheets to help retain moisture. This was done once on the day of the pour, and twice a day for the following three days after the pour. The curing duration followed the requirements for “curing type 1” per Table 19 of CSA A23.1:19/CSA A23.2:19 (Canadian Standards Association, 2019). Ambient temperature was not regulated as it was not deemed a concern because the lab is consistently maintained at a comfortable room temperature. A photo taken during curing is shown in Figure 4-10 (a). Upon the completion of curing, the formwork was removed seven days from the date of the pour. A photo of the bottom footing shortly after formwork removal is shown in Figure 4-10 (b). 73 a) b) Figure 4-10: Footing Beam Construction: a) During Curing and b) After Formwork Removal 4.2.2.2 Construction of Masonry Walls Block cutting and masonry block placement was done by a local masonry contractor, Scorpio Masonry. The reason for block cutting was discussed in Section 4.2.1. Scorpio Masonry sawcut approximately 500 blocks required for construction in their yard. These blocks were transported to the UBC Structures Laboratory prior to the first day of construction of the masonry walls. Two Scorpio Masonry staff aided in the wall construction and grouting: a foreman with 20 years of experience who was primarily responsible for placing the blocks and mortar joints, and a labourer with 7 years of experience who was responsible for finishing the joints (i.e., pointing) and mixing the mortar for the foreman. Table 4-2 summarizes the construction schedule of the masonry walls. 74 Table 4-2: Construction Schedule for the Masonry Walls Construction Day Specimens W-1 & W-4 Specimens W-2 & W-3 1 (August 6, 2024) Laying courses 1 – 5 - 2 (August 7, 2024) Grouting courses 1 – 5 Laying courses 1 – 5 3 (August 8, 2024) Laying courses 6 – 11 Grouting courses 1 – 5 4 (August 9, 2024) Grouting courses 6 – 11 Laying courses 6 – 11 5 (August 12, 2024) Laying courses 12 – 17 Grouting courses 6 – 11 6 (August 13, 2024) - Laying courses 12 – 17 7 (August 15, 2024) Grouting courses 12 – 15 Grouting courses 12 – 15, W-3 Only 8 (August 16, 2024) - Grouting courses 12 – 15, W-2 Only Photos of the specimens taken after Days 2, 4, and 8 are shown in Figure 4-11. Per Table 4-2, the work sequence consisted of building each wall in three segments, such that breaks were taken following completion up to and including courses 5, 11, and 17. The breaks were taken at these intervals once the blocks were placed and cores were grouted. Once the blocks were placed to the specified course level, grouting was delayed until at least the following day to allow hardening of the mortar. The primary reason for constructing the walls in segments was to allow for low lift-grouting (as opposed to high lift grouting, during which the entire wall is grouted at the same time). Low-lift grouting was deemed to be essential for these specimens to allow for better grout consolidation, such that the experimental results were not influenced by inadequate grout placement. Furthermore, the relatively high concentration of reinforcement in the boundary elements of specimens W-2, W-3 and W-4 and wall end zones of specimen W-1 required a very high quality of grout consolidation, which could only be accomplished through low-lift grouting. 75 a) b) c) Figure 4-11: Masonry Wall Construction: a) Day 2; b) Day 4; c) Day 8 The first step in the construction of the walls was to measure the footprint of the masonry walls on the concrete footings and ensure that the dimensions aligned with those shown on the design drawings. The dimensions of interest were the distances between the outside faces of the outermost masonry blocks and the footing edges, as well as the distances between the outermost vertical reinforcement and the outside face of the outermost masonry block (100 mm 76 per Figure 4-1). Once these distances were measured and marked on the footings, the outermost blocks of the walls (i.e., those at the wall ends) were placed first, and the remaining blocks in the first course were placed in between these blocks, marking the completion of the first course. Block and reinforcement placement were executed according to the following steps: 1. Placing the horizontal reinforcement in the bond beam course, starting with the first course. 2. Lowering a sufficient number of confinement ties into the boundary elements from atop the vertical reinforcement (i.e., enough to reach the next horizontal reinforcement placement, see Figure 4-12). Since the spacing of confinement ties was 100 mm on-centre, four ties were sufficient as the distance between horizontal reinforcement bars was 400 mm (i.e., 2 courses). Placement of all confinement ties along the entire wall height prior to wall construction was not done as it would have been impossible to fit the 90-degree hooks of the horizontal reinforcement bars between the confinement ties, since the hook length exceeded 100 mm. This step is applicable to all specimens except specimen W-1. 3. Following assembly of the confinement ties, the masons would resume laying the following course without horizontal reinforcement, and the subsequent course with horizontal reinforcement. The masons employed standard industry practices when laying blocks, which included providing 10 mm joints between blocks, adequate finishing and pointing of the joints, employing a level to ensure that the wall is being built straight in all directions, and other techniques that make masons skilled labourers. Mortar was laid with the assistance of a brick trowel, and the blocks were lifted into the courses manually by the foreman. The mortar was mixed by Scorpio Masonry’s labourer immediately prior to application, which involved mixing a bag of mortar powder and an appropriate amount of water in a pail with a handheld cement mixer. Photos of the masons working are shown in Figure 4-13. 4. Steps 1 – 3 were repeated until the desired course height for the next low-lift grout pour. Scaffolding was built up as necessary to ensure accessibility as the walls became higher. 77 The only minor deviation from this sequence occurred during the construction of courses 1 – 4 for all walls. This deviation consisted of expulsion of strain gauge wires from the bed joints of the walls. This is discussed in greater detail in Section 4.5. Figure 4-12: Assembly of Confinement Ties in the Boundary Elements 78 a) b) c) Figure 4-13: a) Foreman Placing Mortar; b) Foreman Placing Blocks; c) Labourer Pointing a Head Joint As mentioned previously, each specimen was grouted in three separate intervals (lifts). Grout was prepared by emptying bags of grout powder and water into a portable concrete mixer immediately prior to grouting the wall. Two different concrete mixers were used throughout the duration of construction: the first concrete mixer was smaller and the one available at UBC (which could mix roughly 0.05 m3 at a time) and the second concrete mixer was larger and provided by Scorpio Masonry (which could mix roughly 0.15 m3 at a time). The first concrete mixer was used for the first and third grout lifts for all walls, and the second concrete mixer was used for the second lifts for all walls. Careful attention was devoted to ensure that the amount of water mixed with the grout powder was in accordance with the manufacturer’s recommendations, which was accomplished by measuring the amount of water going into the mixer during each mix. A photo of the mixing procedure is shown in Figure 4-14. 79 Figure 4-14: Mixing Grout with Smaller Concrete Mixer Prior to Transportation via a Wheelbarrow During construction, slump testing of the grout was performed. Slump testing was completed during the first four days of construction (Days 2 – 5) and the testing results are summarized in Table 4-3. Slump tests were performed using a sample batch from the first mix of each pour. Testing was performed per CSA A23.2-5C (Canadian Standards Association, 2019). The intent of testing the grout for slump was to assess it for workability and ensure consistency amongst mixes. Per Table 4-3, the testing results satisfied the manufacturer’s prescribed range of 200 mm – 275 mm. Given the consistency of results amongst the tested days, slump testing was omitted for the remaining days during which pours took place (Days 7 and 8). Table 4-3: Slump Test Results for Grout Construction Day Slump Test Result (mm) 2 (August 7, 2024) 220 3 (August 8, 2024) 240 4 (August 9, 2024) 240 5 (August 12, 2024) 230 80 Once a batch of grout was mixed, it was transported to the wall into which it was poured. For courses 1 – 5, grout was transported from the mixer to the wall via a wheelbarrow. The grout was then scooped up with pails and placed into the masonry cores, as shown in Figure 4-15 (a). For courses 6 – 15, grout was transported from the mixer to the walls via a tub that was provided by Scorpio Masonry. As shown in Figure 4-15 (b), the tub was transported via the 10-ton overhead crane in the UBC Structures Laboratory and placed onto the scaffolding. Following, pails were used to scoop up the grout and place it into the masonry cores. a) b) Figure 4-15: a) Grout Placement with Pails and b) Grout Tub Attached to Crane Each grout pour required mixing several batches. Generally, each batch was distributed evenly amongst the block cores and was added in this manner until the desired height was reached. The desired height was approximately 100 mm elevation (i.e., half a course height) below the top of course 5 for the first pour, course 11 for the second pour, and course 15 for the final pour to create a shear key as shown in Figure 4-16. Grout was not poured until course 17 for the final pour to facilitate easier installation of the 15M dowels at the top of the wall, such that the remainder of course 15 and courses 16 and 17 were filled with concrete during the pour of the loading beam. 81 Figure 4-16: Typical Masonry Shear Key Following grout placement, the final step was grout consolidation, which was accomplished by tamping an 8 mm diameter steel rod in each core. The rod length was approximately 1400 mm, which was sufficient to protrude into at least six courses. Each core was tamped generously to ensure adequate grout consolidation, especially within the boundary elements. A photo taken during grout consolidation is shown in Figure 4-17 (a). According to the foreman from Scorpio Masonry, an indicator of good consolidation (a sign that the grout reached the bottom elevation of each pour) was water seepage on the masonry surface, as shown in Figure 4-17 (b). a) b) Figure 4-17: a) Grout Consolidation and b) Water Seepage Following Grout Consolidation 82 During the masonry wall construction, many test samples were prepared, including mortar cubes per CSA A179-14 (Canadian Standards Association, 2014), grout cylinders per CSA A23.2-24 (Canadian Standards Association, 2024), grout prisms per ASTM C1019-24 (ASTM International, 2024), and cut masonry prisms per ASTM C1314-23b (ASTM International, 2023). Table 4-4 summarizes the quantities of the test samples and the days on which they were prepared. Section 4.3 provides the material testing results for specimens W-1 and W-2. Table 4-4: Test Samples Prepared during Masonry Construction Day Work Performed Type & Quantity of Test Specimens Prepared W – 1 & W – 4 W – 2 & W – 3 Mortar Cubes (CSA A179-14) Grout Cylinders (CSA A23.2-24) Grout Prisms (ASTM C1019-24) Cut Masonry Prisms (ASTM C1314-23b) 1 LC 1 – 5 - 3 for W-1 3 for W-4 - - - 2 GC 1 – 5 LC 1 – 5 3 for W-2 3 for W-3 3 for W-1 3 for W-4 3 for W-1 3 for W-4 3 for W-1 3 for W-4 3 LC 6 – 11 GC 1 – 5 3 for W-1 3 for W-4 3 for W-2 3 for W-3 3 for W-2 3 for W-3 3 for W-2 3 for W-3 4 GC 6 – 11 LC 6 – 11 3 for W-2 3 for W-3 3 for W-1 3 for W-4 - - 5 LC 12 – 17 GC 6 – 11 3 for W-1 3 for W-4 3 for W-2 3 for W-3 - - 6 - LC 12 – 17 3 for W-2 3 for W-3 - - - 7 GC 12 – 15 GC 12 – 15, W-3 - 3 for W-1 3 for W-4 3 for W-4 - - 8 - GC 12 – 15, W-2 - 3 for W-2 - - Notes: LC = Laying Courses, GC = Grouting Courses 83 4.2.2.3 Construction of Loading Beams The construction of the loading beams was similar to the footing beams as their dimensions and reinforcement configurations were identical. The formwork used for the footing beams was re-used for the construction of the loading beams. The only variation in formwork consisted of modifications to the bottom panel, which was altered to include an opening for the masonry wall. The reinforcement cages for the loading beams were assembled in a similar manner as for the footing beams. The construction of the loading beams was challenging due to the requirement of having to work at a height. Until the concrete in the footing beams hardened, temporary framework support was required, which was accomplished by designing and fabricating a steel frame used for supporting the formwork. Selected design drawings of the temporary formwork support frame are shown in Figure 4-18, Figure 4-19, and Figure 4-20. 84 Figure 4-18: Front View of Temporary Formwork Support Frame, Section “A” of Figure 4-20 Figure 4-19: Elevation View of Temporary Formwork Support Frame, Section “C” of Figure 4-20 85 Figure 4-20: Plan View of Temporary Formwork Support Frame 86 The formwork for the loading beams was supported by four W310x45 beams (shown in red), which were supported by two W200x46 beams (shown in green). This assembly was connected to four columns that were fixed to the strong floor in the lab. All steel connections were bolted. The design of the steel assembly was performed per CSA S16-24 (Canadian Standards Association, 2024). Finally, four teleposts were added at the underside of the midspan point of the W310x45 beams to minimize their deflections. Although these beams met the strength and serviceability requirements of CSA S16-24 without the telepost support, it was deemed necessary to limit deflection to a more stringent limit such that the loading beams would be constructed straight. A photo of the work area taken the day prior to pouring the loading beams is shown in Figure 4-21. A photo of the same work area following the removal of scaffolding, formwork, and the teleposts is shown in Figure 4-22. Figure 4-21: Wall Specimens Prior to Concrete Pouring for the Loading Beams 87 Figure 4-22: Completed Wall Specimens with the Steel Frame Assembly Following the installation of the steel frame, the following sequence of work was followed for the beam construction: 1. The bottom panel of the formwork was placed on top of the red beams and aligned with the top of the masonry wall. Gaps between the formwork and wall were filled with a combination of mortar and sealant. 2. The pre-assembled reinforcement cages were lifted with the 10-ton crane and placed onto the bottom panel. 3. The remaining reinforcement was placed, including the 15M dowels and lifting hooks. 4. The formwork panels were placed around the reinforcement cages and screwed to the bottom panel. Next, the 2-inch PVC pipes were installed into their final positions. A photo of the completed formwork, shortly before the concrete was poured, is shown in Figure 4-23. 88 a) b) Figure 4-23: Construction of Loading Beams: a) Formwork Detail and b) View of Formwork for All Loading Beams Concrete placement in the loading beams was identical to the footing beams, except that a concrete line pump truck had to be employed to transfer the concrete to the formwork. A photo taken from atop the scaffolding showing the completed loading beams is shown in Figure 4-24. Figure 4-24: Loading Beams Upon Completion 89 4.3 Material Testing 4.3.1 Masonry Prisms The materials used to construct the masonry prisms were the same materials used to construct the masonry walls. These cut masonry prisms were prepared, cured, and tested per ASTM C1314-23b (ASTM International, 2023). The prisms for material testing used double corner blocks that were cut in half due to the constraints related to the capacity of the testing equipment in the UBC Structures Laboratory. The testing equipment used was the Baldwin-Tate-Emery Universal Testing Machine (herein referred to as the “Baldwin”) with the maximum capacity of 1820 kN, corresponding to a regular masonry prism (constructed using a full block) with a compressive strength of 19 MPa, but a cut prism could be crushed with a strength nearly double this value. It is noted that cut prisms and regular prisms constructed using the same materials might provide different testing results due to differences in their aspect ratios. The assembly of the masonry prisms began on Day 1 of the masonry wall construction (August 7, 2024). On this day, the foreman from Scorpio Masonry assembled the blocks and mortar for the prisms. Each prism was prepared by stacking two blocks, with a 10 mm mortar bed joint placed between the blocks. The mortar used for prism assembly is representative of the mortar used to construct the wall specimens. Subsequently, the hollow cores of the blocks were filled with grout, which was obtained from sample batches of grout placed into the specimens. In total, six prisms were cast using the same grout as placed into specimens W-1 and W-4, while the other six prisms were cast using the same grout as placed into specimens W-2 and W-3. The grout was sampled during grout placement of the walls’ bottom thirds, as this is most representative of grout in the specimens’ plastic hinge regions. Since the same grout was used during the pour of specimens W-1 and W-4, the prism strengths are representative of both these specimens (the same is true for specimens W-2 and W-3). After the prisms were grouted, they were left to cure in the UBC Structures Laboratory and were wrapped with moisture-tight bags, 90 which were removed 26 days after casting (2 days prior to the testing). Figure 4-25 depicts a photo taken on Day 2 of construction, showing the wrapped prisms corresponding to specimens W-1 and W-4, and the freshly grouted prisms corresponding to specimens W-2 and W-3. Figure 4-25: Wrapped Prisms for Specimens W-1 and W-4 (Topmost Row) and Freshly Cast Prisms for Specimens W-2 and W-3 (Bottommost Rows) Two days prior to the testing, the prisms were “capped” with gypsum. Gypsum capping for prisms consists of applying a thin layer of high-strength gypsum to the tops and bottoms of the specimens to provide a smooth, level, and even surface to ensure a uniform load distribution during the testing. The material used was Hydro – Stone gypsum cement from USG. This procedure was done in accordance with ASTM C1552-23 (ASTM International, 2023). This procedure is illustrated in Figure 4-26. 91 Figure 4-26: Capping the Masonry Prisms Results from compressive strength testing of the prisms are shown in Table 4-5 and Table 4-6. For each set of prisms (i.e., W-1 / W-4, W-2 / W-3) results from five out of six prisms are included. This is due to technical difficulties observed during the testing for two of the prisms, such that some of the results were deemed inadequate. Only the average height, width, and length values are reported in the tables for brevity, although an industry report conforming to ASTM C1314-23b would also include the individual values (ASTM International, 2023). Table 4-5: Masonry Prism Compressive Strength: Testing Results (Specimens W-1 & W-4) Specimens W-1 and W-4 Prism Number 1/4 – 1 1/4 – 2 1/4 – 3 1/4 – 4 1/4 – 5 Cast Day 2 (Aug 7) Average Height (mm) 390 390 391 389 390 Average Width (mm) 221 221 221 222 221 Average Length (mm) 241 240 240 240 240 Failure Description Conical Break Conical Break Conical Break Conical Break Conical Break Max Load (N) 916,286 968,562 1,218,895 742,679 996,002 Net Compressive Strength (MPa) 17.2 18.3 23.0 14.0 18.8 Height/thickness ratio 1.76 1.77 1.77 1.76 1.76 92 Specimens W-1 and W-4 Prism Number 1/4 – 1 1/4 – 2 1/4 – 3 1/4 – 4 1/4 – 5 Height/thickness correction factor 0.98 0.98 0.98 0.98 0.98 Corrected Net Compressive Strength (MPa) 16.9 17.9 22.5 13.7 18.4 Mean (MPa) 18.0 Standard Deviation (MPa) 2.9 Coefficient of Variation (%) 16.1 Table 4-6: Masonry Prism Compressive Strength: Testing Results (Specimens W-2 & W-3) Specimens W-2 and W-3 Prism Number 2/3 – 1 2/3 – 2 2/3 – 3 2/3 – 4 2/3 – 5 Cast Day 3 (Aug 8) Average Height (mm) 391 389 390 389 389 Average Width (mm) 221 222 221 221 221 Average Length (mm) 240 240 240 241 241 Failure Description Cone & Shear Conical Break Cone & Split Conical Break Cone & Shear Max Load (N) 1,218,895 742,679 996,002 838,370 1,017,211 Net Compressive Strength (MPa) 23.0 14.0 18.8 15.7 19.1 Height/thickness ratio 1.77 1.76 1.76 1.76 1.76 Height/thickness correction factor 0.98 0.98 0.98 0.98 0.98 Corrected Net Compressive Strength (MPa) 22.5 13.7 18.4 15.4 18.7 Mean (MPa) 17.9 Standard Deviation (MPa) 3.1 Coefficient of Variation (%) 17.4 93 A photo of a typical prism taken during testing is shown in Figure 4-27. Figure 4-27: Typical Masonry Prism Subjected to Compression 4.3.2 Concrete Masonry Units The 250 mm concrete masonry units (CMUs) used for wall construction were manufactured by Basalite at their plant in Surrey, BC. These CMUs conformed to the requirements of CSA A165-14 (Canadian Standards Association, 2014). Five full-size stretcher blocks and five half blocks were tested using the Baldwin Universal testing machine in UBC’s Structures Laboratory. Testing conformed to the requirements of CSA A179-14, except that due to laboratory constraints, the blocks did not have gypsum or sulfur capping. Rather, medium density fiberboards (MDF) were placed at the top and bottom of the block during the testing, as shown in Figure 4-28. Although using MDF sheets for capping does not conform to the testing requirements of CSA A179, it is a common approach used by concrete block manufacturers. The measured compressive strengths of CMUs with MDFs are generally lower as compared to when gypsum or sulfur capping is used (Concrete Masonry and Hardscapes Association, 2014). 94 Figure 4-28: a) Stretcher CMU During Testing; b) Half CMU During Testing Compressive strength values obtained through testing are summarized in Table 4-7. The values of the net areas used for converting the applied loads to compressive strengths were provided by Basalite. Values of compressive strength for blocks SB-4 and SB-5 are not provided as during testing, the capacity of the Baldwin machine was reached prior to the blocks experiencing crushing. This implies that the strength of blocks SB-4 and SB-5 was at least 36.67 MPa. Generally, the average compressive strength of 34.1 MPa significantly exceeds the strength based on the manufacturer’s specifications (15 MPa). Table 4-7: Concrete Masonry Units Compressive Test Results Block Type Specimen # Net Area (mm2) Applied Load (kN) Compressive Strength (MPa) Stretcher Block (SB) SB-1 49632 1693.92 34.13 SB-2 49632 1636.27 32.97 SB-3 49632 1753.59 35.33 SB-4 49632 1819.85 - SB-5 49632 1819.85 - 95 Block Type Specimen # Net Area (mm2) Applied Load (kN) Compressive Strength (MPa) Half Block (HB) HB-1 30640 1132.98 36.98 HB-2 30640 1079.18 35.22 HB-3 30640 849.53 27.73 HB-4 30640 1096.48 35.79 HB-5 30640 1090.03 35.58 Mean (MPa) 34.1 Standard Deviation (MPa) 2.7 Coefficient of Variation (%) 7.9 4.3.3 Grout The grout used for wall construction was Basalite’s “BLOCKFILL”, with the specified compressive strength of 25 MPa, which meets the requirements of CSA A179-14 (Canadian Standards Association, 2014). The grout cylinder samples were prepared conforming to CSA A179-14 while the grout prisms were prepared conforming to ASTM C1019-24 (ASTM International, 2024). 4.3.3.1 Grout Cylinders Nine grout cylinders were prepared for each specimen (three per grout pour). Grout was sampled prior to the placement of a fresh batch mix into a given specimen. The sampled grout was placed into 100 mm x 200 mm cylindrical molds and prepared per the requirements of CSA A23.2-24 3C (Canadian Standards Association, 2024). Prior to grout placement into the molds, the interior mold surfaces were coated with hydraulic oil to facilitate easier demolding. After the preparation, the cylinders remained in the original casting spot for the first 20-28 hours “on-site” per the requirements of CSA A23.2-24 (Canadian Standards Association, 2024), following which they were demolded and placed in the curing room in UBC’s Materials Laboratory until the day of testing. A photo of several cylinders taken shortly after preparation is shown in Figure 4-29. 96 Figure 4-29: Grout Cylinders in Molds Following Preparation Compressive strength of all grout cylinders was determined by testing in the Materials Laboratory at UBC. The testing equipment used was the Forney FHS-600-VFD compressive testing machine. All cylinders were tested per CSA A179-14 and CSA A23.2-24 9C at their designated 28-day mark. Prior to testing, both faces of each cylinder were grinded to ensure uniform stress distribution during testing. A photo of a cylinder taken during testing is shown in Figure 4-30. Figure 4-30: Grout Cylinder During Testing The results of compressive strength testing for the grout cylinders are shown in Table 4-8. CSA A179-14 only requires that the compressive strength needs to be recorded, but CSA A23.2-24 is more stringent on what needs to be reported. Upon review of both standards, it was determined 97 that the most relevant information to record for research purposes are the specimen diameter, length, mass, compressive strength, and failure type. The requirement related to a cylinder’s diameter is that it shall not vary by more than 2% compared to other diameters of tested cylinders (Canadian Standards Association, 2024). The requirement for length is that it is required to be 1.8 – 2.2 times greater than the diameter (Canadian Standards Association, 2024). The compressive strength requirement is minimum 10 MPa for fine grout and 12.5 MPa for coarse grout per CSA A179-14 (Canadian Standards Association, 2014). Finally, the requirement for failure types is that it needs to be classified per the six failure types defined in CSA A23.2-24 (Canadian Standards Association, 2024). Note that for all tested cylinders, the failure type observed was Type 3. Type 3 failure consists of columnar vertical cracking through both ends of the cylinder, with no well-formed cones. Table 4-8: Grout Cylinder Compressive Test Results Specimen Cast Day Cylinder # Diameter (mm) Height (mm) Mass (g) Compressive Strength (MPa) W-1 1 (Aug 6) 1 – 1 101.20 195.42 3693.0 26.2 1 – 2 100.93 193.06 3693.5 28.2 1 – 3 100.92 193.36 3692.5 26.0 3 (Aug 8) 1 – 4 101.15 196.48 3710.0 26.3 1 – 5 101.18 196.82 3720.0 26.2 1 – 6 101.15 196.31 3679.0 24.8 5 (Aug 12) 1 – 7 101.90 193.27 3678.0 31.8 1 – 8 101.10 196.20 3714.5 33.1 1 – 9 101.20 198.79 3740.5 32.9 Mean (MPa): 28.2 Standard Deviation (MPa): 3.1 Coefficient of Variation (%): 11.0 W-2 3 (Aug 8) 2 – 1 101.15 195.86 3715.0 30.0 2 – 2 102.67 195.19 3714.0 29.6 2 – 3 102.89 194.60 3708.5 29.4 5 (Aug 12) 2 – 4 100.97 197.90 3736.5 30.3 2 – 5 100.86 197.65 3725.5 31.2 2 – 6 101.33 195.32 3662.5 20.2 98 Specimen Cast Day Cylinder # Diameter (mm) Height (mm) Mass (g) Compressive Strength (MPa) W-2 8 (Aug 16) 2 – 7 101.20 196.09 3719.0 28.1 2 – 8 100.83 195.69 3708.0 28.2 2 – 9 101.38 195.32 3713.0 28.6 Mean (MPa): 28.2 Standard Deviation (MPa): 3.1 Coefficient of Variation (%): 10.8 4.3.3.2 Grout Prisms For each specimen, three grout prisms were prepared. These prisms were prepared during the first grout pour for each specimen (bottom third of the specimen height); hence, the results are deemed to be representative of the grout in each specimen’s plastic hinge region. Sampling was done at the same time when grout was sampled for the grout cylinders. Preparation, curing, and testing of grout prisms was done per ASTM C1019-24 (ASTM International, 2024). The setup used for preparing the grout prisms consisted of several laid-out blocks which were oriented in a way that allowed for casting six prisms at once (also known as a “pinwheel” orientation). The openings between blocks used for casting were lined with cardboard to create a mold. The grout was placed into these molds and followed the initial curing requirements of ASTM C1019-24 (ASTM International, 2024). At the end of this time frame, the prisms were placed in the curing room in UBC’s Materials Laboratory until testing, which took place 28 days after their casting. A photo of the block arrangement used to prepare the grout prisms is shown in Figure 4-31. 99 Figure 4-31: Grout Prisms After Casting Compressive strength of all grout prisms was determined in the Materials Laboratory at UBC, using the Forney FHS-600-VFD universal testing machine. All specimens were tested per ASTM C1019-24 at their designated 28-day mark (ASTM International, 2024). Prior to testing, both faces of each prism were covered with a thin layer of Hydro – Stone gypsum cement from USG to ensure that the surfaces are smooth and levelled (similar to the masonry prisms). Capping was performed per ASTM C617-10 (ASTM International, 2010). A photo of a grout prism in the testing machine is shown in Figure 4-32. Figure 4-32: Grout Prism Before the Compression Testing 100 The test results are summarized in Table 4-9. Note that only the average values for height and width are reported for brevity, although an industry report conforming to ASTM C1314-23b would also include the individual values (ASTM International, 2024). Table 4-9: Grout Prism Compressive Test Results Specimen W-1 Specimen W-2 Cast Day 2 (Aug 7) 3 (Aug 8) Grout Prism Number 1 – 1 1 – 2 1 – 3 2 – 1 2 – 2 2 – 3 Average Height (mm) 192.13 195.47 190.60 203.46 193.50 194.54 Average Width (mm) 92.61 98.93 96.34 90.75 93.00 90.51 Perpendicularity (mm / 50 mm) 0.33 0.33 0.67 0.67 0.33 0.33 Planeness (mm / 50 mm) 0.52 1 0.52 1 1 0.52 Max Load (N) 197,500 245,650 258,950 162,370 237,210 192,860 Failure Description Vertical column cracking through both ends Vertical column cracking through both ends Compressive Strength (MPa) 23.0 25.1 27.9 19.7 27.4 23.5 Mean (MPa) 25.3 23.4 St. Dev. (MPa) 2.0 3.1 COV (%) 7.9 13.5 Per Table 4-9, grout prisms 1 – 2 and 1 – 3 did not meet the ASTM C1314-23b requirement of maintaining an average width to be between 76 mm and 95 mm (ASTM International, 2024). Furthermore, prisms 1 – 1, 2 – 1, 2 – 2, and 2 – 3 passed this requirement but failed to maintain an average height 1.75 – 2 times greater than their average widths, which was another requirement set by the same standard. 101 4.3.4 Mortar Cubes The mortar used during wall construction was Basalite’s “Mortar-TekTM”, which is a Type S mortar conforming to the requirements of CSA A179-14 (Canadian Standards Association, 2014). For each specimen, three 50 mm x 50 mm x 50 mm mortar cubes were prepared during the block placement of each wall’s third; that is, nine cubes per specimen. Sampling of mortar was done at random, and the cubes were prepared per the requirements of CSA A179-14 (Canadian Standards Association, 2014) and Test Method CSA A3004:23-C2 (Canadian Standards Association, 2023). Once the cubes were cast, they were left within the vicinity of casting for the first 24 – 44 hours “on site” per the requirements of CSA A179-14 (Canadian Standards Association, 2014), after which they were placed in the Materials Laboratory at UBC until testing. Figure 4-33 shows a photo of typical cubes immediately after the casting. Figure 4-33: Mortar Cubes in Molds Following Preparation Compressive testing of all mortar cubes took place in the Materials Laboratory at UBC, where they were tested using the Forney FHS-600-VFD universal testing machine. All specimens were tested per CSA A179-14 at the designated 28-day mark (Canadian Standards Association, 2014). Most cubes had smooth surfaces; hence, no additional treatment was required prior to testing. A photo of a mortar cube set for the testing is shown in Figure 4-34. 102 Figure 4-34: Mortar Cube Subjected to Compression in the Testing Machine The results from the compressive strength testing of mortar cubes are shown in Table 4-10. According to the requirements set by CSA A179-14 and Test Method CSA A3004:23-C2, only the applied load and compressive strength need to be reported. It is required to report cube dimensions only if they are found to vary by more than 1.5% from the nominal surface area (i.e., 2500 mm2), which was not the case for any of the cubes. The minimum compressive strength requirements for mortar are 8.5 MPa for job prepared and 12.5 MPa for laboratory prepared per CSA A179-14 (Canadian Standards Association, 2014). 103 Table 4-10: Mortar Cubes Compressive Test Results Specimen # Cast Day Cube # Applied Load (kN) Compressive Strength (MPa) W – 1 1 (Aug 6) 1 – 1 59.88 24.0 1 – 2 59.91 24.0 1 – 3 50.58 20.2 3 (Aug 8) 1 – 4 56.27 22.5 1 – 5 55.07 22.0 1 – 6 52.40 20.9 5 (Aug 12) 1 – 7 68.40 27.4 1 – 8 60.60 24.2 1 – 9 58.74 23.5 Mean (MPa): 23.1 Standard Deviation (MPa): 2.0 Coefficient of Variation (%): 8.6 W – 2 2 (Aug 7) 2 – 1 59.42 23.8 2 – 2 60.44 24.2 2 – 3 55.66 22.3 4 (Aug 9) 2 – 4 61.39 24.6 2 – 5 61.22 24.5 2 – 6 55.90 22.4 6 (Aug 13) 2 – 7 57.08 22.8 2 – 8 65.98 26.4 2 – 9 69.85 28.0 Mean (MPa): 24.3 Standard Deviation (MPa): 1.8 Coefficient of Variation (%): 7.3 4.3.5 Steel Reinforcement The steel reinforcement used for the footing beams, masonry walls, and loading beams was supplied by Nucor and delivered to the UBC Structures Laboratory as part of the same order. As part of this order, nine straight 900 mm bars were provided (three 10M bars, three 15M bars, and three 20M bars) and were used for testing. These bars correspond to the reinforcement sizes used during construction of specimens W-1 and W-2. Unfortunately, the 900 mm 10M bars 104 were misplaced, but were replaced by two 400 mm bars of the same size that were obtained by cutting leftover stirrup reinforcement used during construction of the concrete footing beams. Tensile testing of the bars took place in the UBC Structures Laboratory using the Baldwin universal testing machine. The applied loading rate was in accordance with ASTM A370-24 (ASTM International, 2024). For each bar, stress-strain plots were produced to determine values for the relevant material properties (yield stress and strain, ultimate stress, etc.). Stress was obtained by dividing the force readings from the testing machine by the cross-sectional area of the bar, while strain was obtained by dividing the bar elongation due to tensile loading by the original length. In this case, the original length was set as the length of a 2620 Series dynamic strain gauge extensometer by Instron, which was used to record the displacements. A photo of a typical bar during testing is shown in Figure 4-35. Figure 4-35: Reinforcement Bar Subjected to Tension The results from tensile testing of the reinforcement bars are shown in Table 4-11, which were computed and reported based on the requirements of CSA G30.18-21 (Canadian Standards 105 Association, 2021). Per this standard, the minimum yield strength is 400 MPa, and the minimum tensile strength is 540 MPa for Grade 400 steel. These requirements were met by all samples, with the exception of 20M-3. Furthermore, CSA G30.18-21 specifies a minimum elongation requirement of 13%, which was only achieved by bars 15M-1, 15M-2, and 20M-2. It is believed that this is a result of technical issues observed during testing rather than the quality of reinforcement. Namely, slippage of the bars is presumed to have contributed to incorrect strain readings which were used for computing elongation and were particularly noticeable for bars 10M-1 and 10M-2 what had significantly reduced grip lengths compared to the remaining bars. Based on this, it is expected that the yield strains obtained through testing are also not accurate. Per Table 4-11, the mean yield strain is 0.00304, which is greater than the yield strain of 0.002 for Grade 400 steel. Table 4-11: Steel Reinforcement Tensile Testing Results Bar Yield Load (kN) Yield Stress (MPa) Yield Strain (m/m) Tensile Load (kN) Tensile Stress (MPa) Elongation (%) 10M - 1 44.8 448 0.0031 66.10046 661.0046 9.5 10M - 2 45.8 458 0.002 55.968 559.68 1.8 15M -1 83.45 417.25 0.00369 120.62 603.1 16.6 15M - 2 86.976 434.88 0.00278 124.56 622.8 10.4 15M - 3 84.698 423.49 0.00388 117.898 589.49 13.4 20M - 1 128.706 429.02 0.00189 184.593 615.31 11.9 20M - 2 127.671 425.57 0.00307 183.069 610.23 13.4 20M - 3 127.293 424.31 0.00338 152.166 507.22 4.6 Mean - 432.37 0.00304 - 594.49 10.71 Std. Dev - 12.93 0.00061 - 43.03 3.51 COV (%) - 2.99 20.03 - 7.24 32.77 106 4.3.6 Footing and Loading Beams Concrete Concrete for the footing and loading beams was prepared according to the same mix design specifications and was provided by the same supplier, USC Concrete Solutions. The concrete had a target compressive strength of 40 MPa at 28 days, used GU cement, contained a maximum aggregate size of 14 mm, had a water-to-cement ratio of 0.3, and included superplasticizer as an additive. Several 100 mm x 200 mm cylinders were cast during each of the pours following a similar procedure as for the grout cylinders described in Section 4.3.3.1. The cylinders were tested for compressive strength 28 days after casting in accordance with CSA A23.2-9C (Canadian Standards Association 2019) in the Materials Laboratory at UBC, in the same way as the grout cylinders described in Section 4.3.3.1. The compressive strengths of three cylinders for each beam are presented in Table 4-12. Table 4-12: Compressive Testing Results for Concrete Cylinders Member Cylinder ID 28-day results (MPa) Footing Beam FB-1 44.0 FB-2 46.5 FB-3 44.6 Mean 45.0 Std. Dev. 1.1 COV (%) 2.4 Loading Beam LB-1 50.0 LB-2 51.6 LB-3 51.5 Mean 51.0 Std. Dev. 0.7 COV (%) 1.4 107 4.4 Test Setup The test setup for specimens W-1 and W-2 in UBC’s Structures Laboratory is illustrated in Figure 4-38, while Figure 4-36 and Figure 4-37 show drawings of the test setup for both specimens. The test setup consisted of a horizontal hydraulic actuator which was used to apply the lateral force to the specimen, two steel plates and four rods which were used to connect the actuator to the specimens’ loading beams, two steel box beams which were used to connect the specimens’ footing beams to the laboratory’s strong floor, and four frames (each consisting of a column and cantilevered beam) that provided out-of-plane supports to the specimens during testing. The positive and negative loading directions are shown in Figure 4-36. The north, south, east, and west orientations are also shown in these figures. This section provides a detailed overview of the test setup, instrumentation and controls. 108 Figure 4-36: Elevation View of Test Setup, Facing West Figure 4-37: Elevation View of Test Setup, Facing South 109 Figure 4-38: Test Setup for Specimen W-2 110 4.4.1 Strong Floor and Wall The strong floor in UBC’s Structures Laboratory comprises of a 2-foot (610 mm) thick heavily reinforced post-tensioned slab with 2-inch (51 mm) diameter holes at 2-feet (610 mm) spacing in both directions. The purpose of these holes is to allow fastening of components to the strong floor via steel rods, plate washers and nuts. The strong floor is accessible from both sides via the laboratory’s basement which allows for installation of these connections. For this experimental program, the strong floor was used to fasten the steel box beams, the out-of-plane support frames and the actuator support frame during the testing, as well as the steel columns during construction of the specimens’ loading beams. Since the stiffness of the strong floor is significantly greater than the stiffness of the specimens, it is treated as a rigid base in experimental tests. The L-shaped strong wall is of similar construction to the strong floor, except the thickness is greater (3 feet, 915 mm). For this experimental program, the strong wall was primarily used to handle the actuator’s reaction force but also served as one of the supports for the actuator’s weight. 4.4.2 Horizontal Actuator & Supports The horizontal hydraulic actuator MTS model 244.31 was used for the testing with a 1000 kN force capacity and a ± 260 mm stroke capacity. The actuator was connected to a MTS 506.61 hydraulic pump and was supported at two locations. The first support connected the base swivel head of the actuator to the strong wall. The system employed for this connection was a modification of the system used by Robazza (2013), who used two steel mounts with four threaded holes connected to the actuator’s base swivel head via four threaded rods. The steel mounts were welded to a steel plate with two holes that were used for connecting it to the strong wall with threaded steel rods. The system was modified by welding three 2-inch (51 mm) steel plates to each end of the steel plate (i.e., six plates total), to increase the distance between the actuator and strong wall by 153 mm. Each set of three plates contained drilled holes through 111 which the steel plate was connected to the strong wall. The reason this modification was required was due to the positioning of the specimen relative to the strong wall. Without this modification, the specimen would be unable to achieve the maximum anticipated lateral drift magnitudes in the positive loading direction due to limitations in the actuator’s stroke capacity. This connection detail with annotations is illustrated in Figure 4-39. Figure 4-39: Actuator Connection to Strong Wall The second support for the actuator consisted of a frame and was located at approximately half the distance between the strong wall and the specimen. The frame consisted of two columns, two bracing members, and two cantilever beams, as shown in Figure 4-40. Each column consisted of a wide flange steel section welded to a base plate connected to the strong floor via threaded rods. The columns had two rows of 1-inch (25 mm) diameter holes drilled in each flange at 3 inch (76 mm) spacing vertically on-center, and at 6 inch (152 mm) horizontal spacing along the entire column height. The holes were used to connect the bracing members and 112 cantilever beams using bolts. The bracing members were steel HSS sections with welded plates on both ends with drilled holes to facilitate this connection. Each cantilever beam consisted of two wide flange steel sections rotated by 90 degrees about their strong axis, and connected to one another with bolts through their flanges, as shown in Figure 4-40. Finally, several steel plates and a rubber bearing pad were placed atop these cantilever beams which provided the bearing surface for the actuator, as shown in Figure 4-40. Figure 4-40: Actuator Support Frame 4.4.3 Box Beams Two identical custom-made box beams were manufactured for the test setup, used for connecting the specimens’ footing beams to the laboratory’s strong floor. The box beams were manufactured by George Third and Son (GTS), a local steel fabricator. As shown in Figure 4-41, 113 each box beam had a length of 3300 mm, a width of 500 mm, and a depth of 450 mm. Each beam consisted of 2-inch (51 mm) thick top and bottom plates, 2-inch (51 mm) thick side plates, and identical 3/4-inch (19 mm) stiffener plates to form the box beam. The plates were made of Grade 300W steel conforming to CSA G40.21 (Canadian Standards Association, 2023). The top and bottom plates were painted with an oxide primer to minimize corrosion during exterior storage. Welding details between the plates are shown in Figure 4-42, and the details of each plate are described below. The top and bottom plates contained five 3-inch (76 mm) holes spaced at 2-feet (610 mm) on-center used for connecting the box beam to the strong floor with vertical post-tensioned rods, as shown in Figure 4-37. The side plates each contained sixteen 3-inch (76 mm) holes spaced at 8 inches (203 mm) on-center, which were used to connect the box beams to the specimens’ footing beams using horizontal post-tensioned rods, as shown in Figure 4-37. The rods were placed through the holes of the side plates which then protruded into the 2-inch (51 mm) PVC pipes that were cast into the concrete footing beams (as described previously). Finally, 17 stiffener plates, spaced at 8-inch (203 mm) on-center along the beam length, were provided to increase the stiffness of each box beam, as shown in Figure 4-41. 114 Figure 4-41: A 3-D View of Steel Box Beam Figure 4-42: Front View and Welding Details of Box Beam Post-tensioning rods used for the box beam connections were 1-1/4“(32 mm) G150 THREADBAR by DYWIDAG, with G150 1-1/4“(32 mm) hex nuts and 6 in x 7 in x 1.5 in (152 mm x 178 mm x 38 mm) bearing washer plates (also manufactured by DYWIDAG). Ten vertical rods (five per box beam) and five horizontal rods were installed to connect the box beams to the concrete footing beams and strong floor, as shown in Figure 4-36. The horizontal rods were post-tensioned to approximately 450 kN to increase the shear friction resistance at the interface between the box beams and concrete footing in order to prevent the rocking of the specimen. 115 The vertical rods were post-tensioned to approximately 250 kN to prevent sliding at the base of the specimen. Post-tensioning was done via a hydraulic jack provided by DYWIDAG, and the post-tensioning process is illustrated in Figure 4-43. Figure 4-43: Post-Tensioning of Horizontal Box Beam Rods4.4.4 Loading Beam-to-Actuator ConnectionThe concrete loading beams were connected to the actuator by means of two steel plates andfour threaded rods. The two 1-5/8” (41 mm) thick steel plates with dimensions of 460 mm x 810mm clamped the loading beam, as shown in Figure 4-36. The clamping force was achieved viafour 1-inch (25 mm) diameter threaded rods inserted into holes drilled in the clamping plates.One of the clamping plates was connected to the actuator, and the connection detail is similar tothe connection between the steel mounts and actuator base swivel, described earlier in Section4.4.2.It can be seen from Figure 4-36 that the centerlines of the actuator and loading beams did notalign for either specimen. The vertical offset distance was approximately 125 mm. As a result,116 the full bearing surface of the clamping steel plates could not be utilized, but an alternative arrangement was made to resolve this issue. 4.4.5 Out-of-Plane Support Frames Four out-of-plane support frames were used during testing, two on each side of the loading beam. Each support frame consisted of a column and a cantilevered beam. Each frame’s column was identical to the columns used for the actuator support frames (Section 4.4.2). The beams were custom-made for this project and consisted of steel HSS sections with welded plates on each end. One of the plates was used for the bolted connection between the beam and the column, while the other plate was used as an attachment for a 1/2” (12.7 mm) thick Fluorosint® 207 polytetrafluoroethylene (PTFE) sheet (also known as “Teflon”). These PTFE sheets with identical thicknesses were also affixed to the specimens’ loading beams, such that the PTFE sheets would slide against one another should the specimens experience out-of-plane displacements during testing. Since the coefficient of friction of PTFE is extremely low, the friction resistance developed at the surface interface of the PTFE sheets would also be extremely low. In other words, the additional applied lateral load from the actuator required to overcome the sliding resistance is assumed to be negligible relative to the load required to subject the specimens to the desired lateral displacements. The PTFE sheets affixed to the steel beams were also coated with industrial grease to further decrease the coefficient of friction. A view of the out-of-plane support taken at the loading beam elevation is shown in Figure 4-44. The design gap between the PTFE sheets was 2 inches (51 mm). Figure 4-45 illustrates the method of affixing the PTFE sheets to the loading beam. In essence, two assemblies shown in Figure 4-45 were prepared and placed atop the loading beam, representative of how a saddle is placed atop a horse. The locations of these assemblies aligned with the locations of the out-of-plane support frames. 117 Figure 4-44: Out-of-Plane Support at the Loading Beam Elevation Figure 4-45: Method of Affixing PTFE Sheets to the Loading Beam 118 4.4.6 Miscellaneous Modifications of the Test Setup Two minor modifications were done to the test setup prior to testing. The first modification consisted of filling the gaps between the box beams and concrete footing beam with high-strength gypsum (Hydro – Stone gypsum cement from USG). This was required because the cross section of the footing beams was not constructed to be exactly rectangular, as shown in Figure 4-46. This modification allowed for the horizontal forces from the post-tensioned rods to be distributed evenly to the concrete footing beam, increasing the shear friction resistance at the interface between the footing and box beams, and eliminating potential for cracking in the footing. As shown in Figure 4-46, shear keys were also cast as part of this pour in both the box beam and footing openings which were not used for placement of horizontal rods. Figure 4-46: Minor Modifications and Touch-Ups to the Test Setup The second modification, applicable only to specimen W-2, consisted of adding four HSS125x125x9.5 sections on top of the steel box beams, as illustrated in Figure 4-46, Figure 4-36, Figure 4-37, and Figure 4-38. Two HSS sections were added to each box beam at opposite edges in the north-south direction, and served as a backup in case the shear friction force at the box beam/footing interface was insufficient to prevent rocking of the specimen. As shown in Figure 4-46, the void between the uneven top surface of the footing beam and the 119 underside of HSS section was filled with gypsum to provide a smooth bearing surface. The HSS sections were affixed to the steel box beams with a strong epoxy adhesive designated for metal connections, Loctite EA9466. This modification was not employed during the testing of specimen W-1, because it was learnt from the first test for specimen W-2 that the shear friction force at the box beam/footing interface was sufficient to prevent rocking. 4.5 Instrumentation and Controls The instrumentation for the test specimens consisted of strain gauges used for measuring strains in the reinforcement (Section 4.5.1) and potentiometers used for measuring displacements (Section 4.5.2). The controls in the test setup consisted of the FlexTest controller by MTS Systems. The FlexTest system was used to operate the actuator. 4.5.1 Strain Gauges The layout of the strain gauges for specimen W-2 is shown in Figure 4-47. The layout for specimen W-1 was identical, except that there were no strain gauges S10 through S15 since specimen W-1 did not have boundary elements. All strain gauges except for S16 were installed prior to constructing the masonry walls (after the footing beams were constructed), whereas S16 was installed after the wall construction was completed. Two types of strain gauges were used: FLAB-5-11-3LJC-F by Tokyo Measuring Instruments Laboratory as the primary gauge type, and KFH-6-120-C1-11L1M2R by Omega Engineering as the backup gauge type. 120 a) b) Figure 4-47: Strain Gauge Locations for Specimen W-2 as seen from a) Top of Wall and b) Front of Wall, Facing East 121 Eight strain gauges (labelled S1 through S8) were affixed to the vertical reinforcement in the boundary elements for specimen W-2 (one strain gauge per bar), and the vertical end bars in specimen W-1. The strain gauges were installed to be as close as possible to the footing beam/masonry wall interface since these locations correspond to the highest internal forces in the specimen during the testing. Strain gauges S1, S2, S5 and S6 were the primary gauges and S3, S4, S7 and S8 were backup gauges. Also, one more strain gauge (labelled S9) was installed to a vertical bar located at the mid-length in each specimen. In addition, six strain gauges (labelled S10 though S15) were affixed to the confinement ties in specimen W-2. Three strain gauges were installed in each boundary element at the second, fourth, and sixth ties from the base of the wall (i.e., within the plastic hinge region). The purpose of these gauges was to verify the strains in the confinement ties. Finally, one strain gauge (labelled S16) was affixed to a vertical reinforcement bar in the boundary element for specimen W-2, and to the vertical bar at the same location in specimen W-1. Each strain gauge was installed to a localized grinded surface on the reinforcement bar as shown in Figure 4-48 (a). The strain gauge was attached to the grinded surface via a CN cyanoacrylate adhesive, and a waterproofing agent (M-Coat A by Micro Measurements, a VPG Brand) was applied to protect the gauge during grouting. The strain gauge was then wrapped with 3M self-bonding insulating tape, as shown in Figure 4-48 (b). Finally, during wall construction, the wires of the strain gauges were expelled through the masonry bed joints, as shown in Figure 4-48 (c). The last step is applicable for all strain gauges except for S16, which were expelled from the top of the loading beam. 122 a) b) c) Figure 4-48: Strain Gauge Installation Sequence: a) Strain Gauge Attached to Reinforcement Bar; b) Strain Gauge Wrapped with Tape; c) Strain Gauges Expelled Through Head Joints The strain gauge wiring was connected to a SCXI-1314 terminal block manufactured by the National Instruments. The wires were extended via soldering as required to reach the terminal block, which was connected to a SCXI-1520 signal conditioning module to amplify the signal, that was physically installed in the SCXI-1001 chassis. The chassis provided power and communication to the data acquisition (DAQ) card installed in the computer. The digitalized signal from the DAQ card was read and processed by a real-time data acquisition program DASYLab and subsequently post-processed. 4.5.2 Potentiometers Both string potentiometers and linear potentiometers were utilized during testing of specimens W-1 and W-2. For specimen W-1, twenty-one potentiometers were used as shown in Figure 4-49, and twenty-three potentiometers were used for specimen W-2 as shown in Figure 4-50. The potentiometer layouts for both specimens were almost identical, except that specimen W-1 123 did not utilize potentiometers P8 and P12, and potentiometers P16 and P17 were installed to measure displacements over a greater height for specimen W-1 than specimen W-2 (2.5 masonry courses versus 1.5 courses, respectively). Fewer potentiometers were used for the test setup of specimen W-1, because it was discovered during the testing of specimen W-2 that two of the potentiometers provided poor readings. Note that for both specimens, the potentiometers were installed on the west face of each specimen; hence, the views shown in Figure 4-50 and Figure 4-49 are facing east (opposite of the view shown in Figure 4-36). This is also true for the strain gauges shown in Figure 4-47, as the strain gauges were expelled from the mortar joints in the west faces of the specimens. Figure 4-49: Potentiometer Layout for Specimen W-1, Facing East 124 Figure 4-50: Potentiometer Layout for Specimen W-2, Facing East String potentiometers P1 through P4 were designated for measuring the lateral displacements of the specimens at varying heights to obtain lateral displacement profiles at varying drift levels. These potentiometers were affixed to the bracing members of the actuator support frame (see Section 4.4.2). Linear potentiometer P5 was designated for measuring lateral sliding displacements between the footing beams of the specimens and strong floor, which would be useful if sliding of the specimen would take place during the testing. Linear potentiometers P6 and P7 were designated for measuring lateral sliding displacements between the walls and the footing and loading beams, respectively. These measurements would be useful to observe the extent of the sliding (if any). Linear potentiometers P9, P10, P11, P13, P14, P15, P16, P17, P18 125 and P19 were designated for measuring vertical displacements which could be used for computing average curvature profiles in the specimens at various drifts (see Section 2.2). For specimen W-2, linear potentiometers P8 and P12 measured vertical displacements, which were useful for computing average curvature profiles. Linear potentiometers P20 and P21 were designated for measuring vertical displacements between the specimens’ footing beam and strong floor and provided insight into potential rocking of the specimen. Finally, string potentiometers P22 and P23 were primarily designated for measuring shear displacements. Calibration and installation of all potentiometers were done by the electrical technicians in the UBC Structures Laboratory. Potentiometers P6 through P23 were affixed to the specimen directly, by fixing each potentiometer to a small piece of lumber with self tapping screws, following which the lumber was affixed to the wall with a light-gauge epoxy adhesive (Gorilla Epoxy by Gorilla Glue Inc.). A photo of potentiometer P9 showing this typical arrangement is shown in Figure 4-51 (a). Potentiometers P1 through P4 were affixed to the bracing members with metal clamps; a photo of potentiometer P3 showing this typical arrangement is shown in Figure 4-51 (b). Finally, potentiometer P5 was affixed to a heavy steel block that was placed on the floor. 126 a) b) Figure 4-51: Typical Arrangement of Potentiometers Affixed to a) Specimen; b) Bracing Potentiometers that used strings to measure displacements required a connection point to attach the opposite end of the string (the end furthest away from the potentiometer itself). The connection was achieved by using a small screw eye tapped into a piece of lumber and affixed to the specimen with adhesive. The string was then hooked to the screw eye as shown in Figure 4-52 (a). Since potentiometers P1, P2, P3, P4, P22 and P23 were string potentiometers, they required this type of connection. Also, although potentiometers P9, P10, P11, P13, P14, P15, P18, and P19 were linear potentiometers, they required this connection as they essentially behaved like string potentiometers. A string was attached to the slider (or wiper) of these potentiometers, and the opposite end was attached to the screw eye, as shown in Figure 4-52 (a). The slider tip of potentiometer P5 was in direct contact with footing beam. The slider tip of potentiometers P20, P21, P8, and P12 was in contact with a lumber piece affixed to either the strong floor (for P20 and P21) or the footing beam (For P8 and P12); a photo of potentiometer 127 P21 is shown in Figure 4-52 (b). Finally, the slider tips of potentiometers P6 and P7 were in contact with an L-shaped bracket adhered to the masonry wall as shown in Figure 4-52 (c). a) b) c) Figure 4-52: a) Potentiometers P13 and P14; b) Potentiometer P21; c) Potentiometer P6 Each potentiometer was assigned an analog input channel in the DAQ system. The digitized signals from these channels were read and processed using DASYLab, and the recorded data was subsequently post-processed. 4.6 Testing Procedure and Loading Protocol Testing of specimens W-1 and W-2 took place in the UBC Structures Laboratory. 128 4.6.1 Specimen W-1 The testing procedure for specimen W-1 consisted of applying a reversed cyclic load from the horizontal actuator to achieve desired magnitudes of lateral displacement. The actuator was displacement-controlled and automatically applied the loading protocol which was inputted into the MTS FlexTest system prior to running the test. The loading protocol for specimen W-1 is shown in Figure 4-53. For the first two cycles, the specimen was laterally displaced approximately 3 mm in both the positive and negative loading directions, which corresponded to 0.1% drift, or 0.5Δy. The theoretical value of yield displacement (Δy) was computed using Equation (2-7) for which the section analysis of the specimen was performed (based on the methodology described in Chapter 6) and was found to be equal to 7.1 mm (0.2% drift). For the third and fourth cycles, the specimen was laterally displaced 7.1 mm in both the positive and negative loading directions, corresponding to Δy. For the remaining cycles (cycles 5 through 22), the specimen was laterally displaced in increments of Δy (7.1 mm or 0.2% drift) every two cycles until failure was observed. For specimen W-1, failure was defined as the instance when the specimen experienced significant strength degradation (50% or greater). The testing was discontinued after 22 loading cycles. 129 Figure 4-53: Loading Protocol for Specimen W-1 The testing process for each series of two cycles (corresponding to the same magnitude of lateral drift) followed a similar procedure. First, the specimen was displaced to the desired level of drift in the positive direction. The loading protocol was then manually paused, and the specimen was inspected for deformations (cracking, spalling, etc.). Subsequently, the specimen was displaced to the same drift level in the negative direction, at which point the loading protocol was paused and the specimen was inspected for deformations. The second cycle (identical to the first) was then applied continuously to complete the series of two cycles. Based on this, the experimental results presented in Chapter 5 correspond to observations made during the first of two cycles for each drift increment (unless noted otherwise). The reason for running a second cycle for each drift increment was to ensure distribution of internal forces in the specimen prior to increasing the drift magnitude in the next series of cycles; this is common practice for testing shear walls in cyclic loading tests. Two cycles were applied for all drift increments. 130 4.6.2 Specimen W-2 The testing procedure for specimen W-2 was identical for specimen W-1, and the loading protocol for specimen W-2 was nearly identical to the loading protocol for specimen W-1. Both specimens were displaced to the same maximum magnitude of absolute lateral displacement (i.e., 2% drift, or 76 mm), except that the full two cycles were not applied at the final drift increment for specimen W-2, which did occur for specimen W-1. The second loading cycle was not applied as it was deemed unsafe given that the specimen experienced significant strength degradation at this stage of the testing. Figure 4-54 shows the loading protocol for specimen W-2. Figure 4-54: Loading Protocol for Specimen W-2 4.7 Summary The purpose of this chapter was to summarize the details of the experimental program for regular RMSW specimen W-1 and RMSW specimen W-2 with embedded boundary elements. The chapter focused on discussing the design and construction details for both specimens, and material testing of individual components. The test setup for both specimens was discussed, and details regarding the various testing components were provided. Finally, the loading 131 protocols for both specimens were explained, including intricacies regarding the testing procedure applicable to both specimens. 132 5. EXPERIMENTAL RESULTS & DISCUSSION 5.1 Introduction This chapter focuses on presentation and analysis of results from testing of specimens W-1 and W-2 (described in Chapter 4). Selected results from testing of specimens W-1 and W-2 are presented in Sections 5.2 and 5.3, respectively. Analysis of these results, and the comparison in the performance of the specimens is accomplished in Section 5.4. 5.2 Experimental Results for Specimen W-15.2.1 Hysteretic Force-Displacement PlotThe hysteretic force-displacement plot obtained from experimental testing of specimen W-1 isshown in Figure 5-1. As shown in the figure, the yield displacement in the positive loadingdirection was found to be equal to the theoretical yield displacement (7.1 mm, or 0.2% drift perSection 4.6.1) corresponding to a lateral yield load of 286 kN. The onset of yielding wasconfirmed by analyzing the readings from strain gauges S5, S6, S7, and S8 as well theprogression of cracking described in Section 5.2.2. The yield displacement in the negativeloading direction of -7.1 mm (-0.2% drift) also found to be equal to the theoretical yielddisplacement, although the lateral yield load of -217 kN was lower than the lateral yield load inthe positive direction. Similarly, the onset of yielding in the negative loading direction wasconfirmed by analyzing the readings from strain gauges S1, S2, S3, and S4 and the progressionof cracking. In Figure 5-1, the tick marks for displacement ductility were computed based onEquation (2-16). 133 Figure 5-1: Hysteretic Force-Displacement Plot for Specimen W-1 The ultimate lateral loads in the opposite loading directions were similar: this value was 412 kN in the positive loading direction and -388 kN in the negative loading direction. These ultimate lateral loads were observed at similar lateral displacements of 35.3 mm (1.0% drift) and -42.3 mm (-1.2% drift), respectively. Correspondingly, the lateral loads at 20% strength degradation were similar (329 kN in the positive loading direction, and -310 kN in the negative loading direction) except that the load in the negative loading direction was observed slightly sooner (-56.6 mm, -1.6% drift) compared to the positive loading direction (63.5 mm, 1.8% drift). 5.2.2 Experimental Observations This section provides an overview of experimental observations recorded during testing of specimen W-1. Figure 5-2 shows the progression of cracking and spalling recorded during testing; recordings were captured when the specimen was displaced to absolute drift magnitudes of 0.2%, 0.4%, 0.6%, 0.8%, 1.0%, and 1.4%. In Figure 5-2, the red and blue lines denote cracks, and the red and blue hatched areas denote regions of spalling. The red lines and hatches denote deformations that were observed during the positive loading cycle, and the blue lines and hatches denote deformations that were observed during the negative loading cycle. 134 The positive and negative directions of loading are also shown with arrows, as well as the north-south orientations. Finally, recordings for drifts 1.2%, 1.6%, 1.8% and 2.0% are not available due to time constraints during testing. Recordings for 0.1% drift are not provided as no cracking or spalling was observed at this drift magnitude. Figure 5-2: Cracking and Spalling Recorded in Specimen W-1 at Drifts a) 0.2%; b) 0.4%; c) 0.6%; d) 0.8%; e) 1.0%; f) 1.4% 135 Testing initiated by displacing the specimen to a drift percentage of 0.1% in both the positive and negative loading directions. As mentioned previously, no cracking or spalling was observed at this stage of testing. Analysis of this information in addition to the strain gauge recordings suggests that the specimen behaviour was elastic at this stage of testing. During the positive loading cycle corresponding to 0.2% drift, the first series of cracks were observed in the specimen. As shown in Figure 5-2 (a), most cracks were formed in the bed joints of the bottom seven courses. Two smaller diagonal cracks were also formed in the fifth course. The largest crack width recorded was in the horizontal crack above the fifth course, measuring 0.25 mm. During the negative loading cycle corresponding to 0.2% drift, new deformation consisted entirely of cracks in the bed joints in the bottom six courses. The widest crack was the horizontal crack above the fourth course, measuring 0.25 mm. New deformation observed during the positive loading cycle corresponding to 0.4% drift consisted of a variety of cracks, as shown in Figure 5-2 (b). New vertical cracks formed in the first and second courses, near the specimen’s south toe. New diagonal cracks formed in courses 3, 5, 6, and 9. The horizontal bed joint crack above the sixth course which formed during the previous loading cycle became significantly longer as shown in in Figure 5-2 (b). The horizontal bed joint crack above the fourth course formed during the previous loading cycle also became slightly longer. Finally, new horizontal bed joint cracks above the eighth and tenth courses were formed. The widest crack was the horizontal bed joint crack above the fifth course, measuring 0.45 millimetres. New deformation observed during the negative loading cycle corresponding to 0.4% drift also consisted of a variety of cracks, as shown in Figure 5-2 (b). A new vertical crack formed in the second course, near the specimen’s north toe. New diagonal cracks formed in courses 1, 3, 4, 5, and 7. The remaining deformation consisted of either new horizontal bed joint cracks, or extensions of previously formed bed joint cracks. The 136 highest new bed joint crack (elevation-wise) was formed above the tenth course. The widest crack was the diagonal crack in the first course, measuring 1.0 mm wide. New deformation observed during the positive loading cycle corresponding to 0.6% drift consisted mostly of new diagonal cracks, as shown in Figure 5-2 (c). These were observed in courses 1, 3, 5, 7, and 8. A small vertical crack formed in the tenth course, and a head joint crack formed in the second course. No new horizontal bed joint cracks were formed, but existing horizontal bed joint cracks became longer and/or wider. The largest crack width was measured in the bed joint crack above the second course, which was 1.5 millimetres. New deformation observed during the negative loading cycle corresponding to 0.6% drift also mostly consisted of new diagonal cracks, which formed in courses 1, 3, 6, and 9. A new horizontal bed joint crack formed above the tenth course; otherwise, all existing bed joint cracks became longer and/or wider. The widest crack measured 3 mm, which was the diagonal crack in the first course near the wall’s north toe. This is a relatively wide crack for this drift magnitude (compared to 1.5 mm for specimen W-2, as discussed in Section 5.3.2). A photo of the wall’s north toe, showing this crack, is provided in Figure 5-3. Figure 5-3: North Toe of Specimen W-1 During the Negative Loading Cycle at 0.6% Drift (Facing East) 137 During the positive loading cycle corresponding to 0.8% drift, two new diagonal cracks formed in the sixth and eleventh courses, as shown in Figure 5-2 (d). The horizontal crack above the second course near the wall’s south toe became slightly longer, and a new vertical crack formed in the second course within this region. Also, at this stage of testing, the mortar joint at the wall/foundation interface was fully cracked. The largest crack width measured 4.5 mm, which was the crack in the first course near the specimen’s south toe. A photo of this region showing this crack is provided in Figure 5-4 (a). During the negative loading cycle corresponding to 0.8% drift, new diagonal cracks formed in the first, third, and ninth courses. A vertical crack in the second course also grew longer, and a new vertical crack formed in the first course near the wall’s north toe. The largest crack width measured 4.5 mm, which was the same crack shown being measured in Figure 5-3. A photo of the wall’s north toe is provided in Figure 5-4 (b). a) b) Figure 5-4: Specimen W-1 at 0.8% Drift (Facing East): a) South Toe; b) North Toe 138 During the positive loading cycle corresponding to 1.0% drift, new diagonal cracks formed in courses 1, 2, 3, 4, 9, and 10, as shown in Figure 5-2 (e). A vertical head joint crack also formed in the second course. Finally, a small vertical crack formed in the tenth course. The largest crack width measured 7 mm, which was the crack in the first course near the specimen’s south toe. During the negative loading cycle corresponding to 1.0% drift, new diagonal cracks formed in courses 1 through 7. A vertical head joint crack also formed in the eighth course. Finally, the horizontal bed joint crack above the tenth course became slightly longer. The largest crack width measured 7 mm, which was the same crack shown being measured in Figure 5-3. During the 1.2% drift cycles, crack recordings were not captured due to time constraints. However, during the testing, it was noted that the onset of face shell spalling at both of the wall’s toes had occurred during the second loading cycle. Photos of both toes noting the differences in deformation between the first and second cycles are provided in Figure 5-5 and Figure 5-6. a) b) Figure 5-5: South Toe of Specimen W-1 (Facing West) at 1.2% Drift During a) First Loading Cycle; b) Second Loading Cycle Outermost bars 139 a) b) Figure 5-6: North Toe of Specimen W-1 at 1.2% Drift During a) First Loading Cycle (Facing East); b) Second Loading Cycle (Facing South) New deformation recorded during the positive and negative loading cycles corresponding to 1.4% drift consisted of some new cracking and further deterioration at the wall’s toes, as shown in Figure 5-2 (f). The damage at both toes was significant and is shown in Figure 5-7. The damage at both toes was similar except that spalling of the face shells was prominent in courses 1 through 5 in the south toe and courses 1 through 3 in the north toe. In both toes, both the outermost reinforcement bars were exposed; when subjected to compression loading these bars would buckle (as shown in Figure 5-7) and when subjected to tension loading, they would straighten. Portions of the grout in these regions were significantly damaged such that in both toes, the exposed lengths of the outermost vertical bars were exposed entirely (e.g., no grout cover around the bar’s circumference). However, enough grout remained intact to provide cover to the adjacent set of vertical bars (second outermost set of bars). Outermost bars 140 a) b) Figure 5-7: Specimen W-1 at 1.4% Drift: a) South Toe (Facing West); b) North Toe (Facing West) Detailed deformation recordings were not captured at cycles corresponding to 1.6% and 1.8% drifts. General observations at these drift magnitudes indicated that the toes of the wall were deteriorating further; the deteriorated state during the final loading cycle at 2.0% drift is discussed below. Photos of the specimen’s toes taken during the final cycles corresponding to 2.0% drift are provided in Figure 5-8. Compared to Figure 5-7, the south toe experienced further deterioration of grout, as well as further spalling of face shells. The extent of this damage was enough to just barely expose the second outermost bar as shown in Figure 5-8 (b). However, deterioration of the toe did not extent higher than the fifth course, which was already observed at 1.4% drift. Conversely, the north toe of the wall experienced significantly more damage at 2.0% drift as compared to 1.4% drift, based on the photo in Figure 5-8 (a). Damage had progressed to the fifth course, accompanied by significant face shell spalling and deterioration of grout such that Outermost bars Outermost bars 141 not only the second outermost vertical bars became exposed, but also the hook of the horizontal reinforcement bar in the first course. The extent of bar buckling in the outermost two vertical bars in this toe is also apparent based on Figure 5-8 (a). a) b) Figure 5-8: Specimen W-1 at 2.0% Drift: a) North Toe (Facing South); b) South Toe (Facing West) 5.2.3 Drift Profiles The lateral wall drift profiles that were obtained from experimental testing using potentiometers P1 through P4 are shown in Figure 5-9. Readings at heights 1000 mm, 1700 mm, 2500 mm, and 3100 mm are available based on the installed heights of these potentiometers shown in Figure 4-49. As shown in Figure 5-9, drift profiles obtained at absolute drifts corresponding to Δy, 2Δy, 4Δy, 6Δy, 8Δy, and 10Δy are shown based on the theoretical and experimental value of Δy (7.1 mm or 0.2% drift). Unfortunately, displacement readings at a height of 1000 mm are not provided for absolute drifts corresponding to 8Δy and 10Δy due to onset of face shell spalling Outermost bar Outermost bars 142 which occurred in the specimen’s south toe at 1.2% drift (corresponding to 6Δy). The lumber block which was utilized by potentiometer P4 was attached to one of the CMUs which experienced face shell spalling. a) b) Figure 5-9:Lateral Wall Drift Profiles for Specimen W-1 in a) Negative Loading Direction and b) Positive Loading Direction 5.2.4 Average Curvature Profiles Average curvature profiles obtained at absolute drifts corresponding to Δy, 2Δy, 3Δy, 4Δy, 5Δy, and 6Δy are shown in Figure 5-10. Similar to the previous section, Δy corresponds to the theoretical and experimental value for Δy equalling 7.1 mm or 0.2% drift. The average curvatures were computed using Equation (2-15). The average curvatures at a height of 2953 mm were computed using the instrumentation readings from potentiometers P18 and P19. The readings from potentiometer pairs P11/P15, P10/P14, and P9/P13 were used to compute the average curvatures at heights 2105 mm, 1305 mm, and 453 mm, respectively. Unfortunately, 143 while potentiometer P16 provided good readings during testing, potentiometer P17 did not, which made calculating the average curvatures at a height of 300 mm impossible. Finally, curvature profiles at absolute drifts corresponding to 7Δy (1.4%), 8Δy (1.6% drift), 9Δy (1.8% drift) and 10Δy (2.0% drift) are not provided primarily due to removal of potentiometers P9 and P13 during the 1.2% drift cycle when face shell spalling initiated at the specimen’s toes. Figure 5-10: Average Curvature Profiles for Specimen W-1 The curvature profiles are mostly symmetric amongst the positive and negative loading directions. The average curvatures are slightly greater in the positive loading direction compared to the negative loading direction at all heights. 5.2.5 Strain Readings Selected results from the strain readings for specimen W-1 are provided in this section. The performance of strain gauges during testing is generally unpredictable, and strain gauge readings obtained from testing should be analyzed and interpreted with caution. Strain gauge 144 readings are generally accurate until yielding, after which the readings can become unpredictable and entirely inaccurate. Therefore, if a strain gauge adhered to a reinforcement bar does not yield during testing, its readings throughout the duration of testing are more likely to be reliable. Despite this, strain gauges may malfunction or provide poor results even prior to yielding. A summary of strain observations for the vertical bars in specimen W-1’s wall ends are provided in Table 5-1. As shown in Figure 4-47, strain gauges S1 through S8 were designated for measuring the strains in these bars. Results for strain gauges S1, S2, and S6 are excluded due to their poor output from testing. The remaining strain gauges generally provided reasonable results prior to yielding of the reinforcement bar; hence, recording of the onset of yielding is provided in Table 5-1 for each strain gauge. The criteria for yielding consisted of a strain gauge reading exceeding 0.002, which is the yield strain for Grade 400 steel. Table 5-1: Summary of Strain Observations for Vertical Bars in Wall Ends for Specimen W-1 Strain Gauge # Bars: Wall End Initial Yielding Observed Load (kN) Disp. (mm) Drift (%) S3 Outermost North -216 -6.72 -0.19 S4 Second outermost -215 -6.59 -0.19 S8 Outermost South 356 10.13 0.29 S5 Second outermost 278 5.83 0.17 S7 337 8.66 0.25 Per Figure 4-47, the remaining strain gauges in specimen W-1 consisted of S9 and S16. Strain gauge S9 was adhered to one of the distributed vertical reinforcement bars but unfortunately did 145 not provide reliable readings during the testing. Strain gauge S16 provided very low readings (a maximum strain of 0.000025 was recorded). 5.2.6 Sliding Shear, Rocking, & Shear Displacements Sliding shear displacements between the masonry wall and footing beam were recorded using potentiometer P6. The displacements recorded using this instrument were relatively significant and are provided in Figure 5-11. The sliding displacements between the masonry wall and loading beam were recorded using potentiometer P7. Displacement readings from this potentiometer were available for the entire duration of testing but were generally found to be minimal (-0.02 mm to 0.01 mm); hence, the relative sliding between the masonry wall and loading beam interface is deemed insignificant. Finally, the sliding displacements between the footing beam and strong floor were recorded using potentiometer P5. The readings ranged between 0.44 mm and -0.40 mm; hence, sliding of the specimen is deemed insignificant. Figure 5-11: Sliding Displacements at Masonry Wall and Foundation Interface for Specimen W-1 Specimen rocking was measured using potentiometers P20 and P21. The readings for potentiometer P20 ranged between 0 mm and -1.68 mm. The readings for potentiometer P21 146 ranged between 1.5 mm and -0.5 mm. These readings suggest that minor rocking of the specimen took place during testing. The shear displacements in the masonry wall were measured using potentiometers P22 andP23. The readings from these potentiometers do not provide the shear displacements directly;rather, it is required to compute the shear displacements manually. The method of computingshear displacements from these potentiometer readings is based on the method by Thomsen &Wallace (1995) for reinforced concrete shear walls. Figure 5-12 shows an illustration of theprocedure. If the original lengths of the diagonal potentiometers (d1 and d2) and thecorresponding deformed lengths (d’1 and d’2, respectively) are known, the shear displacementsΔshear can be computed via trigonometry. As shown in the figure, the bottom length of the redright triangle (x) is computed using d’1 and h (the height of the instrumentation), and the bottomlength of the blue right triangle (y) is computed using d’2 and h. Following, it is required tosubtract the value of y from x which yields to 2Δshear and then divide this value by 2 to obtainΔshear. These calculations are summarized in Equation (5-1), where l is the length of theinstrumentation.∆𝑠ℎ𝑒𝑎𝑟=𝑥 − 𝑦2=√𝑑1′2 − ℎ2 −√𝑑2′2 − ℎ22 (5-1) 147 Figure 5-12: Method for Decoupling Shear Displacements from Diagonal PotentiometerReadings (Adapted from Thomsen & Wallace, 1995)The decoupled shear displacements using this method are summarized in Figure 5-13. Thereare two important comments related to these results. First, although Equation (5-1) is intendedfor decoupling shear displacements, the displacements shown in Figure 5-13 include both thedecoupled shear displacements and the sliding shear displacements which occurred in crackedbed joints (except at the wall/foundation interface). Sliding shear displacements in the bed jointswere not measured during testing but based on the progression of cracking and spallingdescribed in Section 5.2.2, are likely to have occurred particularly in the longer and widercracked bed joints. Sliding shear displacements in bed joints are not possible in reinforcedconcrete, which is why Equation (5-1) is more suitable for decoupling shear displacements inreinforced concrete shear walls versus RMSWs. Second, a study by Massone and Wallace(2004) for slender reinforced concrete shear walls suggests that the decoupled sheardisplacements computed using this method may potentially be over-estimated due to theinfluence of flexural displacements. This is particularly relevant if the center of rotation of thewall does not coincide with its geometric center. Their study provides an equation for148 “correcting” the values computed using Equation (5-1) (i.e., the “uncorrected” sheardisplacements) by subtracting the estimated flexural displacements to compute the “corrected”shear displacements. The results using this approach are not provided as for some of thevalues, the estimated flexural displacements were found to be greater than the “uncorrected”shear displacements, which is illogical. Figure 5-13: Combined Shear & Sliding Shear Displacements Between Masonry Courses,Specimen W-15.3 Experimental Results for Specimen W-25.3.1 Hysteretic Force-Displacement PlotThe hysteretic force-displacement plot obtained from experimental testing of specimen W-2 isshown in Figure 5-14. As shown in the figure, the yield displacement in the positive loadingdirection was found to be equal to the theoretical yield displacement (7.1 mm, or 0.2% drift perSection 4.6.2) corresponding to a lateral yield load of 284 kN. The onset of yielding wasconfirmed by analyzing the readings from strain gauges S5, S6, S7, and S8 as well the149 progression of cracking described in Section 5.3.2. The yield displacement in the negative loading direction of -11.6 mm (-0.33% drift) was found to be greater than the theoretical yield displacement, although the lateral yield load of -280 kN was almost equal to the lateral yield load in the positive loading direction. Similarly, the onset of yielding in the negative loading direction was confirmed by analyzing the readings from strain gauges S1, S2, and S3 and the progression of cracking. In Figure 5-14, the tick marks for displacement ductility were computed using Equation (2-16), considering the absolute average yield displacement in the positive and negative loading directions (9.35 mm, or 0.27% drift). Figure 5-14: Hysteretic Force-Displacement Plot for Specimen W-2 A similar trend in the differences between the yield displacements was observed for the displacements corresponding to the ultimate lateral loads. While the ultimate lateral loads in the positive and negative directions were comparable (426 kN and -385 kN, respectively), the displacements corresponding to these loads were significantly different. The displacement corresponding to Qu was 28.4 mm (0.8% drift) and the displacement corresponding to -Qu was -49.7 mm (-1.4% drift). However, the displacements at 20% strength degradation were more 150 comparable. In the positive loading direction, the displacement at 20% strength degradation was 60.3 mm (1.7%) and in the negative loading direction this value was -63.5 mm (-1.8% drift). Generally, while there are differences between the displacements corresponding to the ultimate lateral loads in the opposite loading directions, the behaviour of the specimen is similar. In the positive loading direction, following attainment of Qu at 0.8% drift, the specimen was able to maintain this ultimate load resistance for four drift increments (0.8% through 1.6%) until significant strength degradation was observed at 1.7% drift. Although the specimen did not reach its negative ultimate load resistance until -1.4% drift, the lateral load resistance at -0.8% drift was -369 kN (96% of -Qu), which progressively increased until -Qu was attained. The lateral load resistance at -1.6% drift was -381 kN (99% of -Qu); hence, the behaviour from absolute drifts 0.8% through 1.6% in both loading directions is similar. Also, the specimen experienced 20% of strength degradation at comparable displacement values in both directions. 5.3.2 Experimental Observations This section provides an overview of experimental observations recording during testing of specimen W-2. Figure 5-15 shows the progression of cracking and spalling recorded during testing; recordings were captured when the specimen was displaced to absolute drift magnitudes of 0.2%, 0.4%, 0.6%, 0.8%, 1.0%, and 1.6%. In Figure 5-15, the red and blue lines denote cracks, and the red and blue hatched areas denote regions of spalling. The red lines and hatches denote deformations that were observed during the positive loading cycle, and the blue lines and hatches denote deformations that were observed during the negative loading cycle. The positive and negative directions of loading are also shown with arrows, as well as the north-south orientations. Finally, recordings for drifts 1.2%, 1.4%, 1.8% and 2.0% are not available due to time constraints during testing. Recordings for 0.1% drift are not provided as no cracking or spalling was observed at this drift magnitude. 151 Figure 5-15: Cracking and Spalling Recorded in Specimen W-2 at Drifts a) 0.2%; b) 0.4%; c) 0.6%; d) 0.8%; e) 1.0%; f) 1.6% Testing initiated by displacing the specimen to a drift percentage of 0.1% in both the positive and negative loading directions. As mentioned previously, no cracking or spalling was observed at this stage of testing. Analysis of this information in addition to the strain gauge recordings suggests that the specimen behaviour was elastic at this stage of testing. 152 During the positive loading cycle corresponding to 0.2% drift, the first series of cracks were observed in the specimen. As shown in Figure 5-15 (a), most cracks were formed in the bed joints in the bottom seven courses. Except for the bottommost horizontal crack at the wall/foundation interface, all cracks extended from the edge of the wall and protruded into the specimen with varying lengths. A stepped crack above the fifth course and two diagonal cracks extending from the horizontal bed joint cracks above the first and third courses were also observed. The largest crack width was recorded in the horizontal crack above the third course, which was 0.3 mm. During the negative loading cycle corresponding to 0.2% drift, the deformation pattern was similar to the pattern described for the positive loading direction, except that the overall extent of deformation was less. Noteworthy differences include the appearance of a diagonal crack in the fifth course that did not extend to the edge of the wall, and the formation of a vertical crack that extended to half the course height in the first course. The widest crack was the horizontal bed joint crack above the second course, measuring 0.25 mm wide. New deformation observed during the positive loading cycle corresponding to 0.4% drift mostly consisted of several stepped cracks, as shown in Figure 5-15 (b). These stepped cracks initiated at the wall edge above the seventh, ninth, and eleventh courses. The stepped crack that formed above the eleventh course was relatively long and extended deep into the specimen. Some of the stepped cracks included segments of diagonal cracking. Finally, a horizontal bed joint crack above the sixth course which formed during the positive loading cycle corresponding to 0.2% drift became longer; also, a new horizontal bed joint crack formed above the eighth course. The largest crack width was recorded in the horizontal crack above the third course, which was 0.35 mm (same location as during the positive loading cycle corresponding to 0.2% drift). The new deformation observed during the negative loading cycle corresponding to 0.4% drift mostly consisted of new horizontal bed joint cracks that extended from the edge of 153 the wall into the specimen; the highest location was above the tenth course. Four new diagonal cracks formed in the first, third, and seventh courses, and at the interface of the first and second courses. Finally, two new stepped cracks formed above the sixth and eight courses. The widest crack was the horizontal joint crack above the third course, measuring 0.3 mm wide. New deformation observed during the positive loading cycle corresponding to 0.6% drift included the development of a second horizontal crack above the second course, higher than the horizontal crack that formed during the positive loading cycle corresponding to 0.2% drift (as shown in Figure 5-15 (c)). Both cracks were concentrated in the head joint, except that the new crack was located higher than the older crack, as shown in Figure 5-16. Also, a diagonal crack in the third course became longer, and the diagonal crack in the first course (south toe) developed further (per Figure 5-16). This diagonal crack had the largest width equalling 1.5 mm. For the negative loading cycle corresponding to 0.6% drift, the development of a long horizontal crack above the tenth course was observed. This horizontal crack turned into a stepped crack as it protruded into the wall and terminated as a diagonal crack in the ninth course. Other new cracks included diagonal cracks in the first, second, third, and seventh courses, as well as a small, stepped crack at the edge of the wall above the fifth course. At this point, the concentration of cracking in the north toe was fairly concentrated as shown in Figure 5-17. The largest crack width was measured in the diagonal crack in the first course, equalling to 1.5 mm. 154 Figure 5-16: South Toe of Specimen W-2 During the Positive Loading Cycle at 0.6% Drift (Facing East) Figure 5-17: North Toe of Specimen W-2 During the Negative Loading Cycle at 0.6% Drift (Facing East) 155 During the positive loading cycle corresponding to 0.8% drift, new deformation mostly consisted of diagonal cracking in the first, second, fifth, and seventh courses, as shown in Figure 5-15 (d). The diagonal cracks in the fifth and seventh courses were extensions of existing diagonal cracks, whereas the remaining diagonal cracks were new. Diagonal cracking in the first course was concentrated near the wall’s south toe, which contributed to further deterioration in that region. This diagonal crack had the largest width of 4 mm. During the negative loading cycle corresponding to 0.8% drift, new diagonal cracks formed in courses 1 through 5, seven, nine, ten, and eleven, as shown in Figure 5-15 (d). Also, the mortar joint between the wall and foundation was found to be cracked almost along its entire length, which happened through extension of this crack from previous cycles. A photo showing this crack in addition to cracking in the first five courses is shown in Figure 5-18. The largest crack width was measured in the diagonal crack in the third course, equalling to 2.5 mm. Figure 5-18: Bottom Five Courses of Specimen W-2 During the Negative Loading Cycle at 0.8% Drift (Facing East) During the positive loading cycle corresponding to 1.0% drift, new deformation mostly consisted of diagonal cracking in the fourth, fifth, seventh, eight, and ninth courses. A new horizonal crack in a masonry block also formed in the ninth course, near the edge of the wall, as shown in 156 Figure 5-15 (e). The largest crack width was measured in the diagonal crack in the south toe of the wall, measuring 4 mm. During the negative loading cycle corresponding to 1.0% drift, new diagonal cracks formed in the third and eleventh courses. A vertical crack also formed in the second course, closest to the south toe of the specimen. The widest diagonal crack was located in the first course near the wall’s north toe, measuring 3.5 mm. During the 1.2% and 1.4% drift cycles, thorough crack recordings were not captured due to time constraints. However, it was noted that minor spalling initiated in the wall’s south toe as shown in Figure 5-19 (a) during the 1.2% drift cycles. A photo of this region is also provided during the 1.4 drift cycles in Figure 5-19 (b). The extent of cracking in the toe region, especially in the first and third courses (based on damage described previously) is apparent in these photos as well. a) b) Figure 5-19: Extent of Damage in South Toe of Specimen W-2 During a) 1.2% Drift and b) 1.4% Drift (Facing West) During the positive loading cycle corresponding to 1.6% drift, face shell spalling occurred at two locations in the specimen’s north toe as shown in Figure 5-15 (f). Photos of this spalling are also provided in Figure 5-20. The spalling that occurred closest to the north edge of the specimen 157 exposed the grout in the first course as shown in Figure 5-20 (a). The spalled piece was removed by hand to expose this portion of the grout. At this stage, the grout remained mostly intact, but some cracking was apparent. The spalled face shell located further away from the north edge of the specimen is shown in Figure 5-20 (b). This portion of the face shell was not removed by hand as the lumber block for potentiometer P8 was in the way. a) b) Figure 5-20: Face Shell Spalling in North Toe at 1.6% Drift: a) Closest to North Edge (Facing South); b) Furthest from North Edge (Facing East) 158 In addition to spalling during the positive loading cycle corresponding to 1.6% drift, several new cracks formed. Vertical cracks formed in the second, fourth, and sixth courses, as shown in Figure 5-15 (f). A long diagonal crack extending through courses 11 – 13 was also formed at this stage, as well as two horizontal cracks above the twelfth course, one of which connected to the long diagonal crack. During the negative loading cycle corresponding to 1.6% drift, face shell spalling took place in the south toe, as shown in Figure 5-15 (f). A photo of this spalling is shown in Figure 5-21. This figure also highlights the relatively large widths of the horizontal bed joint cracks at the wall/foundation interface and above the second course, which formed during previous loading cycles but grew in width as testing progressed. Furthermore, new deformation observed during this loading cycle included the formation of new diagonal cracks in courses 1, 3, 5, 7, 10, and 11 – 14 as shown in Figure 5-15 (f). Formation of new vertical cracks also occurred in courses 1, 2, 3, 4, 9, and 10, as shown in Figure 5-15 (f). Figure 5-21: Bottom Two Courses of Specimen W-2 During Negative Loading Cycle at 1.6% Drift (Facing East) During the 1.8% drift cycles, the specimen started to experience significant strength degradation as shown in the hysteretic force-displacement plot of Figure 5-14. Cracking and spalling were no longer recorded at this stage for the remainder of the test. However, several photos were 159 taken to record to the development of spalling at the specimen’s toes, as shown in Figure 5-22. A noteworthy observation relates to the progression of spalling at the specimen’s north toe: as per Figure 5-22 (c), cracking and spalling of the grout progressed to the extent that a portion of one of the vertical bars in the boundary element was exposed. a) b) c) Figure 5-22: Progression of Face Shell Spalling at 1.8% Drift in a) South Toe (Facing West); b) South Toe (Facing East); c) North Toe (Facing South) 160 The final loading cycles in the positive and negative directions at 2.0% drift corresponded to significant strength degradation of the specimen. At this stage, the toe crushing (TC) and bar buckling (BB) failure mechanisms were prevalent in the specimen. A photo of the specimen’s north toe is shown in Figure 5-23. Per the figure, a significant change in deterioration was noticed as compared to the previous loading cycles at 1.8% drift. Face shell spalling was apparent in the first three courses, exposing a large portion of the grouted region in the bottom of the wall. Closest to the wall/foundation interface, a significant portion of the reinforcement in the boundary element was exposed, including the vertical reinforcement and ties. Buckling of the outermost reinforcement in the boundary elements was apparent as shown in Figure 5-23 (b). Also, the confined grout column was significantly deteriorated within the first course, as shown in Figure 5-23 (a). a) b) Figure 5-23: a) Specimen W-2 North Toe at 2.0% Drift (Facing West); b) Close-up of Outermost Buckled Bar in North Toe 161 A photo of the specimen’s south toe taken during the 2.0% drift cycle is shown in Figure 5-24. Per this figure, the grouted portion of the wall was less exposed as compared to the north toe. However, significant face shell spalling and deterioration of the grout is still apparent. Figure 5-24: Specimen W-2 South Toe at 2.0% Drift (Facing West) 5.3.3 Drift Profiles The lateral wall drift profiles that were obtained from experimental testing using potentiometers P1 through P4 are shown in Figure 5-25. Readings at heights 1000 mm, 1700 mm, 2500 mm, and 3100 mm are available based on the installed heights of these potentiometers shown in Figure 4-50. As shown in Figure 5-25, drift profiles obtained at absolute lateral drifts corresponding to Δy, 2Δy, 4Δy, 6Δy, 8Δy, and 10Δy are shown based on the theoretical value of Δy equalling 7.1 mm or 0.2% drift (which is also the experimental value of Δy in the positive loading direction). 162 a) b) Figure 5-25: Lateral Wall Drift Profiles for Specimen W-2 in a) Negative Loading Direction and b) Positive Loading Direction 5.3.4 Average Curvature Profiles Average curvature profiles obtained at absolute drifts corresponding to Δy, 2Δy, 3Δy, 4Δy, 5Δy, 6Δy, and 7Δy are shown in Figure 5-26. Similar to the drift profiles in the previous section, Δy corresponds to theoretical value of Δy equalling 7.1 mm or 0.2% drift. The average curvatures were computed using Equation (2-15). The average curvatures at a height of 2953 mm were computed using the instrumentation readings from potentiometers P18 and P19. The readings from potentiometer pairs P11/P15, P10/P14, P9/P13, and P12/P16 were used to compute the average curvatures at heights 2105 mm, 1305 mm, 453 mm, and 300 mm, respectively. The readings from potentiometers P8 and P17, which were designated for measuring average curvatures, were not utilized to compute the average curvature profiles due to their poor and 163 unreliable readings. Finally, curvature profiles at absolute drifts corresponding to 8Δy (1.6% drift), 9Δy (1.8% drift) and 10Δy (2.0% drift) are not provided primarily due to removal of potentiometers P16, P17, P8, and P12 during the 1.6% drift cycle when face shell spalling initiated at the specimen’s toes. The removal of these potentiometers and their mounting lumber blocks also made it impossible for potentiometers P9 and P13 to record displacements, based on their attachment mechanism described in Section 4.5.2. Also, an average curvature reading in the negative loading direction corresponding to 7Δy at height 453 mm is not provided due to a faulty instrumentation reading, believed to have occurred due to incipient face shell spalling within the vicinity of the instrument. Figure 5-26: Average Curvature Profiles for Specimen W-2 The average curvature profiles are not entirely symmetric between the positive and negative loading directions. The average curvatures are most symmetric at heights of 300 mm, 2105 mm, and 2953 mm. At a height of 1305 mm, the average curvatures in the negative loading direction are generally greater, whereas the opposite is true at a height of 452.5 mm. Nevertheless, it is 164 apparent that the average curvatures at heights of 300 mm and 452.5 mm are significantly greater than the curvatures at the remaining heights in both loading directions. 5.3.5 Strain Readings Selected results from the strain readings for specimen W-2 are provided in this section. The limitations of the performance of strain gauges during testing were discussed in Section 5.2.5. A summary of strain observations for the vertical bars in specimen W-2’s boundary elements are provided in Table 5-2. As shown in Figure 4-47, strain gauges S1 through S8 were designated for measuring the strains in these bars. Results from strain gauges S4 and S6 are excluded due to their poor output from testing. The remaining strain gauges generally provided reasonable results prior to yielding; hence, recording of the onset of yielding is provided in Table 5-2 for each strain gauge. The criteria for yielding consisted of a strain gauge reading exceeding 0.002, which is the yield strain for Grade 400 steel. Table 5-2: Summary of Strain Observations for Vertical Bars in Boundary Elements for Specimen W-2 Strain Gauge # Bars: Wall End Initial Yielding Observed Load (kN) Disp. (mm) Drift (%) S1 Outermost North -248 -9.52 -0.27 S3 -280 -11.64 -0.33 S2 Second outermost -281 -11.93 -0.34 S8 Outermost South 178 2.64 0.08 S5 Second outermost 379 10.76 0.30 S7 259 5.24 0.15 A summary of strain observations for the ties in the boundary elements is provided in Table 5-3. As per the table, strain gauges S11, S14, and S15 were not observed to yield during testing, 165 such that it is possible to provide readings for the tension strain in the ties at ultimate load. Strain gauges S10, S12, and S13 malfunctioned during testing; it is not clear if they malfunctioned due to the onset of yielding or for other reasons. Therefore, Table 5-3 summarizes at which point in testing there was definitely no record of yielding in these strain gauges. Table 5-3: Summary of Strain Observations for Ties in Boundary Elements for Specimen W-2 Strain Gauge # Wall End Course: No yielding at least until: Tension Strain at Ultimate Load Load (kN) Disp. (mm) Drift (%) (mm/mm) x εy S10 North 1 -383 -42.3 -1.2 Unreliable reading S11 2 Did not yield 0.0006 0.3 S12 3 -357 -28.4 -0.8 Unreliable reading S13 South 1 425 28.4 0.8 Unreliable reading S14 2 Did not yield 0.0001 0.05 S15 3 Did not yield 0.0006 0.3 Per Figure 4-47, the remaining strain gauges in specimen W-2 consisted of S9 and S16. Strain gauge S9 was adhered to one of the distributed vertical reinforcement bars but unfortunately did not provide reliable readings during testing. Strain gauge S16 generally provided very low readings (a maximum strain of 0.00004 was recorded). 5.3.6 Sliding Shear, Rocking, & Shear Displacements Sliding shear displacements between the masonry wall and footing beam were recording using potentiometer P6. The displacements recorded using this instrument were relatively significant and are provided in Figure 5-27. Per this figure, displacement records are only available up to an absolute drift of 1.2%, as the L-shaped bracket which touched the wiper tip of the 166 potentiometer fell off during testing once this drift magnitude was reached. The sliding displacements between the masonry wall and loading beam were recorded using potentiometer P7. Displacement readings from this potentiometer were available for the entire duration of testing but were generally found to be minimal (-0.008 mm to 0.008 mm); hence, the relative sliding between the masonry wall and loading beam interface is deemed insignificant. Finally, the sliding displacements between the footing beam and strong floor were recorded using potentiometer P5. The readings ranged between 0.3 mm and -0.6 mm; hence, sliding of the specimen is deemed insignificant. Figure 5-27: Sliding Displacements at Masonry Wall and Foundation Interface for Specimen W-2 Specimen rocking was measured using potentiometers P20 and P21. The readings for potentiometer P20 ranged between 0 mm and -0.922 mm. The readings for potentiometer P21 ranged between 1.6 mm and -2 mm. These readings suggest that minor rocking of the specimen took place during testing. 167 The combined decoupled shear displacements and sliding shear displacements in the wall bed joints are provided in Figure 5-28, similarly to Figure 5-13 for specimen W-1 provided in Section 5.2.6. The method of computing these displacements and the limitations of this method were discussed in the same section. Figure 5-28: Combined Shear & Sliding Shear Displacements Between Masonry Courses, Specimen W-2 5.4 Analysis of Results and Comparison in Specimen Response 5.4.1 Force-Displacement Envelopes Force-displacement envelopes for specimens W-1 and W-2 have been provided in Figure 5-29. Based on this figure, the force-displacement envelopes for both specimens are very similar to one another. In the positive loading direction, the envelopes of specimens W-1 and W-2 are extremely similar between lateral drifts of 0 mm and 56.5 mm (0% drift and 1.6% drift, respectively), except that the lateral load resistances were on average 20.8 kN (5.5%) greater for specimen W-2 versus specimen W-1 within this drift range. The differences in lateral load 168 resistances between the specimens are attributed simply to slight variations in the ways the specimens were constructed and tested. At a displacement of 63.5 mm (1.8% drift), the capacity of specimen W-1 was slightly greater compared to specimen W-2 (relative difference of 25 kN, or 8.4%) and significantly greater at a displacement of 70.6 mm (2.0% drift) (relative difference of 128 kN, or 81%). This implies that, while the force-displacement responses of the specimens in the positive loading direction were similar up to a lateral drift of 63.5 mm (1.8% drift), specimen W-2 experienced significantly greater strength degradation towards the end of the test compared to specimen W-1. At a displacement of 70.6 mm (2.0% drift), specimen W-1 experienced 30% strength degradation, and specimen W-2 experienced 63% strength degradation. Figure 5-29: Force-Displacement Envelopes for Specimens W-1 & W-2 Comparison of the force-displacement envelopes in the negative loading direction generally yields to similar observations as to the positive loading direction. Between drifts of 0 mm and -56.5 mm (0% drift and -1.6% drift, respectively), the envelopes are extremely similar, except the lateral load resistances of specimen W-1 were on average 3.75 kN (1.1%) greater compared to 169 specimen W-2 within this drift range. Similar to the positive loading direction, the differences in lateral load resistances between the specimens are attributed simply to slight variations in the ways the specimens were constructed and tested. At a displacement of -63.5 mm (-1.8% drift), the capacity of specimen W-2 was slightly greater compared to specimen W-1 (relative difference of 37 kN, or 15.6%), but at a drift of -70.6 mm (-2.0% drift) was significantly lower (relative difference of 175 kN, or 921%). This implies that, while the force-displacement responses of the specimens in the negative loading direction were similar up to a lateral drift of -63.5 mm (-1.8% drift), specimen W-2 experienced significantly greater strength degradation towards the end of the test compared to specimen W-1. At a displacement of -70.6 mm (-2.0% drift), specimen W-1 experienced 50% strength degradation, and specimen W-2 experienced 95% strength degradation. Based on the aforementioned comparison, the specimens responded similarly up to an absolute lateral drift of 63.5 mm (1.8% drift), following which specimen W-2 experienced significantly greater strength degradation than specimen W-1 during the final load cycles at an absolute drift of 70.6 mm (2.0% drift). 5.4.2 Wall Capacities The capacity for each wall is defined as the maximum lateral load resisted by the wall during the test. Table 5-4 summarizes the values for the specimens. Table 5-4: Wall Capacities for Specimens W-1 & W-2 Specimen Positive Loading Direction Negative Loading Direction W-1 412 kN -388 kN W-2 426 kN -385 kN Per this table, the capacity of specimen W-2 was 14 kN (3.4%) greater than the capacity of specimen W-1 in the positive loading direction. In the negative loading direction, the capacity of 170 specimen W-1 was 3 kN (0.8%) greater than the capacity of specimen W-2. In practical terms, these differences in capacities are negligible, and are attributed to slight variations in the construction and testing of the specimens. 5.4.3 Displacements In RMSWs, the total in-plane lateral deflection results from three components: flexural, sliding, and shear displacements (Shedid, 2006). From testing results of RMSWs, it can be useful to analyze the portion that each displacement component contributed to the total response. Generally, a larger contribution from flexural displacements is preferred as they correspond to larger contributions of flexural failure mechanisms. Figure 5-30 and Figure 5-31 show the percent contributions of the flexural and shear displacements for specimens W-1 and W-2, respectively. For specimen W-1, the shear displacements are the sum of the sliding shear displacements measured at the wall/foundation interface (Figure 5-11), and the combined shear displacements and sliding displacements in the bed joints (Figure 5-13). The flexural displacements were computed by subtracting these values from the total lateral displacements of the specimen. The same procedure was followed for specimen W-2 considering the values in Figure 5-27 and Figure 5-28. The lateral displacements at which the specimens yielded and provided the ultimate load resistance are also shown. Note that for specimen W-2, since flexural and shear displacement values are not available at the point when the specimen reached ultimate capacity in the negative loading direction, the point when 96% of the ultimate capacity was reached is marked (based on the discussion in Section 5.3.1). Finally, Figure 5-32 shows the flexural displacements for specimens W-1 and W-2 on the same plot for comparison. 171 Figure 5-30: Flexural and Shear Displacements, Specimen W-1 Figure 5-31: Flexural and Shear Displacements, Specimen W-2 172 Figure 5-32: Flexural Displacements, Specimens W-1 & W-2 Per Figure 5-32, the total contribution of flexural displacements in specimen W-1 was generally less compared to the total contribution of flexural displacements in specimen W-2. The values were only comparable at lateral drifts of 7 mm and 14 mm (drift % of 0.2 and 0.4, respectively); otherwise, the values were greater for specimen W-2. The relative differences in flexural displacements amongst the specimens increased as loading progressed in the positive and negative loading directions. Based on this, during testing of both specimens, specimen W-2 generally experienced a larger contribution from flexural displacements compared to specimen W-1. 5.4.4 Extent of Damage & Failure Mechanisms The intent of this section is to discuss the extent of damage and failure mechanisms of specimens W-1 and W-2 based on the classification of failure mechanisms identified in Chapter 2. As discussed in Chapter 2, this classification system states that each RMSW specimen subjected to cyclic loading has two failure mechanisms that generalize its response: a primary and secondary failure mechanism. The primary failure mechanism is observed at ultimate load, 173 and the secondary failure mechanism is observed at 20% strength degradation. For the purposes of this section, in order to compare the failure mechanisms amongst the specimens, the definition of the primary failure mechanism is slightly adjusted. In this section, the primary failure mechanism is the governing failure mechanism at 1.0% drift (35.3 mm of lateral displacement). Per the hysteretic force-displacement plots for specimens W-1 and W-2, the load resistances at 1.0% drift in both loading directions were either at their ultimate values (such as in the positive loading direction for specimen W-1), or a significant fraction of the ultimate values (96% or greater). Based on this, the definition of the primary failure mechanism is not altered significantly. Finally, in addition to comparing the primary and secondary failure mechanisms, commentary regarding the onset of face shell spalling, and the extent of toe crushing, will be provided for both specimens. Figure 5-33 shows photos of the bottom eleven courses for specimens W-1 and W-2, which were taken after the first loading cycle was run in the positive and negative loading directions at 1.0% drift (35.3 mm of lateral displacement). The first eleven courses are shown as this is where deterioration in both specimens was concentrated. In Figure 5-33, markings of the cracks are visible which correspond to the cracks shown in Figure 5-2 for specimen W-1 and Figure 5-15 for specimen W-2. 174 a) b) Figure 5-33: Specimens at 1.0% Drift: a) W-1; b) W-2 Per this figure, the heights in which deterioration was present in both specimens was identical (i.e., within the first eleven courses). However, the amount of deterioration was generally greater in specimen W-1 compared to specimen W-2. At 1.0% drift, specimen W-1 contained significantly more diagonal cracks compared to specimen W-2, although specimen W-2 contained slightly more stepped cracks compared to specimen W-1. The number of horizontal bed joint cracks that were long (i.e., extending across most of the specimen’s length) were similar: this value was 5 for specimen W-1 and 4 for specimen W-1. Recognition of these cracks is important, as it is likely that they contributed to sliding between the courses (in addition to sliding between the wall/foundation interfaces, the displacements for which were recorded). Namely, the wide horizontal bed joint crack observed above the second course for specimen W-2 (based on Figure 5-21) highlights the potential for significant shear sliding at this location. Finally, both specimens contained a significant number of smaller bed joint cracks positioned closer towards the edges of the walls, which are indicative of flexural deformations. 175 From a performance perspective, the extent of damage in specimens W-1 and W-2 at 1.0% is similar. Both specimens experienced significant cracking of the masonry, but no other forms of deterioration. Ultimately, based on the analysis of available data including the experimental observations provided in Sections 5.2.2 and 5.3.2 and the decoupled displacements provided in Section 5.4.3, Ductile Flexure (DF) is deemed to be the primary failure mechanism for both specimens. Prior to discussing the secondary failure mechanism for both specimens, the onset of face shell spalling, and extent of toe crushing, is discussed for both specimens. In flexure-dominated walls, the onset of face shell spalling (which typically initiates at the wall’s toes) is an important milestone in the failure progression as it corresponds to the start of significant damage (typically followed by toe crushing). This damage is significant because it can potentially cause substantial damage to the building’s non-structural components as well as contribute to falling debris during earthquakes, which becomes a safety hazard. Per Sections 5.2.2 and 5.3.2, the onset of face shell spalling for specimen W-1 occurred during the second loading cycle at 1.2% drift, and during the first loading cycle for specimen W-2 at 1.6% drift. Also, the observed extent of face shell spalling and toe crushing during the final loading cycle (at 2.0% drift, 70.6 mm lateral displacement) for specimen W-1 was more significant compared to specimen W-2, based on the photos provided in Sections 5.2.2 and 5.2.3. This implies that in terms of damage caused due to face shell spalling and toe crushing, specimen W-2 performed better compared to specimen W-1. This is justified as specimen W-2 experienced both less overall damage and a later onset of damage compared to specimen W-1. As discussed previously, the secondary failure mechanism is the governing failure mechanism observed at 20% strength degradation. From previous sections, 20% strength degradation in specimen W-1 occurred at a lateral displacement of 63.5 mm (1.8% drift) in the positive loading direction, and -56.6 mm (-1.6% drift) in the negative loading direction. For specimen W-2, these 176 values were 60.3 mm (1.7% drift) and -63.5 mm (-1.8% drift), respectively. Since the failure mechanisms at both toes were similar, and for the purposes of comparison, photos of the specimens’ toes at 1.8% drift (63.5 mm lateral displacement) taken during the positive loading cycle are shown in Figure 5-34. 1.8% drift (63.5 mm lateral displacement) corresponds to exactly 20% strength degradation for specimen W-1, and slightly greater than 20% strength degradation for specimen W-2. a) b) Figure 5-34: Specimens at 1.8% Drift: a) W-1; b) W-2 Based on this figure, the secondary failure mechanism for specimen W-1 is apparent. As shown in Figure 5-34 (a), the presence of significant toe crushing (TC) and bar buckling (BB) is noticeable. However, despite the significant amount of toe crushing (TC), it is deemed most likely that if bar buckling (BB) was not present, the specimen would be able to maintain a lateral load resistance at a value near the ultimate capacity. Hence, bar buckling (BB) is deemed to be the secondary failure mechanism for specimen W-1. For specimen W-2, the secondary failure 177 mechanism is not as apparent based on Figure 5-34 (b). While there is some face shell spalling and toe crushing (TC), it is not deemed to be significant enough to cause 20% strength degradation. Also, based on this figure and Figure 5-22, there does not appear to significant bar buckling (BB) either. Given the experimental observations provided in Section 5.3.2, and the sliding shear and shear displacement readings provided in Section 5.3.6, it is deemed most likely that Sliding Shear Failure (SL) was the secondary failure mechanism. A photo of the specimen’s bottom four courses taken at 1.8% drift is illustrated in Figure 5-35, highlighting the locations at which sliding was deemed to be most significant in the specimen. Figure 5-35: Bottom Four Courses of Specimen W-2 at 1.8% Drift (Facing East) 5.4.5 Energy Dissipation In seismic design, energy dissipation is an important concept as it is linked to the ductility modification factor (Rd) used by NBC 2020 (Canadian Commission on Building and Fire Codes, 2022); similar modification factors are used in other design codes and standards. As discussed in Chapter 1, SFRSs with higher Rd values have greater potential to dissipate energy during earthquakes. SFRSs with higher Rd values are permitted to be designed for reduced seismic demands given their enhanced capabilities to dissipate energy. 178 Figure 5-36 shows the cumulative energy dissipation of specimens W-1 and W-2 at different displacement levels. In this figure, each displacement level corresponds to a loading cycle based on the loading protocols identified in Section 4.6. The area enclosed by each cycle in the hysteretic force-displacement plots for the specimens is equal to the energy dissipated during the loading cycle. For computation purposes, each force-displacement cycle was isolated and exported to a CAD software which easily computes the areas of various shapes. Figure 5-36: Energy Dissipation of Specimens W-1 & W-2 Per this figure, the cumulative energy dissipated by the specimens was almost equal up to a lateral displacement of 49.4 mm (1.4% drift). The rate of energy dissipation up to this point was also almost equal amongst the specimens. After this, the rate of energy dissipation for specimen W-2 slightly increased relative to specimen W-1 at lateral displacements of 56.5 mm and 63.5 mm (1.6% and 1.8% drifts, respectively), but decreased during the final loading cycle at a lateral displacement of 70.6 mm (2.0% drift). The total energy dissipation of specimen W-2 was 118,906 kN*mm, which is 5.3% greater than the energy dissipation of specimen W-1 (112,933 kN*mm). This difference in energy dissipation is generally insignificant in terms of seismic 179 performance. Also, the nearly equal rates of energy dissipation up to a lateral displacement of 49.4 mm (1.4% drift) suggest that the energy dissipation properties of the specimens are similar. 5.4.6 Ductility Ratios As discussed in Chapter 2, the ductility ratio μ can provide insight towards the seismic performance of RMSWs. It was also discussed in this chapter that the drawback of the ductility ratio is that its value can be sensitive to the value of Δy used in its computation. Table 5-5 summarizes the ductility ratios for specimens W-1 and W-2 computed using Equation (2-16). Two sets of ductility ratios have been provided. The first set of ductility ratios was computed considering the absolute average yield displacements (Δy) and ultimate displacements (Δu) in the positive and negative loading directions for both specimens. The second set of ductility ratios was computed considering the yield and ultimate displacements in the positive loading direction only. The second set of ductility ratios was computed to provide a slightly fairer comparison amongst the specimens, since the values of Δy for both specimens were found to be equal in the positive loading direction. Table 5-5: Ductility Ratios for Specimens W-1 & W-2 Specimen Positive & Negative Loading Directions Positive Loading Direction Only Average Δy Average Δu μ Δy Δu μ W-1 7.1 mm 60.1 mm 8.5 7.1 mm 63.5 mm 8.9 W-2 9.4 mm 61.9 mm 6.6 7.1 mm 60.3 mm 8.5 Based on this table, the ductility ratio of specimen W-1 is significantly greater than specimen W-2 if the first set of ductility ratios are used as comparison, and slightly greater if the second set of ductility ratios are used as comparison. Generally, the ductility ratios are comparable if the second set of ductility ratios are considered. 180 5.4.7 Key Takeaways & Conclusions Per Chapter 1, one of the objectives of this thesis was to identify if embedded boundary elements have potential to improve the seismic performance of RMSWs based on the comparison of experimental results from the in-plane reversed cyclic tests of specimens W-1 and W-2. Based on this, if specimen W-2 performed better than specimen W-1, the positive differences in behaviour could be attributed to the effect of the embedded boundary elements. In this section (Section 5.4), various parameters were compared amongst the specimens to assess their performance relative to one another. In summary, the findings were: 1. The force-displacement responses of specimen W-1 and W-2 were generally comparable. This is justified as for most of the testing (0% - 1.8% absolute drifts), the responses were very similar amongst the specimens. 2. The wall capacities of the specimens were comparable; hence, it does not appear that the embedded boundary elements in specimen W-2 increased the wall capacity relative to specimen W-1. 3. The primary failure mechanisms of the specimens were Ductile Flexure (DF), and the second failure mechanisms of specimens W-1 and W-2 were bar buckling (BB) and Sliding Shear Failure (SL), respectively. The extent of damage in the wall’s toes was concentrated within the bottom 5 courses in specimen W-1, and within the bottom 3 courses in specimen W-2. The onset of this damage occurred during the 1.2% drift cycles in specimen W-1, and the 1.6% drift cycles in specimen W-2. 4. The energy dissipation properties of the specimens were similar. 5. The ductility ratio of specimen W-1 was comparable to the ductility ratio of specimen W-2. This is true if the ductility ratio computed using the value of Δy in the positive loading direction is considered in the comparison. 181 Based on these limited experimental results, it is deemed that without applied axial compression, the seismic performance of RMSWs with and without embedded boundary elements is comparable. Since most of the RMSW specimens with external boundary elements that were previously tested in Canada were subjected to axial stress (including all the specimens referenced in Chapter 3), this statement can provide insight towards the seismic performance of RMSWs with external boundary elements without applied axial compression. Ultimately, these findings are important because masonry buildings are often constructed with precast hollow core floor panels, which are designed as one-way structural systems. This means that if a masonry wall is not bearing a hollow core panel, it would be subjected to a very small magnitude of axial stress beyond its self-weight. Given the findings of this chapter, thoughtful consideration should be given if it is worthwhile constructing these types of RMSWs with any type of boundary elements. 5.5 Summary The purpose of this chapter was to provide the results from the experimental program in this research study. Selected experimental results for specimens W-1 and W-2 were provided in Sections 5.2 and 5.3, respectively. Analysis of these results, and the comparison in the performance of the specimens, was accomplished in Section 5.4. 182 6. PROPOSED BACKBONE MODELS FOR REINFORCED MASONRY SHEAR WALLS 6.1 Introduction The purpose of this chapter is to present approaches for developing generalized force-deformation curves for regular RMSWs and RMSWs with boundary elements. A force-deformation curve is a representation of the nonlinear behaviour of a component action based on a smooth or multilinear curve at a discrete location along the length of the component (American Society of Civil Engineers, 2023). In the context of RMSW structures, the “component” is a single RMSW, and the “discrete location along the length of the component” is taken at the bottom of the RMSW as this is where internal forces (shear, bending) are the largest, except that in this context the “length of the component” refers to the height of the RMSW. A force-deformation curve is often less formally referred to as a “backbone” curve, which was previously introduced in Chapter 2 and an example was shown in Figure 2-11. In modern structural engineering, backbone curves are commonly used in applications involving nonlinear static analysis (i.e., pushover analysis). A numerical model for pushover analysis can be developed using various structural elements, and each element can be assigned a backbone curve to capture its nonlinear force-displacement relationship. Once incremental displacements are applied to the model as part of the pushover analysis, the software can generate a force-displacement plot for the entire model. In Chapter 2, Figure 2-7 showed the various models that can be used for nonlinear analysis: plastic hinge, nonlinear spring hinge, finite length hinge zone, fiber section, and finite element model. The nonlinear behaviour of a plastic hinge, nonlinear spring hinge, and finite length hinge zone models are often characterized by backbone curves. This is because backbone curves relate a nonlinear moment-curvature relation in the plastic hinge zone of a model to a 183 nonlinear force-displacement relation of the entire structural element. This is illustrated in Figure 6-1, where a moment (Mi) – curvature (φi) relation for a wall cross section in the plastic hinge zone is used as input, and a force (Qi) vs. displacement (Δi) capacity curve is obtained as a result of the pushover analysis. Figure 6-1: Moment-Curvature Relation and Force-Displacement Relation in a Nonlinear Model The most accurate method for obtaining a backbone curve for a RMSW is from an experimental hysteretic force-displacement plot for a RMSW specimen. A multilinear curve can be created by defining three to four critical points based on experimental results. Usually, point 1 corresponds to the yield point (i.e., when a reinforced concrete or reinforced masonry specimen starts to yield), point 2 corresponds to the ultimate load (capacity) that a structural element can attain, point 3 corresponds to 80% of the ultimate load (20% strength degradation), and point 4 184 corresponds to the ultimate displacement (at failure). A backbone model showing these points is illustrated in Figure 6-2 (a), and a sample backbone curve obtained from an experimental hysteretic force-displacement plot for a RMSW specimen is shown in Figure 6-2 (b). a) b) Figure 6-2: Backbone Curve: a) General Model; b) Backbone Curve Corresponding to a RMSW (Adapted from Shedid et al., 2010) 185 The limitation of the method for developing a backbone curve by obtaining it from an experimental hysteretic force-displacement plot for a RMSW specimen is that the curve becomes unique to a specific specimen, which has its own geometry, material properties, reinforcement amount and configurations, level of axial stress, etc. In practical settings, it is unrealistic to obtain experimental hysteretic force-displacement plots for various RMSW configurations and develop corresponding backbone curves. Therefore, it is required to create generalized force-displacement curves which can be used to characterize nonlinear behaviour of any RMSW. For that reason, seismic design codes and guidelines provide generalized backbone curves for RMSWs and other structural elements. The development of these generalized curves is accomplished based on statistical analysis of experimental test data and numerical modelling, and the resulting generalized modelling parameters can be applied to a wide range of designs. NIST GCR 17-917-45 (Applied Technology Council, 2017) and ASCE 41-23 (American Society of Civil Engineers, 2023) provide generalized backbone curves for flexure-dominated and shear-dominated RMSWs. Backbone curves for flexure-dominated fully grouted regular RMSWs can be obtained by following two steps, which are described below. The first step consists of developing a moment-curvature relation for the wall cross-section within the plastic hinge zone shown in Figure 6-3. This requires computing values for six parameters: i) Mmax, the maximum (or ultimate) moment resistance of the RMSW; ii) M75, the post-peak moment resistance of the RMSW at 25% strength degradation (i.e., 75% of Mmax); iii) Mc, the post-peak moment resistance of the RMSW at which the moment-curvature plot is “capped” (taken as 50% of Mmax), as well as the corresponding curvatures φm, φ75, and φc. The values for Mmax, φm, φ75, and φc are statistically calibrated parameters that are readily obtained from Table 9-1 of NIST GCR 17-917-45 and are functions of the RMSW’s geometry, vertical reinforcement ratio, magnitude of axial stress, steel yield strength, and masonry compressive strength. 186 Figure 6-3: Moment-Curvature Relation for Regular RMSWs per NIST GCR 17-917-45 (Applied Technology Council, 2017) The second step consists of converting the moment-curvature relation obtained in the first step to a backbone curve; the latter is shown in Figure 6-4. This backbone model considers point A as the yield point, point B corresponds to the ultimate capacity (Qmax), point C corresponds to 25% strength degradation, and point D corresponds to 50% strength degradation. The development of this backbone curve requires computing values for eight parameters, including four lateral forces (Qy, Qmax, Q75, and Qc) and the corresponding lateral displacements (Δy, Δm, Δ75, and Δc). For a cantilever RMSW, parameters Qmax, Q75, and Qc are obtained by dividing the values of the corresponding moment resistances Mmax, M75 and Mc by the RMSW’s height hw. Parameters Δm, Δ75, and Δc are determined by converting the corresponding curvatures φm, φ75, and φc to displacements. In NIST GCR 17-917-45, this is accomplished by employing an equation similar to Equation (2-14), except that Equation (2-14) only considers flexural displacements, whereas in NIST GCR 17-917-45 shear displacements are also considered. Finally, parameter Qy is assumed to be equal to 0.8Qmax, and parameter Δy is obtained by dividing Qy by the RMSW’s elastic stiffness k. The elastic stiffness k depends on the boundary conditions and force distributions in a wall. NIST GCR 17-917-45 considers both flexural and shear components of stiffness during the computation. 187 Figure 6-4: Force-Displacement (Backbone) Curve for Flexure-Dominated Regular RMSWs per NIST GCR 17-917-45 (Applied Technology Council, 2017) NIST GCR 17-917-45 provides an approach for developing backbone curves only for regular RMSWs. An approach to develop backbone curves for RMSWs with boundary elements is currently not available. The primary objective of this chapter is to propose a methodology for developing backbone models for fully grouted RMSWs with boundary elements (Section 6.3). This is preceded by presentation of an approach for developing backbone curves for fully grouted regular RMSWs in Section 6.2. The approach presented in Section 6.3 builds upon the approach presented in Section 6.2. 6.2 Backbone Model for Regular RMSWs This section presents a methodology for developing backbone curves for fully grouted flexure dominated regular RMSWs. A backbone curve that can be developed using this methodology is shown in Figure 6-5. Per this figure, the backbone curve is constructed using four points: • Point 1 corresponds to onset of yielding of the RMSW, defined by yield load Qy and yield displacement Δy. • Point 2 corresponds to the ultimate load capacity of the RMSW, defined by Qu and ΔQu. 188 • Point 3 corresponds to the RMSW’s post-peak strength at 20% strength degradation, defined by Q80 and Δ80. • Point 4 corresponds to the final point on the backbone curve (corresponding to failure), defined by Qf and Δf. There is flexibility in terms of selection criterion for point 4: it can either correspond to a certain percentage of strength degradation (for example, 50% per NIST GCR 17-917-45) or a certain drift percentage. In this study, the drift related criterion is adopted to demonstrate the effectiveness of the proposed backbone model, since experimental hysteretic force-displacement plots are characterized by varying magnitudes of strength degradation in the final loading cycle. Figure 6-5: Force-Displacement (Backbone) Curve for Flexure-Dominated Fully Grouted Regular RMSWs The procedure for developing the backbone curve shown in Figure 6-5 consists of performing a section analysis for the RMSW four times (one analysis per point). The objective of section analysis is to ensure equilibrium of internal and external (applied forces) for a given strain profile. Strain profiles for points 1 to 4 of the backbone curve are shown conceptually in Figure 6-6. Each strain profile corresponds to a point (1, 2, 3, or 4) on the backbone curve. Once the 189 force equilibrium is satisfied, the sum of moments about an arbitrary point along the wall length is set to zero, and the corresponding probable moment resistance of the RMSW, Mp, is computed. Mp is computed using a masonry resistance factor Φm taken equal to 1 and a steel resistance factor Φs taken equal to 1.25. Knowledge of the strain profile also allows for computation of the corresponding curvature φ. Once both Mp and φ are known, they are converted to the corresponding Q and Δ values. The procedure is repeated four times to obtain all four points of the backbone curve. Figure 6-6: Conceptual Strain Profiles for a Regular RMSW Corresponding to Points 1-4 on the Backbone Curve Section analyses performed to determine point 1 (Qy and Δy) and point 2 (Qu and ΔQu) on the backbone curve shown in Figure 6-5 are relatively simple. Explanation of this procedure is aided through Figure 6-7, which shows a sample cross-section of a regular RMSW alongside its strain profile and free body diagram that are used in section analyses. Figure 6-7 (a) shows the strain profile and free body diagram used to obtain point 1, and Figure 6-7 (b) shows the strain profile and free body diagram used to obtain point 2. In this figure, lw is the wall length, de is the 190 distance between the center of the outermost vertical reinforcement bar and the end of the section, εsi is the tensile strain in vertical reinforcement bar i, ε’si is the compressive strain in vertical reinforcement bar i, Ti is the tensile force developed in vertical reinforcement bar i, Ci is the compressive force developed in vertical reinforcement bar i, Cm is the compressive force of the masonry, M is the applied bending moment, and P is the applied axial force. a) b) Figure 6-7: Sample RMSW Cross Section, Strain Profile, and Internal Force Distribution for a) Point 1 (Onset of Yielding) and b) Point 2 (Ultimate Moment Capacity) in a Regular RMSW Backbone Curve The first step in section analyses for points 1 and 2 on the backbone curve is to impose a constraint on the strain profile. For point 1, this constraint consists of setting the tensile strain of the outermost vertical reinforcement bar equal to the steel’s yield strain εsy (see Figure 6-7 (a)). For Grade 400 steel, εsy is equal to 0.002. For point 2, this constraint consists of setting the masonry strain equal to the ultimate masonry strain. Since the ultimate masonry strain is not known, the recommended approach is to initially set εmu equal to 0.003, which is the value used in CSA S304-24 (Canadian Standards Association, 2024). Once the constraints on the strain 191 profiles are imposed, the next step is to set a trial value for c in both analyses, which allows the user to determine trial strain profiles. The values from the trial strain profile (i.e., εsn, ε’sn, c) are then converted to internal forces in steel and masonry based on specified relationships. Next, the force equilibrium is verified. If force equilibrium is not attained, a new iteration for c is used, and the procedure is repeated until the equilibrium is attained. Subsequently, the moment resistances and the curvature values for points 1 and 2 are determined and are converted to the force and displacement values (equations for this are provided at the end of this section). The final step in the analysis of point 2 only is to determine the maximum moment resistance. This involves slightly adjusting the values of εmu and c which give the maximum moment resistance of the wall. The reason for initially setting εmu equal to 0.003 is that the computed moment resistance using this value is likely to be close to the maximum moment resistance, which provides estimates for the expected c and Mu values. While the maximum moment resistance is not very sensitive to the value used for εmu, the value for curvature is, why is why this adjustment is required. This procedure for obtaining values for points 1 and 2 is summarized in a flowchart in Figure 6-8. 192 Figure 6-8: Summary of Analytical Procedure to Determine Points 1 & 2 on a Regular RMSW Backbone Curve Conversion of values from the strain profile (i.e., εsi, ε’si, c) to internal forces in the masonry and steel is accomplished via material models. The material model used for steel is shown in Figure 6-9, which relates values of εsi and ε’si to steel stress σs; the latter is multiplied by the bar area to compute forces Ti and Ci. The model is adapted from the cyclic material model from NIST GCR 193 17-917-45, which accounts for bar buckling in compression by neglecting the strength contribution from the reinforcement following yielding, whereas tensile bar fracture from cyclic loading is accounted for by imposing a limit on strain-hardening (corresponding to a strain of 0.003). Figure 6-9: Stress-Strain Relation for Steel Considering Bar Buckling and Fracture in Regular RMSWs (adapted from Applied Technology Council, 2017) For post-yield points on the backbone curve, the internal forces in masonry (the compressive stress resultant) for section analysis are computed using the equivalent rectangular compression stress block for masonry, consistent with CSA S304-24 (Canadian Standards Association, 2024). This approach assumes that the compressive masonry stress is uniformly distributed and is equal to 0.85f’mΦm and acts over a compression zone length a, as shown in Figure 6-7 (b). The parameter a is equal to the product of β1 and c, where β1 is equal to 0.8 when f’m is less than or equal to 20 MPa. Section analyses to obtain points 3 and 4 for the backbone curve in Figure 6-5 are generally similar to the procedure identified for point 2. The primary difference is that in order to capture the strength degradation of points 3 and 4, it is required to employ a “moment arm reduction” approach. Explanation of this approach is aided through Figure 6-10 (which is similar to Figure 194 6-7), which shows a sample cross section of a regular RMSW alongside its strain profile and free body diagram that are used in section analyses of points 3 and 4. It can be seen in Figure 6-6 that as the curvature φ of the RMSW section increases at points 3 and 4 (as compared to point 2), the extreme masonry strains in the strain profile (εm80 at point 3, and εmf at point 4) increase as well. Due to the moment arm reduction approach, the compressive strength resistance of masonry is taken equal to zero when the masonry strain exceeds εmu, as shown in Figure 6-10. In this figure, the portion of the RMSW that is providing compressive resistance is within length c’ (i.e., the strains within this length are less than or equal to εmu), whereas the portion of the RMSW that is not providing compressive resistance is within length c – c’ (i.e., the strains within this length are greater than εmu). Based on this, the hatched portion of the strain profile in Figure 6-10 denotes the length of the moment arm; notice that the strain profile is fully hatched in Figure 6-7. Also, the length of the equivalent stress block a is equal to the product of β1 and c’, as shown in Figure 6-10. In general, neglecting the compressive strength resistance of masonry once its strain exceeds εmu implies that the masonry has experienced significant crushing. Since section analysis is performed at the most critical section of the RMSW (within the plastic hinge zone), this implies that the moment arm reduction approach simulates the toe crushing (TC) failure mechanism in RMSWs. Furthermore, since εmu is typically greater than εsy, the bar buckling (BB) failure mechanism is also simulated within length c – c’. 195 Figure 6-10: Sample RMSW Cross Section, Strain Profile, and Internal Force Distribution used in Section Analysis for Points 3 and 4 in a Regular RMSW Backbone Curve The flowchart for section analyses of points 3 and 4 for the backbone curve in Figure 6-5 is shown in Figure 6-11. Section analysis for point 3 is straightforward – it involves iterating εm80 and c until the strain profile is established, force equilibrium is satisfied, and the moment resistance of the RMSW M80 is roughly equal to 80% of ultimate moment resistance Mu. The section analysis for point 4 is similar, except that the final lateral displacement Δf is verified against the predefined drift ratio. Per earlier commentary in this section, the procedure for point 3 in Figure 6-11 can be adopted for point 4 if attainment of a certain percentage of strength degradation is desired, rather than attainment of a certain drift percentage. 196 Figure 6-11: Summary of Analytical Procedure to Determine Points 3 & 4 on a Regular RMSW Backbone Curve The procedure for developing backbone curves shown in Figure 6-5 for regular flexure-dominated fully grouted RMSWs was implemented and validated against selected experimental hysteretic force-displacement plots from research studies presented in Chapter 3. Namely, the force displacement plots of specimen 1 by Shedid et al. (2008) and specimen W1 by Shedid et 197 al. (2010) were referenced. The former is an analysis case for a specimen tested without axial stress, whereas the latter is a case for a specimen tested with axial stress. The specimen properties employed in the analysis are listed in Table 3-1, and the specimen cross sections are shown in Figure 6-12 and Figure 6-13. Figure 6-12: Cross Section of Specimen 1 (Adapted from Shedid et al., 2008) Figure 6-13: Cross Section of Specimen W1 (Adapted from Shedid et al., 2010) The backbone curves obtained using the procedure described in this section are shown against the experimental results by Shedid et al. (2008, 2010) in Figure 6-14 and Figure 6-15. 198 Figure 6-14: Fitted Backbone Curve to the Hysteretic Force-Displacement Plot of Specimen 1 (Adapted from Shedid et al., 2008) Figure 6-15: Fitted Backbone Curve to the Hysteretic Force-Displacement Plot of Specimen W1 (Adapted from Shedid et al., 2010) The yield displacements Δy were computed using Equation (2-7). The conversion of post-yield curvatures φ to lateral displacements Δ employed an equation similar to Equation (2-14). In 199 Chapter 2, it was mentioned that derivation of Equation (2-14) assumes a finite length hinge zone model, meaning that the idealized plastic hinge height hp is assumed to be fully developed immediately following yielding of the RMSW. Since this does not accurately represent RMSW behaviour in experimental settings, a variable length hinge zone model was employed to convert post-yield curvatures φ to lateral displacements Δ. This model allows for progressive development of the idealized plastic hinge height hp, which is more representative of RMSW behaviour in experimental settings. This requires introduction of variable x into Equation (2-14); the revised equation with this implemented is shown in Equation (6-1). 𝛥𝑄𝑢| 80|𝑓 = 𝛥𝑦 + (𝜑𝑄𝑢| 80|𝑓 − 𝜑𝑦)(𝑥ℎ𝑝)(ℎ𝑤 − 0.5𝑥ℎ𝑝) (6-1) where x equals 0.45 for point 2 in the backbone curve (ΔQu), 0.9 for point 3 in the backbone curve (Δ80) and 1 for point 4 in the backbone curve (Δf) (i.e., hp is fully developed at point 4). Further study is recommended to validate the proposed values of x against a larger set of experimental data. Finally, hp was taken equal to 0.5lw per CSA S304-24 (Canadian Standards Association, 2024). The values from the strain profiles for points 2, 3, and 4 on the backbone curves shown in Figure 6-14 and Figure 6-15 are summarized in Table 6-1. 200 Table 6-1: Summary of Parameters from Strain Profiles from Referenced Studies Specimen Point on Backbone Curve Masonry Strain (εm) [mm/mm] Steel Strain in Outermost Bar (εs1) [mm/mm] Depth of neutral axis (c) [mm] Curvature (φ) [rad/mm E-5] Specimen 1 (Shedid et al. (2008)) 2 0.0075 0.0356 298.2 2.54 3 0.0124 0.0418 388.7 3.19 4 0.0219 0.0342 662.4 3.29 Specimen W1 (Shedid et al. (2010)) 2 0.0074 0.0141 622.8 1.25 3 0.0103 0.0150 713.3 1.45 4 0.0122 0.0140 813.8 1.50 Per Table 6-1, the proposed approach for developing backbone curves conforms to the basic principles of the analytical behaviour of RMSWs in which the masonry strain, depth of the neutral axis, and curvature increase as the RMSW is subjected to increasing lateral displacements. The values of tensile strain in the outermost vertical bar generally remain similar for points 2, 3, and 4 because once this bar yields, the increase in tensile strength relative to the increase in tensile strain is very small, based on the material model shown in Figure 6-9. Finally, the values of εmu of 0.0075 and 0.0074 for specimens 1 by Shedid et al. (2008) and W-1 by Shedid et al. (2010), respectively, are greater than the maximum allowable value of 0.003 for regular RMSWs per CSA S304-24 (Canadian Standards Association, 2024). The value of εmu for specimen W-1 was validated against the experimental compressive strains provided by Shedid (2009), shown in Figure 6-16. Per this figure, the compressive strain values in the first course (height of 50 mm) at ultimate loads 177 kN and -180 kN are 0.011 and 0.006, respectively, the average of which is 0.0085. Based on this, Shedid (2009) stated that “the values of maximum compressive strain are very conservative” in masonry design codes such as CSA S304. This is 201 why it is required to adjust the value of εmu during the analysis of point 2 from the initial trial value of 0.003. Figure 6-16: Compressive Strains vs. Lateral Loads in Courses 1 and 2 of Specimen W-1 (Shedid, 2009) A comparison of the proposed approach for developing backbone curves for regular RMSWs presented in this section, versus the method presented in NIST GCR 17-917-45, is shown in Figure 6-17. Backbone curves developed using both methods are plotted against the experimental hysteretic force-displacement plots of specimen W1 by Shedid et al. (2008). An important observation is related to the differences in displacements between the backbone curves, especially the displacements at point 2 (ΔQu). Per Figure 6-17, the experimental value of ΔQu is 32 mm, the value on the backbone curve using the approach proposed in this study is 34 mm (6% error compared to 32 mm), and the value on the backbone curve using the NIST GCR 17-917-45 is 52 mm (63% error compared to 32 mm). Note that the displacement ΔQu determined using the NIST GCR 17-917-45 approach is overestimated because of the finite length hinge zone model, as discussed previously. 202 Figure 6-17: Fitted Backbone Curves to the Hysteretic Force-Displacement Plot of Specimen 1 using Varying Approaches (Adapted from Shedid et al., 2008) There are several important equations that are used in the proposed approach for developing backbone curves for regular fully grouted flexure-dominated RMSWs that was presented in this section, in addition to Equations (2-7) and (6-1). As shown below, Equation (6-2) is used to obtain curvature φ from a strain profile knowing masonry strain εm and c: 𝜑 =𝜀𝑚𝑐 (6-2) Equation (6-3) is used to obtain parameter a for computation of Cm for points 2, 3, and 4 on the backbone curve. β1 is equal to 0.8 when f’m is less than or equal to 20 MPa. For values greater than 20 MPa, 0.1 is subtracted for every increase in strength of 10 MPa (i.e., β1 equals to 0.7 for 30 MPa, 0.6 for 40 MPa, etc.). 𝑎 = {𝛽1𝑐, 𝑃𝑜𝑖𝑛𝑡 2𝛽1𝑐′, 𝑃𝑜𝑖𝑛𝑡𝑠 3, 4 (6-3) 203 Equation (6-4) is used to obtain masonry compressive strength Cm. Φm is taken equal to 1, a is computed using Equation (6-3), tw is the wall thickness. 𝐶𝑚 = {0.5𝑓’𝑚𝛷𝑚(𝑐𝑡𝑤), 𝑃𝑜𝑖𝑛𝑡 10.85𝑓’𝑚𝛷𝑚(𝑎𝑡𝑤), 𝑃𝑜𝑖𝑛𝑡𝑠 2, 3, 4 (6-4) Equation (6-5) is used to obtain steel tensile force in bar i (Ti). σs is obtained from Figure 6-9 knowing the tensile strain εsi. Ab is the area of the bar. 𝑇𝑖 = 𝜎𝑠𝐴𝑏 (6-5) Equation (6-6) is used to obtain steel compressive force in bar i (Ci). σs is obtained from Figure 6-9 knowing the compression strain ε’si. Ab is the area of the bar. 𝐶𝑖 = 𝜎𝑠𝐴𝑏 (6-6) Equation (6-7) is used to verify the force equilibrium. P is the applied axial force. 𝑃 +∑𝑇𝑛𝑛𝑖=1−∑𝐶𝑛 − 𝐶𝑚 = 0𝑛𝑖=1 (6-7) Finally, Equation (6-8) is used to compute the probable moment resistance of the RMSW (Mp). Note that δ is the distance between the location of the centroid of forces P, Ti, Ci, and Cm and an arbitrary point along the length of the wall (commonly considered at the wall’s centroid for simplicity). In this case, If P is assumed to be applied along the centerline of the wall, then δp is equal to zero, based on the illustration shown in Figure 6-18. 𝑀𝑝 = 𝑃𝛿𝑝 +∑𝑇𝑖𝛿𝑇𝑖𝑛𝑖=1+∑𝐶𝑖𝛿𝐶𝑖 + 𝐶𝑚𝛿𝐶𝑚𝑛𝑖=1 (6-8) 204 Figure 6-18: Internal Force Diagram and Distances for Computation of Probable Moment Resistance of a RMSW Table 6-2 summarizes the approach that was presented in this section. Table 6-2: Design Approach for Developing Backbone Curves for Regular RMSWs Point: Step: Obtain: Description 1 1 Qy Perform section analysis of the regular RMSW to obtain My. Set the strain of the outermost reinforcement steel bar to be equal to the yield strain (taken as 0.002 for Grade 400 steel). Compute Qy using My / hw. 2 Δy Gather εm and c from Step 1; use Equation (6-2) to obtain φy. Use Equation (2-7) to convert φy to Δy. 2 3 Qu Perform section analysis of the regular RMSW to obtain Mu. Set εmu equal to 0.003 to obtain an approximation for Mu. Adjust the values for εmu and c to obtain actual Mu. Compute Qu using Mu / hw. Finally, compute φu. 4 ΔQu Evaluate using Equation (6-1). Use hp = 0.5lw and x = 0.45. 205 Point: Step: Obtain: Description 3 5 Q80 Perform section analysis of the regular RMSW to obtain M80. Use the moment arm reduction approach presented in this thesis. Validate the value of M80 against 80% of Mu obtained in Step 3. Finally, compute φ80. 6 Δ80 Evaluate using Equation (6-1). Use hp = 0.5lw and x = 0.9. 4 7 Qf Perform section analysis of the regular RMSW to obtain Mf. Use the moment arm reduction approach presented in this thesis. Finally, compute φf. 8 Δf Evaluate using Equation (6-1). Use hp = 0.5lw and x = 1. Validate the value of Δf against the desired drift percentage. 6.3 Backbone Model for RMSWs with Boundary Elements This section presents an approach for developing backbone curves for fully grouted RMSWs with boundary elements (BEs). The backbone curve that can be developed using this approach is shown in Figure 6-19. The first two points of this backbone curve are the same as of the backbone curve for regular RMSWs shown in Figure 6-5. However, a prominent difference between backbone curves for regular RMSWs and RMSWs with BEs lies in the definition for point 3. In Chapter 3, it was discussed that BEs in RMSWs are able to delay the onset of strength degradation, meaning that RMSWs with BEs are typically able to maintain ultimate load Qu for several cycles following the cycle in which this load is initially attained. Hence, it is important to capture this phenomenon in backbone curves for RMSWs with BEs, which requires re-defining point 3. In backbone curves for RMSWs with BEs, point 3 is defined by lateral load Q’u and corresponding lateral displacement ΔQ’u. Q’u is taken to be equal to Qu; the difference between these parameters is that Qu corresponds to the initial attainment of the ultimate load, whereas Q’u corresponds to the onset of strength degradation. The definition of point 4 in backbone curves for RMSWs with BEs is identical to regular RMSWs, although the section analysis to obtain the parameters of this point differs; this is described shortly. 206 Figure 6-19: Backbone Curve for Fully Grouted Regular RMSWs with External Boundary Elements Section analyses to obtain the parameters for points 1 and 2 on the backbone curve shown in Figure 6-19 for RMSWs with BEs are similar to regular RMSWs. The differences that need to be considered include accounting for the additional vertical reinforcement in the BEs, the dimensions of the BEs (length of BE, lBE, and thickness of BE, tBE), and the strength of the grouted column for which the compressive strength of grout is used (f’g) rather than the compressive strength of masonry (f’m). These differences are illustrated in Figure 6-20, which shows a sample cross section of a RMSW with BEs, the strain profiles, and free body diagram used in section analyses for points 1 and 2. The notation used in this figure is the same as in Figure 6-7, except that lGC is the length of the grout column, tGC is the thickness of the grout column, tw is the wall thickness, and lweb is the length of the web. An important difference between regular RMSWs and RMSWs with BEs is that if the length of the neutral axis c is greater than lBE, it is required to compute the masonry compressive strengths provided by the BE (labelled Cm(BE) in Figure 6-20) and the web (labelled Cm(web) in Figure 6-20) separately. This is noted in the equations provided at the end of this section. 207 a) b) Figure 6-20: Sample RMSW Cross Section, Strain Profile, & Internal Force Distribution used in Section Analysis for a) Point 1 and b) Point 2 in a Backbone Curve for RMSWs with BEs At point 3, research studies such as those presented in Chapter 3 show that RMSWs with BEs subjected to cyclic loading generally experience significant face shell spalling in the BEs. However, the vertical reinforcement and confined grout column in the BEs, as well as the RMSW web generally remain mostly undamaged. A few changes to the section parameters are needed to capture this, as discussed next. Foremost, the effective cross-section area of the RMSW is reduced to account for face shell spalling in the BEs, as shown in Figure 6-21 (the effective cross-section area is shown hatched). Next, the effect of confinement ties on delaying reinforcement buckling is accounted for by revising the material model for the vertical reinforcement in the boundary elements as shown in Figure 6-22. In the revised model, it is assumed that the vertical reinforcement bars sustain the yield strength after the onset of yielding via a bilinear model in which compressive strain hardening is neglected. The model remains 208 bilinear until the strain of 0.008 after which buckling is assumed to occur; the reasoning for this value is discussed shortly. The unconfined vertical reinforcement in the RMSW’s web conforms to the material model shown in Figure 6-9. At point 4, research studies such as those presented in Chapter 3 show that RMSWs with BEs subjected to cyclic loading experience a strength degradation at higher drift demands, primarily as a result of vertical bar buckling (BB) in the BEs. The confined grout column usually remains mostly undamaged; that is, it is capable to provide compressive resistance. Cracking of the RMSW’s web and oftentimes spalling (especially in the web portion near the boundary elements) is typically observed as well. Based on this, it was assumed that at point 4, the effective cross-section area of the RMSW has an undamaged confined grout column and a deteriorated RMSW web within the neutral axis c, as shown in Figure 6-21. Since it was assumed that the confined grout column remained undamaged, the grout compressive strength is considered in the analysis (i.e., f’g). However, in the RMSW’s web, it is recommended to consider a reduced masonry compressive strength (f’m) to account for material deterioration. The multiplier to consider for this purpose is most likely proportional to the percentage of strength degradation at point 4, but a further study is needed to calibrate the multiplier based on the varying strength degradation. In the model validation examples presented shortly, the value used for the multiplier was 0.8. Finally, buckling of vertical bars in the BEs is considered via the material model for steel shown in in Figure 6-22, in which a rapid compressive strength loss occurs following the attainment of a compressive strain (ε’s) of 0.008. 209 Figure 6-21: Conceptual Evolution (Progression) of Damage and the Corresponding Strain Profiles for Points 1 Through 4 on a Backbone Curve for RMSWs with BEs: a) Points 1 & 2; b) Point 3; c) Point 4 210 Figure 6-22: Stress-Strain Relationship for Steel Considering a Delayed Bar Buckling Due to Confinement Ties & Bar Fracture, RMSWs with External Boundary Elements (Adapted from Applied Technology Council, 2017) As mentioned previously, in Figure 6-22 bar buckling is considering by imposing a limit on the compressive strain of steel (ε’s) of 0.008, following which rapid strength loss occurs. This value is equal to the maximum allowable ultimate masonry strain εmu per CSA S304-24 (Canadian Standards Association, 2024) in RMSWs with BEs. As mentioned previously, the analyses procedures to obtain points 1 and 2 on the backbone curve of Figure 6-19 are similar to the regular RMSWs; hence, flowchart of Figure 6-8 may be utilized to illustrate the procedure. The flowchart for obtaining points 3 and 4 on the backbone curve of Figure 6-19 is shown in Figure 6-23. Similarly to regular RMSWs, in the analysis of point 4 the final lateral displacement Δf is verified against the desired drift percentage. 211 Figure 6-23: Summary of Analytical Procedure to Determine Points 3 & 4 on a Backbone Curve for RMSWs with BEs The method for developing backbone curves shown in Figure 6-19 for fully grouted RMSWs with BEs was implemented and validated against selected experimental hysteretic force-displacement plots from research studies presented in Chapter 3. Namely, the force displacement plots of specimen W6 by Shedid et al. (2010) and specimen W7 by Aly & Galal 212 (2020a) were referenced. Specimen W6 is relevant for the validation because the strength degradation of the RMSW was observed, meaning that all four points on the backbone curve of Figure 6-19 can be considered. However, strength degradation was not reported for specimen W7, hence only the first three points shown in the backbone curve of Figure 6-19 can be considered. Specimen W7 was selected to demonstrate that the approach presented in this section may be used for RMSWs with external boundary elements in which significant strength degradation is not apparent; the only difference lies in the requirement to assume that the idealized plastic hinge height hp is fully developed at point 3 instead of point 4. The specimen properties employed in the analysis are listed in Table 3-2, and cross sections are shown in Figure 6-24 and Figure 6-25. Figure 6-24: Cross-Section of Specimen W3 (Adapted from Shedid et al., 2010) Figure 6-25: Cross-Section of Specimen W6 (Adapted from Aly & Galal, 2020a) The fitted backbone curve for specimen W6 by Shedid et al. (2010) is shown in Figure 6-26, and the fitted backbone curve for specimen W7 by Aly & Galal (2020a) is shown in Figure 6-27. 213 Figure 6-26: Fitted Backbone Curve to the Hysteretic Force-Displacement Plot of Specimen W6 (Adapted from Shedid et al., 2010) Figure 6-27: Fitted Backbone Curve to the Hysteretic Force-Displacement Plot of Specimen W7 (Adapted from Aly & Galal, 2020a) 214 The yield displacements Δy were computed using Equation (2-7). The conversion of post-yield curvatures φ to lateral displacements Δ employed Equation (6-9). This equation is essentially identical to Equation (6-1) for regular RMSWs (including the same values for parameter x at points 2, 3, and 4), but the subscripts for Δ and φ are updated to reflect the points in the backbone curve for RMSWs with external boundary elements shown in Figure 6-19. 𝛥𝑄𝑢|𝑄′𝑢|𝑓 = 𝛥𝑦 + (𝜑𝑄𝑢|𝑄′𝑢|𝑓 − 𝜑𝑦) (𝑥ℎ𝑝)(ℎ𝑤 − 0.5𝑥ℎ𝑝) (6-9) In Equation (6-9), hp was taken to be equal to 0.5lw based on CSA S304-24, similar to regular RMSWs (Canadian Standards Association, 2024). However, based on the discussion in Chapter 3, it was identified that the plastic hinge height in RMSWs with external boundary elements is likely proportional to the wall’s aspect ratio. This implies that if hp is taken to be equal to 0.5lw for RMSWs with external boundary elements with higher aspect ratios, the lateral displacements may be considerably underestimated. Further study is recommended to explore this and identify suitable hp values for RMSWs with external boundary elements that have varying aspect ratios. It was deemed appropriate to use the current estimate for hp for the backbone curves of the two specimens in this section, because both had relatively low aspect ratios. Specimen W6 by Shedid et al. (2010) had an aspect ratio of 1.5, whereas specimen W7 by Aly & Galal (2020a) had an aspect ratio of 1.4. The values from the strain profiles for points 2, 3, and 4 on the backbone curves shown in Figure 6-26 and Figure 6-27 are summarized in Table 6-3. 215 Table 6-3: Summary of Parameters from Strain Profiles from Referenced Studies Specimen Point on Backbone Curve Masonry Strain (εm) [mm/mm] Steel Strain in Outermost Bar (εs1) [mm/mm] Depth of neutral axis (c) [mm] Curvature (φ) [rad/mm E-5] Specimen W6 (Shedid et al. (2010)) 2 0.00297 0.0238 194.14 1.53 3 0.00589 0.0400 218.38 2.72 4 0.01236 0.0444 370.56 3.33 Specimen W7 (Aly & Galal (2020a)) 2 0.00301 0.0123 327.49 0.92 3 0.01432 0.0451 401.02 3.57 Similarly to regular RMSWs, the values for εmu were validated against the respective experimental values by Shedid et al. (2010) and Aly & Galal (2020a). The equations listed in Section 6.2 for analysis of regular RMSWs can be used for analysis of RMSWs with BEs, except for the changes noted. The computation of parameter a for RMSWs with BEs uses Equation (6-10) rather than Equation (6-3): 𝑎 = 𝛽1𝑐 (6-10) Parameter β1 is computed exactly the same as in Equation (6-3). Next, the computation of parameter Cm is performed using different equations rather than Equation (6-4). For point 1 for the backbone curve for RMSWs with BEs, parameter Cm is computed using Equation (6-11): 𝐶𝑚 = {0.5[𝑓’𝑚𝛷𝑚((𝑡𝐵𝐸𝑑𝐸) + (𝑡𝐵𝐸 − 𝑡𝐺𝐶)(𝑐 − 𝑑𝐸)) + 𝑓’𝑔𝛷𝑔(𝑡𝐺𝐶)(𝑐 − 𝑑𝐸)], 𝑖𝑓 𝑐 ≤ 𝑙𝐵𝐸 0.5[𝑓’𝑔𝛷𝑔(𝑡𝐺𝐶𝑙𝐺𝐶) + 𝑓’𝑚𝛷𝑚((𝑡𝐵𝐸𝑙𝐵𝐸 − 𝑡𝐺𝐶𝑙𝐺𝐶) + (𝑡𝑤)(𝑐 − 𝑙𝐵𝑒))], 𝑖𝑓 𝑐 > 𝑙𝐵𝐸 (6-11) where Φg is the resistance factor of grout, taken equal to 1. In this equation, if c is less than or equal to lBE, only the compressive resistance of the boundary element is considered (Cm(BE)). 216 However, if c is greater than lBE, both Cm(BE) and the compressive resistance of the RMSW’s web (Cm(web)) are considered. Next, for point 2, Cm is computed using Equation (6-12): 𝐶𝑚 = {0.85[𝑓’𝑚𝛷𝑚((𝑡𝐵𝐸𝑑𝐸) + (𝑡𝐵𝐸 − 𝑡𝐺𝐶)(𝑎 − 𝑑𝐸)) + 𝑓’𝑔𝛷𝑔(𝑡𝐺𝐶)(𝑎 − 𝑑𝐸)], 𝑖𝑓 𝑐 ≤ 𝑙𝐵𝐸 0.85[𝑓’𝑔𝛷𝑔(𝑡𝐺𝐶𝑙𝐺𝐶) + 𝑓’𝑚𝛷𝑚((𝑡𝐵𝐸𝑙𝐵𝐸 − 𝑡𝐺𝐶𝑙𝐺𝐶) + (𝑡𝑤)(𝑎 − 𝑙𝐵𝐸))], 𝑖𝑓 𝑐 > 𝑙𝐵𝐸 (6-12) Next, for point 3, Cm is computed using Equation (6-13): 𝐶𝑚 = {0.85𝑓’𝑔𝛷𝑔𝑡𝐺𝐶𝑎, 𝑖𝑓 𝑐 ≤ 𝑙𝐺𝐶 0.85[𝑓’𝑚𝛷𝑚𝑡𝑤(𝑙𝐺𝐶 − 𝑎) + 𝑓’𝑔𝛷𝑔𝑡𝐺𝐶𝑙𝐺𝐶], 𝑖𝑓 𝑐 > 𝑙𝐺𝐶 (6-13) The effective area of the compression zone computed using Equation (6-13) corresponds to the effective area shown in Figure 6-21 (b). Finally, for point 4, Cm is computed using Equation (6-14): 𝐶𝑚 = {0.85𝑓’𝑔𝛷𝑔𝑡𝐺𝐶𝑎, 𝑖𝑓 𝑐 ≤ 𝑙𝐺𝐶 0.68𝑓’𝑚𝛷𝑚𝑡𝑤(𝑙𝐺𝐶 − 𝑎) + 0.85𝑓’𝑔𝛷𝑔𝑡𝐺𝐶𝑙𝐺𝐶 , 𝑖𝑓 𝑐 > 𝑙𝐺𝐶 (6-14) Equation (6-14) is nearly identical to Equation (6-13), except that the multiplier of 0.8 is applied during the computation of the compressive resistance of the RMSW’s web to account for material deterioration (discussed previously). Table 6-4 summarizes the approach for developing backbone curves for fully grouted RMSWs with external boundary elements that was presented in this section. 217 Table 6-4: Design Approach for Developing Backbone Curves for RMSWs with BEs Point: Step: Obtain: Description 1 1 Qy Similar to regular RMSWs per Table 6-2. However, employ the material model for vertical reinforcement steel in the boundary elements per Figure 6-22. Also, account for f’g when computing the compressive resistance of the grout column, and consider the boundary element dimensions lBE and tBE. 2 Δy Identical to regular RMSWs per Table 6-2. 2 3 Qu Similar to regular RMSWs per Table 6-2. However, employ the material model for vertical reinforcement steel in the boundary elements per Figure 6-22. Also, account for f’g when computing the compressive resistance of the grout column, and consider the boundary element dimensions lBE and tBE. 4 ΔQu Similar to regular RMSWs per Table 6-2, except for the employment of Equation (6-9) versus Equation (6-1). 3 5 Q’u Perform section analysis of the RMSW with boundary elements to obtain M’u. Use the section shown in Figure 6-21 (b). Use the material model material model for vertical reinforcement steel in the boundary elements per Figure 6-22. Consider f’g for the compressive strength of the grout column. Validate the value of M’u against Mu obtained in Step 3. Finally, compute φ’u. 6 ΔQ’u Compute using Equation (6-9). Use hp = 0.5lw and x = 0.9, unless point 4 is not considered in the backbone curve. In this case, use hp = 0.5lw and x = 1.0. 4 7 Qf Perform section analysis of the RMSW with boundary elements to obtain Mf. Use the section shown in Figure 6-21. Use the material model for vertical reinforcement steel in the boundary elements per Figure 6-22. Consider f’g for the compressive strength of the confined grout column. Consider a multiplier of 0.8 for f’m for the strength of the RMSW’s web. Finally, compute φf. 8 Δf Compute using Equation (6-9). Use hp = 0.5lw and x = 1.0. Validate the value of Δf against the desired drift percentage. 218 6.4 Summary This chapter presents a new framework for developing force-displacement (backbone) curves for regular RMSWs and RMSWs with boundary elements. The start of the chapter focused on introducing backbone curves, discussing their applications, and presenting an overview of an existing method of their development for regular RMSWs per NIST GCR 17-917-45. This was followed by presentation of a new approach for developing backbone curves for regular RMSWs. Following this, a new approach for developing backbone curves for RMSWs with BEs was presented. The approaches were implemented and validated against selected experimental results from studies by Shedid et al. (2008, 2010) and Aly and Galal (2020a). 219 7. CONCLUSIONS 7.1 Summary The purpose of this thesis was to present the experimental and analytical studies of RMSWs with and without boundary elements subjected to in-plane reversed cyclic loading. The focus of the experimental study was to study the influence of embedded boundary elements in RMSWs by subjecting two full-size 240 mm RMSW specimens (W-1 and W-2) to reversed cyclic loading without applied axial compression. Specimen W-1 was a regular RMSW specimen (without boundary elements), whereas specimen W-2 was a RMSW specimen with embedded boundary elements. Specimen W-2 was designed to be identical to specimen W-1, except for the presence of the embedded boundary elements. Details regarding their design, construction, material properties, test setup, and testing procedure were provided in this thesis. Selected results from the testing of both specimens were presented, and the response of the specimens was compared to understand the potential advantages of embedded boundary elements for improving the seismic performance of RMSWs. The construction and testing of the specimens were performed in UBC’s Structures Laboratory. Material testing was performed in UBC’s Structures Laboratory and UBC’s Materials Laboratory. The focus of the analytical study was to present approaches for developing generalized force-displacement (backbone) curves for regular RMSWs and RMSWs with boundary elements, which were implemented and validated against selected experimental data by other researchers. 7.2 Key Findings The primary finding of the experimental study was that, without applied axial compression, the seismic performance of RMSWs with and without embedded boundary elements was comparable. This statement was justified by analyzing and comparing the responses of the 220 specimens based on the force-displacement responses, wall capacities, the progressions/extents of damage and failure mechanisms, energy dissipation properties, and ductility ratios. The key findings are summarized below: 1. The force-displacement response of specimen W-1 was comparable to the response of specimen W-2. The force-displacement responses of the specimens were similar up to a lateral drift of 1.8% in both loading directions. During the final loading cycles at 2.0% drift for both specimens, specimen W-2 experienced a significantly greater extent of strength degradation (63% and 95% in the positive and negative loading directions, respectively) compared to specimen W-1 (30% and 50% in the positive and negative loading directions, respectively). 2. The wall capacities (ultimate lateral load resistances) of specimen W-2 (412 kN and -388 kN in the positive and negative loading directions, respectively) were comparable to specimen W-1 (426 kN and -385 kN in the positive and negative loading directions, respectively). Hence, the presence of embedded boundary elements did not appear to provide a measurable increase in the RMSW’s capacity. 3. The onset of significant damage (face shell spalling and grout crushing at the wall’s toes) occurred slightly sooner in specimen W-1 (second cycle at 1.2% drift) compared to specimen W-2 (first cycle at 1.6% drift). The overall extent of damage at the wall’s toes was greater in specimen W-1 compared to specimen W-2. In specimen W-1, damage was concentrated in the bottom five courses, and in specimen W-2 it was concentrated in the bottom three courses. 4. The energy dissipation properties of specimens W-1 and W-2 were similar. The rate of energy dissipation up to a lateral drift of 1.4% was nearly identical for both specimens, and the cumulative energy dissipated at this drift level was nearly equal (66,324 kN*mm for specimen W-1, and 68,080 kN*mm for specimen W-2). The rate of energy dissipation for the 221 remainder of the testing increased for specimen W-2 relative to specimen W-1, such that the cumulative energy dissipated was 112,933 kN*mm for specimen W-1 and 118,905 kN*mm for specimen W-2. Based on this, the energy dissipated by specimen W-2 is comparable to the energy dissipated by specimen W-1. 5. The ductility ratio of specimen W-1 was comparable to the ductility ratio of specimen W-2. Two ductility ratios were computed in this thesis. The first ratio was computed considering the responses in the positive and negative loading directions (different values of yield displacements amongst the specimens), whereas the second ratio was computed considered the responses in the positive loading direction only (equal values of yield displacements amongst the specimens). Based on the first ratio, the values were 8.5 and 6.6 for specimens W-1 and W-2, respectively, and based on the second ratio, the values were 8.9 and 8.5, respectively. If the second ratio is used as a comparison, then the ductility ratios amongst the specimens are comparable. Based on the analysis of results, both specimens experienced Ductile Flexure (DF) as the primary failure mechanism (governing failure mechanism at ultimate capacity). The secondary failure mechanisms (governing failure mechanisms at 20% strength degradation) were Bar Buckling (BB) and Sliding Shear Failure (SL) for specimens W-1 and W-2, respectively. The key finding of the analytical study was that the proposed approaches for developing generalized force-displacement curves for RMSWs with and without boundary elements provide reasonably accurate results which can be used as input for nonlinear static structural analyses. The approaches were implemented and validated against selected experimental results from studies by Shedid et al. (2008, 2010) and Aly and Galal (2020a). 222 7.3 Future Research Needs Based on the findings of this thesis, several recommendations are provided towards potential future works and studies for RMSWs with and without boundary elements subjected to reversed in-plane cyclic loading. Future experimental studies on RMSWs with and without embedded boundary elements subjected to axial compression are needed. The implementation of a similar program in this thesis is recommended, in which at least two specimens (with and without embedded boundary elements) are subjected to reversed cyclic loading with axial compression. The data from this type of research study can be utilized to further understand the potential of embedded boundary elements in RMSWs to improve their seismic performance. As discussed in Chapter 5, the findings of this thesis are mostly relevant for RMSWs bearing little to no axial load beyond their self-weight, which are not uncommon in buildings constructed using RM. However, loadbearing RMSWs are more critical in RM buildings compared to non-loadbearing RMSWs, which is why further research is recommended. Finally, given that most of the past Canadian experimental studies on RMSWs with external boundary elements under reversed cyclic loading have been performed with applied axial compression, it may be useful to evaluate the performance without applied axial compression (similar to the work done in this thesis). Given the relatively difficult construction of boundary elements in RMSWs, it is important for engineers to consider them in design scenarios where their application is most effective. Additional analytical studies could be performed by validating the proposed approaches for regular RMSWs and RMSWs with boundary elements against a larger set of experimental data, to confirm whether the proposed approaches are sufficiently accurate, or requiring any modifications. 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Thesis/Dissertation
eng
Civil Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Yang, Tony T. Y.
Experimental and analytical studies of reinforced masonry shear walls with and without boundary elements subjected to in-plane cyclic loading
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