Behavior of Masonry Walls Constructed Using Locally

AIN SHAMS UNIVERSITY FACULTY OF ENGINEERING Structural Engineering

Behavior of Masonry Walls Constructed Using Locally Available Dry-Stack Interlocking Masonry Units A Thesis submitted in partial fulfillment of the requirements of the degree of Doctor of Philosophy in Civil Engineering (Structural Engineering) by

Mohamed Kohail M. Fayez Master of Science in Civil Engineering (Structural Engineering) Faculty of Engineering, Ain Shams University, 2009 Supervised By Dr. Hany Mohamad El-Shafie Associate Professor of Structural Engineering Faculty of Engineering Ain Shams University

Dr. Ahmed Rashad Mohamed

Dr. Hussein Osama Okail

Assistant Professor of Structural Engineering Faculty of Engineering Ain Shams University

Assistant Professor of Structural Engineering Faculty of Engineering Ain Shams University

Cairo - (2015)

AIN SHAMS UNIVERSITY FACULTY OF ENGINEERING Structural Engineering

Behavior of Masonry Walls Constructed Using Locally Available Dry-Stack Interlocking Masonry Units by

Mohamed Kohail M. Fayez Master of Science in Civil Engineering (Structural Engineering) Faculty of Engineering, Ain Shams University, 2009 Examiners’ Committee Name and Affiliation

Prof. Dr. Ahmed A. Hamid

Signature ……………….

Professor and Director of the Masonry Research Laboratory, Drexel University, Philadelphia, USA.

Prof. Dr. Ahmed Sherif Essawy

……………….

Professor of Reinforced Concrete Structures, Structural Engineering Department, Faculty of Engineering, Ain Shams University.

Dr. Hany M. El-Shafie

……………….

Associate Professor, Structural Engineering Department, Faculty of engineering, Ain Shams University. Date: 06 May 2015

Statement This thesis is submitted as a partial fulfillment of Doctor of Philosophy in Civil Engineering (Structural Engineering), Faculty of Engineering, Ain shams University. The author carried out the work included in this thesis, and no part of it has been submitted for a degree or a qualification at any other scientific entity.

Student name Mohamed Kohail M. Fayez Signature …………...……….

Date: 06 May 2015

Researcher Data Name

: Mohamed Kohail M. Fayez

Date of birth

: 08 January 1982

Place of birth

: El-Kalyobia, Egypt

Last academic degree

: Master of Science

Field of specialization

: Structural Engineering

University issued the degree

: Ain Shams

Date of issued degree

: September 2009

Current job

: Teaching Assistant

THESIS SUMMARY This thesis contains analysis details of an experimental and analytical study conducted to evaluate the in-plane behavior of dry-stacked masonry shear walls under cyclic loading and to study the effect of the reinforcement configurations, grouting and post-tension on the failure mode and lateral load capacity of the dry-stacked masonry shear walls. The test program consists of ten masonry shear walls constructed with three different types of locally available concrete masonry blocks (conventional, Azar and Spar-lock), the walls were tested under reversed cyclic lateral load with a displacement controlled loading protocol up to failure. Key experimental results showed that the similarity behavior of Azar system shear walls to the conventional masonry system, and the brittle failure of Spar-lock system walls even after rearrangement because the system doesn’t allow horizontal reinforcement. Post-tensioning is an effective method to construct un-grouted dry-stacked shear walls with minimum or no reinforcement, which resists 62.00% of the ultimate load capacity of fully-grouted reinforced shear walls. The usage of sliding control can improve the ductility of post-tensioned dry-stacked shear walls. An analytical study using FEM to extend the experimental results of post-tensioned dry-stacked shear walls by studying other parameters as initial post-tensioning level and position of post-tensioning bars. Key analytical results showed that the ultimate load capacity for both grouted and un-grouted dry-stacked shear wall is directly proportional to the initial post-tensioning level with almost no effect of the position of bars. The grouting of wall’s first course can increase the ultimate load by 11%, and the grouting of two courses increases the ultimate load by 28% for the same post-tensioning level. The usage of sliding control decreases the ultimate i

Thesis Summary load by 15% but with a significant improvement of ductility. The ultimate load capacity of partially-grouted walls with sliding control directly proportional with the initial post-tension stress, and the usage of central bars can improve the ultimate load by 40%. Keywords:

Dry-stacked

Masonry,

Post-Tensioning,

Behavior, Interlocking Masonry, In-plane cyclic loading

ii

Seismic

ACKNOWLEDGEMENT I would like to express my deepest thanks and appreciation to my supervisor, Dr. Hany El-Shafie for his guidance and advice throughout this work. I am grateful to him all for having the opportunity to work under his supervision. Special thanks for my supervisors, Dr. Ahmed Rashad and Dr. Hussein Okail for their valuable assistance, guidance, patience and endless support throughout this research, and reviewing of the manuscript are greatly acknowledged. The experimental work was carried out at the Properties and Testing of Materials Laboratory of the Structural Engineering Department of AinShams University. The help of the laboratory staff in developing work is greatly appreciated. For thier distinguished assistance during the experimental work. Finally, I would like to thank my family for their continuous encouragement, overwhelming support, fruitful care and patience, especially during the hard times.

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TABLE OF CONTENTS Abstract .................................................... Error! Bookmark not defined. Acknowledgement .................................................................................... iii Table of Contents....................................................................................... v List of Figures ......................................................................................... xiii List of Tables ......................................................................................... xxv CHAPTER (1) ........................................................................................... 1 Introduction................................................................................................ 1 1.1. 1.2.

Background.................................................................................... 1 Dry-Stacked Masonry.................................................................... 2

1.3.

Definition of the Problem .............................................................. 2

1.4.

Research Objectives ...................................................................... 3

1.5.

Thesis Organization ....................................................................... 4

CHAPTER (2) ........................................................................................... 7 Literature Review ...................................................................................... 7 2.1.

Introduction ................................................................................... 7

2.2.

Dry-Stacked Masonry.................................................................... 8

2.2.1. Dry-Stacked Masonry Systems ................................................... 11 2.2.2. Properties of Dry-Stacked Masonry ............................................ 16 2.2.2.1. Compressive Strength.................................................................. 16 2.2.2.2. Initial Settlement ......................................................................... 20 2.2.2.3. In-Plane behavior of Dry-Stacked Masonry Walls ..................... 22 2.3.

Grouting Effect ............................................................................ 31

2.4.

Post-Tensioned Masonry ............................................................. 32

2.5. 2.6.

The Codification of Pre-Stressed Masonry ................................. 37 Behavior of Reinforced Masonry Shear Walls ........................... 45

2.7.

Behavior of Post-Tensioned Masonry Shear Walls .................... 57

2.8.

Needed Research ......................................................................... 59

CHAPTER (3) ......................................................................................... 61 Research Plan and Design of Test Walls ................................................. 61 3.1.

Introduction ................................................................................. 61 v

Table of Contents 3.2.

Research Plan .............................................................................. 61

3.2.1. Objectives .................................................................................... 61 3.2.2. Scope ........................................................................................ 62 3.3. Test Program ............................................................................... 63 3.4.

Pre-Test Analysis ........................................................................ 71

3.4.1. Design of Walls W1 (C:RVH:FG) and W2 (A:RVH:FG) .......... 71 3.4.2. Design of Wall W3 (S:RV:FG) ................................................... 74 3.4.3. Design of Wall W4 (A:RH:FG:PT) ............................................ 76 3.4.4. Design of Wall W5 (A:RH:UG:PT) and W6 (C:RH:UG:PT) .... 78 3.4.5. Design of Wall W7 (S:RH:UG:PT) ............................................ 81 3.4.6. Design of Wall W8 (A:RH:UG:PT:Sl) ....................................... 83 3.4.7. Design of Wall W9 (A:RH:PG:PT:Sl) ........................................ 84 CHAPTER (4) ......................................................................................... 87 Material Characterization ........................................................................ 87 4.1.

Introduction ................................................................................. 87

4.2.

Material Testing........................................................................... 87

4.2.1. Concrete Block Units .................................................................. 87 4.2.2. Masonry Mortar ........................................................................... 90 4.2.3. Grout ........................................................................................ 92 4.2.4. Masonry Prisms ........................................................................... 93 4.2.5. Diagonal Tension (Shear) Test .................................................... 98 4.2.6. Shear Friction (Triplet Test) ...................................................... 100 4.2.7. Reinforcing Steel ....................................................................... 103 4.2.8. Post-Tensioning Bars ................................................................ 103 CHAPTER (5) ....................................................................................... 105 Construction and Testing the Masonry Shear Walls ............................. 105 5.1.

Introduction ............................................................................... 105

5.2.

Specimen Construction and Preparation ................................... 105

5.2.1. General Description ................................................................... 105 5.2.2. Reinforced Concrete Footings ................................................... 108 5.2.3. Masonry Panels ......................................................................... 109 5.2.3.1. Masonry Blocks ......................................................................... 109 vi

Table of Contents 5.2.3.2. Reinforcement ........................................................................... 110 5.2.3.3. Post-Tensioning Bars ................................................................ 111 5.2.3.4. Grout 111 5.2.3.5. Sliding control ........................................................................... 111 5.2.4. Reinforced Concrete Top Beam ................................................ 112 5.3.

Test Setup .................................................................................. 112

5.3.1. Reaction System ........................................................................ 114 5.3.2. Lateral Load System .................................................................. 117 5.3.3. Out-of-Plane Bracing System.................................................... 118 5.4. Instrumentation .......................................................................... 119 5.5.

Data Acquisition System ........................................................... 122

5.6.

Test Procedure ........................................................................... 123

CHAPTER (6) ....................................................................................... 125 Test Results and Analysis of Wall Response ........................................ 125 6.1.

Introduction ............................................................................... 125

6.2.

Test Results for Wall W1 (C:RVH:FG) .................................... 129

6.2.1. General ...................................................................................... 129 6.2.2. Crack Patterns............................................................................ 129 6.2.3. Lateral Load – Overall Drift Angle Curve ................................ 129 6.2.4. Flexural Strain – Overall Drift Angle Curves ........................... 130 6.2.5. Panel Drift Angle – Displacement Curves ................................ 130 6.2.6. Sliding ...................................................................................... 130 6.2.7. Failure Mechanism .................................................................... 131 6.2.8. Summary of Major Events ........................................................ 131 6.3. Test Results for Wall W2 (A:RVH:FG).................................... 136 6.3.1. General ...................................................................................... 136 6.3.2. Crack Patterns............................................................................ 136 6.3.3. Lateral Load – Overall Drift Angle Curve ................................ 136 6.3.4. Flexural Strain – Displacement Curves ..................................... 136 6.3.5. Panel Drift Angle – Displacement Curves ................................ 137 6.3.6. Sliding ...................................................................................... 137 6.3.7. Failure Mechanism .................................................................... 137 6.3.8. Summary of Major Events ........................................................ 137 vii

Table of Contents 6.4.

Test Results for Wall W3 (S:RV:FG) ....................................... 142

6.4.1. General ...................................................................................... 142 6.4.2. Crack Patterns............................................................................ 142 6.4.3. Lateral Load – Overall Drift Angle and Displacement Curves 142 6.4.4. Flexural Strain – Displacement Curves ..................................... 142 6.4.5. Panel Drift Angle – Displacement Curves ................................ 143 6.4.6. Sliding ...................................................................................... 143 6.4.7. Failure Mechanism .................................................................... 143 6.4.8. Summary of Major Events ........................................................ 143 6.5. Test Results for Wall W4 (A:RH:FG:PT) ................................. 148 6.5.1. General ...................................................................................... 148 6.5.2. Crack Patterns............................................................................ 148 6.5.3. Lateral Load – Overall Drift Angle Curve ................................ 148 6.5.4. Flexural Strain – Displacement Curves ..................................... 148 6.5.5. Panel Drift Angle – Displacement Curves ................................ 149 6.5.6. Sliding ...................................................................................... 149 6.5.7. Post-Tension Forces – Drift Angle Curves ............................... 149 6.5.8. Failure Mechanism .................................................................... 149 6.5.9. Summary of Major Events ........................................................ 150 6.6. Test Results for Wall W5* (A:RH*:UG:PT) ............................ 156 6.6.1. General ...................................................................................... 156 6.6.2. Crack Pattern ............................................................................. 156 6.6.3. Lateral Load – Overall Drift Angle and Displacement Curves 156 6.6.4. Flexural Strain – Displacement Curves ..................................... 157 6.6.5. Panel Drift Angle – Displacement Curves ................................ 157 6.6.6. Sliding ...................................................................................... 157 6.6.7. Post-Tension Forces - Displacement Curves ............................ 157 6.6.8. Failure Mechanism .................................................................... 158 6.6.9. Summary of Major Events ........................................................ 158 6.7.

Test Results for Wall W5 (A:RH:UG:PT) ................................ 165

6.7.1. General ...................................................................................... 165 6.7.2. Crack Pattern ............................................................................. 165 6.7.3. Lateral Load – Overall Drift Angle Curve ................................ 165 viii

Table of Contents 6.7.4. Flexural Strain – Displacement Curves ..................................... 166 6.7.5. Panel Drift Angle – Displacement Curve.................................. 166 6.7.6. Sliding ...................................................................................... 166 6.7.7. Post-Tension Forces - Displacement Curves ............................ 166 6.7.8. Failure Mechanism .................................................................... 167 6.7.9. Summary of Major Events ........................................................ 167 6.8.

Test Results for Wall W6 (C:RH:UG:PT) ................................ 174

6.8.1. General ...................................................................................... 174 6.8.2. Crack Pattern ............................................................................. 174 6.8.3. Lateral Load – Overall Drift Angle Curve ................................ 174 6.8.4. Flexural Strain – Displacement Curves ..................................... 174 6.8.5. Panel Drift Angle – Displacement Curves ................................ 175 6.8.6. Sliding ...................................................................................... 175 6.8.7. Post-Tensioned Forces - Displacement Curves......................... 175 6.8.8. Failure Mechanism .................................................................... 175 6.8.9. Summary of Major Events ........................................................ 176 6.9.

Test Results for Wall W7 (S:RH:UG:PT) ................................. 183

6.9.1. General ...................................................................................... 183 6.9.2. Crack Pattern ............................................................................. 183 6.9.3. Lateral Load – Overall Drift Angle Curve ................................ 183 6.9.4. Flexural Strain – Displacement Curves ..................................... 184 6.9.5. Panel Drift Angle – Displacement Curves ................................ 184 6.9.6. Sliding ...................................................................................... 184 6.9.7. Post-Tensioned Forces - Displacement Curves......................... 184 6.9.8. Failure Mechanism .................................................................... 185 6.9.9. Summary of Major Events ........................................................ 185 6.10. Test Results for Wall W8 (A:RH:UG:PT:Sl)............................ 192 6.10.1. General ...................................................................................... 192 6.10.2. Crack Pattern ............................................................................. 192 6.10.3. Lateral Load – Overall Drift Angle Curve ................................ 192 6.10.4. Flexural Strain – Displacement Curves ..................................... 192 6.10.5. Panel Drift Angle – Displacement Curve.................................. 193 6.10.6. Sliding ...................................................................................... 193 ix

Table of Contents 6.10.7. Post-Tensioned Forces - Displacement Curves......................... 193 6.10.8. Failure Mechanism .................................................................... 193 6.10.9. Summary of Major Events ........................................................ 193 6.11. Test Results for Wall W9 (A:RH:PG:PT:Sl) ............................ 201 6.11.1. General ...................................................................................... 201 6.11.2. Crack Pattern ............................................................................. 201 6.11.3. Lateral Load – Overall Drift Angle Curve ................................ 201 6.11.4. Flexural Strain – Displacement Curves ..................................... 201 6.11.5. Panel Drift Angle – Displacement Curves ................................ 202 6.11.6. Sliding ...................................................................................... 202 6.11.7. Post-Tensioned Forces - Displacement Curves......................... 202 6.11.8. Failure Mechanism .................................................................... 203 6.11.9. Summary of Major Events ........................................................ 203 6.12.

Discussion of Test Results ........................................................ 210

6.12.1. General Behavior ....................................................................... 210 6.12.2. Lateral Load-Displacement Response ....................................... 211 6.12.3. Modes of Deformation .............................................................. 216 6.12.4. Residual Displacement .............................................................. 223 6.12.5. Displacement Ductility .............................................................. 225 6.12.6. Variation in Stiffness ................................................................. 230 6.12.7. Identification of Damage State and Development of Fragility curves ...................................................................................... 237 6.12.8. Energy Dissipation .................................................................... 239 6.12.9. Equivalent Viscous Damping .................................................... 242 CHAPTER (7) ....................................................................................... 245 Finite Element Analysis And Parametric Study .................................... 245 7.1. 7.2.

Introduction ............................................................................... 245 General Behavior ....................................................................... 245

7.3.

Model Geometry........................................................................ 247

7.4.

Elements .................................................................................... 249

7.5.

Assembly ................................................................................... 249

7.6. 7.7.

Finite Element Meshing ............................................................ 252 Material Models......................................................................... 253 x

Table of Contents 7.8.

Boundary Conditions and Initial Conditions ............................. 254

7.9.

Model Verification .................................................................... 255

7.10. Parametric Study Using FE Models .......................................... 258 7.10.1. Fully-Grouted Post-Tensioned Walls ........................................ 258 7.10.2. Un-Grouted Post-Tensioned Walls ........................................... 263 7.10.3. Partially-Grouted Post-Tensioned Walls................................... 267 7.10.4. Partially-Grouted Post-Tensioned Walls with Sliding Control. 270 7.11.

Summary of Parametric Study .................................................. 276

CHAPTER (8) ....................................................................................... 279 Summary, Conclusions, and Recommendations ................................... 279 7.1.

Summary.................................................................................... 279

7.2.

Conclusions ............................................................................... 280

7.3.

Recommendations for Further Studies ...................................... 286

References.............................................................................................. 287

xi

LIST OF FIGURES Figure (2.1): Haener Block System ......................................................... 12 Figure (2.2): Raised Lugs for the Haener Block ..................................... 12 Figure (2.3): Horizontal Reinforcement in the Haener Block ................. 12 Figure (2.4): Azar Blocks ........................................................................ 13 Figure (2.5): Filling Azar Blocks with Grout .......................................... 13 Figure (2.6): Vertical & Horizontal Rft. With Azar Blocks .................... 14 Figure (2.7): Spar-lock system ................................................................ 15 Figure (2.8): Hydraform Block System ................................................... 15 Figure (2.9): Stress-Strain Curve for Walls with and without Mortar [Marzahn, G. (1997)] ............................................................................... 17 Figure (2.10): Comparison between Stress-Strain Curves [Marzahn, G. (1999)] ..................................................................................................... 21 Figure (2.11): Test setup to determine the internal friction coefficient between the brick layers [Marzahn, G. (1998)]....................................... 23 Figure (2.12): Shearing test results [Marzahn, G. (1998)] ...................... 23 Figure (2.13): Test set-up for full-scale shearing tests on a mortar-less masonry wall [Marzahn, G. (1998)] ........................................................ 24 Figure (2.14): Walls Detailing for [Ingham et al. (2006)] ...................... 25 Figure (2.15): Construction of Dry-Stacked Wall [Ingham et al. (2006)] ................................................................................................................. 25 Figure (2.16): Test Setup used by [Ingham et al. (2006)] ....................... 26 Figure (2.17): Used Loading Cycles [Ingham et al. (2006)] ................... 27 Figure (2.18): Load-Displacement Curve [Ingham et al. (2006)] ........... 28 Figure (2.19): ICEB System [Bland (2011)] ........................................... 29 Figure (2.20): Detailing of Tested walls [Bland (2011)] ........................ 30 Figure (2.21): Typical Load-Displacement Curve [Bland (2011)] ......... 30 Figure (2.22): Typical Mode of Failure [Bland (2011)].......................... 31 xiii

List of Figures Figure (2.23): Plain masonry walls to axial load and bending [Marzahn (1997)] ..................................................................................................... 35 Figure (2.24): Principal construction of a post-tensioned dry-stacked masonry wall [Marzahn (1997)] .............................................................. 36 Figure (2.25): Flexural Stress Distribution throughout Loading History. (a) Beam Section. (b) Initial Pre-stressing Stage (c) Self Weight and Effective Pre-stress (d) Full Dead Load plus Effective Pre-stress (e) Full Service Load plus Effective Pre-stress (f)Limit State of Stress at Ultimate Load [Nawy (2003)] ................................................................................ 39 Figure (2.26): Load-Deformation Curve of Typical Pre-stressed Flexural Member [Nawy (2003)] ........................................................................... 40 Figure (2.27): Idealized Flexural Strain and Stress [Islam, M. (2008)] .. 46 Figure (2.28): Idealized Load-Displacement Curve for Shear Walls [Paulay and Priestly (1992)] .................................................................... 56 Figure (2.29): Centroid of the Regular Reinforcing 𝑑 [Salah (2010)] .... 58 Figure (3.1): Test Setup for Diagonal Tension Test ................................ 64 Figure (3.2): Test Setup of Triplet Test ................................................... 65 Figure (3.3): Details of Tested Walls ...................................................... 70 Figure (3.4): Cracked Section of Walls W1 (C:RVH:FG) and W2 (A:RVH:FG) ............................................................................................ 71 Figure (3.5): Dimension and Reinforcement Detailing of W1................ 73 Figure (3.6): Dimension and Reinforcement Detailing of W2................ 73 Figure (3.7): Dimension and Reinforcement Detailing of W3 ................ 74 Figure (3.8): Cracked Section of Wall W3 .............................................. 76 Figure (3.9): Cracked Section of Wall W4 .............................................. 76 Figure (3.10): Dimension and Detailing of W4 ...................................... 77 Figure (3.11): Cracked Section Walls W5 and W6 ................................. 78 Figure (3.12): Dimension and Detailing of W5* .................................... 80 xiv

List of Figures Figure (3.13): Dimension and Detailing of W5 ...................................... 80 Figure (3.14): Dimension and Detailing of W6 ...................................... 80 Figure (3.15): Horizontal Reinforcement in Spar-lock Modified Configuration ........................................................................................... 81 Figure (3.16): Dimension and Detailing of W7 ...................................... 82 Figure (3.17): Dimension and Detailing of W8 ...................................... 84 Figure (3.18): Dimension and Detailing of W9 ...................................... 85 Figure (4.1): Concrete Blocks Used to Construct Test Specimens ......... 87 Figure (4.2): Uniaxial Compression Test for Concrete Blocks ............... 89 Figure (4.3): Axial Compression Test for Mortar Cubes ........................ 91 Figure (4.4): Compression Test for Grout ............................................... 93 Figure (4.5): Axial Compression Test for Masonry Prisms .................... 95 Figure (4.6): Stress-Strain Curve for Conventional Block Prisms .......... 96 Figure (4.7): Stress-Strain Curve for Azar Block Prisms ........................ 96 Figure (4.8): Stress-Strain Curve for Spar-lock Block Prisms ................ 97 Figure (4.9): Stress-Strain Curve for Tested Prisms .............................. 97 Figure (4.10): Test Setup for Diagonal Tension Test .............................. 98 Figure (4.11): Failure Modes for Diagonal Tension Test ....................... 99 Figure (4.12): Test Result of B-B Triplet Specimens ........................... 101 Figure (4.13): Test Result of B-C Triplet Specimens ........................... 101 Figure (4.14): Test Result of B-C-SL Triplet Specimens ..................... 102 Figure (4.15): Test Result of All Triplet Specimens ............................. 102 Figure (4.16): Typical Failure Mode for Tested Post-Tensioning Bars 104 Figure (5.1): Geometry and Dimensions of the Tested Specimens.. Error! Bookmark not defined. Figure (5.2): Dimensions and Reinforcement Details of the R.C. Footing ............................................................................................................... 109 xv

List of Figures Figure (5.3): Face-Shells Grooves for Un-Grouted Walls .................... 110 Figure (5.4): Construction of Wall Panels ............................................. 110 Figure (5.5): Dimensions and Reinforcement Details of the R.C. TopBeam ...................................................................................................... 112 Figure (5.6): Schematic of Test Setup ................................................... 113 Figure (5.7): Test Setup with a Typical Wall in Position ...................... 114 Figure (5.8): Reaction Steel Frame ....................................................... 116 Figure (5.9): The Additional In-Plane Bracing ..................................... 117 Figure (5.10): Lateral Loading System. ................................................ 117 Figure (5.11): Out-of-Plane Bracing System. ....................................... 118 Figure (5.12): Wheatstone Bridge Electrical Circuit............................. 120 Figure (5.13): Fabricated Load Cells..................................................... 120 Figure (5.14): Reinforced Walls W1, W2 and W3 Instrumentation ..... 121 Figure (5.15): Post-Tensioned Walls W4 and W9 Instrumentation ...... 121 Figure (5.16): Post-Tensioned Walls W5*, W5, W6, W7 and W8 Instrumentation ...................................................................................... 122 Figure (5.17): Cyclic Displacement Protocol [Ingham et al (2006)] .... 123 Figure (6.1): Wall Designation. ............................................................. 128 Figure (6.2): Wall W1 (C:RVH:FG): Crack Patterns............................ 132 Figure (6.3): Wall W1 (C:RVH:FG): Lateral Load – Overall Drift Angle. ............................................................................................................... 133 Figure (6.4): Wall W1 (C:RVH:FG): Flexural Strain at North Toe...... 133 Figure (6.5): Wall W1 (C:RVH:FG): Flexural Strain at South Toe...... 134 Figure (6.6): Wall W1 (C:RVH:FG): Panel Drift Angle. ..................... 134 Figure (6.7): Wall W1 (C:RVH:FG): Sliding. ...................................... 135 Figure (6.8): Wall W1 (C:RVH:FG): Failure Mechanism. ................... 135 Figure (6.9): Wall W2 (A:RVH:FG): Crack Patterns. .......................... 138

xvi

List of Figures Figure (6.10): Wall W2 (A:RVH:FG): Lateral Load –Overall Drift Angle. ............................................................................................................... 139 Figure (6.11): Wall W2 (A:RVH:FG): Flexural Strain at North Toe. .. 139 Figure (6.12): Wall W2 (A:RVH:FG): Flexural Strain at South Toe. .. 140 Figure (6.13): Wall W2 (A:RVH:FG): Panel Drift Angle. ................... 140 Figure (6.14): Wall W2 (A:RVH:FG): Sliding. .................................... 141 Figure (6.15): Wall W2 (A:RVH:FG): Failure Mechanism .................. 141 Figure (6.16): Wall W3 (S:RV:FG): Crack Patterns. ............................ 144 Figure (6.17): Wall W3 (S:RV:FG): Lateral Load – Overall Drift Angle. ............................................................................................................... 145 Figure (6.18): Wall W3 (S:RV:FG): Flexural Strain at North Toe. ...... 145 Figure (6.19): Wall W3 (S:RV:FG): Flexural Strain at South Toe. ...... 146 Figure (6.20): Wall W3 (S:RV:FG): Panel Drift Angle. ....................... 146 Figure (6.21): Wall W3 (S:RV:FG): Sliding. ........................................ 147 Figure (6.22): Wall W3 (S:RV:FG): Failure Mechanism. .................... 147 Figure (6.23): Wall W4 (A:RH:FG:PT): Crack Patterns. ..................... 150 Figure (6.24): Wall W4 (A:RH:FG:PT): Lateral Load – Overall Drift Angle...................................................................................................... 151 Figure (6.25): Wall W4 (A:RH:FG:PT): Flexural Strain at North Toe. 151 Figure (6.26): Wall W4 (A:RH:FG:PT): Flexural Strain at South Toe. 152 Figure (6.27): Wall W4 (A:RH:FG:PT): Panel Drift Angle. ................ 152 Figure (6.28): Wall W4 (A:RH:FG:PT): Sliding. ................................. 153 Figure (6.29): Wall W4 (A:RH:FG:PT): North Bar Post-Tension Force. ............................................................................................................... 153 Figure (6.30): Wall W4 (A:RH:FG:PT): Middle Bar Post-Tension. Force ............................................................................................................... 154 Figure (6.31): Wall W4 (A:RH:FG:PT): South Bar Post-Tension Force. ............................................................................................................... 154 Figure (6.32): Wall W4 (A:RH:FG:PT): Total Post-Tension Force. .... 155 xvii

List of Figures Figure (6.33): Wall W4 (A:RH:FG:PT): Failure Mechanism ............... 155 Figure (6.34): Wall W5* (A:RH*:UG:PT): Crack Patterns .................. 159 Figure (6.35): Wall W5* (A:RH*:UG:PT): Lateral Load – Overall Drift Angle...................................................................................................... 160 Figure (6.36): Wall W5* (A:RH*:UG:PT): Flexural Strain at North Toe. ............................................................................................................... 160 Figure (6.37): Wall W5* (A:RH*:UG:PT): Flexural Strain at South Toe. ............................................................................................................... 161 Figure (6.38): Wall W5* (A:RH*:UG:PT): Panel Drift Angle. ............ 161 Figure (6.39): Wall W5* (A:RH*:UG:PT): Sliding.............................. 162 Figure (6.40): Wall W5* (A:RH*:UG:PT): North Bar Post-Tension Force. ............................................................................................................... 162 Figure (6.41): Wall W5* (A:RH*:UG:PT): South Bar Post-Tension Force. ............................................................................................................... 163 Figure (6.42): Wall W5* (A:RH*:UG:PT): Total Post-Tension Force. 163 Figure (6.43): Wall W5* (A:RH*:UG:PT): Failure Mechanism. ......... 164 Figure (6.44): Wall W5 (A:RH:UG:PT): Crack Patterns. ..................... 168 Figure (6.45): Wall W5 (A:RH:UG:PT): Lateral Load – Overall Drift Angle...................................................................................................... 169 Figure (6.46): Wall W5 (A:RH:UG:PT): Flexural Strain at North Toe.169 Figure (6.47): Wall W5 (A:RH:UG:PT): Flexural Strain at South Toe.170 Figure (6.48): Wall W5 (A:RH:UG:PT): Panel Drift Angle. ................ 170 Figure (6.49): Wall W5 (A:RH:UG:PT): Sliding. ................................. 171 Figure (6.50): Wall W5 (A:RH:UG:PT): North Bar Post-Tension Force. ............................................................................................................... 171 Figure (6.51): Wall W5 (A:RH:UG:PT): South Bar Post-Tension Force. ............................................................................................................... 172 Figure (6.52): Wall W5 (A:RH:UG:PT): Total Post-Tension Force. ... 172 Figure (6.53): Wall W5 (A:RH:UG:PT): Failure Mechanism. ............. 173 xviii

List of Figures Figure (6.54): Wall W6 (C:RH:UG:PT): Crack Patterns. ..................... 177 Figure (6.55): Wall W6 (C:RH:UG:PT): Lateral Load – Overall Drift Angle...................................................................................................... 178 Figure (6.56): Wall W6 (C:RH:UG:PT): Flexural Strain at North Toe. 178 Figure (6.57): Wall W6 (C:RH:UG:PT): Flexural Strain at South Toe. 179 Figure (6.58): Wall W6 (C:RH:UG:PT): Panel Drift Angle. ................ 179 Figure (6.59): Wall W6 (C:RH:UG:PT): Sliding. ................................. 180 Figure (6.60): Wall W6 (C:RH:UG:PT): North Bar Post-Tension Force. ............................................................................................................... 180 Figure (6.61): Wall W6 (C:RH:UG:PT): South Bar Post-Tension Force. ............................................................................................................... 181 Figure (6.62): Wall W6 (C:RH:UG:PT): Total Post-Tension Force..... 181 Figure (6.63): Wall W6 (C:RH:UG:PT): Failure Mechanism. ............. 182 Figure (6.64): Wall W7 (S:RH:UG:PT): Crack Patterns. ..................... 186 Figure (6.65): Wall W7 (S:RH:UG:PT): Lateral Load – Overall Drift Angle...................................................................................................... 187 Figure (6.66): Wall W7 (S:RH:UG:PT): Flexural Strain at North Toe. 187 Figure (6.67): Wall W7 (S:RH:UG:PT): Flexural Strain at South Toe. 188 Figure (6.68): Wall W7 (S:RH:UG:PT): Panel Drift Angle. ................ 188 Figure (6.69): Wall W7 (S:RH:UG:PT): Sliding. ................................. 189 Figure (6.70): Wall W7 (S:RH:UG:PT): North Bar Post-Tension Force. ............................................................................................................... 189 Figure (6.71): Wall W7 (S:RH:UG:PT): South Bar Post-Tension Force. ............................................................................................................... 190 Figure (6.72): Wall W7 (S:RH:UG:PT): Total Bar Post-Tension Force. ............................................................................................................... 190 Figure (6.73): Wall W7 (S:RH:UG:PT): Failure Mechanism. .............. 191 Figure (6.74): Wall W8 (A:RH:UG:PT:Sl): Crack Patterns. ................ 195

xix

List of Figures Figure (6.75): Wall W8 (A:RH:UG:PT:Sl): Lateral Load – Overall Drift Angle...................................................................................................... 196 Figure (6.76): Wall W8 (A:RH:UG:PT:Sl): Flexural Strain at North Toe. ............................................................................................................... 196 Figure (6.77): Wall W8 (A:RH:UG:PT:Sl): Flexural Strain at South Toe. ............................................................................................................... 197 Figure (6.78): Wall W8 (A:RH:UG:PT:Sl): Panel Drift Angle. ........... 197 Figure (6.79): Wall W8 (A:RH:UG:PT:Sl): Sliding. ............................ 198 Figure (6.80): Wall W8 (A:RH:UG:PT:Sl): North Bar Post-Tension Force. ............................................................................................................... 198 Figure (6.81): Wall W8 (A:RH:UG:PT:Sl): South Bar Post-Tension Force. ............................................................................................................... 199 Figure (6.82): Wall W8 (A:RH:UG:PT:Sl): Total Post-Tension Forces. ............................................................................................................... 199 Figure (6.83): Wall W8 (A:RH:UG:PT:Sl): Failure Mechanism. ......... 200 Figure (6.84): Wall W9 (A:RH:PG:PT:Sl): Crack Patterns. ................. 204 Figure (6.85): Wall W9 (A:RH:PG:PT:Sl): Lateral Load – Overall Drift Angle...................................................................................................... 205 Figure (6.86): Wall W9 (A:RH:PG:PT:Sl): Flexural Strain at North Toe. ............................................................................................................... 205 Figure (6.87): Wall W9 (A:RH:PG:PT:Sl): Flexural Strain at South Toe. ............................................................................................................... 206 Figure (6.88): Wall W9 (A:RH:PG:PT:Sl): Panel Drift Angle. ............ 206 Figure (6.89): Wall W9 (A:RH:PG:PT:Sl): Sliding. ............................. 207 Figure (6.90): Wall W9 (A:RH:PG:PT:Sl): North Bar Post-Tension Force. ............................................................................................................... 207 Figure (6.91): Wall W9 (A:RH:PG:PT:Sl): Middle Bar Post-Tension Force. ..................................................................................................... 208

xx

List of Figures Figure (6.92): Wall W9 (A:RH:PG:PT:Sl): South Bar Post-Tension Force. ............................................................................................................... 208 Figure (6.93): Wall W9 (A:RH:PG:PT:Sl): Total Post-Tension Forces. ............................................................................................................... 209 Figure (6.94): Wall W9 (A:RH:PG:PT:Sl): Failure Mechanism. ......... 209 Figure (6.95) Envelope of Load-Drift Angle Curves for Tested Walls 212 Figure (6.96): Comparison of Predicted and Measured Lateral Load Capacities ............................................................................................... 215 Figure (6.97): Predicted Lateral Load Capacities versus Measured Capacities ............................................................................................... 215 Figure (6.98): Deformation Modes for Solid Wall................................ 216 Figure (6.99): W1 (C:RVH:FG): Contribution of Different Deformation Modes. ................................................................................................... 218 Figure (6.100): W2 (A:RVH:FG): Contribution of Different Deformation Modes. ................................................................................................... 218 Figure (6.101): W3 (S:RV:FG): Contribution of Different Deformation Modes. ................................................................................................... 219 Figure

(6.102):

W4

(A:RH:FG:PT):

Contribution

of

Different

Deformation Modes. .............................................................................. 219 Figure (6.103): W5* (A:RH*:UG:PT): Contribution of Different Deformation Modes. .............................................................................. 220 Figure

(6.104):

W5

(A:RH:UG:PT):

Contribution

of

Different

Deformation Modes. .............................................................................. 220 Figure

(6.105):

W6

(C:RH:UG:PT):

Contribution

of

Different

Deformation Modes. .............................................................................. 221 Figure

(6.106):

W7

(S:RH:UG:PT):

Contribution

of

Different

Deformation Modes. .............................................................................. 221 Figure (6.107): W8 (A:RH:UG:PT:Sl): Contribution of Different Deformation Modes. .............................................................................. 222 xxi

List of Figures Figure (6.108): W9 (A:RH:PG:PT:Sl): Contribution of Different Deformation Modes. .............................................................................. 222 Figure (6.109): Calculation of Residual Displacement ......................... 224 Figure (6.110): Maximum and Residual Displacements for Tested Walls ............................................................................................................... 224 Figure (6.111): Relationship between Ductility and Force Reduction Factor [Paulay and Priestley (1992)]. .................................................... 227 Figure (6.112): Actual and Idealized Load-Displacement Relationships for the Test Walls Used for Ductility and Response Modification Factor Calculation [Tomazevic (1998)]............................................................ 227 Figure (6.113): Variation of Wall Stiffness ........................................... 232 Figure (6.114): Predicted Stiffness versus Measured Stiffness............. 235 Figure (6.115): Predicted Stiffness versus Measured Stiffness for PostTension Walls (Second Approach) ........................................................ 237 Figure (6.116): Fragility Curves for Flexure Demand of Un-Grouted PostTensioned Shear Walls. ......................................................................... 239 Figure (6.117): Calculation of Energy Dissipation [Shedid et al. (2009)] ............................................................................................................... 240 Figure (6.118): Energy Dissipation for Tested Walls ........................... 241 Figure (6.119): Equivalent Viscous Damping Ratio ............................. 242 Figure (7.1): Modeling Strategies for Masonry Structures ................... 248 Figure (7.2): Model for Grouted Shear Walls ....................................... 250 Figure (7.3): Model Interfaces for Grouted Shear Walls ...................... 250 Figure (7.4): Model for Un-Grouted Shear Walls ................................. 252 Figure (7.5): Model Interfaces for Un-Grouted Shear Walls ................ 252 Figure (7.6): Meshing of the Walls Models .......................................... 253 Figure (7.7): Boundary Conditions for Models ..................................... 254

xxii

List of Figures Figure (7.8): W4 (A:FG): Load-Displacement Curves for FE Models of Tested Walls (Test vs. FEM) ................................................................. 256 Figure (7.9): W5 (A:UG): Load-Displacement Curves for FE Models of Tested Walls (Test vs. FEM) ................................................................. 256 Figure (7.10): W8 (A:UG:Sl): Load-Displacement Curves for FE Models of Tested Walls (Test vs. FEM) ............................................................ 257 Figure (7.11): W9 (A:PG:Sl): Load-Displacement Curves for FE Models of Tested Walls (Test vs. FEM) ............................................................ 257 Figure (7.12): Specimens Configurations for FE Models of Grouted Walls ............................................................................................................... 260 Figure (7.13): Predicated load-Displacement Curves for FE Models of Grouted Walls ........................................................................................ 261 Figure (7.14): Principle Stress Contours for FE Models of Grouted Walls ............................................................................................................... 262 Figure (7.15): Specimens Configurations for FE Models of Un-Grouted Walls ...................................................................................................... 264 Figure (7.16): Predicated load-Displacement Curves for FE Models of UnGrouted Walls ........................................................................................ 265 Figure (7.17): Principle Stress Contours for FE Models of Grouted Walls ............................................................................................................... 266 Figure (7.18): Specimens Configurations for FE Models of PartiallyGrouted Walls ........................................................................................ 268 Figure (7.19): Predicated load-Displacement curves for FE Models of Partially- Grouted Walls ........................................................................ 269 Figure (7.20): Principle Stress Contours for FE Models of PartiallyGrouted Walls ........................................................................................ 269 Figure (7.21): Specimens Configurations for FE Models of PartiallyGrouted Walls with Sliding Control ...................................................... 273

xxiii

List of Figures Figure (7.22): Predicated load-Displacement curves for FE Models of Walls with Sliding control ..................................................................... 274 Figure (7.23): Principle Stress Contours for FE Models of Grouted Walls ............................................................................................................... 276

xxiv

LIST OF TABLES Table (3.1): Test Program for Triplet Test .............................................. 65 Table (3.2): Details of Tested Walls........................................................ 67

Table (4.1): Average Dimensions for Different Blocks .......................... 88 Table (4.2): Uniaxial Compressive Strength of Different Concrete Blocks ................................................................................................................. 90 Table (4.3): Results of Axial Compression Test for Mortar. .................. 92 Table (4.4): Compressive Strength for Grout: ......................................... 93 Table (4.5): Compressive Strength for Prisms ........................................ 94 Table (4.6): Diagonal Tension (Shear) Test for Grouted Specimens ...... 99 Table (4.7) Test Result of Shear Friction Test ...................................... 103

Table (6.1): Summary of Major Events for Wall W1 (C:RVH:FG) ..... 131 Table (6.2): Summary of Major Events for Wall W2 (A:RVH:FG) ..... 138 Table (6.3): Summary of Major Events for Wall W3 (S:RV:FG) ........ 144 Table (6.4): Summary of Major Events for Wall W4 (A:RH:FG:PT) .. 150 Table (6.5): Summary of Major Events for Wall W5* (A:RH*:UG:PT) ............................................................................................................... 158 Table (6.6): Summary of Major Events for Wall W5 (A:RH:UG:PT) . 167 Table (6.7): Summary of Major Events for Wall W6 (C:RH:UG:PT).. 176 Table (6.8): Summary of Major Events for Wall W7 (S:RH:UG:PT) .. 185 Table (6.9): Summary of Major Events for Wall W8 (A:RH:UG:PT:Sl) ............................................................................................................... 194 Table (6.10): Summary of Major Events for Wall W9 (A:RH:PG:PT:Sl) ............................................................................................................... 203 Table (6.11): Summary of Major Events for Tested Walls: .................. 211

xxv

List of Tables Table (6.12): Predicted and Measured Lateral Load Capacities for the Tested Walls .......................................................................................... 214 Table (6.13): Residual Displacement .................................................... 225 Table (6.14): Measured Values for Displacement Ductility of the Tested Walls ...................................................................................................... 228 Table (6.15): Measured Walls Stiffnesses ............................................. 231 Table (6.16): Predicted and Measured Stiffnesses for Tested Walls .... 234 Table (6.17): Predicted and Measured Stiffnesses Post-Tension Walls 235

Figure (7.1): Modeling Strategies for Masonry Structures ................... 248 Figure (7.2): Model for Grouted Shear Walls ....................................... 250 Figure (7.3): Model Interfaces for Grouted Shear Walls ...................... 250 Figure (7.4): Model for Un-Grouted Shear Walls ................................. 252 Figure (7.5): Model Interfaces for Un-Grouted Shear Walls ................ 252 Figure (7.6): Meshing of the Walls Models .......................................... 253 Figure (7.7): Boundary Conditions for Models ..................................... 254 Figure (7.8): W4 (A:FG): Load-Displacement Curves for FE Models of Tested Walls (Test vs. FEM) ................................................................. 256 Figure (7.9): W5 (A:UG): Load-Displacement Curves for FE Models of Tested Walls (Test vs. FEM) ................................................................. 256 Figure (7.10): W8 (A:UG:Sl): Load-Displacement Curves for FE Models of Tested Walls (Test vs. FEM) ............................................................ 257 Figure (7.11): W9 (A:PG:Sl): Load-Displacement Curves for FE Models of Tested Walls (Test vs. FEM) ............................................................ 257 Figure (7.12): Specimens Configurations for FE Models of Grouted Walls ............................................................................................................... 260 Figure (7.13): Predicated load-Displacement Curves for FE Models of Grouted Walls ........................................................................................ 261 xxvi

List of Tables Figure (7.14): Principle Stress Contours for FE Models of Grouted Walls ............................................................................................................... 262 Figure (7.15): Specimens Configurations for FE Models of Un-Grouted Walls ...................................................................................................... 264 Figure (7.16): Predicated load-Displacement Curves for FE Models of UnGrouted Walls ........................................................................................ 265 Figure (7.17): Principle Stress Contours for FE Models of Grouted Walls ............................................................................................................... 266 Figure (7.18): Specimens Configurations for FE Models of PartiallyGrouted Walls ........................................................................................ 268 Figure (7.19): Predicated load-Displacement curves for FE Models of Partially- Grouted Walls ........................................................................ 269 Figure (7.20): Principle Stress Contours for FE Models of PartiallyGrouted Walls ........................................................................................ 269 Figure (7.21): Specimens Configurations for FE Models of PartiallyGrouted Walls with Sliding Control ...................................................... 273 Figure (7.22): Predicated load-Displacement curves for FE Models of Walls with Sliding control ..................................................................... 274 Figure (7.23): Principle Stress Contours for FE Models of Grouted Walls ............................................................................................................... 276

xxvii

CHAPTER (1) INTRODUCTION 1.1. Background Masonry is one of the oldest construction materials. But there are several disadvantages of using masonry units in construction when compared with other construction materials such as concrete or steel. Masonry construction often requires long time spent by highly skilled laborers which means added cost to the project. This problem is now being magnified by the fact that the low number of qualified masons is shrinking quickly. Another disadvantage to typical masonry construction is the amount of mortar that is required to be mixed on-site. This makes construction time consuming and also makes construction during inclement weather very difficult. Shrinkage cracking is another significant issue that faces concrete masonry units construction. An important disadvantage in typical masonry construction is the weak joints between blocks due to mortar decrease the bearing capacity of the wall compared to the individual block. One method that has been suggested to minimize some of these disadvantages is to dry-stack the blocks. Dry-stacked masonry is manufactured as traditional brick work but without mortar joints. The drystack method makes construction significantly easier and thus reduces the need for skilled labor. However, dry-stack systems are not without their disadvantages. One of the major issues is that without the mortar between courses of blocks, there is no easy way to deal with irregularities in the individual blocks. There is no economical method of producing concrete masonry blocks with little or no variation in height. Dry-stack masonry contractors have come up with several methods to address this issue 1

Chapter 1

Introduction

including used of metal shims between blocks, using small amounts of mortar where required, or placing the blocks in a stack bond. Development in block production led to well leveled artificial units with small tolerances of shape, making possible to work without any mortar in the bed joints. This offers great advantages for the construction process by acceleration, cost reduction as well as independence from climate conditions. 1.2. Dry-Stacked Masonry The advantage of fast erection is induced by elimination of mortar in head joints as well as in bed joints. The costs of production and supply of mortar are cut away. Dry-stacked bricks and blocks can be laid much easier and quicker. Simultaneously, the moisture degree in masonry is reduced. The risk of moisture damages and shrinkage will be decreased. Compared with traditional masonry in fresh state, dry-stacked masonry has more stability during construction. The application of this kind of brick work can be especially recommended if the erection time is short because the drystacked walls can be loaded immediately after construction. 1.3. Definition of the Problem Although the worldwide interest for the dry-stack masonry construction technique because of its attractive advantages, the lack of wide knowledge of loading and deformation behavior of dry-stacked masonry structures exists till now in contrast to this of mortar layered brickwork. There are many available systems of interlocked mortar-less structures already available in the local and worldwide markets. But these systems are based only on a small number of observations on the specific structures without gaining general information. Therefore, these systems are very restricted in design and application. 2

Chapter 1

Introduction

The knowledge of the failure mechanisms is essential for evaluating performance of mortar-less masonry structures. Different investigations on the load bearing behavior were made in the last decade [Murray (2007)], but they did not include systematic examinations, and did not include the shear behavior of the dry-stacked masonry walls which considered one of the most disadvantages of these systems due to the absence of mortar. 1.4. Research Objectives Extensive research program has been initiated at the Faculty of Engineering, Ain Shams University to investigate the behavior of drystacked masonry systems, focusing on how to improve the shear behavior and ductility of the locally available dry-stacked masonry systems. The main objective of the current research is to investigate the inplane behavior of locally available dry-stacked masonry systems in Egypt, (i.e. Azar and Spar-lock systems) and comparing between these two systems and traditional masonry blocks system. The specific objectives of the research plan are to: 1. Investigate the properties of locally available dry-stacked masonry systems 2. Evaluate the in-plane behavior of full-scale dry-stacked shear walls under cyclic loading. The effect of the different variables (reinforcement configurations, grouting, post-tension and sliding control) on the failure mode and lateral load capacity of the wall was studied also. 3. Develop an analytical study of dry-stacked masonry shear walls subjected to in-plane cyclic load and use it to evaluate the effect of untested parameters through an extensive parametric study.

3

Chapter 1

Introduction

1.5. Thesis Organization The following gives a brief description for the chapters’ contents: Chapter (1): Introduces a general statement of the problem of the dry-stacked system, the objectives of this research work, and the thesis layout. Chapter (2): Reviews the available literature discussing various studies conducted on behavior of dry-stacked masonry systems and relevant topics. The chapter includes a literature survey on previous research carried out to develop a dry-stacked system, create new systems that can overcome the defects of the existing systems or these researches that carried out to investigate the behavior of dry-stacked interlocking masonry systems. At the end of this chapter, the research areas which needed to be studied were identified. Chapter (3): Presents an overview for the research plan, pre-test analysis of tested walls. The configurations of the test specimens are also described in this chapter. Chapter (4): Reports the properties of materials used in the research program. Different tests for a mechanical characterization of materials used in the present research are also described and discussed in this chapter. The shear and shear friction properties of the concrete dry-stacked masonry block systems are also studied and discussed in this chapter. Chapter (5): Includes a complete description for the tested walls, details of construction, test setup, instrumentations, and test procedure. Chapter (6): Presents the test results of the full-scale shear walls subjected to in-plane cyclic loading. The behavior of dry-stacked masonry shear walls under cyclic loading is studied and discussed in this chapter. The test results, and the effect of different factors like grout, post4

Chapter 1

Introduction

tensioning, and sliding control on the behavior of dry-stacked shear walls are also presented and discussed in this chapter. Chapter (7): Provides a brief overview of the difficulties associated with modelling the post-tensioned dry-stacked masonry walls. Finite element models are developed to verify the experimental test results and to extend the experimental program using finite element modeling in order to provide more results for untested parameters. Results from the analytical investigation and parametric study are presented along with the experimental test results in this chapter. Chapter (8): Provides summary, conclusions, and recommendations for future work in the area of dry-stacked masonry systems

5

CHAPTER (2) LITERATURE REVIEW 2.1.

Introduction

Conventional masonry is a composite construction material consisting of masonry units and mortar built following certain pattern. The mechanical properties of masonry vary considerably due to variable material properties of units and joining mortar. Masonry units are made from clay, shale, concrete, calcium silicate, stone, and glass, but the most commonly available units are bricks and blocks made from clay or concrete. Concrete blocks masonry is the focus of this research, because it is similar to the dry-stacked concrete block systems. Compressive strength of concrete units varies from as low as 5 MPa to as high as 140 MPa [El-Shafie (1997)]. There are several disadvantages of using concrete masonry units (CMU) in construction when compared with other methods such as concrete or steel construction. CMU construction often requires long time spent by highly skilled laborers which means added cost to the project. This problem is now being magnified by the fact that the low number of qualified masons is shrinking quickly. Another disadvantage to typical CMU construction is the amount of mortar that is required to be mixed onsite. This makes construction time consuming and also makes construction during inclement weather very difficult. Shrinkage cracking is another significant issue that faces CMU construction [Beall (2000)]. The construction industry is acknowledging the strong need to accelerate the masonry construction process, as the traditional method is labor intensive, and hence slower, due to the presence of a large number of mortar joints [Anand et al., (2000)]. 7

Chapter 2

Literature Review

Early attempts were made to increase the size of masonry units (block instead of brick), thereby reducing the number of mortar joints, wherein the use of bedding mortar imposed constraints on the number of layers to be constructed in a day. The need for further acceleration of the rate of construction led to the elimination of bedding mortar and the development of non-conventional methods of masonry construction techniques such as the Hydraform Dry-Stack Block masonry [Agreement South Africa (1996)]. One method that has been suggested to minimize some of these disadvantages is to dry-stack the blocks. The dry-stack method makes construction significantly easier and thus reduces the need for skilled labor, and makes year round construction more feasible [Murray (2007)]. 2.2.

Dry-Stacked Masonry

Traditional masonry construction consists of bricks or blocks jointed together by mortar. Dry-stacked masonry is also manufactured as traditional brickwork but without mortar joints. The advantage of erecting is induced by elimination of mortar in head joints as well as in bed joints. The costs of production and supply of mortar are cut away. Dry-stacked bricks and blocks can be laid much easier and quicker. Simultaneously, the moisture degree in masonry is reduced. The risk of moisture damages as well as shrinkage cracking will be decreased. Compared with traditional masonry in fresh states, dry-stacked masonry has more stability during construction, because the bricks do not float in mortar. The strength of masonry with mortar increases with age, like concrete, particularly as the mortar hardens. Dry-stacked walls can be loaded immediately after construction. The application of this kind of brickwork can be especially recommended if the erection time is short. The first layer in dry-stacked walls has to be stacked carefully, because the absence of the mortar layer 8

Chapter 2

Literature Review

may affect the bricklayers in vertical and horizontal direction. Therefore, the blocks lying below must be put in mortar and straightened out [Marzahn (1997)]. The technique of dry-stacking masonry units in construction has existed in Africa for thousands of years. The Egyptian pyramids and the Zimbabwe ruins, a capital of ancient Shona Kingdom around 400AD, are good examples. Innovative mortar-less system has improved with time since mid-1980’s and is now more competitive in the market than before. The time consuming, the on-site mixed mortar with low quality control, the shrinkage of mortar, and the low number and high cost of skilled masons are some of the problems facing the conventional masonry construction. Several institutions in America, Africa and Asia are now involved in the development of this technology. However, little attention has been given to research on the structural behavior of the systems. In conventional masonry, mortar is used for bonding the masonry units. Drystacking relies mainly on the mechanical interlocking features of the units, which assist alignment and provide stability during construction. Drystacking reduces the requirement for skilled labor and a costly bonding material like cement and allows floor and roof Loadings to be applied immediately upon completion of walls. It reduces building costs due to savings in construction time. Overall savings of up to 27% compared to conventional masonry have been reported [Agreement South Africa (1996)]. The savings are mainly due to savings in cost of mortar, the block units and construction time. A crew could output approximately 60% more using interlocking dry-stacked blocks than with traditional hollow block masonry [Anand et al. (2003)]. Using of mortar-less technique will save

9

Chapter 2

Literature Review

50% of wall construction cost and 50% cement consumption, which ultimately will reduce 40% of carbon emissions [Kintingu (2009)]. However, dry-stack systems are not without their disadvantages. One of the major issues is that without the mortar between courses of block there is no easy way to deal with irregularities in the individual blocks. There is no economical method of producing concrete masonry blocks with little or no variation in height. Dry-stack masonry contractors have come up with several methods to address this issue including using metal shims between blocks, using small amounts of mortar where required, or placing the blocks in a stack bond [Murray (2007)]. In order to attain alignment accuracy in accordance with BS 56283:2005 in a dry-stack mortar-less wall, using of full bricks with top and bottom surface irregularities not exceeding ±0.5mm for un-grooved bricks, and up-to ±0.9mm for grooved bricks is recommend [Kintingu (2009)]. Although the worldwide interest for the dry-stack masonry construction technique because of its attractive advantages, the lack of wide knowledge of loading and deformation behavior of dry-stacked masonry structures exists up to now in contrast to this of mortar layered brickwork. Mortar-less masonry construction is not included in most concrete masonry design standards [Ingham et al., (2006)]. Many of drystacked systems are based only on a small number of observations on the specific structures without gaining general information. Therefore, these systems are very restricted in design and application [Marzahn (1999)]. Although the behavior of interlocking block walls have been studied and reported by several researchers [Drysdale et al. (1991), Gazzola et al. (1989), Harris et al. (1992), Harris et al. (1993), Hatzinikolas et al. (1986), Hansen (1998), and Uzoegbo et al. (2007)], the geometric changes of each system required more effort to investigate each unique system. 10

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2.2.1. Dry-Stacked Masonry Systems There are many systems of interlocking dry-stack masonry all over the world. Hydraform of South Africa, Azar and Spar-lock both of Canada and Haener, Durisol, Faswall and Endura of USA are among many companies that are currently developing and marketing dry-stack masonry. Dry-stack masonry units of different geometry, sizes and interlocking features have been developed in recent years. Researches are done every day to develop it and create new systems that can overcome the defects of the existing systems. Each system has its advantages and disadvantages. Some of these system are now available in the Egyptian market. All dry-stacked systems are constructed without mortar between courses of blocks. The individual blocks of some systems such as Azar, Durisol, and Endura are generally the same size as a typical 40x20x20 cm, but each system is unique. Other systems like Durisol and Faswall are made of composite materials consisting of soft wood fibers and Portland cement. Because of their decreased compressive strength, these systems require all walls to be solid grouted. The advantage of these composite block systems is that they are light weight and therefore construction is easier and faster. [Agreement South Africa (1996) and Murray (2007)]. I. Haener Block Haener block has been on the US market longer than any other dry-stack system. Figure (2.1) presents Haener blocks. It is an interlocking system; the individual blocks have raised lugs that align with the block above as shown in Figure (2.2). Figure (2.3) represents the ability of using horizontal and vertical reinforcement with this system. The system requires the same amount of grout as conventional CMU construction.

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Figure (2.1): Haener Block System The raised lugs

Figure (2.2): Raised Lugs for the Haener Block

Figure (2.3): Horizontal Reinforcement in the Haener Block 12

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II. Azar Block Azar block walls are similar dry-stack interlocking system. Figure (2.4) shows the variable blocks of Azar system. The bed and head joints are manufactured to interlock with adjacent blocks. Azar block, as mentioned in the company recommendations, requires that all walls be solid grouted [Murray (2007)], as shown in Figure (2.5). Vertical and Horizontal reinforcements can be used as can be seen in Figure (2.6).

Figure (2.4): Azar Blocks

Figure (2.5): Filling Azar Blocks with Grout

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Figure (2.6): Vertical & Horizontal Rft. With Azar Blocks III. Spar-lock The Spar-lock system, as can be seen in Figure (2.7) uses unique shaped blocks that slide together. The blocks are placed in a stack bond arrangement. The unique Spar-lock system is one feature that achieves interlocking of individual units in both the horizontal and vertical directions by use of built in shear keys. This system enables the interlocking to be continued around corners. Because the bed and head joints are not continuous straight through the wall there is no straight path for weather to penetrate to the other side of the wall. Spar-lock is not typically used in bearing wall situations but has been employed heavily on the firewall market. Vertical reinforcement and grout may be used but typically are not required for non-bearing situations [Murray (2007)].

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Figure (2.7): Spar-lock system

IV. Hydraform Block The Hydraform block system is not currently available in the Egypt but widely used in many African countries like South Africa, Mozambique, and Ethiopia. Figure (2.8) presents Hydraform block system. The Hydraform system is an interlocking system that uses the interlocking ability of the individual blocks to provide stability and strength lost when mortar is not used. The Hydraform blocks production, like other solid blocks is simple. It can be made in suite by a simple machine.

Figure (2.8): Hydraform Block System

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2.2.2. Properties of Dry-Stacked Masonry 2.2.2.1. Compressive Strength Masonry is usually compressed perpendicular to the bed plane, as this is where masonry exhibits its greatest compressive strength. Mortar tends to be more flexible than the brick unit induced by a lower modulus of elasticity. Thus in unrestrained masonry mortar tends to want to expand more than the unit due to the Poisson’s effect. As mortar and unit are bonded together, the unit resists the extra lateral expansion of the mortar. Therefore the mortar in bed joint and brick unit are subjected to triaxial stress state. Deducing from the triaxial stress state of mortar and bricks, solid masonry compressive strength is above that of mortar but below that of bricks. In addition, mortar is to be used to balance height tolerances of units in order to produce linear stresses perpendicular to the surface of a stressed cross section. Generally, it was observed that thicker mortar layers related to a lower strength of masonry, while brickwork erected with thin joints has a higher compressive resistance. [Marzahn, G. (1997)]. However, the lack of mortar may also be a disadvantage because of slight variations in individual block heights. Marzahn, G. (1997) compared stress versus strain for walls built with and without mortar. The stress-strain curve for the mortar jointed walls, as can be seen in Figure (2.9) appeared to be nearly linear until failure suggesting that there was nearly a constant modulus of elasticity. However, the dry-stacked wall’s stress-strain curve showed large initial deflections and modulus of elasticity that increased as vertical load increased. As can be seen, the dry-stacked units had to settle down in order to balance uneven surfaces and notches before they were able to carry loads. The strength up to 85-95 percent of the compressive strength of thin mortar layered 16

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masonry is possible. Marzahn also suggest pre-stressing the masonry walls to minimize that effect.

Figure (2.9): Stress-Strain Curve for Walls with and without Mortar [Marzahn, G. (1997)]

Uzoegbo, et al. (2007), investigate the axial compressive capacity of Hydraform block system. The general failure mode of the unreinforced system was vertical cracks at the mid section of the walls. When some walls constructed by lower strength units were tested the top courses of block were crushed at failure loads. Crushing usually occurred as the ratio of unit strength to overall wall panel strength decreases. The results of the testing were used to develop a proprietary “relationship between the unit strength and the masonry panel strength.” Results of these tests showed a 65% increase in axial strength when mortar was used in the bed joints. The difference in strength was attributed to a difference in failure mode. The dry stack walls tended to fail in shear and splitting of the head joints. When

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mortar was used in the bed joints, the mortar resisted the shear, which slightly increased the axial capacity of those walls. The main disadvantage of dry stacked masonry systems is that geometric imperfections in individual blocks and varying individual block heights play an increased role in the performance of a system [Jaafar et al. (2006)]. In traditional concrete block construction, these imperfections are compensated for by the mortar in the bed joints. Jaafar et al. investigated two types of geometric imperfections. The first type is caused by the variation of regularity and roughness of the block bed interfaces, while the second is caused by variations in individual block height. When neighboring blocks are slightly different heights, a gap can form when blocks are placed in a running bond. Two different tests were performed. The first test was a “Single Joint” test. The single joint test was comprised of two blocks stacked on top of each other. Small mechanical gauge Demec Points (DPs) were placed near the block interfaces. These DPs were placed near the interface to measure only the deflection caused by the first type of geometric irregularities. The results of the single joint test showed that there was a change in stiffness during testing. The initial stiffness was attributed to settling of the blocks and the closing of block irregularities. As more of the block areas came into contact the stiffness increased slightly. The second test was a “Multiple Joint” test. In this test, blocks were placed in a running bond. The test was to simulate both types of irregularities in a dry stack wall. The results of this test showed large differences in displacement between tested walls. These large differences were attributed to the varying block heights which caused small gaps between interfaces. The sized of these gaps varied from walls to wall, thus the differences in deflection. 18

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Dry-stacked system is effective only if “its performance is at least equal or superior to that of normal blocks.”, “the system must provide adequate bending strength in both the vertical and horizontal directions.”, and “the system must provide adequate resistance to water penetration and have good insulation properties.” [Klausmeier (1978)] Numerical values were obtained for the axial capacities of G. R. drystacked masonry system walls, which is a proprietary system similar to the Spar-lock system. However these values are only applicable to the G. R. system. As ultimate loads were approached, vertical face shell cracking developed. This vertical cracking was attributed to the lateral tensile stresses that develop in the block as the interior grout expands under compression. [Klausmeier (1978)] Murray (2007) investigate the compressive strength of ENDURA system, after testing only 10 different wall configurations concluded that; First, the amount of grouted cells in the walls directly influences the overall strength of the wall. Second, the ultimate capacity of typical built ENDURA Walls is approximately the same as the ENDURA Walls built with the thin set mortar. Additional small scale testing could be performed in order to better understand the effects of the dry interface between blocks. In a small scale test the contact points between blocks could be more easily isolated. Testing with and without the surface bonding cement could also be performed in order to determine whether this component of the system has an effect on axial capacity. Third, the walls reinforced with rebars placed in the center of the corner blocks appeared to have greater ultimate capacities than the walls with eccentrically placed rebars. However, it is unclear whether this difference is due to reinforcing eccentricity, the amount of grout used in the walls, or the type of block used. More testing should be carried out in order to ascertain the effects of eccentricity on 19

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ENDURA block walls. Finally, the researcher suggested that more research is required to develop an analytical procedure to determine the design capacities of ENDURA walls. 2.2.2.2. Initial Settlement Marzahn, G. (1999) investigated the initial settlement of dry-staked masonry under compression. Short term and long term tests were performed on dry stacked masonry walls built using varying individual block strengths. Walls using a thin mortar layer were also tested as a means of comparison. The results of the testing showed that while the ultimate capacities of the dry stacked and mortar jointed walls were similar; the failure or deformation behavior was quite different. The walls built using mortar tended to have a nearly linear relationship between stress and strain from the beginning of the test up to failure. However, the stress-strain behavior of dry masonry was somewhat bi-linear. The first part of the curve, which extended to approximately one third of the failure load, was linear which resulted from the initial settlement of uneven surfaces and block inaccuracies. The second part of the curve depended more on the deformation of the bricks. Dry stacked walls tended to have large initial deformations. Marzahn suggests that prestressing the walls could be a viable method of limiting these large initial deflections.

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Figure (2.10): Comparison between Stress-Strain Curves [Marzahn, G. (1999)] Similar observations were made by Jaafar et al. (2007). The researchers studied the characteristics of dry joints under compressive load, and their effect on the overall behavior of the interlocking mortarless system, are still not well understood. The experimental program designed to investigate the behavior of both grouted and un-grouted specimens. The un-grouted prisms showed extensive axial deformation at lower load levels due to the initial deformation. This behavior occurred mainly because of variation in the contact behavior of dry joints, which was affected by the geometric imperfection caused by block bed irregularity and variation of block height. The grouted prisms showed completely different behavior from that of the un-grouted system. The initial large deformation at the lower loads disappears, and also the prisms had a higher average stress at which cracks in the web were initiated. The concrete grout core area was added to the face-shell’s bedded area to find the total loaded area in stress calculation 21

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of the grouted prisms. Because the effect of the dry joint is reduced in the grouted prisms, the variation in their strength becomes less than in the ungrouted prisms. The results indicate that the overall behavior of the mortar-less system is strongly affected by dry joint behavior. Similar to conventional mortared masonry, web splitting takes place in the mortar-less masonry. Web splitting occurs at higher stress in grouted prisms than in un-grouted prisms. In un-grouted prisms web splitting occurs via a mechanism similar to deep beam bending, whereas in grouted specimens it occurs as a result of lateral expansion of the grout. 2.2.2.3. In-Plane behavior of Dry-Stacked Masonry Walls Similar to normal masonry with mortar bedding, dry-stacked masonry must be designed to withstand shear forces. The shear strength of masonry in general is influenced by several factors, the most important being the joint friction and the unit tensile strength. Bearing walls may design to carry in-plane horizontal loads, induced by wind, bracing effects or earthquake; they are transferred to the walls primarily via diaphragms such as floors or roofs.

Marzahn, G. (1998) studied the effect of static loads on shear walls. First Marzahn performed many tests to investigate the unit material properties (compressive strength, splitting tensile strength, axial tensile strength, internal friction coefficient between the brick layers, and modulus of elasticity). Figure (2.11) present test setup to determine the internal friction coefficient between the brick layers. Figure (2.12) present the individual block shearing test results

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Figure (2.11): Test setup to determine the internal friction coefficient between the brick layers [Marzahn, G. (1998)]

Figure (2.12): Shearing test results [Marzahn, G. (1998)]

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Figure (2.13): Test set-up for full-scale shearing tests on a mortar-less masonry wall [Marzahn, G. (1998)] Then Marzahn performed a full-scale shearing tests on a mortar-less masonry wall as shown in Figure (2.13). And he concluded that, the shear strength of mortar-less masonry is very low compared to its compressive strength. As a result it cannot be used for flexural members, which cause additionally shear stresses in the wall section, as well as for shear walls, which are subjected to pure shear due to bracing forces or earthquake. This deficiency can be compensated by additional compressive stresses normal to the bedding area of the units, efficiently done by prestressing. Ingham et al. (2006) studied the behavior of in-plane dry-stacked masonry walls constructed by using Formblock® system. Two walls were prepared to be tested under cyclic loading with length of 2600 mm and a height of 2400 mm. As shown in Figure (2.14), the walls were conventionally reinforced and fully-grouted. Figure (2.15) shows the

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method used to place the horizontal reinforcement and the plastic shims used to fix the dry-stacked blocks tolerance problem and make them leveled. Lateral force was provided by a hydraulic actuator mounted horizontally at the height of the top surface of the wall, as shown in Figure (2.16).

Figure (2.14): Walls Detailing for [Ingham et al. (2006)]

Figure (2.15): Construction of Dry-Stacked Wall [Ingham et al. (2006)]

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Figure (2.16): Test Setup used by [Ingham et al. (2006)] The loading cycle used for the tests is illustrated in Figure (2.17). This loading cycle was consist of several stages. 1. The system was first taken to the serviceability level load in each of the push and pull directions. 2. A load of 0.75Fn (max. lateral force) was applied in each direction. From this cycle an average displacement was extrapolated to find the ductility one displacements. 3. The structure was then taken through two full (±) cycles to ductility 2, then two to ductility 4, proceeding to increase the displacement in increments of ductility 2 until failure occurred. Failure was defined as having occurred when the lateral force sustained by the structure falls below 80% of the peak value sustained by the structure or when rupture occurred.

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Figure (2.17): Used Loading Cycles [Ingham et al. (2006)]

The research was concluded that, the feasibility of using Formblock® as a dry-stack concrete block system when it used as fully-grouted conventionally reinforced walls, the vertical alignment of wall and accurate placement of reinforcement was achieved without difficulty using Form Bridges. Figure (2.18) presents the load-displacement curve for tested wall.

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Figure (2.18): Load-Displacement Curve [Ingham et al. (2006)]

Bland (2011) studied the behavior of dry-stacked shear walls made of compressed earth block system named ICEB shown in Figure (2.19), all tested walls were grouted and conventionally reinforced as shown in Figure (2.20). The author concluded that the fully grouted reinforced ICEB shear walls behave similarly to conventional reinforced shear walls, and that some of the theory that is used for design conventional reinforced masonry or concrete can be applied to ICEB structures. However, experimental results also indicated some significant differences between the expected and actual shear capacity. The shear strength of fully grouted ICEB walls is significantly higher than that of partially grouted walls. This also suggests that ICEB shear strength is not directly proportional to net area, and is attributed to more continuous distribution of grouting, and better “shear continuity”. Simple flexural theory, based on the assumptions that plane sections remain plane and an equivalent rectangular masonry stress

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block, provides a fairly close prediction of the flexural capacity of ICEB shear walls based on tensile yielding of longitudinal reinforcement. Figures (2.21 and 2.22) show typical load-displacement cure and the modes of failure of the tested walls.

Figure (2.19): ICEB System [Bland (2011)]

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Figure (2.20): Detailing of Tested walls [Bland (2011)]

Figure (2.21): Typical Load-Displacement Curve [Bland (2011)]

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a) control wall

a) with shear panel

Figure (2.22): Typical Mode of Failure [Bland (2011)] 2.3.

Grouting Effect

The recognized procedure for estimating the strength of a grouted masonry wall is based on the gross cross sectional bearing area of the wall. The gross area includes the area of masonry and grout. The grout is required to have at least the same strength as the concrete block. Thus, the strength of the gross cross section may be conservatively based on the strength of the weaker concrete block. Hamid et al. (1978) reviewed the validity of this method through several tests performed on both grouted and un-grouted masonry prisms. Through testing, the researchers also sought to determine the influence of grout strength on the overall prism strength. The prisms tested consisted of three half block courses with varying mortar and grout characteristics. The results of these tests indicated that only small increases in prism strength were achieved with large increases in grout strength. The tests also showed that a superposition of grout strength multiplied by grout area and block strength multiplied by block area greatly overestimates the strength of the prisms. The researchers concluded that mortar strength was not the most significant parameter in determining axial strength.

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Post-Tensioned Masonry

Pre-stressing, usually achieved by post-tensioning, takes advantage of the compressive strength of masonry and improves the carrying behavior by reducing or eliminating tensile stresses, bending cracks, and enhancing the friction resistance in the bed joints to a required amount. The methods of pre-stressing in masonry are similar to those of concrete, but un-bonded post-tensioning is most often used in practice. The bars or wires are tensioned against the masonry and anchored by special anchoring devices like special designed concrete blocks or steel plates. The bars and anchorage elements used are protected against corrosion with plastic coats. [Marzahn (1998)] One of the first experimental investigations on un-bonded posttension (UPT) masonry shear walls was that by Hinkley (1966), who tested five UPT and two unreinforced brickwork shear walls. Square walls as well as rectangular walls were tested and the post-tensioning was applied either uniformly or at the wall ends. Post-tensioning was applied first and then a bond beam was constructed to which the horizontal load was applied. It is mentioned that only horizontal load was assumed to be transferred, although there was some unknown vertical restraint by friction. Monotonic loading was applied at a very slow pace until failure occurred after approximately six hours. the behavior was linear-elastic until cracking first occurred, while the ultimate load could be approximated most accurately by assuming a rectangular stress block and yield of all post-tensioned wires outside the compressed zone.

Page et al. (1988) investigated the racking behavior of pre-stressed and reinforced hollow clay masonry walls. Three tests were conducted: one with grouted reinforcement, one with un-bonded vertical post32

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tensioning and one with un-bonded vertical and horizontal post-tensioning the load was applied with a spherically seated hydraulic jack via a steel bearing plate directly to the top courses of the masonry. This way of applying the load caused local failure of the hollow masonry in the third test. Uplift (base separation) was measured, but the walls failed by diagonal cracking of the masonry. Kurama et al. (1999) investigated the lateral load behavior of UPT precast concrete walls. They found that, although horizontal displacements during seismic loading were larger than in conventional reinforced concrete (RC), plastic deformations and damage were smaller. Since concrete masonry material properties are similar to those of (precast) concrete, Laursen et al. (2001) applied the concept of UPT to single-storey concrete masonry shear walls. Eight walls were tested, of which six were fully grouted, one was partially grouted and one was ungrouted. Cyclic loading was applied. All fully grouted walls exhibited rocking response, but one wall with a higher axial load ratio failed by diagonal cracking. In addition to tests on single storey walls, tests on enhanced single-storey concrete masonry walls and three-storey concrete masonry walls with confinement plates in the toe zones were conducted [Laursen et al. (2004)]. Rosenboom et al. (2004) tested UPT clay masonry and found the same rocking mechanism to occur as in UPT concrete masonry.

The behavior of dry-stacked post-tensioned masonry is characterized by dry friction, zero tensile strength at the interfaces and non-linear contact in compression [Marzahn (2007)]. Tolerances for unit dimensions are even smaller than for masonry with thin-layer mortar, and sufficient axial force

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from building weight or post-tensioning is crucial for the coherence of a dry-stacked masonry wall. Marzahn (1997) discussed the application of post-tensioned drystacked masonry. Like mortar jointed masonry, dry-stacked walls have a good resistance against compression but slightly weak against shear, bending or tension. As dry-stacked masonry is not able to resist tensile stresses perpendicular to bed planes, cracks running along the bed planes will occur. Therefore the bed planes become planes of weaknesses under direct tension or flexure. If actions induce shear, bending or tension, additional compression stresses in vertical direction are needed. Obviously, any increase in axial load, either caused by additional dead load or better by pre-stressing, will induce friction to sustain shear as well as reduce the maximum crack width due to bending or direct tension, respectively. Therefore actions such as flexure which induce tension require the dry-stacked masonry to be posttensioned. Post-tensioning enhances the resistance to flexure as well as shear and tension. The governing criterion for post-tensioning forces is the limitation of the crack width, besides the masonry strength in general. The ultimate load level mainly depends on the deformation of the entire wall between anchorages, as shown in Figure (2.23).

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Figure (2.23): Plain masonry walls to axial load and bending [Marzahn (1997)]

On the other hand the strength of masonry under local compression due to the pre-stressing forces at anchorage elements on the top and bottom is not allowed to be neglected. Masonry constructed from all types of units may be post-tensioned with bars running through pockets formed in the masonry or cores in the units themselves. A lack of shear strength or bending resistance and the static system of most of the walls clearly favor the vertical axis of a wall to be the best direction for placing bars. Commonly the bars are located at the center of the wall. For special applications, such as basement walls, bars might be tensioned at a constant eccentricity. For post-tensioned masonry pre-stressing bars or monostrands are usually used. While for grouted masonry structures a bonded post-tensioning system might be used similar to concrete structures, an un-bonded system using monostrands offers major advantages in un-grouted and in drystacked masonry structures both for constructability and durability reasons. Un-bonded monostrands are provided now with an excellent 35

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double corrosion protection of the pre-stressing steel by grease and plastic ducts or simply by means of plastic coat. Post-tensioned dry-stacked walls demonstrate how masonry can be turned into a new structural material which is suitable for a wide range of buildings as well as engineering works like bridges or shells. In Figure (2.24) the principal construction of a dry-stacked masonry wall is illustrated.

Figure (2.24): Principal construction of a post-tensioned dry-stacked masonry wall [Marzahn (1997)]

It can be concluded that research on UPT shear walls has intensified over the last ten years, especially in the field of earthquake engineering. The type of failure of UPT shear walls depends on the type of loading (seismic or wind loading), the aspect ratio of the wall, the boundary conditions imposed by the storey floor(s) and the axial load level. Shear 36

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failure mechanisms, which include gaping, sliding and diagonal cracking, are associated with a brittle response and global damage, whereas the flexural failure mechanisms characterized by toe crushing, local damage and a high degree of ductility. 2.5.

The Codification of Pre-Stressed Masonry

2.5.1. Background In the next issues, we will highlight the development of the prestressed masonry code in the United States. This is, because we will relate to this Code [MSJC (2008)] in our research work. The United Kingdom (1988), Switzerland (1995) and Europe (1996) have successfully incorporated pre-stressed masonry into their codes [Biggs (1999)]. Without a code, pre-stressed masonry has been used in the United States in proprietary systems for commercial buildings, retrofit applications and research. Wherever in the following the term “Code” is mentioned, the “MSJC” is meant. 2.5.2. Code Development Biggs (1999) stated the first MSJC (Masonry Standards Joint Committee) began its development of a pre-stressed masonry code in 1992 with the creation of a pre-stressed masonry subcommittee. In 1999, the first pre-stressed masonry chapter of the MSJC has been published. It has been part of the MSJC Code for inclusion in the 2000 International Building Code (IBC). The MSJC is a committee sponsored by three professional organizations, which deal with masonry. These organizations are the Masonry Society, American Society of Civil Engineers and American 37

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Concrete Institute. MSJC’s Code is a consensus document developed in accordance with criteria of the American National Standards Institute (ANSI). ANSI requires committee review and input which culminates in balloting for the code. All negative comments within the MSJC must be addressed before any addition or change to the code is approved. Between 1992 and 1998, there were six official drafts and four ballots. MSJC approval was obtained in May 1998; the approval of the sponsoring organizations was finalized in March 1999. Publication is stated for July 1999. Next editions were published at years 2002 and 2005, every with its changes and modifications up to the committees’ continuous activities. The pre-stressed masonry chapter was developed using information obtained from the United Kingdom and Switzerland. This information was used with the existing MSJC Code to create criteria for pre-stressed masonry. While the MSJC Code does not preclude other uses for prestressing, the primary emphasis is on wall. 2.5.3. Basic Theory Prestressing forces are used in masonry walls to reduce or eliminate tensile stresses due to externally applied loads by using controlled precompression. The pre-compression is generated by prestressing bars, either bars, wires, or strands, that are contained in openings in the masonry, which may be grouted. The prestressing bars can be pre-tensioned (stressed against external abutments prior to placing the masonry), or post-tensioned (stressed against the masonry after it has been placed). Most construction applications to date have involved post-tensioned, un-grouted masonry for its ease of construction and overall economy. Consequently, these code provisions primarily focus on post-tensioned masonry. Although not very common, pre-tensioning has been used to construct prefabricated masonry panels. 38

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The elastic theory of combined bending and direct stresses is used for the design and analysis of pre-stressed masonry flexural elements. The criteria used in the design of such elements are the allowable stresses in compression and tension at transfer and at service loads. It is to be insured that the stresses developed at the extreme top and bottom fibers of the flexural member during pre-stressing and at service loads are less than or equal to the allowable tensile and compressive stresses for the masonry. Figure (2.25) represents a typical loading history and corresponding stress distribution across the depth of the critical section, whereas Figure (2.26) is a schematic plot of the load versus deformation for the various loading stages from the self-weight effect up to rupture.

Figure (2.25): Flexural Stress Distribution throughout Loading History. (a) Beam Section. (b) Initial Pre-stressing Stage (c) Self Weight and Effective Pre-stress (d) Full Dead Load plus Effective Pre-stress (e) Full Service Load plus Effective Pre-stress (f)Limit State of Stress at Ultimate Load [Nawy (2003)]

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Figure (2.26): Load-Deformation Curve of Typical Pre-stressed Flexural Member [Nawy (2003)]

For the design of pre-stressed masonry with laterally restrained prestressing bars, a combination of allowable stress design and strength design is proposed. The strength design is included to insure adequate strength and ductility of the member in flexure under strength level loading. Wherever possible the MSJC Code requirements for unreinforced masonry have been applied to pre-stressed masonry. Bonded as well as un-bonded but laterally restrained bars may be considered to contribute to the minimum reinforcement requirements. Bars contribute their force to the moment strength. Thus, the bars remain in tension at moment strength

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condition, they are not subjected to buckling, and hence no lateral support (i.e. lateral tie) will be needed. Often, the masonry member will be pre-stressed prior to 28 days after construction. The specified compressive strength of the masonry at the time of pre-stressing (f'mi) is used to determine the allowable prestressing levels. This strength will likely be a fraction of the 28-day specified compressive strength. Assessment of compressive strength at the time of pre-stress transfer should be by testing of masonry prisms or by a record of strength gain over time of masonry prisms constructed of similar masonry units, mortar and pre-stressing grout when subjected to similar curing conditions. A detailed design procedure built upon the MSJC Code (2008) provisions will be discussed in Section (2.7) leading to the pre-test analysis. A distinction can be made between un-bonded post-tensioning (UPT) and bonded posttensioning (BPT). In the case of BPT masonry, prestressing bars in cavities in the masonry are anchored and prestressed, after which bond between masonry and prestressing bars is achieved by grouting the cavities. In the case of UPT masonry, prestressing bars are either applied in cavities in the masonry or externally, and bond between masonry and prestressing bars is not obtained. BPT and UPT shear walls exhibit fundamentally different mechanical behavior. While the mechanical behavior of BPT shear walls is based on strain compatibility of the shear wall material and the prestressing bars, the mechanical behavior of UPT shear walls relies on global compatibility of wall and bar deformations between the anchorages. BPT shear walls generally have a higher stiffness after cracking than UPT shear walls [Kurama et al (1999)], but stiffness was not the primary concern of the investigation described in

41

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this dissertation. Moreover, grouting is an additional, time-consuming and expensive operation, which contains the risk of grout leakage. 2.5.4. Permissible Stresses in Pre-stressing Bars The stress in pre-stressing bars due to wrenching or jacking force shall not exceed 0.94 fpy (specified yield strength of pre-stressing bar) nor 0.80 fpu (specified tensile strength of pre-stressing bar) nor the maximum value recommended by the manufacturer of the pre-stressing bars or anchorages. Immediately after transfer of pre-stressing force to the masonry it shall not exceed 0.82 fpy nor 0.74f pu. When computing the prestressing-bar stress immediately after transfer of pre-stress, all sources of pre-stress short term losses are to be considered. These sources include anchorage seating loss, elastic shortening of masonry, and friction losses. After transfer and the masonry have gained its compressive strength the effective pre-stress fse shall not exceed 0.78fpy nor 0.70fpu and its computation includes the following pre-stress loss sources: creep of masonry, shrinkage of concrete masonry, relaxation of pre-stressing bar stress and irreversible moisture expansion of clay masonry. As seen above that the state of stress in a pre-stressed masonry member must be checked for all stages of loading. Effective pre-stress is not a fixed quantity over time. Research in loss and gain of pre-stress in pre-stressed masonry is extensive and include testing of time dependent phenomena such as creep, shrinkage, moisture expansion, and pre-stressing bar stress relaxation. Instantaneous deformation of masonry due to the application of pre-stress may be computed by the modulus of elasticity Em=700 fmi for clay masonry;

(2.1)

Em=900 fmi for concrete masonry.

(2.2)

42

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Or the chord modulus of elasticity taken between 0.05 and 0.33 of the maximum compressive strength of each prism determined by test in accordance with the prism test method, article 1.4 B.3 OF ACI 530.1/ASCE 6/TMS602 and ASTM E 111. Changes in pre-stress due to thermal fluctuations may be neglected if masonry is pre-stressed with high strength pre-stressing steels. Calculations should be based on the particular construction materials and methods as well as the climate and environmental conditions. 2.5.5. Brief Notes about Pre-stress Losses Essentially, the reduction in the pre-stressing force can be grouped into two categories:  Immediate elastic loss during the fabrication or construction process, including: 1. Elastic shortening of the masonry. 2. Anchorage seating loss. 3. Friction loss.  Time-dependent losses such as: 1. Creep of masonry. 2. Shrinkage of concrete masonry. 3. Relaxation of prestressing bar stress. In the next brief notes about prestress losses will be mentioned in the guidance of the of the prestressed concrete studies. The MSJC experience, as dated in the commentary on the masonry building code, indicates that the prestress losses are expected to be in the following ranges: a) Initial loss after jacking- 1% to 3% b) Total losses after long-term service for concrete masonry- 30% to 35% 43

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c) Total losses after long-term service for clay masonry- 20% to 25% The values in (b) and (c) include both the short-term and longterm losses expected for post-tensioning. 2.5.5.1. Effect of Prestress Losses on the Study None of the two types mentioned in Section (2.5.5) will affect the prestress level. The friction loss relates to the draped strand shape, resulting from the friction between the strand and the covering sheath. Due to the difficulty in shaping the high strength bars draped, this shape has been considered out of scope. The anchorage loss results from the wire sliding in the conical anchorage. The used anchorage type is the threaded bar tightened with a nut, with no expectation of anchorage loss. Finally, elastic shortening does not relate to the post-tensioning technique, but the pretensioning one, existing immediately after loosening the prestressing wires from the outer supports, when transferring their stress to the intended member. Thus the panels in study are loaded just after exerting the prestress, no time-dependent losses will affect the test results. 2.5.6. Prestressing Bar Anchorages, Couplers, and End Blocks Prestressing bars in masonry construction are anchored either by mechanical devices bearing directly on masonry, or by bond in reinforced concrete end blocks or members. Anchorages and couplers for prestressing shall develop at least 95% of the specified tensile strength of the prestressing bars when tested in an unbonded condition. Also reinforcement shall be provided in masonry members near anchorages if tensile stresses created by spalling forces induced by the prestressing bar exceed the capacity of the masonry. The bearing stresses due to maximum jacking force of the prestressing bar shall not exceed 0.5 f m 44

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2.5.7. Protection of Prestressing Bars and Accessories Prestressing bars, anchorages, couplers and end fittings in exterior walls exposed to earth or weather or walls exposed to relative mean humidity exceeding 75% are to be protected against corrosion. The guidelines of the corrosion protection are as following: 1. Bonded bars are to be encapsulated in corrosion resistant and watertight corrugated ducts, which are to be filled with prestressing grout. The ducts are made of high density polypropylene or polyethylene. The prestressing grout should be of minimum water content limited by a maximum by weight water-cement ratio of 0.45. The water used is to be potable and free of materials known to be harmful to masonry and bars. 2. Unbonded bars are to be coated with a corrosion-inhibiting coating material, which is chemically stable and nonreactive with bar sheathing material and masonry. A sheath should cover the entire bar length, in order to prevent loss of coating material during bar installation and stressing procedure. 2.6.

Behavior of Reinforced Masonry Shear Walls

2.6.1. Flexural Strength It has been reported [Abboud (1987), Shing et al (1989), Shing and Hoskere (1990), Shing et al (1990), and Paulay and Priestly (1992)] that the flexural strength of reinforced masonry sections can be reasonably estimated using simple flexural theory which is based on the assumption that plane sections remain plane after bending (i.e. similar to the approach followed for reinforced concrete sections). The ultimate flexural strength may be determined by assuming rectangular stress block with average /

/

strength of 0.85 𝑓𝑚 and a depth of 0.85𝑐 where 𝑓𝑚 is the masonry 45

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compressive strength and 𝑐 is the distance of the neutral axis from the extreme compression fibers as shown in Figure (2.27a).

Wall Section

a) Strain

b) Stress

c) Stress (approximated)

Figure (2.27): Idealized Flexural Strain and Stress [Islam, M. (2008)] Based on the idealized flexural strain and stress shown in Figure (2.27), the flexural strength (𝑀𝑢 ) of reinforced masonry wall section subjected to axial force (𝑃) can be determined by applying the equilibrium equations as follows: /

𝑃 = 𝛾𝛽𝑓𝑚 𝑐𝑏 − ∑𝑛𝑖=1 𝐴𝑠𝑖 𝑓𝑠𝑖 𝑙

/

𝑀𝑢 = 𝛾𝛽𝑓𝑚 𝑐𝑏 ( 𝑤 − 2

(2.3)

𝛽𝑐

𝑙

+ ∑𝑛𝑖=1 𝐴𝑠𝑖 𝑓𝑠𝑖 (𝑑 − 𝑤) ) 2 2

(2.4)

Where 𝑑𝑖 −𝑐

𝑓𝑢 = 𝐸𝑠 𝜀𝑚𝑢 (

𝑐

)

𝑑𝑖 −𝑐

𝑓𝑢 = 𝐸𝑠 [𝛼𝜀𝑚𝑢 (

𝑐

) + (1 − 𝛼)𝜀𝑦 ] 46

for

𝑓𝑢 ≤ 𝑓𝑦

(2.5)

for

𝑓𝑢 > 𝑓𝑦

(2.6)

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In which 𝐴𝑠𝑖 and 𝑓𝑠𝑖 are the cross-sectional area and stress of a vertical bar 𝑖 distanced 𝑑𝑖 from the compression edge, 𝐸𝑠 is the steel elastic modulus, 𝜀𝑦 and 𝑓𝑦 are the yield strain and stress of the vertical steel, 𝛼 is a strain-hardening parameter of steel, 𝑛 is the number of reinforcing bars, 𝛾 and 𝛽 are the stress and length parameters for the masonry stress block (see Figure (2.27b)), 𝜀𝑚𝑢 is the masonry ultimate compressive strain, and 𝑙𝑤 and 𝑏 are the length and width of horizontal cross section of the wall. The value of 𝛼 depends on characteristic properties of reinforcing bars. Typical values of 𝛼 range between 0.01 and 0.02 [Kurkchubasche et al (1994)]. Shing et al (1990) reported that simple flexural theory consistently underestimates the experimental results by 10 – 13%. Since the ultimate compressive strain of masonry (𝜀𝑚𝑢 ) will normally exceed the reinforcement yield strain (𝜀𝑦 ), virtually all the reinforcement will be at yield in either tension or compression. Therefore, it is reasonable to be consider all reinforcement is at yield (i.e. replacing 𝑓𝑠𝑖 by 𝑓𝑦 in Equations (2.3) and (2.4)). Since the error in estimating the moment capacity, due to overestimating the stress of bars close to neutral axis, will be small [66]. Furthermore, error resulting from assuming that bars situated close to neutral axis yield in tension or compression is offset by relatively early onset of strain hardening of bars near the extreme tension fibers [Paulay and Priestly (1992)]. It is recommended [Paulay and Priestly (1992) and Priestly (1997)] to use uniformly distributed flexural reinforcement rather than end cells reinforcement (jamb steel). Using uniformly distributed flexural reinforcement eases construction process, enhances the resistance to 47

Chapter 2

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diagonal and sliding shear failure of masonry panels, and reduces potential problems regarding out-of-plane buckling of compression zones. The use of uniformly distributed flexural reinforcement instead of wall ends reinforcement is supported by the fact that for typical levels of axial load and flexural reinforcement content, the flexural capacity of wall sections is insensitive to the reinforcement distribution [Paulay and Priestly (1992)]. For design purposes a quick estimation for required amount of flexural reinforcement (∑𝑛𝑖=1 𝐴𝑠𝑖 ) (as uniformly distributed) for wall section subjected to moment (𝑀) and axial force (𝑃) can be carried out by considering the moment resisting of section is resolved into moment sustained by axial force (𝑀𝑝 ) and moment sustained by reinforcement (𝑀𝑠 ). Also the depth of equivalent rectangular compressive strength is divided into parts, (𝑎1 ) is the depth of compression zone due to bending moment carried by axial force and (𝑎2 ) is depth due to moment carried by reinforcement distribution. Therefore, for simplicity of calculations, it is assumed that all the uniformly distributed flexural reinforcing bars are lumped at the middle of the wall section as shown in Figure (2.27c). Based on these assumptions the amount of reinforcement can be estimated using the following equations [Paulay and Priestly (1992)]. ∑𝑛𝑖=1 𝐴𝑠𝑖 ≥

𝑀𝑠 𝑙𝑤⁄ 𝑎 𝑓𝑦 [ 2−𝑎1 − 2⁄2]

(2.7)

Where 𝑎1 =

𝑃

(2.8)

/

𝛾𝑓𝑚 𝑏

𝑙 𝑎 𝑀𝑢 = 𝑃 [ 𝑤⁄2 − 1⁄2] 𝑎2 = 𝑎1 (

𝑀𝑠 𝑀𝑝

) = 𝑎1 (

𝑀−𝑀𝑝 𝑀𝑝

(2.9) )

(2.10) 48

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It should be noted that masonry sections should be reinforced with enough flexural reinforcement so that flexural strength exceeds cracking strength by a reasonable margin of safety to insure ductile performance [UBC (1997)]. Moreover, the vertical (flexural) reinforcement should be kept to the minimum required because the ductility of reinforced sections reduces as flexural reinforcement increases [Paulay and Priestly (1992), Shedid (2008)]. 2.6.2. Diagonal Shear Strength The diagonal shear strength of reinforced masonry walls comprises of two main components, masonry shear strength (𝑉𝑚 ), and shear strength (𝑉𝑠 ) provided by the shear reinforcement. The masonry shear strength usually represents shear strength of different mechanisms such as aggregate interlock, dowel action of flexural reinforcement and shear transferred by the masonry at the compression toe. Several studies have been carried out to study the shear behavior of reinforced masonry shear walls [Matsumura (1987),Shing et al (1990), Matsumura (1990), Anderson and Priestley (1992), Shing et al (June 1993), and Shing et al (August 1993)]. Through these studies different formulas have been developed to predict shear strength. Formulas proposed by Paulay and Priestley (1992) are chosen herein to design the shear reinforcement for the tested walls. These formulas were developed and verified based on the results of several research studies for masonry strength. In addition, Paulay and Priestley shear formulas are design formulas so they are more conservative compared to other formulas which usually are based on best fit of experimental results [El-Shafie (1997)]. Using these formulas, the masonry shear strength (𝑉𝑚 ) and the reinforcement shear strength (𝑉𝑠 ) can be estimated as follows:

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a) Contribution of Masonry, 𝑽𝒎 1- In all regions except potential plastic hinges, /

𝑉𝑚 = (0.17√𝑓𝑚 +

0.3𝑃 𝑙𝑤 𝑏

) 𝑑𝑏

(2.11)

but not greater than 𝑉𝑚 = (0.75 +

0.3𝑃 𝑙𝑤 𝑏

) 𝑑𝑏

(2.12)

nor greater than 𝑉𝑚 = 1.3𝑑𝑏

(2.13)

Where 𝑑 is the effective depth, normally taken as 0.8𝑙𝑤 for rectangular sections with distributed reinforcement. It should be noted that experimental data support an increased shear strength for walls with aspect ratio less than one. However, more research is needed to quantify such increase. 2- Plastic hinge regions At plastic hinge, the masonry shear strength (𝑉𝑚 ) reduces due to masonry deterioration at this region. Paulay and Priestley suggested the following equations to predict masonry shear strength at plastic hinge regions: /

𝑉𝑚 = (0.05√𝑓𝑚 +

0.2𝑃 𝑙𝑤 𝑏

) 𝑑𝑏

(2.14)

but not greater than 𝑉𝑚 = (0.25 +

0.3𝑃 𝑙𝑤 𝑏

) 𝑑𝑏

(2.15)

nor greater than 𝑉𝑚 = 0.65𝑑𝑏

(2.16) 50

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b) Contribution of Shear Reinforcement, 𝑽𝒔 The design of horizontal shear reinforcement for masonry walls follows the same principles used for reinforced concrete. The required area (𝐴𝑠ℎ ) of horizontal (shear) reinforcing bar spaced at 𝑆ℎ can be calculated from the following equation: 𝐴𝑠ℎ =

(𝑉−𝑉𝑚 )𝑆ℎ

(2.17)

𝑓𝑦 𝑑

Where 𝑉 is total shear force carried by the wall panel Although many test results showed that horizontal reinforcement is much more efficient than vertical reinforcement in resisting shear forces, research work results for reinforced masonry tested under pure shear forces [43] showed that shear reinforcement should be distributed between the vertical and horizontal directions to be able to resist the excess of forces that cannot be carried by the masonry after the formation of diagonal cracks. Therefore the vertical reinforcement may have to be designed to resist part of the shear force in addition to the bending moment. It has been also shown the importance of proper detailing of shear reinforcement to insure adequate anchorage. It was concluded that properly detailed shear reinforcement of total percentages higher than 0.2% or 0.3% helped to avoid brittle shear failure and improved both the strength and the ductility of masonry walls. 2.6.3. Sliding Shear Sliding shear failure is limited to shear walls subjected to reversal loads, where the wall may slides along interconnected flexural crack especially at wall footing and plastic hinge regions [El-Shafie (1997)]. Test results [Shing et al (1988)] showed that for walls with low axial loads, sliding shear controlled the failure and prevented the development of wall flexural

51

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capacity and significantly reduced wall stiffness and ductility. Based on the test results of testing concrete masonry coupled shear walls, Merryman et al (1990) recommended that sliding shear at the wall footing should be limited by using shear keys, or roughening of the bed joint at the base of the wall. The sliding strength is provided by frictional resistance along the crack surface which depends on wall compression force and clamping forces (dowel action) provided by flexural reinforcement at wall ends should not be considered for sliding resistance mechanism, because, at potential sliding planes, the flexural reinforcement at wall ends is usually at yield due to flexural stresses. It is recommended [Paulay and Priestley (1992)] that only the flexural reinforcement in the middle third of the wall and crossing the sliding plane may be considered as shear-friction reinforcement.

Moreover,

using

uniformly

distributed

flexural

reinforcement enhances the sliding resistance of the wall panel because of better crack control and better dowel shear resistance. The following equation has been proposed [Anderson et al (1992)] to predict the amount of shear-friction reinforcement (𝐴𝑠𝑓 ) required to resist the shear force (𝑉): 𝐴𝑠𝑓 =

𝑉−𝜇𝑃

(2.18)

𝜇𝑓𝑦

Where 𝜇 is friction coefficient. Based on results of testing masonry shear walls [Anderson et al (1992)] a value of 1.3 was proposed for friction coefficient for masonry walls. 𝑃 is axial load carried by the wall. Shear-friction reinforcement (𝐴𝑠𝑓 ) in accordance with Equation (2.18), should be uniformly distributed in the middle third of the wall crossing the potential sliding plane and adequately anchored on both sides of the sliding plane. All flexural reinforcement within the middle third of

52

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the wall may be included in determining the shear-friction reinforcement [Paulay and Priestley (1992)]. 2.6.4. Stiffness Cantilever wall stiffness (force per unit displacement of mass relative to base) can be calculated based on the elastic theory approach by the following equation [Pauley and Priestly (1992)]: 𝐾=

1

(2.19)

ℎ3 ℎ + 3𝐸𝑚 𝐼 𝐴𝐺𝑚

Where 𝐸𝑚 is the masonry elasticity modulus, 𝐼 the moment of inertia, 𝐴 the effective shear area, 𝐺𝑚 the masonry shear modulus (0.4𝐸𝑚 ). The two terms in the denominator of Equation (2.19) represents the flexural and shear flexibility, respectively. It should, however, be noted that masonry as well as concrete structures cannot strictly be considered linear elastic systems. 𝐼 and 𝐴 in Equation (2.19) depend on the extent of cracking, and hence the lateral force levels, 𝐸𝑚 and 𝐺𝑚 are dependent on the stress level, and unloading stiffness is different from elastic stiffness. Thus even at levels of force less than at yield strength of the cantilever, 𝐾 is a variable [Paulay and Priestley (1992)]. It is worth to mentioning that the approximate methods based on the elastic theory approach does not account for some of the important modes of deformation for reinforced concrete shear walls such as sliding at the base and flexural rotation concentrated at the base due to extensive cracking [El-Shafie (1997)]. In order to use these approximate method for stiffness prediction of reinforced masonry shear walls, it should be modified to take into consideration the effects of cracking, axial load, and flexibility due to modes of deformation which are not considered by elastic theory.

53

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Several approaches were proposed to account for the effect of cracks, tension stiffening, axial load, and flexibility due to unaccounted modes of deformation on the stiffness of reinforced masonry shear walls. Some of these approaches are reviewed hereinafter. The Uniform Building Code (UBC) (1997) stated that the effective moment of inertia (𝐼𝑒 ) for reinforced masonry sections, tacking into consideration the effects of cracking and tension stiffening, can be calculated, in a way similar to that followed to reinforced concrete sections, by using gross and cracked moment of inertia in accordance with Equation (2.20). 𝑀𝑐𝑟

𝐼𝑒 = (

𝑀𝑎

3

𝑀

) 𝐼𝑔 + [1 − ( 𝑀𝑐𝑟 ) ] 𝐼𝑐𝑟 𝑎

≤ 𝐼𝑔

(2.20)

Where 𝑀𝑐𝑟 is the nominal cracking moment strength, 𝑀𝑎 is maximum moment in the member at the stage deflection is computed, and 𝐼𝑔 and 𝐼𝑐𝑟 are the gross and cracked moment of inertia of the wall cross section. It should be noted that Equation (2.20) is an empirical equation which has been long used for estimating the post cracking flexural stiffness for outof-plane flexural walls. However, the application of this equation to shear walls (walls with low aspect ratios) needs further verification. Moreover, this equation gives a constant effective flexural stiffness for the member based on the bending moment value (𝑀𝑎 ) at only one section, therefore it may lead to a significant error for particular distribution of bending moments along the member (i.e. members with constant bending moments along the member length). Further investigation is needed to study the adequacy of using Equation (2.20) in estimating effective flexural stiffness for members subjected to bending moments combined with axial forces. Priestley and Hart (1989) developed a new equation for preliminary prediction of effective moment of inertia for reinforced masonry sections 54

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tacking into consideration the effects of cracking, tension stiffening, and axial force. This equation proportions the effective moment of inertia (𝐼𝑒 ) to the gross moment of inertia (𝐼𝑔 ) as follows: 103

𝐼𝑒 = [

𝑓𝑦

+

𝑃 / 𝑓𝑚 𝑙𝑤 𝑏

] 𝐼𝑔

(2.21)

Moreover, Priestley and Hart proposed that the influence of cracking on shear deformation is proportional to the influence of cracking on flexural deformation. Hart et al (1992) suggested that for analysis purposes, the initial stiffness of reinforced wall-frame elements can be approximated by using 25% and 50% of gross moment of inertia for beams and piers, respectively. Based on a correlation study between stiffness values determined analytically (using elastic theory principles and effective properties of wall sections) and those determined experimentally (at first yield) for cantilever reinforced masonry shear walls, Hart et al (1988) reported that the ratio of experimentally determined stiffness to that determined analytically ranges from a low of 0.26 and a high of 0.3. Accordingly, Hart et al suggested that, for cantilever reinforced masonry shear walls, the stiffness (𝐾) determined analytically at first yield using the elastic theory should be scaled down by a factor of 0.3, accordingly: 𝐾=

𝑉 ∆

=

0.3

(2.22)

ℎ3 ℎ + 3𝐸𝑚 𝐼 𝐴𝐺𝑚

2.6.5. Ductility The ductility of the wall represents its ability to deform beyond elastic limits without excessive strength degradation. The ductility is an important measure for the ability of the wall to sustain large deformations and absorb the energy induced by earthquake loading. In most of building codes 55

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[Aoyama (1981), NEHRP (1988), UBC (1997), and NZS (2004)], the equation of equivalent static load for seismic loading is a function of the available ductility of the structural system. Therefore a reasonable estimate for the ductility is one of the most important parameters in seismic design. The ductility concept may be applied to strain, curvature at certain sections or overall displacement of the wall. The latter is the most convenient way to evaluate the wall overall ductility. The displacement ductility (𝜇𝑢 ) is defined as the ratio of the ultimate displacement (∆𝑢 ) to the yield displacement (∆𝑦 ). The yield displacement (∆𝑦 ) can be defined from an equivalent idealized elasto-plastic response where the lateral loaddisplacement response is replaced by bilinear curve as shown in Figure (2.28) with an initial stiffness defined by a line from the origin to a point on the actual curve corresponding to 75% of the peak lateral load [Paulay and Priestly (1992)].

Figure (2.28): Idealized Load-Displacement Curve for Shear Walls [Paulay and Priestly (1992)] Different approaches have been used to define the ultimate displacement (∆𝑢 ), Shing et al [Shing et al (1986)] defined it as the displacement at which the peak lateral resistance is reduced to 50% of 56

Chapter 2

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ultimate resistance. Priestley and Park (1987) defined the ultimate displacement for concrete columns as the displacement corresponding to the

ultimate

concrete

compressive

strain

or

the

displacement

corresponding to 20% drop of lateral load capacity wherever is smaller. 2.7.

Behavior of Post-Tensioned Masonry Shear Walls

2.7.1. Flexural Strength Based on the elastic theory, MSJC (2008) give equation to predict the flexural strength (𝑀𝑢 ) of post-tensioned masonry shear walls with uniform width (𝑏) and subjected to axial load (𝑃), as follows: 𝑎

𝑀𝑢 = (𝑓𝑝𝑠 𝐴𝑝𝑠 + 𝑓𝑦 𝐴𝑠 + 𝑃𝑢 ) (𝑑 − ) 2

(2.23)

Where 𝑓𝑝𝑠 is the post-tension stress, 𝐴𝑝𝑠 is the total area of posttension bars, 𝑓𝑦 and 𝐴𝑠 are the yielding stress and the cross section area of reinforcing bars (if used), 𝑑 is the distance between the center of tension bars and the extreme compression fiber, and 𝑎 are the effective depth and the equivalent compression stress block. The equivalent compression stress block (𝑎) for cross sections with uniform width (𝑏) over the depth of the compression zone shall be determined by the following equation: 𝑎=

𝑓𝑝𝑠 𝐴𝑝𝑠 +𝑓𝑦 𝐴𝑠 +𝑃𝑢

(2.24)

/

0.80𝑓𝑚 𝑏

The post-tension stress (𝑓𝑝𝑠 ) for shear walls with bonded posttensioning bars shall be taken equal to the yielding stress of post-tensioning bars 𝑓𝑝𝑦 . For walls with unbonded post-tensioning bars 𝑓𝑝𝑠 shall be considered equal the effective post-tension stress in bars (after all losses). The distance d shall be computed as the actual distance from the centerline of the bar to the compression face of the member. For walls with 57

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laterally unrestrained post-tension bars and loaded out of plane (𝑑) shall not exceed the face-shell thickness plus one half the bar diameter plus 12 mm. The ratio 𝑎⁄𝑑 shall not exceed 0.425.

Figure (2.29): Centroid of the Regular Reinforcing (𝑑) [Salah (2010)] 2.7.2. Diagonal Shear Strength The shear strength of post-tensioned shear walls could be calculated by the same equations proposed for reinforced shear walls [MSJC (2008)]. 2.7.3. Sliding Shear Unlikely the reinforced shear walls, the sliding shear does not considered as brittle failure for post-tensioned shear wall especially for walls with unbonded bars. The post-tensioned shear walls with un-bonded bars have the ability of self-restoring the deformation because of the increase and eccentricity in post-tension forces with loading. The proper design of sliding at wall footing could enhance the wall ductility and energy absorption. 2.7.4. Ductility The MSJC (2008) reported that the response modification coefficient (𝑅) and deflection amplification factor (𝐶𝑑 ) used for unreinforced masonry are also used in the design of pre-stressed masonry. This requirement ensures 58

Chapter 2

Literature Review

that the structural response of pre-stressed masonry structures, designed in accordance with these provisions, will essentially remain in the elastic range. The Code also mentioned that “When more experimental and field date are available on the ductility of both bonded and un-bonded systems, 𝑅 and 𝐶𝑑 factors can be reviewed”. According to this restrictive recommendations the post-tensioned shear walls in high seismic zones should be fully-grouted fully-reinforced to ensure elastic response of post-tension structure. 2.8.

Needed Research

Literature review has revealed that the advantages of the dry-stacked masonry systems comparing with the conventional masonry, the properties of these dry-stacked systems had not been fully investigated. It has been also shown that there is a need for further investigation of post-tensioned shear walls constructed with these dry-stacked masonry systems. Moreover, there is a need to verify the proposed methods to predict flexural and shear strengths of dry-stacked shear walls. Also, the underestimation of ductility of post-tensioned shear walls needs to be investigated and finding a simple method to enhance the ductility of post-tensioned shear walls to be able to construct un-grouted post-tensioned dry-stacked shear walls in moderate or high seismic zones, that will minimize the cost of labor, time, grouting, and reinforcement. Therefore, this research program has been initiated to study the behavior of the post-tensioned dry-stacked masonry shear walls with special attention to address the points which have not been fully investigated in previous research studies. It is hoped that this study will result in a better understanding of behavior of post-tensioned shear walls

59

Chapter 2

Literature Review

constructed using available dry-stacked masonry systems and improve the ductility of these walls.

60

CHAPTER (3) RESEARCH PLAN AND DESIGN OF TEST WALLS 3.1. Introduction As presented earlier in Chapter (2), the literature review has demonstrated the need for further research to study the behavior of dry-stacked interlocking shear walls under cyclic loading, the effect of using posttension bars in these walls, and develop a new technique to enhance the shear wall ductility and to prevent the shear brittle failure in un-grouted walls. In this chapter, the details of the current research plan and test program are presented. 3.2. Research Plan 3.2.1. Objectives The main objective of this research is to study the behavior of the drystacked masonry, using locally available interlocking block systems (i.e. Azar and Spar-lock systems) under in-plane loading. The specific objectives of the research plan are to:  Investigate the behavior of masonry assemblages under in-plane loading.  Study the shear-friction behavior of dry-stacked masonry blocks under different conditions.  Investigate the behavior of the fully-grouted dry-stacked reinforced shear walls in comparison with the behavior of conventional blocks shear walls.

61

Chapter 3

Research Plan and Design of Test Walls

 Study the effect of applying locally available post-tensioning technique on the behavior of grouted and un-grouted dry-stacked masonry shear walls.  Investigate the effect of the initial post-tensioning level on the behavior of the un-grouted dry-stacked masonry shear walls.  Develop a new technique using sliding control reinforcement to improve the ductility performance of in-plane un-grouted and partially grouted post-tensioned dry-stacked masonry shear walls. 3.2.2. Scope The scope of the current research is limited to post-tensioned dry-stacked masonry shear walls. To achieve the previously mentioned objectives, the current research program has been developed. This includes: Literature review: It includes review previous research work in the area of behavior of masonry shear walls, dry-stacked masonry systems, post-tensioned masonry shear walls and the relevant topics. Experimental study: It consists of two main phases: Phase (I): This phase is designed to study the behavior of dry-stacked masonry blocks assemblages in comparison with the conventional assemblages using mortared concrete blocks. Diagonal tension and shear friction properties were investigated for Azar and spar-lock systems. Phase (II): This phase is designed to investigate the behavior of fullscale dry-stacked masonry shear walls with different types of dry-stacked masonry systems under cyclic in-plane lateral loading in comparison with conventional reinforced fully-grouted shear walls, and to investigate the effect of post-tensioning on the behavior of dry-stacked masonry shear grouted and un-grouted walls. The enhancement of the ductility of the dry-

62

Chapter 3

Research Plan and Design of Test Walls

stacked shear walls using sliding control technique was also investigated in this phase. Analytical study: A numerical study was conducted using the finite element method to simulate the behavior of the tested post-tensioned walls. The models were validated in light of the experimental results. The calibrated models were used to perform a parametric study including parameters other than the experimentally studied parameters such as the post-tensioning stress level, position of post-tensioned bars and partial grouting. 3.3. Test Program As previously mentioned, the experimental investigation of the current research consists of two phases to study the diagonal tension and shear friction behavior of dry-stack assemblages and the behavior of dry-stack shear walls under in-plane cyclic loading. The designed test program for conducting this research consists of the following: 3.3.1. Phase (I) In this phase, diagonal tension and shear friction tests were performed to investigate the shear and shear friction properties of used dry-stack masonry systems. The following subsections give more details about the test specimens and test setup. 3.3.1.1. Diagonal Tension Assemblages Four dry-stacked fully grouted specimens with overall dimensions of 800×800×200 mm were prepared and tested according to ASTM E 519. The specimens were cured for 28 days, and then tested by applying a diagonal compression force that would cause a diagonal tension failure, this failure mechanism will represent the shear strength of the specimens.

63

Chapter 3

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All specimens were tested in a reaction frame using 500 kN hydraulic jack to apply load, and the load was measured with a 400 kN load cell. Two steel shoes were used to applying the concentrated load at the corners of the wallettes as shown in Figure (3.1).

Figure (3.1): Test Setup for Diagonal Tension Test 3.3.1.2. Triplet Assemblages The shear friction behavior of blocks was determined by triplet test. The special interlocking shape of Spar system prevents constructing its specimens, so in this test we concentrated only to study the Azar blocks system. Ten triplet specimens were constructed and tested using Azar blocks, each set consisted of three specimens as shown in Table (3.1). The specimens represent the surface between two blocks courses, the first course and the concrete base, and the first course and the base using sliding control. After many iterations, the sliding control was chosen a galvanized steel sheet lied in mortar with 2/3 of its area. Each specimen was subjected to a different normal stress using post-tensioning bars, that normal force

64

Chapter 3

Research Plan and Design of Test Walls

was measured using full bridge load cell. Specimens were subjected to a shear force till failure, the shear forces were measured using 40 kN load cell, Figure (3.2) shows the test setup for the test. Table (3.1): Test Program for Triplet Test No.

Specimen Code

1

B-B-1

Description

Surface Condition

Friction between two Azar blocks

Dry-stacked blocks

Normal Stress (MPa) 0.33

2

B-B-2

3

B-B-3

1.33

4

B-C-1

0.00

5

B-C-2

6

B-C-3

7

B-C-4

8

B-C-SL-1

9

B-C-SL-2

10

B-C-SL-3

Friction between Azar blocks and concrete

Mortar

0.67

0.33 0.67 1.33

Friction between Azar blocks and concrete with sliding control

0.33 Mortar with sliding control

0.67 1.33

Figure (3.2): Test Setup of Triplet Test

3.3.2. Phase (II) The experimental program of this phase includes testing of ten full scale masonry shear walls. The specimens were designated by W1 to W9. All 65

Chapter 3

Research Plan and Design of Test Walls

tested walls were eight courses high with three and half block per course, as shown in Figure (3.3) (approximately 1600×1400×200mm). Three specimens (W1, W2, and W3) were constructed with each block type, typically reinforced and fully grouted. Specimen (W4) was post-tensioned and fully-grouted. The wall was designed to have the same ultimate load of the typically reinforced walls. Each block system was used to construct a post-tensioned un-grouted specimen (W5*, W5, W6 and W7). Unfortunately the Azar wall was constructed by mistake with inadequate horizontal reinforcement, so this wall was replaced with wall W5. The last two specimens (W8 and W9) were un-grouted and partiallygrouted post-tensioned walls constructed with sliding control. The details of all wall specimens are given in table (3.2).

66

Table (3.2): Details of Tested Walls Reinforcement Grout

Number and Initial PostTensioning Force (kN)

1Ø12/400mm

Fully

----

----

----

87.0

4ɸ16

1Ø12/400mm

Fully

----

----

----

87.0

Spar-lock

4ɸ16

----

Fully

----

----

----

22.80

A:RH:FG:PT

Azar

----

1Ø12/400mm

Fully

3×50.0 kN

0.066

----

86.30

W5*

A:RH*:UG:PT

Azar

----

2Ø6/400mm

Un-grouted

2×60.0 kN

0.159

----

21.70

W5

A:RH:UG:PT

Azar

----

2Ø6/200mm

Un-grouted

2×60.0 kN

0.159

----

44.70

W6

C:RH:UG:PT

Conventional

----

2Ø6/200mm

Un-grouted

2×60.0 kN

0.144

----

44.70

W7

S:RH:UG:PT

Spar-lock

----

2Ø6/200mm

Un-grouted

2×45.0 kN

0.162

----

22.80

W8

A:RH:UG:PT:Sl

Azar

----

2Ø6/200mm

Un-grouted

2×60.0 kN

0.159

Yes

37.00

W9

A:RH:PG:PT:Sl

Azar

----

2ɸ6/200mm

Partially

3×50.0 kN

0.199 – 0.066

Yes

69.20

Wall

Code

Block Type

W1

C:RVH:FG

W2

Vl.

Hl.

Conventional

4ɸ16

A:RVH:FG

Azar

W3

S:RV:FG

W4

67

(fa/f/m)

Sliding control

Predicted Lateral Load Capacity (kN)

Stress Level

Chapter 3

Research Plan and Design of Test Walls

The specimen code in Table (3.2) refers to the variables. The first character identifies the block type (“C” for conventional, “A” for Azar and “S” for Spar-lock). The second character identifies the reinforcement (“RVH” for vertically and horizontally reinforced, “RV” for only vertically reinforced and “RH” for only horizontally reinforced). The third character identifies the grouting (“FG” for fully-grouted, “UG” for ungrouted and “PG” for partially-grouted). The fourth character, if any, identifies the post-tensioning (“PT” for post-tension). The fifth character identifies the sliding control (“SL” for sliding control). For example specimen (A:RH:UG:PT:Sl) refers to Azar horizontally reinforced ungrouted post-tension wall with sliding control.

a) W1 (C:RVH:FG) b) W2 (A:RVH:FG) Figure (3.3): Details of Tested Walls

68

Chapter 3

Research Plan and Design of Test Walls

c) W3 (S:RV:FG)

d) W4 (A:RH:FG:PT)

e) W5* (A:RH*:UG:PT) f) W5 (A:RH:UG:PT) Figure (3.4): Details of Tested Walls “continued”

69

Chapter 3

Research Plan and Design of Test Walls

g) W6 (C:RH:UG:PT)

h) W7 (S:RH:UG:PT)

i) W8 (A:RH:UG:PT:Sl) j) W9 (A:RH:PG:PT:Sl) Figure (3.5): Details of Tested Walls “continued”

70

Chapter 3

Research Plan and Design of Test Walls

3.4. Pre-Test Analysis A pre-test analysis for the proposed tested walls was carried out using MSJC (2008) to determine the reinforcement and post-tension bars used in the tested shear walls. The calculations to determine the maximum load expected for the wall specimens to reach its ultimate strength will also be presented. The properties of materials needed in the design calculations have been determined through tests and presented in Chapter (4). 3.4.1. Design of Walls W1 (C:RVH:FG) and W2 (A:RVH:FG) The conventional and Azar blocks specimens W1 (C:RVH:FG) and W2 (A:RVH:FG) were decided to be typically reinforced with 4Φ16 vertical bars (every other cell ) and four horizontal bars (every other course), and the two walls are fully-grouted. As shown in the following designing equations, the walls would have 87.0 kN ultimate lateral load capacity.

Figure (3.6): Cracked Section of Walls W1 (C:RVH:FG) and W2 (A:RVH:FG) a) Flexural Design As can be seen in Figure (3.4), the length of compression area, Kd, and the cracked moment of inertia, Inv, can be determined as follows; 𝑆𝑛𝑣 = 0 𝑏(𝑘𝑑 )2 + 𝑛𝐴𝑠 (𝑘𝑑 − 100) = 3𝑛𝐴𝑠 (900 − 𝑘𝑑 ) 2 𝑘𝑑 = 261.86 𝑚𝑚

71

Chapter 3 𝐼𝑛𝑣

Research Plan and Design of Test Walls

𝑏(𝑘𝑑 )3 = + 𝑛𝐴𝑠 (𝑘𝑑 − 100)2 + 3𝑛𝐴𝑠 (900 − 𝑘𝑑 )2 3

𝐼𝑛𝑣 = 6,213,484,748 𝑚𝑚4 Assuming the average compressive strength of masonry prisms equal 9.00 MPa and the steel yielding stress equal 510 MPa, as described in chapter (4), the lateral load capacity of both tension and compression sides can be determines as follows; 𝑓𝑐 =

𝑀 × 𝑘𝑑 𝐼𝑛𝑣

𝑀𝑡 = 213,554,428.9 𝑁. 𝑚𝑚 𝑉=

𝑀 ℎ𝑤

𝑉 = 133.5 𝑘𝑁

𝑓𝑠 =

𝑀 × (1400 − 𝑘𝑑 ) ×𝑛 𝐼𝑛𝑣

𝑀𝑐 = 139,212,980 𝑁. 𝑚𝑚 𝑉=

𝑀 ℎ𝑤

𝑉 = 87.0 𝑘𝑁

b) Shear Design Shear (horizontal) reinforcement was decided to be distributed every other course leaving 400 mm spacing. The shear failure is one of the brittle failure modes, so the design of shear walls was made to avoid this failure mechanism. So it was decided to design the shear reinforcement to carry 1.5 the ultimate flexural load (i.e. 130.5 kN). The required horizontal reinforcement can predicted as follows; 𝑞𝑠ℎ =

𝑉 𝑏𝑑

𝑞𝑠ℎ = 0.466 𝑀𝑃𝑎 𝑞𝑠ℎ =

𝐴𝑠 𝑓𝑦 𝑏𝑆

𝐴𝑠 = 73.11 𝑚𝑚2 Using a 12 mm bar every other course 72

Chapter 3

Research Plan and Design of Test Walls

Figures (3.5) and (3.6) shows the dimension and reinforcement detailing of walls W1 (C:RVH:FG) and W2 (A:RVH:FG) respectively.

Figure (3.7): Dimension and Reinforcement Detailing of W1

Figure (3.8): Dimension and Reinforcement Detailing of W2 73

Chapter 3

Research Plan and Design of Test Walls

3.4.2. Design of Wall W3 (S:RV:FG) The Spar-lock wall W3 (S:RV:FG) was fully grouted and conventionally reinforced like the previous walls. Spar-lock system refuse the inclination of horizontal reinforcement because of its vertically interlocking system, so its shear resistance depends only on the blocks resistance. Figure (3.7) shows the dimension and reinforcement detailing of wall W3 (S:RV:FG).

Figure (3.9): Dimension and Reinforcement Detailing of W3 a) Shear Design As will be described in Chapter (4) the 800×800×200 mm diagonal tension specimen failed in sliding at 8.00 kN. Where fsh =

0.707 P Aav

So the diagonal forces (P) directly proportional with the average cross section area of the wall (Aav)

74

Chapter 3

Research Plan and Design of Test Walls

Therefore for the shear wall with dimensions 1600×1400×200 mm was expected to fail in sliding along the wall cells at 15.00 kN diagonal force, which means 22.80 kN lateral force (V). b) Flexural Design After the sliding of wall cells over each other and according to the location of the sliding, each part of the wall was predicted to resist the overturning moment by its own which decreases its capacity relative to conventional and Azar walls. If we assuming that each cell will behave by its own, the wall will consist of four grouted reinforced cells. Each cell will have dimensions of 402×143 mm with a 16 mm diameter reinforcing bar as shown in Figure (3.8), and the unreinforced cells will be neglected. Each of these cells can resist an overturning moment caused by 3.82 kN lateral force as illustrate in the following equations. 𝑆𝑛𝑣 = 0 𝑏(𝑘𝑑 )2 = 𝑛𝐴𝑠 (200 − 𝑘𝑑 ) 2 𝑘𝑑 = 80.66 𝑚𝑚 𝐼𝑛𝑣

𝑏(𝑘𝑑 )3 = + 𝑛𝐴𝑠 (200 − 𝑘𝑑 )2 3

𝐼𝑛𝑣 = 82,267,345.4 𝑚𝑚4 Assuming the average compressive strength of masonry prisms equal 6.00 MPa and the steel yielding stress equal 510 MPa, as described in Chapter (4).

75

Chapter 3

Research Plan and Design of Test Walls

𝑉 = 3.82 𝑘𝑁

𝑉 = 4.08 𝑘𝑁

The lateral load capacity of the four separated cells was assumed to be 15.30 kN. So when the sliding took place along the cells at 22.80 kN, the wall would suddenly fail.

Figure (3.10): Cracked Section of Wall W3 3.4.3. Design of Wall W4 (A:RH:FG:PT) The design philosophy of fully grouted post-tensioned wall W4 (A:RH:FG:PT) was using post-tension technique instead of the conventional vertical reinforcement and keep the same ultimate lateral load capacity of the wall (87.0 kN). Three post-tension bars were used each with 50 kN initial post-tension force. a) Flexural Design Figure (3.9) shows the cross section of wall W4 (A:RH:FG:PT).

Figure (3.11): Cracked Section of Wall W4 76

Chapter 3 a=

Research Plan and Design of Test Walls

fps Aps /

0.8fm b Using the post-tension stress (fps) is equal the yielding stress for the

bars (1080 MPa), and the compressive strength of masonry prisms equal 8.15 MPa, as described in chapter (4) a = 172.55 mm a M = fps Aps (d − ) 2 M = 138,088,125 N. mm V = 86.30 kN b) Shear Design Horizontal reinforcement was decided to be a 12 mm bar every other course just like the previous walls. Figure (3.10) shows the detailing of wall W4 (A:RH:FG:PT)

Figure (3.12): Dimension and Detailing of W4 77

Chapter 3

Research Plan and Design of Test Walls

3.4.4. Design of Wall W5 (A:RH:UG:PT) and W6 (C:RH:UG:PT) The un-grouted post-tensioned walls W5 (A:RH:UG:PT) and W6 (C:RH:UG:PT) were constructed using Azar and Conventional blocks respectively with face-shell horizontal reinforcement. The aim of the design these un-grouted post-tension walls is to have the maximum possible ultimate lateral load capacity of the wall. a) Flexural Design To have no tensile stresses on the wall section after loading, the initial stress on masonry due to initial post-tension force was considered to be half the allowable compressive strength (fm = 0.165 f/m), the net area of the wall is 92400 mm2 as shown in Figure (5.8). Therefore the allowable initial post-tension force is 137.214 kN (f/m = 9.00 MPa). The effective posttension stress after losses (fse) for the used bars shall not exceed 885.60 MPa (0.82 fpy nor 0.74 fpu), according to MSJC (2008). So it was decided to use two bars each with 60 kN post-tension force to satisfy these recommendations. The wall's ultimate lateral load was predicted to be 44.70 kN as illustrated in the following equations.

Figure (3.13): Cracked Section Walls W5 and W6

As shown in Figure (3.11) /

fps Aps = 0.8fm (30 × 200 + (a − 30) × 30 × 2) a a = 207.8 mm … … … … … … … … ≤ 0.425 d 78

Chapter 3

Research Plan and Design of Test Walls

a M = fps Aps (d − ) 2 M = 71,533,333 N. mm V = 44.70 kN b) Shear Design Horizontal reinforcement was decided to be two mild-steel bars (fy=280 MPa) lays in face shell grooves and distributed every course leaving 200 mm spacing. The shear design was performed to carry 1.5 the flexural failure load (i.e. 67.05 kN). 𝑞𝑠ℎ =

𝑉 𝐴

𝑞𝑠ℎ = 0.726 𝑀𝑃𝑎 𝑞𝑠ℎ =

𝐴𝑠 𝑓𝑦 𝑏𝑆

𝐴𝑠 = 31.11 𝑚𝑚2 , Using 2ø5 mm every course Unfortunately, by mistake the wall W5 (A:RH:UG:PT) was constructed using 2ø5 mm every other course (400mm spacing) instead of every course, so the wall was replaced. The mistaken wall named by W5* (A:RH*:UG:PT). that wall with inadequate horizontal reinforcement was predicted to fail in shear mode at 21.17 kN ultimate lateral load. Figures (3.12) to (3.14) show the detailing of walls W5* (A:RH*:UG:PT), W5 (A:RH:UG:PT) and W6 (C:RH:UG:PT).

79

Chapter 3

Research Plan and Design of Test Walls

Figure (3.14): Dimension and Detailing of W5*

Figure (3.15): Dimension and Detailing of W5

Figure (3.16): Dimension and Detailing of W6

80

Chapter 3

Research Plan and Design of Test Walls

3.4.5. Design of Wall W7 (S:RH:UG:PT) In the post-tensioned spar-lock wall W7 (S:RH:UG:PT), the blocks were rearranged to allow a horizontal reinforcement to trying to improve its shear capacity, two mild steel sheets with dimensions of 35.0×1.0mm were used as horizontal reinforcement, as shown in Figure (3.15). Even with the new arrangement, there was a shortage in the horizontal reinforcement at the corner blocks. The shear properties would be improved except for this region and the shear failure was expected at almost the same of the Sparlock wall W7 (S:RH:UG:PT) (22.80 kN). Figure (3.16) shows the detailing of wall W7 (S:RH:UG:PT). The initial post-tension force were decided to be 45.00 kN in two bars, to provide masonry compressive stress fm = 0.165 f/m, as described before (average compressive strength Spar-lock prisms was 6.00 MPa).

Hl. Reinforcement Unreinforced Area

Figure (3.17): Horizontal Reinforcement in Spar-lock Modified Configuration

81

Chapter 3

Research Plan and Design of Test Walls

Figure (3.18): Dimension and Detailing of W7

82

Chapter 3

Research Plan and Design of Test Walls

3.4.6. Design of Wall W8 (A:RH:UG:PT:Sl) The aim of using sliding control in wall W8 (A:RH:UG:PT:Sl) was trying to force the wall to slide before the flexural failure took place, which expected to happen at 44.70 kN lateral force as shown in the design of wall W5 (A:RH:UG:PT). The shear friction between the base and first course was determine by triplet test as shown in Chapter (4), the shear friction equation was 𝜏 = 0.20 𝜎 + 0.14 The normal stress (σ) for the un-grouted post-tensioned walls can be calculated as follows: 𝜎= 𝜎=

𝑃𝑝𝑠 𝐴𝑤 𝑛𝑒𝑡 2×60000 92400

= 1.30 𝑀𝑃𝑎

So

𝜏 = 0.40 𝑀𝑃𝑎

And

𝑉 = 𝜏 × 𝐴𝑤 𝑛𝑒𝑡 = 37.00 𝑘𝑁

That means the sliding of the wall was predicted to occurs at 37.00 kN lateral load (i.e. 82.8% of the flexural lateral load capacity) The friction between dry-stacked courses will be enough to prevent the in-between sliding (𝜏 = 0.60 𝜎, so the courses need 72.0 kN to slide over each other). Figure (3.17) shows the detailing of wall

83

Chapter 3

Research Plan and Design of Test Walls

Figure (3.19): Dimension and Detailing of W8 3.4.7. Design of Wall W9 (A:RH:PG:PT:Sl) Wall W9 (A:RH:PG:PT:Sl) was designed to improve the behavior of wall W8 (A:RH:UG:PT:Sl), so the first course was decided to be grouted; the grouted course would prevent the crushing of thin face-shells when it slides, also the initial total post-tension force could be enlarged to improve the ultimate lateral load capacity of the wall. As shown in Figure (3.18), three post-tension bars were decided to use each with 50 kN initial post-tension force, gives 1.62 MPa compression stress for the un-grouted courses (0.199 f/m). The sliding control would be used as wall W8 (A:RH:UG:PT:Sl). The ultimate lateral load would be 60.20 kN as shown in the following equations. a=

fps Aps /

0.8fm b

84

Chapter 3

Research Plan and Design of Test Walls

Where the post-tension stress (fps) is assumed equal the initial stress for unbonded bars, and the compressive strength of masonry prisms equal 8.15 MPa. a = 115 mm a M = fps Aps (d − ) 2 M = 186,375,000 N. mm V = 116.48 kN By using the sliding control with shear friction of 𝜏 = 0.20 𝜎 + 0.14, and the normal stress (σ) at the base section equal 0.535 MPa. The wall would slide over its base at 69.20 kN.

Figure (3.20): Dimension and Detailing of W9

85

CHAPTER (4) MATERIAL CHARACTERIZATION 4.1. Introduction This chapter presents the properties of the materials used in the experimental program. These materials included three different types of concrete blocks, grout, mortar, conventional reinforcing steel bars, and post-tension bars. Standard tests were performed to determine the mechanical properties of these materials. It also include evaluating of masonry assemblages properties via testing of prisms, diagonal tension assemblages and triplets 4.2. Material Testing 4.2.1. Concrete Block Units Three different types of concrete blocks were used to construct the different specimens used in this research namely; Conventional, Azar, and Spar-lock blocks. Figure (4.1) shows the used blocks.

Intermediate Block

Half Block

Intermediate Block

a) Conventional

Edge Block

b) Azar

Intermediate Block

Edge Block

c) Spar-lock Figure (4.1): Concrete Units Used to Construct Test Specimens

87

Half Block

Chapter 4

Material Characterization

4.2.1.1. Unit Dimensions The dimensions of 5 intermediate and edge blocks from each type of blocks were measured according to ASTM C 140, and the average dimensions are represented in Table (4.1). Table (4.1): Average Dimensions for Different Blocks

No.

Block Type

Average Overall Dimensions (mm)

Average Face Average Web Shell Thickness Thickness (mm) (mm)

Length

Width

Height

Inter.

400

200

198

20.5

21

Edge

200

200

200

21

21

Inter.

404

200

200

31

30.5

Edge

201

200

200

31

31

402/210

143

198 - 99

38

37

402/210

200/143

198 - 99

38

37

1

Con.

2

Azar

3

Spar- Inter. lock Edge

4.2.1.2. Compressive Strength The compressive strength test was carried out on three blocks from each type of concrete blocks according to ASTM C 140. A gypsum capping was spread on the two opposite bearing surfaces of each block to eliminate the stress concentration. The test setup and the failure modes are shown in Figure (4.2). Table (4.2) represents the test results of uniaxial compression test for different concrete blocks.

88

Chapter 4

Material Characterization

Test Setup

Failure Mode a) Conventional Block

Test Setup

Failure Mode b) Azar Block

Test Setup

Failure Mode c) Spar-lock Block

Figure (4.2): Uniaxial Compression Test for Concrete Units

89

Chapter 4

Material Characterization

Table (4.2): Uniaxial Compressive Strength of Different Concrete Units Failure Load (kN)

Compressive Strength “f/u” (MPa)

318.0

12.04

245.0

9.27

3

300.0

11.35

4

241.0

7.20

364.0

10.87

239.0

7.14

158.0

6.87

185.0

7.88

135.0

6.02

No

Code

Cross Section Net Area (mm2)

1 2

5

Con.

Azar

26417

33466

6 7 8

Sparlock

26874

9

Average Compressive Strength “f/u” (MPa)

C.O.V* (%)

10.88

13.12

8.40

25.44

6.92

15.68

* Coefficient of variation.

The high coefficient of variation reflects the low quality of the block units used in this research which match the types of blocks were produced and used in masonry constructions in Egypt. 4.2.2. Masonry Mortar The mortar used for construction the conventional specimens and bonding the first course in dry-stacked specimens was Type M mortar in accordance with ASTM C 270-04a (Type 1 according to ECP 204), that is the most type used in dry-stacked masonry system construction to bond the first course of blocks to the concrete base. The mix of mortar consists of Portland cement, hydrated lime, sand, and water. The type of cement used was ordinary Portland cement (Type I, ASTM C 150). The sand used was natural sand in accordance with ASTM C 144. The mix proportions of the mortar were as follows:

90

Chapter 4

Material Characterization

Cement

:

Lime

:

Sand

1.00

:

0.25

:

3.00

by Volume

1.00

:

0.12

:

3.44

by Weight

The water content was adjusted to provide a workable mix. The water/cement ratio was about 1.1. Three 50 mm cubes were taken from the mortar during construction. The specimens were cast and tested for compressive strength, at 28-day age, according to ASTM C 109/C 109M. All specimens failed by shear as shown in as shown in Figure (4.3). Table (4.3) summarizes the results of axial compressive strength for mortar cubes.

Test Setup

Typical Failure Mode

Figure (4.3): Axial Compression Test for Mortar Cubes

91

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Material Characterization

Table (4.3): Results of Axial Compression Test for Mortar. Average C.O.V Compressive (%) Strength (MPa)

Construction Day

Specimen Constructed

1

Masonry Prisms

21.3

10.5

2

Diagonal Tension Specimens

22.4

14.7

3

Triplet Specimens

20.2

9.4

4

W1

20.0

11.2

5

W2

22.3

12.3

6

W3

19.8

10.5

7

W4

21.7

8.4

8

W5*

22.2

13.3

9

W5

20.4

10.6

10

W6

23.1

9.4

11

W7

19.5

15.0

12

W8

20.5

13.0

13

W9

13.0

12.4

4.2.3. Grout A self-compacted grout was used to fill cells in the grouted specimens. The mix of grout consists of Portland cement, natural sand, water, and admixture. The type of cement used was ordinary Portland cement (Type I, ASTM C 150), and the admixture used was high range water reducer (Type G, Sikament® 163). The mix proportions by weight of the grout were as follows: Cement 1

: :

Sand 2.5

: :

Water

:

Admixture

0.4

:

0.02

The slump was measured for the grout after mixing, and five 75×75×150mm prisms were taken from the grout during construction for 92

Chapter 4

Material Characterization

compression test, a gypsum capping was spread on the bearing surfaces of each specimen to eliminate the stress concentration. The specimens were

casted and tested in compression according to ASTM C476. The test setup and the failure mode for the grout specimen are shown in Figure (4.4). All specimens failed by splitting as shown in Figure (4.4). Table (4.4) represents the results of the slump test and compression test of grout for each wall.

Test Setup

Typical Failure Mode

Figure (4.4): Compression Test for Grout Table (4.4): Compressive Strength for Grout: No.

Specimen

Slump (mm)

Average Compressive Strength (MPa)

C.O.V (%)

1 2 3 4 5

W1 W2 W3 W4 W9

220 210 230 220 230

21.5 22.5 22.0 22.5 18.0

5.3 6.0 8.9 11.4 6.8

4.2.4. Masonry Prisms Three masonry prisms for each type of used blocks were built in stack bond to determine masonry compressive strength in accordance with ASTM C1314-03b. Each prism was three blocks high and all prisms were built 93

Chapter 4

Material Characterization

using intermediate blocks. The conventional blocks were built with mortar, and the Azar and Spar blocks built without mortar (dry-stacked). All prisms were fully grouted. A gypsum capping was spread on the two opposite bearing surfaces of each prism in order to create a uniform distribution of compression stresses. All prisms were failed by face shell delimitation as shown in Figure (4.5).

The axial load and corresponding strain were measured using load cell and two LVDTs (having 400 mm gage length) in order to plot the stress-strain response for the masonry in compression and the modulus of elasticity are shown in Figures (4.6) to (4.8). Data from load cell and LVDTs were electronically recorded using a computerized data acquisition system. Representative stress-strain curves for the three types of used blocks in compression are shown in Figures (4.6) to (4.9). Table (4.5) represents the compressive strength and modulus of elasticity for each type of blocks. Table (4.5): Compressive Strength for Prisms No. 1 2 3 4 5 6 7 8 9

Code

Con.

Azar Sparlock

Compressi ve Strength (MPa) 9.20 9.40 8.50 8.50 8.10 7.85 5.62 6.25 6.12

Average Compressive Strength “f/m” (MPa)

Average Modulus of Elasticity “E” (MPa)

9.03

8136

8.15

7350

6.00

5800

94

Chapter 4

Material Characterization

Test Setup

Typical Failure Mode a) Conventional Block

Test Setup

Typical Failure Mode b) Azar Block

Test Setup

Typical Failure Mode c) Spar-lock Block

Figure (4.5): Axial Compression Test for Masonry Prisms 95

Chapter 4

Material Characterization

Figure (4.6): Stress-Strain Curve for Conventional Block Prisms

Figure (4.7): Stress-Strain Curve for Azar Block Prisms

96

Chapter 4

Material Characterization

Figure (4.8): Stress-Strain Curve for Spar-lock Block Prisms

Figure (4.9): Stress-Strain Curve for Tested Prisms

97

Chapter 4

Material Characterization

4.2.5. Diagonal Tension (Shear) Test Four dry-stacked fully grouted specimens with overall dimensions of 800×800×200 mm were prepared and tested according to ASTM E 519. The specimens were cured for 28 days, and then tested by applying a diagonal compression force that would cause a diagonal tension failure, this failure mechanism will represent the shear strength of the specimens. All specimens were tested in a reaction frame using 500 kN hydraulic jack to apply load, and the load was measured with a 450 kN load cell. Two steel shoes were used to applying the concentrated load at the corners of the wallettes as shown in Figure (4.10).

Figure (4.10): Test Setup for Diagonal Tension Test The failure modes of the Azar tested specimens were typically diagonal tension (shear) failure. The Spar-lock blocks’ specimen, on the other hand, failed by sliding with almost no shear resistance, Spar system 98

Chapter 4

Material Characterization

works as separated cells with a poor connection between. The failure modes of tested specimens are shown in Figure (4.11). Table (4.6) shows summary of test result for diagonal tension test.

Table (4.6): Diagonal Tension (Shear) Test for Grouted Specimens No.

Code

1

Azar 1

2

Azar 2

3

Azar 3

4

Spar-lock

Cross Section Area (mm2)

160000 160000

Max. Diagonal Load (kN) 340

Tensile Strength "fd" (MPa)

Average Tensile Strength "fd" (MPa)

1.50

370

1.63

350

1.55

Sliding @ 8.00 kN

a) Azar

b) Spar-lock Figure (4.11): Failure Modes for Diagonal Tension Test

99

1.56

0.04

Chapter 4

Material Characterization

4.2.6. Shear Friction (Triplet Test) Shear friction behavior is an important property which decides the type and the place of failure; furthermore it controls the amount of energy dissipation before failure which means the wall ductility. The higher shear friction between block courses due to pure friction or due to cohesion of mortar in addition of friction, tends to higher shear resistance for the shear wall. Also the higher shear friction between the first course and the concrete base, limit the sliding failure mechanism which means a lower ductility. But on the other hand too low shear friction with the concrete base tends the wall to slide very early with low load carrying capacity which allows the wall to dissipate small amount of energy. The shear friction behavior of blocks was determined by triplet test. The special interlocking shape of Spar system prevents constructing its specimens, so in this test we concentrated only to study the Azar blocks system. Shear bond strength (𝜏𝜊 ) and coefficient of friction (𝜇𝜊 ) according to the Coulomb friction relationship (𝜏 = 𝜏𝜊 + 𝜇𝜊 𝜎𝑛 ) were calculated by means of linear interpolation of the data provided by the tests as shown in Figures (4.12) to (4.15) and summarized in Table (4.7)

100

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Material Characterization

Figure (4.12): Test Result of B-B Triplet Specimens

Figure (4.13): Test Result of B-C Triplet Specimens

101

Chapter 4

Material Characterization

Figure (4.14): Test Result of B-C-SL Triplet Specimens

Figure (4.15): Test Result of All Triplet Specimens

102

Chapter 4

Material Characterization

Table (4.7) Test Result of Shear Friction Test No.

Description

𝜇𝜊

𝜏𝜊 (MPa)

1

Friction between two Azar blocks

0.60

0.00

2

Friction between Azar blocks and concrete base

0.65

0.64

3

Friction between Azar blocks and concrete base with sliding control

0.20

0.14

4.2.7. Reinforcing Steel All reinforcing steel used in the current research was high strength deformed steel. In order to determine the mechanical properties of the reinforcing steel, three specimens from each diameter were prepared and tested under uniaxial tensile load. The average yield and ultimate tensile strength were 510, and 690 MPa respectively, and the average maximum elongation was 18 %. 4.2.8. Post-Tensioning Bars High strength post-tension steel bars were used for post-tensioning of concrete masonry shear walls. The post-tensioning bars were 9.4 mm in diameter and 2100 mm in length with 100 mm threaded part at each bar end. These bars had special lock nuts in order to provide adequate locking for the post-tensioning system to bear the high tension force in the bar. This high tensile steel is used as a post-tensioning system in the prestressed concrete railway sleepers. Three post-tension bars were tested in tension to find out the elastic and ultimate tensile strengths, which would be used to calculate the

103

Chapter 4

Material Characterization

maximum allowed initial post-tension force in each bar and to determine number of bars used in each shear wall. The tested bars had average proof strength at 0.1% strain and ultimate tensile strength 1080 and 1570 MPa respectively, where the modulus of elasticity was 216 GPa. Figure (4.16) shows the typical failure mode of the tested post-tension bars. As shown in Figure the fracture occurred in the threaded part.

Figure (4.16): Typical Failure Mode for Tested Post-Tensioning Bars

104

CHAPTER (5) CONSTRUCTION AND TESTING OF MASONRY SHEAR WALLS 5.1. Introduction As proposed in Chapter (3), the experimental program phase (II) consists of testing ten masonry shear walls. The details of construction, test setup, and instrumentation are presented in this chapter. 5.2. Specimen Construction and Preparation 5.2.1. General Description All tested shear walls were constructed on a pre-cast reinforced concrete footing having dimensions 200×200×1800 mm. After construction of masonry panel and allowing grout to cure in grouted specimens, a pre-cast reinforced concrete top beam, having dimensions 150×200×1400 mm. was fixed on the top of specimen using a strong mortar (Type M mortar). As shown in previous sections, the masonry panel for all specimen having overall

dimensions

1400×1600×200

mm,

changing

slightly

in

conventional walls because of mortar layers between blocks to 1430×1680×200 mm. Figure (5.1) shows the geometry and dimensions of the tested specimens.

105

Chapter 5

Construction and Testing of Masonry Shear Walls

a) W1 (C:RVH:FG)

b) W2 (A:RVH:FG)

c) W3 (S:RV:FG)

d) W4 (A:RH:FG:PT)

Figure (5.1): Geometry and Dimensions of the Tested Specimens

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Chapter 5

Construction and Testing of Masonry Shear Walls

e) W5* (A:RH*:UG:PT)

f) W5 (A:RH:UG:PT)

g) W6 (C:RH:UG:PT)

h) W7 (S:RH:UG:PT)

Figure (5.2): Geometry and Dimensions of the Tested Specimens (continued)

107

Chapter 5

Construction and Testing of Masonry Shear Walls

i) W8 (A:RH:UG:PT:Sl)

j) W9 (A:RH:PG:PT:Sl)

Figure (5.3): Geometry and Dimensions of the Tested Specimens (continued) 5.2.2. Reinforced Concrete Footings The reinforced concrete footing was constructed to support the masonry panel, to fix the tested wall to the test bed, and to anchor the vertical reinforcement and the post-tension bars. All footings having dimensions 200×200×1800mm and were reinforced with 2ɸ12 upper and lower longitudinal bars and

1Ø8/150mm stirrups. Each footing had ten steel bolts each with 16mm diameter, to insure the fixation of the footing with the test bed. The vertical reinforcement of the reinforced walls was established with the footing reinforcement before pouring concrete to insure anchorage. The footings of the post-tension walls had groves with the alignment of the post-tension bars to allow constructing the bars and applying the post-tension force.

108

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The concrete mixture used for the footing consisted of ordinary Portland cement Type I, natural sand, crushed dolomite, water, and super plasticizer admixture with proportion of 1: 2: 3: 0.4 :0.02 respectively. An electrical vibrator was used to compact the poured concrete. The top surface of the concrete footing was roughened wising wire brush to provide a good bond with the concrete panel. The footing was wet cured for one week. All masonry panels (conventional and interlocking) were constructed on the reinforced concrete footing, after setting and leveling it in a horizontal position. The dimensions and reinforcement details of the footing are shown in Figure (5.2)

Figure (5.4): Dimensions and Reinforcement Details of the R.C. Footing 5.2.3. Masonry Panels The masonry panels were changed according to the studied parameters as block type, reinforcement configuration and post-tensioning.

5.2.3.1. Masonry Blocks As described before, three different concrete blocks were used in this research. All the properties of these concrete blocks were illustrated early in chapter (4).

109

Chapter 5

Construction and Testing of Masonry Shear Walls

Conventional masonry panels were laid in a running bond pattern by a professional mason, on the other hand the interlocking systems masonry panels were constructed by ordinary labors in its own pattern.

Some 10×10mm grooves are made by saw cutting in the face-shells of the un-grouted walls to allow the horizontal reinforcements. Figure (5.3) shows the grooves. The construction of wall panels are shown in Figure (5.4)

Figure (5.5): Face-Shells Grooves for Un-Grouted Walls

a) Conventional

b) Spar-lock

Figure (5.6): Construction of Wall Panels 5.2.3.2. Reinforcement All used horizontal and vertical reinforcement were high tensile deformed bars grade 400/600 in accordance with ECCS 203 (2007). The properties of the used reinforcement were described in Chapter (4).

110

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Construction and Testing of Masonry Shear Walls

Four vertical steel bars each with 16 mm diameter were fixed in the concrete footing for all reinforced walls as described before, the bars were applied every other cell according to the walls design. The spacing between vertical bars may slightly change because of the unique dimensions of each block system, as shown in Figure (5.1).

During the construction of grouted walls masonry panels, a 16 mm steel bar was placed every other course as a horizontal reinforcement according to the wall design, the horizontal reinforcing bars were anchored around the end vertical bars or bars by 180o hooks. 5.2.3.3. Post-Tensioning Bars All used bars were with 9.4 mm diameter with 100 mm threaded ends, having 1570 MPa ultimate tensile strength as described in Chapter (4). The post-tensioning forces were applied to bars with special lock nuts. 12mm diameter tubes were placed in the grouted wall W4 (A:RH:FG:PT) for the construction of un-bonded post-tensioning bars . 5.2.3.4. Grout Fixing the reinforced concrete top beam always was after pouring and curing of grout.

5.2.3.5. Sliding control Masonry panels of walls W8 (A:RH:UG:PT:Sl), and W9 (A:RH:PG:PT:Sl) were constructed on two galvanized steel sheets with 2/3 the area of mortar or grouting contact to concrete base, these sheets works as a sliding control which minimize the friction between masonry panel and the concrete footing, the shear friction properties enhancement due to these sheets was shown in the triplet test results in Chapter (4).

111

Chapter 5

Construction and Testing of Masonry Shear Walls

5.2.4. Reinforced Concrete Top Beam All reinforced concrete top beams having dimensions 150×200×1400 mm and were reinforced with 4ɸ12 longitudinal reinforcement bars and with

1Ø8/150mm stirrups, as shown in Figure (5.5). The top beams were fixed on the top of specimen using a strong mortar (Type M mortar). Each beam had four steel bolts at each side to be connected to the loading system. The concrete top beams for all reinforced walls were solid, but ones for post-tensioned walls must have holes to passing the bars throw it. The concrete mixture used for the top beam was similar to that used for reinforced concrete footing.

Figure (5.7): Dimensions and Reinforcement Details of the R.C. TopBeam 5.3. Test Setup The function of test setup was to load the tested wall by in-plane cyclic loading similar to that imposed on typical shear walls in real buildings subjected to seismic load. The test setup used in the current study is shown in Figures (5.6)

112

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and (5.7). As shown in these Figures, the test setup consisted mainly of three parts: 1) Reaction system, 2) Lateral loading system, and 3) Out-of-plane bracing system.

Figure (5.8): Schematic of Test Setup

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Figure (5.9): Test Setup with a Typical Wall in Position

5.3.1. Reaction System An adjustable multi-proposes space steel frame that accommodates different specimen sizes under different loading conditions was used to provide fixed support condition along the wall footing and to support the lateral loading device. The details of the steel frame are shown in Figure (5.8). The space steel frame consists basically of two steel frames of span 3.0 m. the spacing between the two frames is 2.0 m. Each steel frame consists of two broad flange I-beam (B.F.I.B No. 200) columns. The two columns connected together by two horizontal steel I-beams (I.P.E No.300) as shown in Figure (5.8). The lower beam served as testing bed to support and fix the test specimen. The two frames braced against out-ofplane movement using a bracing system as shown in Figure (5.8). All frame members were provided with uniformly distributed holes to provide a flexibility to change the beams positions and to enable the attachment of 114

Chapter 5

Construction and Testing of Masonry Shear Walls

the testing devices and the test specimens. The test specimen was fixed to the lower beam using the anchor bolts, which were embedded, in the reinforced concrete footing. Moreover, the lateral load capacity of the steel frame was estimated, it was found to be not more than 60 KN. So it was required to increase the capacity of the steel frame to meet the expected lateral load capacity of tested specimens. In-plane bracing was used to increase the lateral load capacity of the steel frame from 60 KN to 120 KN. The in-plane bracing consisted of four high strength wires with diameter of 22 mm with its accessories (such as four hooks and four stringers) and four channels fixed to the column's flange (B.F.I.B No. 200) with six bolts as shown in Figure (5.9).

115

Chapter 5

Construction and Testing of Masonry Shear Walls

Figure (5.10): Reaction Steel Frame

116

Chapter 5

Construction and Testing of Masonry Shear Walls

Figure (5.11): The Additional In-Plane Bracing 5.3.2. Lateral Load System The test specimen was displaced horizontally using two ways 450-kN hydraulic actuator with a maximum stroke of 150 mm. The actuator was driven in displacement control. The fixed end of the actuator was attached to the column of the reaction frame and the movable end was pin connected to a distributor steel plate. The lateral load transmitted from the hydraulic actuator to a distributor steel plate which consequently transmitted the load to two angles as shown in Figure (5.10). The lateral load transmitted from the two angles to the center of another two angles which fixed to the top beam through eight anchor bolts (four per side) which were embedded in the top beam.

Figure (5.12): Lateral Loading System.

117

Chapter 5

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5.3.3. Out-of-Plane Bracing System The test specimen was braced against out-of-plane distortion by a pair of rollers on both sides of the wall as shown in Figure (5.10). The rollers were fixed to two angles 100×10 mm running horizontally on both sides of the wall. The steel beams were fixed to the frame columns as shown in Figure (5.11).

Figure (5.13): Out-of-Plane Bracing System. 118

Chapter 5

Construction and Testing of Masonry Shear Walls

5.4. Instrumentation Different types of instrumentation were used to monitor the wall behavior. The following measurements were recorded during the wall testing. The actuator load was measured using 450 kN capacity two ways load cell attached to the movable end of the actuator as shown in Figure (5.6). The horizontal in-plane displacement at the top of the wall was measured relative to the reinforced concrete footing using linear variable transducer (LVDT) having a 50 mm stroke. The LVDT was set in horizontal position. The fixed base of the LVDT was attached to the stationary reference (fixed to the concrete base) and the end of movable chord was attached to the center of the last masonry course. The flexural deformations at the expected critical sections were measured using LVDTs or combination of LVDTs and dial gages. The shear deformations were measured following the panel drift angle approach, proposed by El-Shafie (1997), which reflects both shear and flexural deformations. In this approach, the panel drift angle was determined by measuring the deformation along the panel diagonal as well as the panel vertical edge. Sliding of the masonry panel over the reinforced concrete footing was measured using dial gage. Additionally, three load cells have been fabricated relying on the Wheatstone bridge electrical circuit. Figure (5.12) shows the circuit with four active electrical gages (resistances) build together a full bridge circuit, where the compressive cylindrical load cell is instrumented with gages R1 and R3 in the longitudinal direction and with gages R2 and R4 around the 119

Chapter 5

Construction and Testing of Masonry Shear Walls

circumference. The latter gages will go into tension because of the Poisson effect. This will cause the longitudinal strain to be magnified by a factor 2(1+υ) over that of a single gage. The load cells have been calibrated under axial compression, in the way of reporting the strain output with the accompanying machine load. A load-strain graph was drawn for every load cell. Figure (5.13) shows the fabricated load cells. Figures from (5.14) to (5.16) show the instrumentation locations for the tested walls.

Figure (5.14): Wheatstone Bridge Electrical Circuit

Figure (5.15): Fabricated Load Cells

120

Chapter 5

Construction and Testing of Masonry Shear Walls

Figure (5.16): Reinforced Walls W1, W2 and W3 Instrumentation

Figure (5.17): Post-Tensioned Walls W4 and W9 Instrumentation

121

Chapter 5

Construction and Testing of Masonry Shear Walls

Figure (5.18): Post-Tensioned Walls W5*, W5, W6, W7 and W8 Instrumentation 5.5. Data Acquisition System The main load cell and LVDTs were connected to conditioners which served to convert the change in the instrument condition, due to any physical change, into electrical signal which can be collected by the computer. The instruments reading were acquired, at a prescribed time rate, by the same computer used for controlling the load. The system does not support acquisitioning electrical strain gage readings, so the forces in the post-tensioned bars were collected manually after each cycle. And also the dial gage reading was recorded manually.

122

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5.6. Test Procedure All specimens were tested via controlled displacement at a rate of 60 µm/s, full displacement protocol was programmed for each amplitude increment aiming at strength and degradation assessment as shown in Figure (5.17). Measured response was examined as the testing progressed to discern Variations in strength, stiffness, and damage at each drift level. During the test, the specimen was visually inspected, location of cracks were noted and Photographed as testing proceeded.

Figure (5.19): Cyclic Displacement Protocol [Ingham et al (2006)]

123

CHAPTER (6) TEST RESULTS AND ANALYSIS OF WALL RESPONSE 6.1. Introduction In this chapter, results and observations of ten full scale masonry shear walls are reported. Test results are presented and discussed, the measured and calculated parameters that characterize the behavior of the tested walls are also summarized and studied in this chapter. The test results as observed by visual inspection during the test and as measured by instrumentation are presented in different forms such as crack patterns, lateral load-displacement/overall drift angle curves, deformations and strains at critical wall locations, and summary of major events. The following gives a brief description of different test indicators as presented in this chapter: 1. Crack patterns: Crack patterns show the cracks as detected by visual inspection during the test. On these diagrams, heavy lines indicate major cracks and hatched areas indicate spalling of masonry. 2. Lateral load – displacement/overall drift angle curves: The lateral loaddisplacement/overall drift angle response of the wall is presented in the form of x-y plot where the vertical axis represents the lateral load and the horizontal axis represents the displacement and the overall drift angle. On these plots a positive sign indicates push direction, and a negative sign indicates pull direction. The overall drift angle is defined as the in-plane displacement at the top of the wall divided by the wall height. The envelop curve is also plotted, the envelop is the curve along the peak points of the loops. 3. Flexural strain – overall drift angle (envelope) curve: Flexural strain measurements at the extreme fibers of critical sections are given in the 125

Chapter 6

Test Results and Analysis of Wall Response

form of x-y plots where the vertical axis shows the flexural strain and the horizontal axis gives the corresponding overall drift angle, only the peak points of the loading loops are presented in this curve. On these plots a positive sign represents tensile strain and a negative sign represents compressive strain. The strain in flexural reinforcing bars was interpolated using measured flexural strains of the masonry extreme fibers. This interpolation is based on the assumptions that: Plane sections remain plane after deformation and no relative movement between the reinforcing bars and the surrounding masonry exists (full bond without sliding). Though these assumption ignore any sliding and shear distortion, it is expected to yield a reasonable estimate of strain in the reinforcing bars before yielding where sliding can be ignored and the effect of shear forces in disturbing the linear distribution of the strain along the section is not significant (based on experimental results of full-scale walls, Shing (1993) demonstrated that up to yielding distortion of linear distribution of the strain along deep wall section is not significant). [El-Shafie (1997)]. The first yield in flexural reinforcement can be determined as the strain at 0.24%, as illustrated in Chapter (4). The first yield displacement (∆y) can be defined from idealized elasto-plastic response as the displacement at 75% of ultimate load [El-Shafie (1997), Priestley (2000) and Shedid et al. (2009)]. 4. Panel drift angle – overall drift angle (envelope) curve: As proposed by El-Shafie (1997), the panel drift angle was determined by measuring the deformation along the panel diagonal as well as the panel vertical edge from the following equation 𝐷𝑝𝑎 =

∆𝑝𝑎 ℎ

=

𝜉𝑝𝑎 𝐷 𝑙𝑤 ℎ

−

𝜉ℎ 𝑙𝑤

126

Chapter 6

Test Results and Analysis of Wall Response

In which 𝐷𝑝𝑎 is panel drift angle determined using the axial deformations measurements along the tension diagonal 𝜉𝑝𝑎 and along vertical edge 𝜉ℎ . h, lw and D are the wall height, length and diagonal. Panel drift angle results are presented in the form of x-y plots where the vertical axis shows panel drift angle and the horizontal axis shows the overall drift angle. On these graphs the positive sign indicates that the panel rotates in the push direction and the negative sign indicates that the panel rotates in the pull direction. 5. Sliding – overall drift angle (envelope) curve: Sliding of the masonry panels relative to the reinforced concrete base is reported as a sliding displacement and the maximum sliding is also reported as a percentage of the wall total displacement. Sliding results are presented in the form of xy plots where the vertical axis shows sliding and the horizontal axis shows the drift angle. The positive and negative signs on these plots indicate push and pull direction respectively. 6. Post-tensioned forces – overall drift angle curves: This measurement describes the post-tensioning force throughout the test. Post-tensioned forces results are presented in the form of x-y plots where the vertical axis shows post-tensioned force and the horizontal axis shows the overall drift angle. The positive and negative signs on these plots indicate push and pull direction respectively. The envelop curve of the loading loops is also plotted which made of the end point of each loop. 7. Failure mechanism: Based on the analysis of the test results, the wall failure mechanism is identified and shown in a simple sketch. 8. Summary of major events: A summary of the test major events (such as first crack, post-tensioned forces, ultimate lateral load, etc.) together with corresponding lateral displacement, overall drift angle and wall lateral load is presented in a tabular form.

127

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The nomenclature shown in Figure (6.1) has been used to describe the test results.

Figure (6.1): Wall Designation.

128

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6.2. Test Results for Wall W1 (C:RVH:FG) 6.2.1. General The conventional typically reinforced and grouted wall W1 was tested under increasing displacement cyclic load until the used LVDT reached its maximum displacement at 25.00 mm (1.56% drift). 6.2.2. Crack Patterns Crack patterns are shown in Figure (6.2). The first observed flexural crack initiated at the wall footing at 2.58 mm displacement (0.16% drift) in the push direction and 2.51 mm displacement (0.16% drift) in the pull direction. With further loading, the crack along the base started widen and cracks initiated and developed at the wall north and south toes. To the end of test, the wall north and south toes were locally crushed, and the wall footing crack was widen up and the wall rocked in-plane with observed sliding in both push and pull directions. 6.2.3. Lateral Load – Overall Drift Angle Curve The lateral load – overall drift angle is given in Figure (6.3). As shown in figure, the wall's initial stiffness started to decrease at 0.16% drift in the push and pull directions. This confirms the visual inspection where the first crack was detected at those drifts. It is clear that the wall reached its ultimate lateral load resistance of 76.40 kN at 0.68% drift (10.86 mm) in the push direction and 82.50 kN at 0.39% drift (6.23 mm) in the pull direction. At the end of test, (when the used LVDT reached its maximum displacement at 1.56% drift) the wall could resist 67.00 kN (87.70% of ultimate load) and 66.40 kN (80.50% of ultimate load) in push and pull directions.

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6.2.4. Flexural Strain – Overall Drift Angle Curves Flexural strain measurements at the extreme fibers of the base section are shown in Figures (6.4) and (6.5). The analysis of flexural strain measurements shows that the first yield in the flexural reinforcement occurred at 5.00 mm displacement in the push direction and 4.80 mm displacement in the pull direction. It should be noted that, the first yield displacements at 75% of ultimate load are 4.00 mm (0.25% drift) and 4.53 mm (0.28% drift) in push and pull directions respectively. The strain measurements clearly demonstrate that the wall developed a plastic hinge at its base where the tensile strains well exceeded the yield strain. The high compression strain 0.46% in the wall north toe and 0.47% in the wall south toe (which exceeded the design ultimate strain for masonry of 0.3%) caused crushing at both north and south toes. 6.2.5. Panel Drift Angle – Displacement Curves The panel drift angle measurements along the tension diagonal is shown in Figure (6.6). It is evident from Figure (6.6) that the panel drift angle measurements for the wall recorded very low values during test. This reflects the low contribution of the shear deformation to the wall lateral displacement. 6.2.6. Sliding Sliding of the masonry wall panel relative to the reinforced concrete footing is shown in Figure (6.7). The dial gage used to measure the sliding was removed after the crushing of wall toe took place (at displacement of 13.40 mm in push direction and 15.90 mm in pull direction. It is clear that up to 0.50% drift, the sliding of the wall was around 10% of the total drift after that the sliding contribution increased to exceed 20% of the total drift.

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6.2.7. Failure Mechanism The analysis of the results shows clearly that the specimen behaved mainly in a ductile rocking mode with sliding and failed by developing flexural cracks at the both wall north and south toes, Figure (6.8) shows failure mechanism of wall W1. 6.2.8. Summary of Major Events A summary of major events which happened during the test together with the corresponding displacement and lateral load is given in Table (6.1). Table (6.1): Summary of Major Events for Wall W1 (C:RVH:FG)

Event Description

Lateral Displacement (mm)

Overall Drift Angle (%)

Lateral Load (kN)

(%)*

Crack Initiation: Flexural crack between the wall panel and concrete footing 75% of Ultimate Load: Crack propagation and crushing at wall north and south toes

Push

2.58

0.16

60.10

78.66

Pull

2.51

0.16

67.65

82.00

Push

4.00

0.25

57.30

75.00

Pull

4.53

0.28

61.88

75.00

Ultimate Lateral Load Capacity:

Push

10.86

0.68

76.40

100

Pull

6.23

0.39

82.50

100

1.56

67.00

87.70

1.56

66.40

80.48

End of the Test: The test 25.00 Push was stopped because the used LVDT reached its 25.00 Pull maximum displacement. *Percentage of the ultimate load of same direction

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(a) At First Crack.

(b) At First Yield.

(c) At Ultimate Load.

(d) At Failure.

Figure (6.2): Wall W1 (C:RVH:FG): Crack Patterns. 132

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Figure (6.3): Wall W1 (C:RVH:FG): Lateral Load – Overall Drift Angle.

Figure (6.4): Wall W1 (C:RVH:FG): Flexural Strain at North Toe.

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Figure (6.5): Wall W1 (C:RVH:FG): Flexural Strain at South Toe.

Figure (6.6): Wall W1 (C:RVH:FG): Panel Drift Angle.

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Figure (6.7): Wall W1 (C:RVH:FG): Sliding.

Figure (6.8): Wall W1 (C:RVH:FG): Failure Mechanism. 135

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6.3. Test Results for Wall W2 (A:RVH:FG) 6.3.1. General The Azar typically reinforced and grouted wall W2 was tested under increasing displacement cyclic load until the used LVDT reached its maximum displacement at 25.00 mm (1.56% drift) and the wall lost 20% of its ultimate load. 6.3.2. Crack Patterns Crack patterns are shown in Figure (6.9). The first observed crack initiated at the wall footing at 3.00 mm displacement (0.19% drift) in the push direction and 2.83 mm displacement (0.18% drift) in the pull direction. With further loading, the crack along the base started widen and other cracks initiated and developed along the wall north and south toes. To the end of test, the wall footing crack was widen up while the wall rock in place and the toe crushing took place at both north and south toes. 6.3.3. Lateral Load – Overall Drift Angle Curve The lateral load – overall drift angle curve is given in Figure (6.10). As shown in Figure (6.10), the wall's initial stiffness started to decrease at 0.20% overall drift angle in the both. This confirms the visual inspection where the first crack was detected at those drifts. It is clear that the wall reached its ultimate lateral load resistance of 79.35 kN at 0.42% drift (6.64 mm) in the push direction and 80.37 kN at 0.55% drift (8.72 mm) in the pull direction. 20% degradation in wall’s lateral load capacity took place at 1.25% and 1.56% drifts in the push and pull directions. 6.3.4. Flexural Strain – Displacement Curves Flexural strain measurements at the extreme fibers of the base section are shown in Figures (6.11) and (6.12). The analysis of flexural strain measurements shows that the first yield in the flexural reinforcement 136

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occurred at 7.50 mm displacement in the push direction and 6.30 mm displacement in the pull direction. It should be noted that, the first yield displacements at 75% of ultimate load are 8.00 mm (0.50% drift) and 7.68 mm (0.48 drift) in push and pull directions respectively. The strain measurements clearly demonstrate that the wall developed a plastic hinge at its base where the tensile strains well exceeded the yield strain. The high compressive strain 0.42% at wall north toe and 0.72% at wall south toe caused crushing at both wall north and south toes. 6.3.5. Panel Drift Angle – Displacement Curves The panel drift angle measurements along the tension diagonal is shown in Figure (6.13). It is evident from Figure (6.13) that the panel drift angle measurements for the wall recorded very low values during test. This reflects the low contribution of the shear deformation to the wall lateral displacement. 6.3.6. Sliding Sliding of the masonry wall panel relative to the reinforced concrete footing is shown in Figure (6.14). It is clear that the sliding contribution of the wall gradually increased with the lateral drift angle recording 3.00 mm at the end of test 1.2% drift angle (19.00 mm). 6.3.7. Failure Mechanism The analysis of the results shows clearly that the specimen behaved mainly in a ductile rocking mode and failed by developing flexural cracks at the both north and south toes, Figure (6.15) shows failure mechanism of wall W2. 6.3.8. Summary of Major Events A summary of major events which happened during the test together with the corresponding displacement and lateral load is given in Table (6.2) 137

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Table (6.2): Summary of Major Events for Wall W2 (A:RVH:FG) Event Description

Lateral Displacement (mm)

Overall Drift Angle (%)

Lateral Load (kN)

(%)*

Crack Initiation: Flexural crack between the wall and concrete base 75% of Ultimate Load: Crack propagation and crushing at wall north and south toes

Push

3.00

0.19

46.07

58.06

Pull

2.83

0.18

43.93

54.66

Push

8.00

0.50

59.51

75.00

Pull

7.68

0.48

60.28

75.00

Ultimate Lateral Load Capacity:

Push

6.64

0.42

79.35

100

Pull

8.72

0.55

80.37

100

1.25

63.50

80.03

1.56

64.30

80.00

End of the Test: The test 20.00 Push was stopped because the used LVDT reached its maximum displacement and 25.00 the wall lost 20% of its Pull ultimate load. *Percentage of the ultimate load of same direction

(a) At first crack.

(b) At first yield.

(c) At ultimate load.

(d) At failure.

Figure (6.9): Wall W2 (A:RVH:FG): Crack Patterns. 138

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Figure (6.10): Wall W2 (A:RVH:FG): Lateral Load –Overall Drift Angle.

Figure (6.11): Wall W2 (A:RVH:FG): Flexural Strain at North Toe.

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Figure (6.12): Wall W2 (A:RVH:FG): Flexural Strain at South Toe.

Figure (6.13): Wall W2 (A:RVH:FG): Panel Drift Angle.

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Figure (6.14): Wall W2 (A:RVH:FG): Sliding.

Figure (6.15): Wall W2 (A:RVH:FG): Failure Mechanism 141

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6.4. Test Results for Wall W3 (S:RV:FG) 6.4.1. General The Spar-lock conventionally reinforced and grouted wall W3 was tested under increasing displacement cyclic load until the used LVDT reached its maximum displacement at 25.00 mm (1.56% drift). 6.4.2. Crack Patterns Crack patterns are shown in Figure (6.16). The shear cracks were observed at many blocks at 2.00 mm displacement (0.13% drift) in the push direction and 2.27 mm displacement (0.14% drift) in the pull direction. With further loading separating vertical cracks along wall cells were initiated. To the end of test, the vertical cracks between wall cells and shear cracks in blocks were widening up, and the wall rocked in-plane with observed sliding in both directions. 6.4.3. Lateral Load – Overall Drift Angle and Displacement Curves The lateral load – overall drift angle is given in Figure (6.17). It is clear that the wall reached its ultimate lateral load resistance of 22.59 kN at 1.16% drift (18.51 mm) in the push direction and 14.82 kN at 1.07% drift (17.18 mm) in the pull direction. Till the end of test at 1.56% drift the wall could resist 98.45% and 92.78% of its ultimate lateral load capacity. 6.4.4. Flexural Strain – Displacement Curves Flexural strain measurements at the extreme fibers of the base section are shown in Figures (6.18) and (6.19). The analysis of flexural strain measurements shows that the flexural reinforcement reach first yield at 10.20 mm displacement in the push direction and 13.00 mm displacement in the pull direction. It should be notes that, the first yield displacements at 75% of ultimate lateral load are 9.50 mm (0.59% drift) and 14.00 mm

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(0.88% drift) in push and pull directions respectively. The compressive strains did not exceed 0.17%, this low strain didn’t cause toe crushing. 6.4.5. Panel Drift Angle – Displacement Curves The panel drift angle measurements along the tension diagonal is shown in Figure (6.20). It is evident from Figure (6.20) that the panel drift angle measurements for the wall recorded high values during test. This reflects the high contribution of the shear deformation to the wall lateral displacement, and the wall acted mainly in shear distortion behavior. 6.4.6. Sliding Sliding of the masonry wall panel relative to the reinforced concrete footing is shown in Figure (6.21). It is clear that up to the end of the test the sliding of the wall did not exceed 15% of the total drift, which reflect low contribution of the sliding to the wall lateral displacement. 6.4.7. Failure Mechanism The analysis of the results shows clearly that the specimen behaved as separated cells, the wall distortion was the main wall deformation, Figure (6.22) shows failure mechanism of wall W3. 6.4.8. Summary of Major Events A summary of major events which happened during the test together with the corresponding displacement and lateral load is given in Table (6.3)

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Table (6.3): Summary of Major Events for Wall W3 (S:RV:FG)

Event Description

Lateral Displacement (mm)

Overall Drift Angle (%)

Lateral Load (kN)

(%)*

Crack Initiation: Shear cracks at many blocks

Push

2.00

0.13

5.42

23.99

Pull

2.27

0.14

2.80

18.89

75% of Ultimate Load: Vertical cracks between wall cells

Push

9.50

0.59

16.94

75.00

Pull

14.00

0.88

11.12

75.00

Ultimate Lateral Load Capacity:

Push

18.51

1.16

22.59

100

Pull

17.18

1.07

14.82

100

1.56

22.24

98.45

1.42

13.75

92.78

End of the Test: The test 25.00 Push was stopped because of excessive increase in the 22.71 vertical crack opening Pull between cells. *Percentage of the ultimate load of same direction

(a) At first crack.

(b) Vertical crack separating cells

(c) At ultimate load

(d) At failure.

Figure (6.16): Wall W3 (S:RV:FG): Crack Patterns.

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Figure (6.17): Wall W3 (S:RV:FG): Lateral Load – Overall Drift Angle.

Figure (6.18): Wall W3 (S:RV:FG): Flexural Strain at North Toe.

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Figure (6.19): Wall W3 (S:RV:FG): Flexural Strain at South Toe.

Figure (6.20): Wall W3 (S:RV:FG): Panel Drift Angle.

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Figure (6.21): Wall W3 (S:RV:FG): Sliding.

Figure (6.22): Wall W3 (S:RV:FG): Failure Mechanism. 147

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6.5. Test Results for Wall W4 (A:RH:FG:PT) 6.5.1. General The post-tensioned grouted wall W4 was tested under increasing displacement cyclic load until the used LVDT reached its maximum displacement at 25.00 mm (1.56% drift). 6.5.2. Crack Patterns Crack patterns are shown in Figure (6.23). The first crack initiated at the wall footing at 9.65 mm displacement (0.60% drift angle) in the push direction and 9.90 mm displacement (0.62% overall drift angle) in the pull direction. With further loading the crack was developed along the wall footing due to wall rotation. To the end of test, the base crack was widened up while the wall rocked in-plane and minor splitting of face shell at wall south toe took place. 6.5.3. Lateral Load – Overall Drift Angle Curve The lateral load – overall drift angle curve is given in Figure (6.24). As shown in Figure (6.24), the wall reached its ultimate lateral load resistance of 83.60 kN at 1.47% drift (23.58 mm) in the push direction and 84.60 kN at 1.28% drift (20.46 mm) in the pull direction. To the end of test at 1.56% drift the wall could resist 97.85% and 81.44% of its ultimate load capacity in push and pull directions respectively. 6.5.4. Flexural Strain – Displacement Curves Flexural strain measurements at the extreme fibers of the base section are shown in Figures (6.25) and (6.26). The high values of tensile strains in both directions reflects the opening crack along the wall footing while the wall panel rock in-plane.

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6.5.5. Panel Drift Angle – Displacement Curves The panel drift angle measurements along the tension diagonal is shown in Figure (6.27). It is evident from Figure (6.27) that the panel drift angle measurements for the wall recorded very low values during test. This reflects the low contribution of the shear deformation to the wall lateral displacement. 6.5.6. Sliding Sliding of the masonry wall panel relative to the reinforced concrete footing is shown in Figure (6.28). The dial gage at the wall footing recorded very low values of sliding during the test, the sliding contribution did not exceed 0.8 mm (3.50% of overall drift). This reflects the high friction caused by post-tensioning stress. 6.5.7. Post-Tension Forces – Drift Angle Curves The post-tension forces, for the used three bars, are shown in Figures (6.29) to (6.32). The initial post-tension force in every bar was 50 kN as described before in the pretest design in Chapter (3). It is clear from Figure (6.30) that minimal changes in post-tension force of the middle bar with the wall drift in both directions. On the other hand, Figure (6.29) and Figure (6.31) shows significant changes in post-tension forces of outer bars, the bars reached yield stress at 0.55% and 0.45% drift for push and pull directions respectively. Generally, the total post-tension force increases gradually with the drift angle in both directions, as shown in Figure (6.32). 6.5.8. Failure Mechanism The analysis of the results shows clearly that the specimen behaved mainly in a ductile rocking mode and failed by developing flexural cracks at the both ends, Figure (6.33) shows failure mechanism of wall W4.

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6.5.9. Summary of Major Events A summary of major events which happened during the test together with the corresponding displacement and lateral load is given in Table (6.4) Table (6.4): Summary of Major Events for Wall W4 (A:RH:FG:PT) Lateral Displacement (mm)

Overall Drift Angle (%)

Push

8.80

0.55

Pull

7.20

Crack Initiation: Flexural crack between the wall and concrete base

Push

Event Description

Total PostTension Force (kN)

Lateral Load (kN)

(%)*

175.00

59.50

71.17

0.45

194.00

60.00

70.92

9.65

0.60

172.00

66.39

79.41

Pull

9.90

0.62

195.00

65.55

77.48

Ultimate Lateral Load Capacity:

Push

23.58

1.47

189.70

83.60

100

Pull

20.46

1.28

214.00

84.60

100

End of the Test: The test was stopped because the used LVDT reached its maximum displacement.

Push

25.00

1.56

188.30

81.80

97.85

25.00

1.56

224.40

68.90

81.44

First Yield of Bar:

Pull

*Percentage of the ultimate load of same direction

(a) At first yield.

(b) At ultimate load.

(c) At failure.

Figure (6.23): Wall W4 (A:RH:FG:PT): Crack Patterns. 150

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Figure (6.24): Wall W4 (A:RH:FG:PT): Lateral Load – Overall Drift Angle.

Figure (6.25): Wall W4 (A:RH:FG:PT): Flexural Strain at North Toe.

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Figure (6.26): Wall W4 (A:RH:FG:PT): Flexural Strain at South Toe.

Figure (6.27): Wall W4 (A:RH:FG:PT): Panel Drift Angle.

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Figure (6.28): Wall W4 (A:RH:FG:PT): Sliding.

Figure (6.29): Wall W4 (A:RH:FG:PT): North Bar Post-Tension Force.

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Figure (6.30): Wall W4 (A:RH:FG:PT): Middle Bar Post-Tension. Force

Figure (6.31): Wall W4 (A:RH:FG:PT): South Bar Post-Tension Force.

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Figure (6.32): Wall W4 (A:RH:FG:PT): Total Post-Tension Force.

Figure (6.33): Wall W4 (A:RH:FG:PT): Failure Mechanism 155

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6.6. Test Results for Wall W5* (A:RH*:UG:PT) 6.6.1. General The un-grouted post-tension wall W5* was constructed with inadequate horizontal reinforcement as described before in Chapter (3). The wall was tested under increasing displacement cyclic load up to 7.50 mm (0.47% drift) in push direction, and 8.90 mm (0.56% drift) in pull direction. The test was stopped because magnificent reduction of lateral load took place due to shear failure. 6.6.2. Crack Pattern Crack patterns are shown in Figure (6.34). Shear cracks initiated at 4.26 mm displacement (0.27% drift) in the push direction and 2.86 mm displacement (0.18% drift) in the pull direction. At the second loop in pull direction at 0.26% drift, the upper south half-block crushed causing a significant loss in its post-tension bar. The crushing of the block was believed because the bad quality control in manufacturing concrete blocks especially in dry-stacked blocks, defects in blocks shape with the exist of post-tension can easily generate high value of stress concentration, so these defects can't be accepted in manufacturing dry-stacked concrete blocks. With further loading shear crack initiated and developed along the wall and the lateral load significantly dropped. To the end of test, the wall shear cracks were widened up and the wall failed in shear mode because of wrong horizontal reinforcement, so this wall will be replaced with W5 (A:RH:UG:PT). 6.6.3. Lateral Load – Overall Drift Angle and Displacement Curves The lateral load – overall drift angle is given in Figure (6.35). It is clear that the wall lost its initial stiffness when shear cracks took place at the ultimate lateral load. The wall reached its ultimate lateral load resistance 156

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of 21.70 kN at 0.27% drift (4.26 mm) in the push direction and 18.10 kN at 0.18% drift (2.86 mm) in the pull direction. 20% degradation of lateral load took place at 0.47% and 0.56% drift in push and pull directions respectively. 6.6.4. Flexural Strain – Displacement Curves Flexural strain measurements at the extreme fibers of the base section are shown in Figures (6.36) and (6.37). Tension and compression strains in both directions were minimal, which reflects the shear behavior of the wall. 6.6.5. Panel Drift Angle – Displacement Curves The panel drift angle measurements along the tension diagonal is shown in Figure (6.38). It is evident from Figure (6.38) that the panel drift angle measurements for the wall recorded high values during test. This reflects the high contribution of the shear deformation to the wall lateral displacement, and the wall acted mainly in shear distortion behavior. 6.6.6. Sliding Sliding of the masonry wall panel relative to the reinforced concrete footing is shown in Figure (6.39). It is clear that the high friction at wall footing due to post-tension force suppressed the wall sliding. So to the end of test the wall sliding didn't exceed 2.8% of the total drift. 6.6.7. Post-Tension Forces - Displacement Curves The post-tensioned forces, for the used two bars, are shown in Figures (6.40) to (6.42). The initial post-tension force in every bar was 60 kN as described before in Chapter (3). It is clear from Figure (6.41) that the posttension force for the south bar had magnificent drop after the crushing of the upper block at 0.26% overall drift angle. None of both bars reached yield stress because of the brittle failure of wall at low drifts.

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6.6.8. Failure Mechanism The analysis of the results shows clearly that the specimen behaved mainly in a brittle shear mode and failed by developing shear cracks, Figure (6.43) shows failure mechanism of wall W5*. 6.6.9. Summary of Major Events A summary of major events which happened during the test together with the corresponding displacement and lateral load is given in Table (6.5) Table (6.5): Summary of Major Events for Wall W5* (A:RH*:UG:PT)

Event Description

Lateral Displacement (mm)

Overall Drift Angle (%)

Total PostTension Force (kN)

Lateral Load (kN)

(%)*

Ultimate Lateral Load Capacity: Shear cracks

Push

4.26

0.27

115.80

21.70

100

initiated at many blocks Crushing of Concrete Block: The upper south half-block was crushed causes a drop in the post-tension force

Pull

2.86

0.18

118.30

18.10

100

Push

----

----

----

----

----

Pull

4.20

0.26

96.19

17.60

97.24

Push

7.50

0.47

75.00

18.00

82.95

Pull

8.90

0.56

60.00

14.00

79.55

End of the Test: The test was stopped because 20% degradation of load took place due to shear failure

*Percentage of the ultimate load of same direction

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(a) At first crack.

(b) Drop in post-tension force.

(c) Cracks Propagation.

(d) At failure.

Figure (6.34): Wall W5* (A:RH*:UG:PT): Crack Patterns

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Figure (6.35): Wall W5* (A:RH*:UG:PT): Lateral Load – Overall Drift Angle.

Figure (6.36): Wall W5* (A:RH*:UG:PT): Flexural Strain at North Toe.

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Figure (6.37): Wall W5* (A:RH*:UG:PT): Flexural Strain at South Toe.

Figure (6.38): Wall W5* (A:RH*:UG:PT): Panel Drift Angle.

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Figure (6.39): Wall W5* (A:RH*:UG:PT): Sliding.

Figure (6.40): Wall W5* (A:RH*:UG:PT): North Bar Post-Tension Force.

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Figure (6.41): Wall W5* (A:RH*:UG:PT): South Bar Post-Tension Force.

Figure (6.42): Wall W5* (A:RH*:UG:PT): Total Post-Tension Force.

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Figure (6.43): Wall W5* (A:RH*:UG:PT): Failure Mechanism.

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6.7. Test Results for Wall W5 (A:RH:UG:PT) 6.7.1. General The Azar un-grouted post-tensioned wall W5 was tested under increasing displacement cyclic load up to 17.00 mm (1.06% drift) in push direction and 13.20 mm (0.83% drift) in pull direction. The test was stopped after 20% degradation of lateral load took place. 6.7.2. Crack Pattern Crack patterns are shown in Figure (6.44). With cyclic lateral loading, the joints of un-grouted dry-stacked masonry opened and closed each loading cycle in addition to sliding of wall courses along each other. These repeated movements caused a damage in the thin face-shells. The first observed crack initiated at 9.50 mm displacement (0.59% drift) in the push direction and 10.97 mm displacement (0.69% drift) in the pull direction. The crack initiated at the face shell of second course’s block. With further loading crack initiated and developed between the first two courses, then the half-block of second course was crushed due to sliding of courses. To the end of test, the second course was crushed and the wall failed with minimal sliding relative to the base. 6.7.3. Lateral Load – Overall Drift Angle Curve The lateral load – overall drift angle curve is given in Figure (6.45). As shown in figure, the wall loses its initial stiffness from the first loop even before observed cracking. This clarify that the dry-stacked joints opening could delay the flexural cracking. It is clear that the wall reached its ultimate lateral load resistance of 51.90 kN at 0.76% drift (12.17 mm) in the push direction and 46.70 kN at 0.69% drift (10.97 mm) in the pull direction, then the lateral load reduced rapidly because of the demolishing

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of second course blocks and reach 20% degradation at 1.06% and 0.83 drifts in the push and pull directions respectively. 6.7.4. Flexural Strain – Displacement Curves Flexural strain measurements at the extreme fibers of the base section are shown in Figures (6.46) and (6.47). It is evident that the minimal strains at extreme fibers, that reflects that the opening joints of dry-stacked courses away from the wall footing. 6.7.5. Panel Drift Angle – Displacement Curve The panel drift angle measurements along the tension diagonal is shown in Figure (6.48). It is evident from Figure (6.48) that the panel drift angle measurements for the wall recorded high values during test. This reflects the LVDTs collect the courses movement. 6.7.6. Sliding Sliding of the masonry wall panel relative to the reinforced concrete footing is shown in Figure (6.49). It is clear that the high friction at wall footing due to post-tension force and the existence of mortar suppressed the wall sliding relative to the concrete base. So to the end of test the wall sliding didn't exceed 2.0% of the total drift. Most sliding occurred above the first course. 6.7.7. Post-Tension Forces - Displacement Curves The post-tensioned forces, for the used two bars, are shown in Figures (6.50) to (6.52). The initial post-tension force in every bar was 60 kN, as described before in Chapter (3). It is clear that the bars reached yield stress at 0.59% and 0.30% drift for push and pull directions respectively. The post-tension force decreases in both bars at 0.70% drift in both directions, that believed because the post-tension losses due to second course crushing. 166

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6.7.8. Failure Mechanism The analysis of the results shows clearly that the specimen behaved mainly in a brittle shear mode and failed by developing shear cracks, Figure (6.53) shows failure mechanism of wall W5. 6.7.9. Summary of Major Events A summary of major events which happened during the test together with the corresponding displacement and lateral load is given in Table (6.6) Table (6.6): Summary of Major Events for Wall W5 (A:RH:UG:PT) Lateral Displacement (mm)

Overall Drift Angle (%)

Push

9.44

0.59

Pull

4.80

Crack Initiation: Flexural shear crack at toe of second course of the wall

Push

Ultimate Lateral Load Capacity: Crushing of face-shells of second course End of the Test: The test was stopped because of 20% degradation of load took place

Event Description

Total PostTension Force (kN)

Lateral Load (kN)

(%)*

102.90

47.70

91.91

0.30

112.50

40.00

85.65

9.50

0.59

120.90

47.70

91.91

Pull

10.97

0.69

108.70

46.70

100

Push

12.17

0.76

104.94

51.90

100

Pull

10.97

0.69

108.70

46.70

100

Push

17.00

1.06

78.90

41.54

80.04

Pull

13.20

0.83

100.00

39.98

85.61

Yield of Bars:

*Percentage of the ultimate load of same direction

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(a) At first loop.

(b) At first crack.

(c) At ultimate load.

(d) At failure.

(e) At Failure.

(f) At Failure.

Figure (6.44): Wall W5 (A:RH:UG:PT): Crack Patterns. 168

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Figure (6.45): Wall W5 (A:RH:UG:PT): Lateral Load – Overall Drift Angle.

Figure (6.46): Wall W5 (A:RH:UG:PT): Flexural Strain at North Toe.

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Figure (6.47): Wall W5 (A:RH:UG:PT): Flexural Strain at South Toe.

Figure (6.48): Wall W5 (A:RH:UG:PT): Panel Drift Angle.

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Figure (6.49): Wall W5 (A:RH:UG:PT): Sliding.

Figure (6.50): Wall W5 (A:RH:UG:PT): North Bar Post-Tension Force.

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Figure (6.51): Wall W5 (A:RH:UG:PT): South Bar Post-Tension Force.

Figure (6.52): Wall W5 (A:RH:UG:PT): Total Post-Tension Force.

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Figure (6.53): Wall W5 (A:RH:UG:PT): Failure Mechanism.

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6.8. Test Results for Wall W6 (C:RH:UG:PT) 6.8.1. General The conventional un-grouted post-tensioned wall W6 was tested under increasing displacement cyclic load up to 18.90 mm (1.18% drift) in push direction and 18.63 mm (1.16% drift) in pull direction. The test was stopped after 20% degradation of lateral load took place in push direction and sudden collapse of wall. 6.8.2. Crack Pattern Crack patterns are shown in Figure (6.54). The first crack initiated in bed joint between the first and second courses at 4.89 mm displacement (0.31% drift) in the push direction and 4.75 mm displacement (0.30% drift) in the pull direction. With further loading flexural cracks initiated and developed at both wall ends along the wall footing. To the end of test, all wall cracks widened up and the wall rocked in-plane almost, north and south toes crushing took place at 0.8% drift, then the wall’s first course was demolished. 6.8.3. Lateral Load – Overall Drift Angle Curve The lateral load – overall drift angle is given in Figure (6.55). It is clear that the wall reached its ultimate lateral load resistance of 50.80 kN at 0.77% drift (12.35 mm) in the push direction and 52.60 kN at 0.95% drift (15.25 mm) in the pull direction. The brittle failure took place at 1.18% drift in push direction and 1.16% drift in pull direction, with 20% degradation of lateral load in push direction and minimal decrease in the pull direction. 6.8.4. Flexural Strain – Displacement Curves Flexural strain measurements at the extreme fibers of the base section are shown in Figures (6.56) and (6.57). It is evident that the high compressive 174

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strain of 0.84% in the push direction and 0.60% in the pull direction caused crushing at both north and south toes. 6.8.5. Panel Drift Angle – Displacement Curves The panel drift angle measurements along the tension diagonal is shown in Figure (6.58). It is evident from Figure (6.58) that the panel drift angle measurements for the wall recorded low values during test. This reflects the low contribution of shear deformations to the wall lateral displacement. 6.8.6. Sliding Sliding of the masonry wall panel relative to the reinforced concrete footing is shown in Figure (6.59). It is clear that the minimal wall sliding which didn't exceed 1.90% of the total drift. 6.8.7. Post-Tensioned Forces - Displacement Curves The post-tensioned forces, for the used two bars, are shown in Figures (6.60) to (6.62). The initial post-tension force in every bar was 60 kN as described before Chapter (3). It is clear that the post-tension force in the bars had significant changes due to cyclic loading, the load increased when the bar in the tension zone and decreased when otherwise. The bars reached yield stress at 0.30% drift in both directions (almost at the first crack of the wall), after that the total post-tension force, as shown in Figure (6.62), started to decrease in both directions, that believed because the posttension losses due to wall cracks and crushing at north and south toes. 6.8.8. Failure Mechanism The analysis of the results shows clearly that the specimen behaved mainly in a ductile rocking mode and failed by developing flexural cracks at the both toes, Figure (6.63) shows failure mechanism of wall W6.

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6.8.9. Summary of Major Events A summary of major events which happened during the test together with the corresponding displacement and lateral load is given in Table (6.7) Table (6.7): Summary of Major Events for Wall W6 (C:RH:UG:PT) Overall Drift Angle (%)

Total PostTension Force (kN)

(kN)

(%)*

Push

4.89

0.31

133.80

43.16

84.96

Pull

4.75

0.30

142.00

41.10

78.14

Push

12.35

0.77

143.20

50.80

100

Pull

15.25

0.95

128.30

52.60

100

Push

18.90

1.18

121.50

40.64

80.00

Pull

18.63

1.16

113.30

52.05

98.95

Event Description Crack Initiation and Yield of Bars: Crack between first and second courses Ultimate Lateral Load Capacity: End of the Test: The test was stopped because of crushing of first course

Lateral Load

Lateral Displacement (mm)

*Percentage of the ultimate load of same direction

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(a) first crack at south toe

(b) Crack propagation at south toe

(c) At ultimate load at south toe

(d) At ultimate load at north toe

(e) At Failure

(f) After Failure

Figure (6.54): Wall W6 (C:RH:UG:PT): Crack Patterns. 177

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Figure (6.55): Wall W6 (C:RH:UG:PT): Lateral Load – Overall Drift Angle.

Figure (6.56): Wall W6 (C:RH:UG:PT): Flexural Strain at North Toe.

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Figure (6.57): Wall W6 (C:RH:UG:PT): Flexural Strain at South Toe.

Figure (6.58): Wall W6 (C:RH:UG:PT): Panel Drift Angle.

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Figure (6.59): Wall W6 (C:RH:UG:PT): Sliding.

Figure (6.60): Wall W6 (C:RH:UG:PT): North Bar Post-Tension Force.

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Figure (6.61): Wall W6 (C:RH:UG:PT): South Bar Post-Tension Force.

Figure (6.62): Wall W6 (C:RH:UG:PT): Total Post-Tension Force.

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Figure (6.63): Wall W6 (C:RH:UG:PT): Failure Mechanism.

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6.9. Test Results for Wall W7 (S:RH:UG:PT) 6.9.1. General The Spar-lock un-grouted post-tensioned wall W7 was tested under increasing displacement cyclic load up to 19.50 mm (1.22% drift) in push direction and 20.36 mm (1.27% drift) in pull direction. The test was stopped after 20% degradation of lateral load took place in due to shear failure. 6.9.2. Crack Pattern Crack patterns are shown in Figure (6.64). The first shear cracks initiated at many blocks at 8.30 mm displacement (0.52% drift) in the push direction and 8.00 mm displacement (0.50% drift) in the pull direction. With further loading shear cracks developed at cells of both ends due to absence of shear reinforcement at this parts. To the end of test, the shear cracks widened up and the wall rocked in-plane. 6.9.3. Lateral Load – Overall Drift Angle Curve The lateral load – overall drift angle is given in Figure (6.65). As shown in Figure (6.65), the wall kept its initial stiffness almost up to ultimate load then the wall's stiffness decreased. This confirms the visual inspection where the first cracks were detected at 0.52% overall drift angle in the push direction 0.50% overall drift angle in the pull direction. It is clear that the wall reached them ultimate lateral load resistances of 26.64 kN at 0.62% drift (9.84 mm) in the push direction and 24.90 kN at 0.50% drift (8.00 mm) in the pull direction. 20% degradation in lateral load took place at 1.22% and 1.27 drifts in push and pull directions respectively. It was believed Spar-lock walls can be more ductile if it allow the inclusion of sufficient horizontal reinforcement.

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6.9.4. Flexural Strain – Displacement Curves Flexural strain measurements at the extreme fibers of the base section are shown in Figures (6.66) and (6.67). Tension and compression strains in both directions were minimal, which reflect the shear behavior of the wall. 6.9.5. Panel Drift Angle – Displacement Curves The panel drift angle measurements along the tension diagonal is shown in Figure (6.68). It is evident from Figure (6.68) that the panel drift angle measurements for the wall recorded high values during test. This reflects the high contribution of the shear deformation to the wall lateral displacement, and the wall acted mainly in shear distortion behavior. 6.9.6. Sliding Sliding of the masonry wall panel relative to the reinforced concrete footing is shown in Figure (6.69). It is clear that the minimal wall sliding which didn't exceed 2.20% of the total drift. 6.9.7. Post-Tensioned Forces - Displacement Curves The post-tensioned forces, for the used two bars, are shown in Figures (6.70) to (6.72). The initial post-tension force in every bar was reduced to 45 kN because of the lower compressive strength of Spar-lock prisms, as described before Chapter (3). It is clear that the post-tension forces in both bars changed normally with the cyclic loading until initiation of shear cracks (0.52% and 0.50% in the push and pull direction respectively). After the shear cracks development, a remarkable losses in the post-tension forces took place, especially for the south bar because of great cracks at its underneath blocks, as shown in the crack pattern Figure (6.64).

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6.9.8. Failure Mechanism The analysis of the results shows clearly that the specimen behaved as separated cells, the wall distortion was the main wall deformation, Figure (6.73) shows failure mechanism of wall W7. 6.9.9. Summary of Major Events A summary of major events which happened during the test together with the corresponding displacement and lateral load is given in Table (6.8),

Table (6.8): Summary of Major Events for Wall W7 (S:RH:UG:PT)

Crack Initiation: Flexural crack at the wall footing Ultimate Lateral Load Capacity: End of the Test: The test was stopped because of 20% degradation of load took place due to local shear failure

Lateral Load

Lateral Displacement (mm)

Overall Drift Angle (%)

Total PostTension Force (kN)

(kN)

(%)*

Push

8.30

0.52

73.30

23.80

89.31

Pull

8.00

0.50

88.55

24.90

100

Push

9.84

0.62

66.58

26.65

100

Pull

8.00

0.50

88.55

24.90

100

Push

19.50

1.22

36.25

21.32

80.00

Pull

20.36

1.27

48.17

20.90

83.94

Event Description

*Percentage of the ultimate load of same direction

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(a) At first crack.

(b) Crack propagation.

(d) At Failure.

Figure (6.64): Wall W7 (S:RH:UG:PT): Crack Patterns.

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Figure (6.65): Wall W7 (S:RH:UG:PT): Lateral Load – Overall Drift Angle.

Figure (6.66): Wall W7 (S:RH:UG:PT): Flexural Strain at North Toe.

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Figure (6.67): Wall W7 (S:RH:UG:PT): Flexural Strain at South Toe.

Figure (6.68): Wall W7 (S:RH:UG:PT): Panel Drift Angle.

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Figure (6.69): Wall W7 (S:RH:UG:PT): Sliding.

Figure (6.70): Wall W7 (S:RH:UG:PT): North Bar Post-Tension Force.

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Figure (6.71): Wall W7 (S:RH:UG:PT): South Bar Post-Tension Force.

Figure (6.72): Wall W7 (S:RH:UG:PT): Total Bar Post-Tension Force.

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Figure (6.73): Wall W7 (S:RH:UG:PT): Failure Mechanism.

191

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6.10.Test Results for Wall W8 (A:RH:UG:PT:Sl) 6.10.1. General The un-grouted wall with sliding control W8 was tested under increasing displacement cyclic load up to 15.65 mm (0.98% drift) in push direction and 13.90 mm (0.87% drift) in pull direction. The test was stopped after 20% degradation of lateral load took place. 6.10.2. Crack Pattern Crack patterns are shown in Figure (6.74). The first observed crack initiated at the wall footing at 5.30 mm displacement (0.64% drift) in the push direction and 4.70 mm displacement (0.64% drift) in the pull direction, while the dry-stacked joints were opened and closed with cyclic loading. With further loading crack initiated and developed at many blocks, it was believed, the thin face-shells of un-grouted blocks damaged while the wall sliding. To the end of test, all wall cracks were widening up and face-shells of first course were crushed. 6.10.3. Lateral Load – Overall Drift Angle Curve The lateral load – overall drift angle is given in Figure (6.75). It is clear that the wall reached its ultimate lateral load resistance of 50.07 kN at 0.64% drift (10.21 mm) in the push direction and 48.60 kN at 0.76% drift (12.14 mm) in the pull direction. The wall lost its resistance rapidly because of excessive cracking, and the lateral load decreased by 20% at 0.98% and 0.87 drifts in push and pull directions. 6.10.4. Flexural Strain – Displacement Curves Flexural strain measurements at the extreme fibers of the base section are shown in Figures (6.76) and (6.77). It is evident that the high compressive strain of 0.5% caused crushing at wall north and south toes.

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6.10.5. Panel Drift Angle – Displacement Curve The panel drift angle measurements along the tension diagonal is shown in Figure (6.78). It is evident from Figure (6.78) that the panel drift angle measurements for the wall recorded high values during test. This reflects the high contribution of the shear deformation to the wall lateral displacement. 6.10.6. Sliding Sliding of the masonry wall panel relative to the reinforced concrete footing is shown in Figure (6.79). It is evident from the Figure (6.79) the sliding control effect, the recorded wall sliding relative to the concrete base was up to 20% of the total drift. 6.10.7. Post-Tensioned Forces - Displacement Curves The post-tensioned forces, for the used two bars, are shown in Figures (6.80) to (6.82). The initial post-tension force in each bar was 60 kN as described before in Chapter (6). It is clear that the bars reached yield stress at 0.33% and 0.29% drift for push and pull directions respectively. The post-tension force decreases in both bars at 0.70% drift in both directions due to excessive cracking. 6.10.8. Failure Mechanism The analysis of the results shows clearly that the specimen behaved mainly in a ductile rocking mode with remarkable contribution of sliding and failed by demolishing of face-shells due to sliding, Figure (6.83) shows failure mechanism of wall W8. 6.10.9. Summary of Major Events A summary of major events which happened during the test together with the corresponding displacement and lateral load is given in Table (6.9)

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Table (6.9): Summary of Major Events for Wall W8 (A:RH:UG:PT:Sl)

Event Description

Lateral Load

Lateral Displacement (mm)

Overall Drift Angle (%)

Total PostTension Force (kN)

(kN)

(%)*

Crack Initiation and Yield of Bars: Flexural crack between the wall and concrete base

Push

5.30

0.33

125.20

40.07

80.03

Pull

4.70

0.29

139.30

42.36

87.14

Ultimate Lateral Load Capacity:

Push

10.21

0.64

121.50

50.07

100

Pull

12.14

0.76

116.62

48.61

100

Push

15.65

0.98

110.88

41.16

82.20

Pull

13.90

0.87

116.62

38.92

80.07

End of the Test: The test was stopped because of 20% degradation of load took place

*Percentage of the ultimate load of same direction

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(a) At first crack.

(b) Crack propagation.

(c) sliding of wall courses

(e) At Failure.

Figure (6.74): Wall W8 (A:RH:UG:PT:Sl): Crack Patterns. 195

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Figure (6.75): Wall W8 (A:RH:UG:PT:Sl): Lateral Load – Overall Drift Angle.

Figure (6.76): Wall W8 (A:RH:UG:PT:Sl): Flexural Strain at North Toe.

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Figure (6.77): Wall W8 (A:RH:UG:PT:Sl): Flexural Strain at South Toe.

Figure (6.78): Wall W8 (A:RH:UG:PT:Sl): Panel Drift Angle.

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Figure (6.79): Wall W8 (A:RH:UG:PT:Sl): Sliding.

Figure (6.80): Wall W8 (A:RH:UG:PT:Sl): North Bar Post-Tension Force.

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Figure (6.81): Wall W8 (A:RH:UG:PT:Sl): South Bar Post-Tension Force.

Figure (6.82): Wall W8 (A:RH:UG:PT:Sl): Total Post-Tension Forces.

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Figure (6.83): Wall W8 (A:RH:UG:PT:Sl): Failure Mechanism.

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6.11.Test Results for Wall W9 (A:RH:PG:PT:Sl) 6.11.1. General The partially-grouted wall with sliding control W9 was tested under increasing displacement cyclic load until the used LVDT reached its maximum displacement at 25.00 mm (1.56% drift). 6.11.2. Crack Pattern Crack patterns are shown in Figure (6.84). The first crack initiated at wall footing at 5.30 mm displacement (0.33% drift) in the push direction and 4.70 mm displacement (0.29% drift) in the pull direction, while the drystacked joints were opened and closed with cyclic loading. With further loading crack developed along the base due to wall sliding. To the end of the test the wall moved along the base due to the sliding control recording remarkable sliding. At 9.90 mm displacement (0.62% drift) in the pull direction, the upper south half-block was crushed. At the end of test, remarkable sliding was observed in both directions and the crack along the wall footing was widening up. 6.11.3. Lateral Load – Overall Drift Angle Curve The lateral load – overall drift angle is given in Figure (6.85). It is clear that the wall reached its ultimate lateral load resistance of 64.50 kN at 0.52% drift (8.03 mm) in the push direction and 68.30 kN at 0.78% drift (12.44 mm) in the pull direction. The wall can keep its ultimate resistance to the end of test at 1.56% drift in the pull direction. Unfortunately, the wall lost its resistance in the push direction after the demolishing of upper south half-block. 6.11.4. Flexural Strain – Displacement Curves Flexural strain measurements at the extreme fibers of the base section are shown in Figures (6.86) and (6.87). It is evident that both tensile and 201

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compressive strains was minimal in both directions, it is believed because the low rocking of wall panel due to sliding. 6.11.5. Panel Drift Angle – Displacement Curves The panel drift angle measurements along the tension diagonal is shown in Figure (6.88). It is evident from Figure (6.88) that the panel drift angle measurements for the wall recorded low values during test. This reflects the low contribution of the shear deformation to the wall lateral displacement. 6.11.6. Sliding Sliding of the masonry wall panel relative to the reinforced concrete footing is shown in Figure (6.89). It is evident that the effect of sliding control on wall sliding, which up to 40% of the total drift angle in the push direction (with loose bar) and 30% of total drift in pull direction. 6.11.7. Post-Tensioned Forces - Displacement Curves The post-tensioned forces, for the used three bars, are shown in Figures (6.90) to (6.93). The initial post-tension force in each bar was 50 kN as described before in Chapter (3). It is clear from Figure (6.92) that the posttension force for the middle bar stayed almost constant with a small increase in its value with the wall drift in both directions. On the other hand, Figure (6.90) shows clearly the normal changes of post-tension force in the north bar with cyclic loading. The south bar, as shown in Figure (6.92), worked as usual with cyclic loading until the crushing of its upper half-block took place, this crushing made a significant loss in post-tension force. By loading, the total post-tension force was increased by 20% of its initial value, as shown in Figure (6.93). Even after the crushing of hell cell block, the total post-tension force stayed at that range for the pull direction

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when the toe and middle bars were in action, and the total post-tension force dropped to 67% of its initial value for the push direction. 6.11.8. Failure Mechanism The analysis of the results shows clearly that the wall behaved mainly in a sliding mode. Figure (6.94) shows failure mechanism of wall W9. 6.11.9. Summary of Major Events A summary of major events which happened during the test together with the corresponding displacement and lateral load is given in Table (6.10) Table (6.10): Summary of Major Events for Wall W9 (A:RH:PG:PT:Sl)

Event Description

Lateral Load

Lateral Displacement (mm)

Overall Drift Angle (%)

Total PostTension Force (kN)

(kN)

(%)*

Crack Initiation: Flexural crack between the wall and concrete base Ultimate Lateral Load Capacity: Crushing of upper south half-block

Push

5.30

0.33

179.17

56.80

88.06

Pull

4.70

0.29

177.54

52.50

76.87

Push

8.30

0.52

179.00

64.50

100

Pull

12.44

0.78

153.60

68.30

100

End of the Test: The test was stopped because the used LVDT reached its maximum displacement

Push

25.00

1.56

101.40

27.10

42.02

Pull

25.00

1.56

167.20

68.30

100

*Percentage of the ultimate load of same direction

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(c) At ultimate load.

(f) After Failure.

Figure (6.84): Wall W9 (A:RH:PG:PT:Sl): Crack Patterns.

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Figure (6.85): Wall W9 (A:RH:PG:PT:Sl): Lateral Load – Overall Drift Angle.

Figure (6.86): Wall W9 (A:RH:PG:PT:Sl): Flexural Strain at North Toe.

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Figure (6.87): Wall W9 (A:RH:PG:PT:Sl): Flexural Strain at South Toe.

Figure (6.88): Wall W9 (A:RH:PG:PT:Sl): Panel Drift Angle.

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Figure (6.89): Wall W9 (A:RH:PG:PT:Sl): Sliding.

Figure (6.90): Wall W9 (A:RH:PG:PT:Sl): North Bar Post-Tension Force.

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Figure (6.91): Wall W9 (A:RH:PG:PT:Sl): Middle Bar Post-Tension Force.

Figure (6.92): Wall W9 (A:RH:PG:PT:Sl): South Bar Post-Tension Force.

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Figure (6.93): Wall W9 (A:RH:PG:PT:Sl): Total Post-Tension Forces.

Figure (6.94): Wall W9 (A:RH:PG:PT:Sl): Failure Mechanism. 209

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6.12.Discussion of Test Results In the previous sections the observed response of the tested specimens was presented. The test results are discussed in this section. Wall response is discussed in terms of failure mechanism, lateral load-displacement response, modes of deformation, residual displacement, displacement ductility, fragility curves, variation in stiffness, energy dissipation and equivalent viscus damping. 6.12.1. General Behavior In this section the general observations for walls' behavior are presented. The analysis of the test results reveals the following: 1. All Conventional and Azar walls behaved mainly in flexural mode, as designed, and failed by flexural cracks at wall footing and toe crushing. 2.

All Spar-lock walls behaved mainly in shear mode because the lack of horizontal reinforcement.

3. The similar behavior of Azar blocks walls and conventional blocks walls, regardless any other parameter like reinforcement, grouting and post-tensioning. 4. As designed, the ultimate lateral load carrying capacity of the posttensioned fully grouted wall W4 (A:RH:FG:PT) was 84.60 kN, equal to 1.03 and 1.05 of the ultimate load carrying capacity of the conventionally reinforced fully-grouted walls W1 (C:RVH:FG) and W2 (A:RVH:FG) respectively. And the wall W4 (A:RH:FG:PT) also can sustain 1.56% overall drift angle. 5. The dry-stacked joints of un-grouted Azar walls opened with lateral loads, which could delay the wall cracking at wall base to 0.60% drift comparing with the un-grouted conventional walls which initiate cracks at 0.30% drift.

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6. The sliding control can improve the maximum drift angle more than 1.50% drift with 20% degradation of load. This is considered the drift limit specified by NBCC (2005) for important buildings, which require some repair after earthquake event. 7. The Spar-lock walls can sustain the same displacements as Azar and conventional walls. But the vertical cracks between cells turns the Spar-lock walls into separated cells with low ultimate lateral load capacity. 6.12.2. Lateral Load-Displacement Response The drift angle and its corresponding lateral load at the first observed crack, the ultimate load and the end of test of tested walls were summarized in Table (6.11). Figure (6.95) represents the load-drift angle curves of the tested walls. Table (6.11): Summary of Major Events for Tested Walls: Wall

Direction

First Observed Crack Drift (%) Load (kN)

Ultimate Load Drift (%) Load (kN)

Maximum Displacement Drift (%) Load (kN)

Push 0.16 60.10 0.68 76.40 1.56* Pull 0.16 67.65 0.39 82.50 1.56* Push 0.19 46.07 0.42 79.35 1.25 W2 (A:RVH:FG) Pull 0.18 43.93 0.55 80.37 1.56* Push 0.13 5.42 1.16 22.59 1.56* W3 (S:RV:FGT) Pull 0.14 2.80 1.07 14.82 1.42 Push 0.60 66.39 1.47 83.60 1.56* W4 (A:RH:FG:PT) Pull 0.62 65.55 1.28 84.60 1.56* Push 0.59 47.67 0.76 51.93 1.06 W5 (A:RH:UG:PT) Pull 0.69 46.74 0.69 46.74 0.83 Push 0.31 43.16 0.77 50.80 1.18 W6 (C:RH:UG:PT) Pull 0.30 41.10 0.95 52.60 1.16 Push 0.52 23.80 0.62 26.65 1.22 W7 (S:RH:UG:PT) Pull 0.50 24.90 0.50 24.90 1.27 Push 0.33 40.07 0.64 50.07 0.98 W8 (A:RH:UG:PT:Sl) Pull 0.29 42.36 0.76 48.61 0.87 Push 0.33 56.80 0.52** 64.50 1.56* W9 (A:RH:PG:PT:Sl) Pull 0.29 52.50 0.78 68.30 1.56* * The test was stopped because the used LVDT reached its maximum displacement. W1 (C:RVH:FG)

67.00 66.40 63.50 64.30 22.24 13.75 81.80 68.90 41.54 39.98 40.64 52.05 21.32 20.90 41.16 38.92 27.10** 68.30

** The wall loses its strength due to the loss of post-tensioning force as a result of crushing of upper south half-block.

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Figure (6.95) Envelope of Load-Drift Angle Curves for Tested Walls Generally for the reinforced masonry walls W1, W2 and W3, the Azar wall behave similar to the conventional block one, and the Spar-lock wall on the other hand has almost 27% of the ultimate capacity of the conventional block wall. All reinforced walls reached more than 1.56% drift with less than 20% degradation of lateral load. The fully-grouted post-tensioned wall W4 could reach the same ultimate load and maximum drift as the reinforced walls. The un-grouted post-tensioned walls W5 and W6 had almost 65% of the conventionally reinforced fully-grouted walls W1 and W2 but with low maximum displacement of 17.00 and 18.90 mm respectively. Adding horizontal reinforcement to Spar-lock post-tensioned wall W7 increases its ultimate load capacity by 17.90% comparing with the conventionally reinforced Spar-lock wall W3. The Spar-lock posttensioned wall can keep 80% of its ultimate load up to 1.27% drift, where

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the Azar and conventional walls reached between 0.83% and 1.18% drifts at the same degradation of load. The sliding control failed to improve the maximum displacement of the un-grouted wall W8 because of premature rupture of first course face shells due to out-of-plane sliding. While the grouting of first course in wall W9 helps the sliding control to improve the maximum displacement. For the wall W9, the upper south half-block was crushed at 0.78% drift (12.44mm) in push direction causing a sudden drop in the north posttensioned bar which directly affect the other loops in the push direction. As discussed earlier in Chapter (3), all the tested walls were designed so that all failure modes but flexural are suppressed, except for spar-lock system which prevent the inclusion of horizontal reinforcement. A prediction of the ultimate lateral load capacity was made. Based on pretest analysis enough shear reinforcement was provided to suppress any shear failure. Only for the Spar system walls were predicted to fail in shear mode. The lateral load capacities of the tested walls, as predicted by the design equations as given in MSJC (2008), are shown in Table (6.12) along with the measured experimentally values. A graphical comparison of the predicted and measured lateral load capacities is given in Figure (6.96).

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Table (6.12): Predicted and Measured Lateral Load Capacities for the Tested Walls Lateral Load Capacity Wall

W1 (C:RVH:FG) W2 (A:RVH:FG) W3 (S:RV:FGT) W4 (A:RH:FG:PT) W5* (A:RH*:UG:PT) W5 (A:RH:UG:PT) W6 (C:RH:UG:PT) W7 (S:RH:UG:PT) W8 (A:RH:UG:PT:Sl) W9 (A:RH:PG:PT:Sl)

Direction Push Pull Push Pull Push Pull Push Pull Push Pull Push Pull Push Pull Push Pull Push Pull Push Pull

Predicted (kN)

87.00 87.00 22.80 86.30 21.17 44.70 44.70 22.80 44.70 69.20

214

Measured (kN) Value

76.40 82.50 79.35 80.37 22.59 14.82 83.60 84.60 21.70 18.10 51.93 46.74 50.80 52.60 26.65 24.90 50.07 48.61 64.50 68.30

Average

Predicted/ Measured

79.45

1.10

79.86

1.09

18.71

1.22

84.10

1.03

19.90

1.06

49.34

0.91

51.70

0.86

25.78

0.88

49.34

0.91

66.40

1.04

Chapter 6

Test Results and Analysis of Wall Response

Figure (6.96): Comparison of Predicted and Measured Lateral Load Capacities

Figure (6.97): Predicted Lateral Load Capacities versus Measured Capacities 215

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It is evident from Table (6.12) and Figure (6.96) that the proposed method by MSJC (2008) provides a good estimate for lateral load capacity with about 15% variation, as shown in Figure (6.97), except of Spar-lock W3 which predicted load based on not separating cell performance that could be overestimate the each cell active width as shown in Chapter (3). The following equations summarizes the designing equations proposed by MSJC (2008) for post-tension shear walls. 𝑎

𝑀𝑢 = (𝑓𝑝𝑠 𝐴𝑝𝑠 + 𝑓𝑦 𝐴𝑠 + 𝑃𝑢 ) (𝑑 − ) 2 𝑎=

𝑓𝑝𝑠 𝐴𝑝𝑠 +𝑓𝑦 𝐴𝑠 +𝑃𝑢

(6.1) (6.2)

/

0.80𝑓𝑚 𝑏

6.12.3. Modes of Deformation As illustrated briefly in El-Shafie (1997), top lateral displacement of solid walls is attribute to three distinctive deformation mechanisms, namely; sliding at the wall footing (Δs), concentrated flexural rotation at the wall footing (Δr), and panel displacement (Δpa) which consists of flexural and shear deformations. These different mechanisms are shown in Figure (6.98).

Figure (6.98): Deformation Modes for Solid Wall

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The overall drift angle (D) of the wall may be considered as the sum of the equivalent drift angles due to different modes of deformation according to the following equation: D = Ds + Dr + Dpa

(6.3)

Where, Ds = Equivalent overall drift angle due to sliding at the wall footing (Δs/h) Dr = Equivalent overall drift angle due to concentrated flexural rotation (Δr/h) Dpa = Equivalent overall drift angle due to panel displacement (Δpa/h) h

= Wall height.

This concept for solid wall modes of deformation will be applied to the tested shear walls. The contributions of different deformation modes to the overall drift angle are calculated and represented graphically, along with the sum of these contributions and measured overall drift angle, in Figures (6.99) to (6.108) for the tested walls. The difference between the measured overall drift angle and the sum of the modal contributions represents the error due to neglecting some of minor deformation mechanisms or due to any uncontrolled play in the instrumentation.

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Figure (6.99): W1 (C:RVH:FG): Contribution of Different Deformation Modes.

Figure (6.100): W2 (A:RVH:FG): Contribution of Different Deformation Modes. 218

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Figure (6.101): W3 (S:RV:FG): Contribution of Different Deformation Modes.

Figure (6.102): W4 (A:RH:FG:PT): Contribution of Different Deformation Modes. 219

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Test Results and Analysis of Wall Response

Figure (6.103): W5* (A:RH*:UG:PT): Contribution of Different Deformation Modes.

Figure (6.104): W5 (A:RH:UG:PT): Contribution of Different Deformation Modes. 220

Chapter 6

Test Results and Analysis of Wall Response

Figure (6.105): W6 (C:RH:UG:PT): Contribution of Different Deformation Modes.

Figure (6.106): W7 (S:RH:UG:PT): Contribution of Different Deformation Modes. 221

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Test Results and Analysis of Wall Response

Figure (6.107): W8 (A:RH:UG:PT:Sl): Contribution of Different Deformation Modes.

Figure (6.108): W9 (A:RH:PG:PT:Sl): Contribution of Different Deformation Modes. 222

Chapter 6

Test Results and Analysis of Wall Response

For conventionally reinforced fully-grouted walls, the main behavior of conventional block and Azar block walls W1 and W2 was rocking mechanism (flexural rotation) with minimal panel distortion. The high contribution of panel distortion in Spar-lock wall W3 reflects the reasonable value of shear deformation as a result of vertical separating cracks along the cells. The reinforced walls had average sliding contribution of 17% of total displacement due to the absence of normal stress. The flexural rotation was the main contribution of deformation for fully-grouted post-tensioned wall W4 with minimal sliding and panel distortion. For un-grouted post-tensioned walls, all dry-stacked walls W5, W7 and W8 had 45% average contribution of panel distortion as a result of the open/close movement of dry-stack joints. The panel distortion of conventional block wall W6, on the other hand, was minimal and the wall main behavior was flexural rotation. The sliding contribution was minimal for all un-grouted post-tension walls as a result of high friction due to high normal stress. The wall with sliding control W9 recorded a high sliding contribution about 35% of total displacement. 6.12.4. Residual Displacement The residual displacement can be defined as the displacement of the wall after unloading (x-axis value at zero lateral load in the lateral loaddisplacement curve), as shown in Figure (6.109). It can be an indication of the effectiveness of usage of un-bonded post-tensioning bars with drystacked shear walls. The residual displacements at the end of test for tested

223

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walls are given in Table (6.13). A graphical comparison of the residual and maximum displacements for tested walls is given in Figure (6.110).

Figure (6.109): Calculation of Residual Displacement

Figure (6.110): Maximum and Residual Displacements for Tested Walls 224

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Test Results and Analysis of Wall Response

Table (6.13): Residual Displacement

W1 (C:RVH:FG) W2 (A:RVH:FG) W3 (S:RV:FGT) W4 (A:RH:FG:PT) W5 (A:RH:UG:PT) W6 (C:RH:UG:PT) W7 (S:RH:UG:PT)

Direction

Wall

Push Pull Push Pull Push Pull Push Pull Push Pull Push Pull Push Pull

W8 (A:RH:UG:PT:Sl)

Push

W9 (A:RH:PG:PT:Sl)

Push

Pull

Maximum Drift Angle (%)

Residual Displacement (mm)

Drift (%)

21.9 15.9 11.7 7.3 9.1 13.0 11.1 3.8 9.1 6.4 3.9 2.2 11.5 8.8 9.8 3.8 2.7 16.8**

1.37 0.99 0.73 0.46 0.57 0.81 0.69 0.24 0.57 0.40 0.24 0.14 0.72 0.55 0.61 0.24 0.17 ---**

Average Drift (%)

Value

1.18 0.60 0.69 0.47 0.49 0.19 0.64 0.43 0.17

1.56 1.56 1.25 1.56 1.56 1.42 1.56 1.56 1.06 0.83 1.18 1.16 1.22 1.27 0.98 0.87 1.56 1.56

Average

Residual/ Max. Drift (%)

1.56*

75.64

1.41*

42.35

1.49*

46.31

1.56*

29.81

0.95

51.32

1.17

16.24

1.25

51.00

0.93

45.95

1.56*

10.90

Pull * The test was stopped because the used LVDT reached its maximum displacement. ** The wall loses its strength due to the loss of post-tensioning force as a result of crushing of upper south half-block.

As shown in Table (6.13) and Figure (6.110), the average residual displacement is 59% of the maximum displacement for conventionally reinforced walls, 37% for the post-tensioned walls without sliding control and only 10.9% for the wall with sliding control W9. 6.12.5. Displacement Ductility The term ductility defines the ability of the wall to deform beyond elastic limits without excessive strength degradation. The ductility is an important measure for the ability of the wall to sustain large inelastic deformation and to absorb the energy induced by earthquake loading. For this reason,

225

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it is the single important property sought by the designer of buildings located in active seismic zones. The displacement ductility (µ∆) is defined herein as the ratio between the measured top displacement at a specified displacement level beyond yielding (∆i), and at the yield displacement (∆y). There are several discussions in the literature regarding the appropriate definition of displacement ductility, but, as indicated by Priestley (2000), there is no general consensus or a unified definition for the yield and the ultimate displacements. Two approaches can be used to describe the relationship between the wall displacement ductility (µ∆) and the response modification factor (R); the response modification factor (R) could be assumed equal the displacement ductility (µ∆) based on equal displacement approach, as shown in Figure (6.111a) or could be calculated form the equal energy approach, as shown in Figure (6.111b) [Newmark and Hall (1973), Paulay and Priestly (1992), and Priestly (2000)]. In this study, the definition proposed by Tomazevic (1998), shown in Figure (6.112a) is used for the construction of the equivalent system and for the calculation of the equivalent displacement ductility for all walls. The method is based on equal areas under the measured and idealized curves for an ultimate level corresponding to 20% strength degradation and an initial stiffness equivalent to the secant stiffness at the first major crack (taken at the 75% of ultimate load). The yield displacement (∆y) can be defined from idealized elasto-plastic response as the displacement at 75% of ultimate load. Measured displacement ductility at maximum load (µ∆u) = ∆𝑢 ⁄∆𝑦 and at 20% degradation in strength (µ0.8∆) = ∆0.8𝑢 ⁄∆𝑦 are listed in Table (6.14) for all walls. The given response modification factors (R), given in Table

226

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(6.14), were calculated based on the equal energy approach, as shown in Figure (6.112b).

a) Equal Displacement

b) Equal Energy

Figure (6.111): Relationship between Ductility and Force Reduction Factor [Paulay and Priestley (1992)].

a) Idealized load-displacement relationships.

b) Ductility-related response modification factor.

Figure (6.112): Actual and Idealized Load-Displacement Relationships for the Test Walls Used for Ductility and Response Modification Factor Calculation [Tomazevic (1998)].

227

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Test Results and Analysis of Wall Response

Table (6.14): Measured Values for Displacement Ductility of the Tested

Measured Displacement (mm) ∆y

∆u

∆0.8u

Displacement Ductility At Max. Load µ∆u

Push

4.00

10.86 25.00

2.72

Pull

4.53

6.23

25.00

1.38

Push

8.00

6.64

20.00

0.83

Pull

7.68

8.72

25.00

1.14

Push

9.50

18.51 25.00

1.95

Pull

14.00 17.18 22.71

1.23

Push 10.67 23.58 25.00

2.21

Pull

10.67 20.46 25.00

1.92

Push

4.67

12.17 17.00

2.61

Pull

4.27

10.97 13.20

2.57

Push

4.89

12.35 18.90

2.53

Pull

4.75

15.25 18.63

3.21

Push

6.00

9.84

19.50

1.64

Pull

8.67

8.00

20.36

0.92

W8 (A:RH:UG:PT:Sl)

Push

4.67

10.21 15.65

2.19

Pull

4.67

12.14 13.90

2.60

W9 (A:RH:PG:PT:Sl)

Push

4.31

8.30

1.93

W1 (C:RVH:FG) W2 (A:RVH:FG) W3 (S:RV:FGT) W4 (A:RH:FG:PT) W5 (A:RH:UG:PT) W6 (C:RH:UG:PT) W7 (S:RH:UG:PT)

25.00

Av. 2.05 0.99 1.59 2.07 2.59 2.87 1.28 2.40 2.08

At 20% Degradation µ0.8∆ 6.25 5.52 2.50 3.26 2.63 1.62 2.34 2.34 3.64 3.09 3.87 3.92 3.25 2.35 3.35 2.98

Av.

Response Modification Factor (R)

Wall

Direction

Walls

5.89*

3.10*

2.88*

2.20*

2.13*

1.24*

2.34*

3.16*

3.37

2.12

3.90

2.49

2.80

1.94

3.17

2.19

5.80

5.13* 2.83* Pull 5.60 12.44 25.00 2.22 4.46 * The test was stopped because the used LVDT reached its maximum displacement.

Displacement ductility values at 20% strength degradation for conventionally reinforced walls were 2.88 and 2.13 for Azar and Spar-lock walls respectively (average of both directions), while the conventional block wall W1 had 5.88 average displacement ductility. The displacement ductility at 20% strength degradation (µ0.8∆) of post-tensioned walls W4, W5, W6, W7 and W8 had ranged from 2.34 and 3.92. 228

Chapter 6

Test Results and Analysis of Wall Response

The sliding control in wall W9 could enhance the displacement ductility to reach more than 5.80 at 20% degradation. Comparing the displacements at 20% degradation of lateral capacity (∆0.8u) and the displacements at maximum load (∆u) listed in Table (6.14), it can be seen that, on average, the conventionally reinforced Azar and conventional block walls maintained 80% of their maximum lateral capacity up to 3.05 ∆u (the average value of ∆0.8𝑢 ⁄∆𝑢 for W1 and W2). The post-tensioned walls on the other hand had a brittle behavior (the average value of ∆0.8𝑢 ⁄∆𝑢 for W4, W5, and W6 walls = 1.27). The sliding control in wall W9 able the wall to maintain 80% of their maximum lateral capacity up to 2.51 ∆u. The brittle shear failure of Spar-lock walls affected the ductility, as clearly shown in Table (6.14). The average values of ∆0.8𝑢 ⁄∆𝑢 1.34 the conventionally reinforced Spar-lock wall W3 and 2.26 for post-tension wall W7. The International Building Code (2000) specifies an upper bound of the maximum amount of flexure reinforcement in order to ensure that, at least, 1% wall drift will be reached prior to developing a strain of 0.0025 in masonry. Test results showed that all walls reached a drift limit of 1.0% (16mm for 1600mm height walls). The partially-grouted wall with sliding control A:RH:PG:P:Sl reached a drift limit of 1.0% with almost no strength degradation (in pull direction), which is the limit specified by the NBCC (2005) for Post-disaster buildings, required to be fully operational after an earthquake event. The un-grouted post-tensioned walls couldn’t reached, a drift limit of 1.5% (24mm) with about 20% degradation in strength. This is considered the drift limit specified by the NBCC (2005) for important buildings, which require some repair after earthquake event.

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The ASCE 7 (2005) given the response modification factor (R) for intermediate reinforced masonry shear walls equal 3.5 and treat the prestressed masonry shear walls as plain masonry shear walls with 1.5 response modification coefficient. The value of R factor for reinforced walls increased from 1.9 to 3.5, corresponding to a decrease in the vertical reinforcement ratio from 1.31% (which is a considerably high ratio) to 0.29% [Shedid et al (2009)]. The tested walls results showed that the ASCE code is underestimate the ductility of post-tension walls. The R factor could be assumed between 2.15 and 2.50 for the post-tensioned un-grouted shear walls and could be more than 2.83 if using sliding control with post-tension shear walls. 6.12.6. Variation in Stiffness To assess the variation of the stiffness with increased loading and top displacement, the secant stiffness defined as the ratio between the lateral resistance and the corresponding top lateral wall displacement was used. The initial stiffness (ki) for all walls was defined as the secant stiffness at 75% of maximum load capacity. Measured values of wall stiffness at 75% of ultimate load, at maximum load and at different wall drifts (0.5%, 1.0% and 1.5%) are given in Table (6.15). Figure (6.113) shows the variation in stiffness for tested walls.

230

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Table (6.15): Measured Walls Stiffnesses Measured Stiffness at 75% Ultimate 0.5% 1.0% Ultimate Load Drift Drift

Wall

16.90 5.23 9.00 (%)* 100 30.95 53.25 (kN/mm) 10.35 9.30 10.00 W2 (A:RVH:FG) (%)* 100 89.86 96.62 (kN/mm) 1.00 1.12 1.20 W3 (S:RV:FGT) (%)* 100 112.00 120.00 (kN/mm) 18.50 9.14 16.50 W4 (A:RH:FG:PT) (%)* 100 49.41 89.19 (kN/mm) 9.00 4.26 5.60 W5 (A:RH:UG:PT) (%)* 100 47.33 62.22 (kN/mm) 9.90 3.80 6.30 W6 (C:RH:UG:PT) (%)* 100 38.38 63.64 (kN/mm) 3.10 2.30 3.10 W7 (S:RH:UG:PT) (%)* 100 74.19 100.00 (kN/mm) 8.70 4.40 5.50 W8 (A:RH:UG:PT:Sl) (%)* 100 50.57 63.22 (kN/mm) 12.00 8.50 8.00 W9 (A:RH:PG:PT:Sl) (%)* 100 70.83 66.67 * Percentage of measured stiffness at 75% of ultimate load capacity W1 (C:RVH:FG)

(kN/mm)

231

4.50 26.63 4.90 47.34 0.92 92.00 12.11 65.46 2.70 30.00 2.90 29.29 1.15 37.10 2.20 25.29 3.00 25.00

1.5% Drift 2.90 17.16 2.30 22.22 0.70 70.00 7.70 41.62 ----------------2.10 17.50

Chapter 6

Test Results and Analysis of Wall Response

Figure (6.113): Variation of Wall Stiffness For conventionally reinforced walls, the Spar-lock wall W3 had very low stiffness comparing with the Conventional block and Azar walls W1 and W2. The separating cell behavior due to absence of horizontal reinforcement in Spar-lock system causes that minimal stiffness. However the Spar-lock wall didn’t lose its stiffness as rabid as other systems. Walls W1 and W2 lost 70% of its stiffness at the 1.0% drift, as shown in Figure (6.113) and Table (6.15). The fully-grouted post-tension wall W4 had almost same initial stiffness of the conventionally reinforced walls W1 and W2. It is clear from Table (6.15) that post-tensioning could resist the losses in stiffness, W4 could keep more than 65% of its initial stiffness up to 1.0% drift. The un-grouted post-tension walls constructed with conventional or Azar blocks (W5, W6, W8) had stiffness almost half the stiffness of the fully-grouted wall W4 at 75% of ultimate load.

232

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Test Results and Analysis of Wall Response

Although the horizontal reinforcement in wall W7 improved the initial stiffness of Spar-lock system, but its stiffness less than 25% of other wall systems due to the shortage of horizontal reinforcement at both sides of wall. The wall with sliding control W9 lost its stiffness more gradually than other post-tension walls. The stiffness of cantilever reinforced shear walls can be calculated based on flexure and shear deformations using the elastic theory equation 𝐾 = 1⁄ ℎ3 1.2ℎ (3𝐸 𝐼 + 𝐴𝐺 ) 𝑚 𝑒

(6.4)

𝑚

Where, Em and Gm are the modulus of elasticity and shear modulus of masonry, h is the wall height, and Ae and Ie are the cross section area and moment of inertia. The effective moment of inertia (Ie) of the cracked section of reinforced masonry shear wall can be estimated according to the following equation which developed by Priestly and Hart (1989) 𝐼𝑒 = (

103 𝑓𝑦

+

𝑃 / 𝑓𝑚 𝑙𝑤 𝑏

) 𝐼𝑔

(6.5)

Where 𝑃 is the axial force on wall (equal to post-tension force in the post-tension walls) Table (6.16) represents the predicted walls stiffnesses for tested walls along with the measured stiffnesses.

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Table (6.16): Predicted and Measured Stiffnesses for Tested Walls Wall

Predicted

Measured

Measured/ Predicted

W1 (C:RVH:FG)

49.40

16.90

2.92

W2 (A:RVH:FG)

44.55

15.30

2.91

W3 (S:RV:FG)

3.62

1.40

2.59

W4 (A:RH:FG:PT)

23.60

18.50

1.28

W5 (A:RH:UG:PT)

10.07

9.00

1.12

W6 (C:RH:UG:PT)

10.82

9.90

1.09

W7 (S:RH:UG:PT)

3.70

3.10

1.19

W8 (A:RH:UG:PT:Sl)

11.17

9.70

1.15

W9 (A:RH:PG:PT:Sl)

12.08

12.00

1.01

It is evident from Table (6.16) that the proposed method provides a good estimate for the stiffness of post-tension walls W4 to W9, and the predicted stiffness of reinforced walls W1, W2 and W3 should be scaled down by 1/3 in order to estimate the stiffness at yield, as illustrated before in the literature review [Pauley and Priestly (1992), Hart et al (1988)], taking into consideration that the predicted stiffness for the Spar-lock wall W3 considered the cross section as a separated four cells as described before in the pre-test analysis in Chapter (3). The predicted stiffness values are plotted versus the measured stiffness values in Figure (6.114) after scaling down the predicted stiffness of reinforced walls as illustrated.

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Figure (6.114): Predicted Stiffness versus Measured Stiffness

The elastic theory equation may be used to predict the initial stiffness of post-tensioned shear walls using the gross moment of inertia and gross section area as follows: 𝐾 = 1⁄ ℎ3 1.2ℎ (3𝐸 𝐼 + 𝐴 𝐺 ) 𝑚 𝑔

(6.6)

𝑔 𝑚

Table (6.17) represents the predicted walls stiffnesses for post-tension walls along with the measured stiffnesses. Table (6.17): Predicted and Measured Stiffnesses Post-Tension Walls Wall

Predicted

Measured

Measured/ Predicted

W4 (A:RH:FG:PT)

118.50

18.50

0.156

W5 (A:RH:UG:PT)

46.92

9.00

0.192

W6 (C:RH:UG:PT)

52.02

9.90

0.190

W8 (A:RH:UG:PT:Sl)

46.92

8.70

0.185

W9 (A:RH:PG:PT:Sl)

46.92

12.00

0.256

235

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It is evident from Table (6.17) that the elastic equation should be scaled down by a factor of 0.2, in order to calculate the initial stiffness of un-grouted post-tension walls (at 75% of ultimate lateral load). The stiffness of post-tension walls at 75% of ultimate lateral load can be calculated by the following equation. 𝐾 = 0.2⁄ ℎ3 1.2ℎ (3𝐸 𝐼 + 𝐴 𝐺 ) 𝑚 𝑔

(6.7)

𝑔 𝑚

Where, 𝐸𝑚 and 𝐺𝑚 are the modulus of elasticity and shear modulus of masonry, h is the wall height, and 𝐴𝑔 and 𝐼𝑔 are the gross area and gross moment of inertia. The predicted stiffness values of post-tension walls based on this approach are plotted versus the measured stiffness values in Figure (6.115). The flexural contribution calculated by Equation (6.7) was equal to 1.74 times the shear contribution, which agreed with the ratio between the flexural (base rotation) and the shear (panel distortion) contributions measured for post-tensioned walls prior to 75% of ultimate load as shown in Figures (6.103) to (6.107) in Section (6.12.3). Also Figures (6.103) to (6.107) shows that the sliding were minimal for all post-tension walls in this zone included wall with sliding control W9, so Equation (6.6), which neglecting the sliding deformation, can be used to predict the stiffness at 75% of ultimate load.

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Figure (6.115): Predicted Stiffness versus Measured Stiffness for Post-Tension Walls (Second Approach)

It is evident from Figures (6.114) and (6.115) that the first approach gives a better estimation of stiffness for both post-tension and reinforced shear walls. 6.12.7. Identification of Damage State and Development of Fragility curves The fragility curves have been developed using experimental data from quasi-static tests of reinforced masonry shear walls, which were mostly fully-grouted concrete masonry walls [Delso et al. (2011)]. For the purpose of developing the fragility curves, different damage states that require different levels of repair and restoration effort and costs have been identified. The damage states are associated with different behavior modes of a wall.

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Fragility curves for un-grouted post-tensioned walls have been developed based on the methodology established in the ATC-58 50% draft guidelines [ATC (2009), Delso et al. (2011)]. The fragility functions are assumed to take the form of a lognormal cumulative distribution function, as shown in following equation. 𝐹𝑖 (𝐷) = Φ (

ln(𝐷 ⁄𝜃𝑖 ) 𝛽𝑖

)

(6.8)

in which θ is the median, β is the logarithmic standard deviation (or dispersion), Fi (D) is the conditional probability that a component will have a damage state i or a more severe damage state when the value of the demand parameter is D, and Φ is the standard normal (Gaussian) cumulative distribution function. Both fully and partially grouted walls are considered here. The fragility curves for flexure-critical un-grouted posttensioned shear walls are shown in Figure (6.116). The fragility curves are based on experimental data of post-tension walls W5, W6, W7, W8 and W9, considering the first yield (75% of ultimate load) as damage state 1 (DS-1), the ultimate load as DS-2 and 20% degradation of ultimate load as DS-3.

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Figure (6.116): Fragility Curves for Flexure Demand of Un-Grouted Post-Tensioned Shear Walls.

6.12.8. Energy Dissipation Energy dissipation through hysteretic damping (Ed) is an important aspect in seismic design since it reduces the amplitude of the seismic response and, thereby, reduces the ductility and strength demands of the structure. The envelope of the load-displacement hysteresis loops is relatively insensitive to the imposed displacement increments and to the number of cycles [Shedid et al. (2009)]. Therefore, the energy dissipation (Ed) will be represented, as suggested by the area enclosed by the force-displacement curve at each displacement level (the horizontally hatched area), as shown in Figure (6.117). The vertically hatched region in the same figure represents the elastic strain energy stored in an equivalent linearelastic system (Es).

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Figure (6.117): Calculation of Energy Dissipation [Shedid et al. (2009)] The energy dissipation values for the walls at different displacement levels are plotted versus the overall drift angle in Figure (6.118). As shown in Figure (6.118) for low displacement levels, the energy dissipation was low before significant inelastic deformation in the masonry took place. For higher displacement levels, the energy dissipation increased significantly for different walls compared to early stages of loading.

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Figure (6.118): Energy Dissipation for Tested Walls The energy dissipation of post-tensioned fully-grouted wall W4 (A:RH:FG:PT) is equal twice the un-grouted wall W6 (C:RH:UG:PT), and almost 75% of the energy dissipated by the conventionally reinforced wall W1 (C:RVH:FG). The Azar post-tensioned un-grouted walls W5 (A:RH:UG:PT) and W8 (A:RH:UG:PT:Sl) dissipate energy 2.5 times the conventional wall W6, and even 35% more than the fully-grouted wall W4. It is believed because the absent of mortar in dry-stacked Azar system the wall courses can separate freely and dissipate more energy. Due to the low ultimate load capacity of Spar-lock walls, the walls W3 (S:RV:FG) and W7 (S:RH:UG:PT) dissipate 25% and 50% of the Azar wall W5 (A:RH:UG:P) respectively. The wall with sliding control W9 (A:RH:PG:PT:Sl) can dissipate energy more than the conventionally reinforced walls up to 0.5% drift when the loosing of north post-tensioning force took place. The sliding due 241

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to sliding control help the wall to keep the same amount of energy dissipation each loop up to failure. 6.12.9. Equivalent Viscous Damping Hysteretic damping can be described by an equivalent viscous damping ratio (𝜉𝑒𝑞 ) which is based on an equal area approach [Shedid (2009)] that represents the same amount of energy loss per loading cycle. The relationship between the dissipated energy (Ed), the stored strain energy (Es) and the equivalent viscous damping ratio (𝜉𝑒𝑞 ) (see Figure (6.119)) is given by following equation: 𝜉𝑒𝑞 =

1

𝐸

( 𝑑) 4𝜋 𝐸

(6.9)

𝑠

The equivalent viscous damping ratio (𝜉𝑒𝑞 ) is plotted versus the drift angle in Figure (6.120) for all tested walls.

Figure (6.119): Equivalent Viscous Damping Ratio

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The viscous damping of conventionally reinforced walls W1, W2 and W3 ranged between 10% and 20%, where the fully-grouted post-tension wall had viscous damping between 7% and 12%. The figure shows that, the dry-stack (Azar and Spar-lock) un-grouted post-tension walls W5, W7 and W8 had increasing viscous damping with increased displacements. Disturbance in W9 damping curve was occurred due to the loss in wall stiffness as described before. The average equivalent viscous damping ratio calculated at 0.5% drift and 1% drift for dry-stacked un-grouted post-tension walls was about 13% and 25%, respectively. This indicates that dry-stacked un-grouted shear wall buildings can be expected to experience high levels of damping which would reduce the seismic demand. The increase of the equivalent viscous damping ratio with increased displacements indicates that different values for the damping ratio may be assigned to structures depending on their design limit state. Structures designed for collapse prevention can be assigned a higher damping ratio as they are expected to exhibit high inelastic deformation and damage, whereas structures designed for a fully operational limit state, or serviceability limit state, can be assigned lower damping values since lower levels of deformations and cracking are permitted [Shedid (2009)].

243

CHAPTER (7) FINITE ELEMENT ANALYSIS AND PARAMETRIC STUDY 7.1. Introduction This chapter will help establish the potential of finite element (FE) analysis to provide dependable results of masonry structures and thus help reduce expensive laboratory experiments by adding some extra analytical models that can extend the experimental program and provide more results. The analysis was focused on post-tensioned dry-staked shear walls. 7.2. General Behavior Another approach to analyze the tested wall specimens is by using the nonlinear finite element method (FEM). In such a FE-analysis, it is possible to have better control over the varied parameters compared with full-scale tests and consequently it is easier to draw conclusions. Furthermore, FE-analyses give the opportunity to study the wall specimens more thoroughly because of the larger amount of results that can be analyzed. Hence, FE-analyses give the possibility to understand how a parameter affects the results. This means that the need for experiments can be greatly reduced by using the finite element method. However, the experiments are still needed to verify that the FE-analyses correspond to the actual behavior. Accordingly, when experiments and non-linear finite element analyses are used together they can become very powerful tools in gaining a better understanding of the structural behavior of posttensioned dry-stacked masonry shear walls. Many factors are need to be considered when trying to model the behavior of post-tensioned dry-stacked masonry shear walls such as the nonlinearity of materials, the boundary conditions, the interaction between the structure’s constituents, etc.. 245

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Often the influences from constituent materials and boundary conditions in masonry structures are too complex to be simplified to a degree that a reasonable analytical expression can be derived. Therefore, a numerical approach must be selected to capture behavior of the structure. If a masonry structure is properly defined, a careful finite element analysis, linear elastic or nonlinear, can give new insights and explanations to sparse and sometimes contradicting results from physical experiments . In this chapter, detailed structural analysis of the wall specimens has been done using the nonlinear finite element program, ABAQUS/Standard 6.10.1 (henceforth referred to as ABAQUS). ABAQUS has the capability of modeling nonlinear behavior of concrete, masonry and steel. In addition it is also capable of treating steel as a separate input entity, allowing it to be modeled independently of concrete elements. At first, a general overview about the formulation of the finite element approach is presented to define the technique, also the solution strategy used in the analysis by the finite element program (ABAQUS) is briefly introduced to interpret the iterative numerical technique for solving nonlinear problems. Secondly, all modeling parameters are discussed such as elements used for modeling of concrete and steel reinforcement, material models, boundary conditions, loading and interactions between model parts. Then, FE models are presented to simulate the post-tensioned dry-stacked shear wall specimens of the achieved experimental program. At last, the validated model will be used to assess the behavior of untested design configuration and further investigate various possible retrofitting schemes for post-tensioned dry-stacked shear walls.

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7.3. Model Geometry ABAQUS does not have a specific constitutive model for masonry structures, but the ones given for concrete elements and other quasi-brittle materials could be properly used to model the masonry, for example, the concrete damage plasticity model, where the material is characterized for tensile cracking or compressive crushing. Even, damage and stiffness recovery factors in compression and tension could be specified. Many researches have shown that analysis of masonry structures can be successfully described using modeling techniques usually applied to concrete mechanics [Lotfi (1994)]. According to Lourenco, the numerical modeling of masonry can be represented by micro-modeling of each of its components or by macro-modeling assuming the masonry to be homogeneous. Depending on the level of accuracy, the following strategies can be used: a. Detailed micro-modeling. Units and mortar joints are represented by continuum (solid) elements, where the unit-mortar interface is represented by discontinuous elements [Ali (1988), and Rots (1991)]; b. Simplifies micro-modeling. The expanded units are represented by continuum (solid) elements, where the behavior of the mortar joints and unit-mortar interface is lumped in discontinuous elements [Arya (1978) and Page (1978)]; c. Macro-modeling. Units, mortar and unit-mortar interface are smeared

out in the continuum (solid) elements and the masonry is treated as an isotropic material.

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Figure (7.1): Modeling Strategies for Masonry Structures The first two approaches are computationally intensive analysis of large masonry structures; however, it can be an important research tool in comparison with the costly and often time consuming laboratory experiments. In this research, the macro-modeling was used for the fully grouted walls, and the modified micro-modeling was used for un-grouted ones. Lourenco (2005) reported on experimental research on the structural behavior of dry joint masonry subjected to in-plane combined loading and also addressed a simplified method of analysis based on a continuum of diagonal struts. He [Lourenco (2004)] also contributes the knowledge of dry joints under cyclic loading where focuses on the characterization of Coulomb failure criterion and the load-displacement behavior including aspects as surface roughness and inelastic behavior. Due to the requirement of capturing plane response, a 3D model was selected, with (a) constituent material representing the behavior of 248

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Masonry prism using 3D continuum (solid) elements (C3D8), (b) concrete modeled with 3D continuum (solid) elements (C3D8), and (c) the reinforcement and post-tensioned bars modeled as truss elements (T3D2). The horizontal reinforcement and the post-tension bars were simulated as embedded truss elements using the “Embedded Region Constraint” option in Abaqus. 7.4. Elements Abaqus offers both linear and quadratic elements for shell and solid elements with rectangular shapes. Moreover, the accuracy of the analysis depends not only on the order of the element’s interpolation function (linear or quadratic), but also on the element formulation, and the level of integration. This research began by investigating the appropriateness of linear elements specifically, the model employed (1) element C3D8, which is a linear 8-node 3D-continuum (solid) element for concrete and masonry elements, and (2) element T3D2 a linear 2-node 3D-Truss for steel bars and bars. 7.5. Assembly 7.5.1. Fully-Grouted Post-Tensioned Shear Wall (W4) As described early, a macro-modeling technique was used to simulate the fully-grouted masonry wall panel, in which all the masonry units and the grout were simulate as one 3D continuum (solid) element (C3D8), as shown in Figure (7.2), the horizontal reinforcement and the vertical posttension bars were simulated as embedded truss elements using the “Embedded Region Constraint” option in Abaqus. however the bars were unboned to the wall panel to simulate the tested wall W4 (A:RH:FG:PT). Both the concrete base and the top beam also were simulated as C3D8 elements, the interface between the wall panel with concrete base and top beam were simulated as a surface-to-surface interface with “hard 249

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contact” for normal direction and with 0.65 coefficient of friction as illustrated before in the friction triplet tests at Chapter (4). All interfaces between wall courses were simulated as a surface-tosurface interface with “hard contact” for normal direction and with 0.65 coefficient of friction. Only in case of sliding control the interface between the lower masonry course and base was simulated with 0.2 the coefficient of friction as shown in Figure (7.3).

Figure (7.2): Model for Grouted Shear Walls

Figure (7.3): Model Interfaces for Grouted Shear Walls 7.5.2. Un-Grouted Post-Tensioned Shear Walls (W5, W8 and W9) 250

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For un-grouted walls, each masonry course was simulated as a 3D continuum (solid) element (C3D8), as shown in Figure (7.4), the interface between each two courses was simulated as a surface-to-surface interface with “hard contact” for normal direction and with 0.60 coefficient of friction as illustrated before in the friction triplet tests at Chapter (4), the horizontal reinforcement and the vertical post-tension bars were simulated as embedded truss elements using the “Embedded Region Constraint” option in Abaqus. The interface between the upper masonry course and the top beam was simulated with 0.65 coefficient of friction. And the interface between the lower masonry course was simulated with 0.65 coefficient of friction in case of W5 (A:RH:UG:PT) without sliding control, and in walls W8 (A:RH:UG:PT:Sl) and W9 (A:RH:PG:PT:Sl) the coefficient of friction equal 0.2 because of sliding control as illustrated before in the friction triplet tests at Chapter (4). All interfaces between wall courses were simulated as a surface-tosurface interface with “hard contact” for normal direction and with 0.65 coefficient of friction. Only in case of sliding control the interface between the lower masonry course and base was simulated with 0.2 the coefficient of friction as shown in Figure (7.5).

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Figure (7.4): Model for Un-Grouted Shear Walls

Figure (7.5): Model Interfaces for Un-Grouted Shear Walls 7.6. Finite Element Meshing Mesh size of 30 mm was chosen for both concrete and masonry. Also the horizontal reinforcement was meshed with approximate maximum size of 30 mm, as shown in Figure (7.6). For the post-tension bars in order to make them un-bonded with the wall panel, the whole bar was simulated as one part (mesh size equal to the bar length). 252

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a) Grouted Walls

b) Un-Grouted Walls

Figure (7.6): Meshing of the Walls Models 7.7. Material Models In order to obtain accurate analysis, proper material models are needed. To be able to understand the mechanical behavior up to final failure, it is important that this non-linear behavior can be simulated in the FEanalyses. The non-linearities of the concrete in compression and the steel were accounted for with plasticity models. Three major effects cause the non-linear response of reinforced concrete namely, a) crushing in compression, b) cracking of concrete in tension and c) yielding of reinforcement. Nonlinearities also arise from the interaction of the constituents of reinforced concrete such as, bond-slip between reinforcing steel and surrounding concrete, aggregate interlock at a crack and dowel action of the reinforcing steel crossing a crack. The concrete and masonry materials was simulated using “concrete damaged plasticity” criteria in Abaqus with 9.00 MPa compressive strength and modulus of elasticity of 1850 MPa, and the post-tension bars materials were simulated as bilinear plastic material with 1080 MPa 253

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yielding stress, 210 GPa modulus of elasticity and 18% maximum elongation, as described before in in Chapter (4). Kmiecik (2011) described the Modelling of reinforced concrete structures using concrete damaged plasticity and how to consider concrete strength degradation and the coefficients used with concrete. 7.8. Boundary Conditions and Initial Conditions All nodes of the bottom surface of the concrete base were locked against translation and rotation in all directions as shown in Figure (7.7). The bars were subjected to an “initial condition type stress” to represent the post-tension forces in these bars. In order to simulate the displacement-control loading of the tested walls, another boundary condition was created at the top beam in the loading step. The loading boundary condition had one way loading to give the envelop of loading cycles, and with a high displacement in the direction of loading enough to lead wall to failure.

Figure (7.7): Boundary Conditions for Models

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7.9. Model Verification Having considered all FE modeling and analysis aspects, ABAQUS was used to investigate Post-tensioned dry-staked tested wall specimens. The predicted in-plane behavior and failure mode for each wall specimens obtained from the corresponding model were then examined against the test results. A comparison of the results from tests and those from the FE analyses was made in the following sections in order to verify the FE models. Load-displacement curves for both tested and FE-model for all the four walls are represented in Figures (7.8) to (7.11). Walls results were summarized in Table (7.1). Results from the finite element analysis of showed that the developed models are capable with sufficient degree of accuracy to capture the ultimate load, stiffness and deformation capacity of the tested walls. The model is considered satisfactory for capturing the global response and ultimate capacities of the walls. Table (7.1): Summary of Model vs Test Comparison Wall

Ultimate Load (KN) Exp.

Num.

Exp./Num.

Max. Displacement (mm) Exp.

Num.

Exp./Num.

W4 (A:FG) 84.60 80.25 1.05 25.0* 48.0 --W5 (A:UG) 51.90 53.05 0.98 17.7 15.0 1.18 W8 (A:UG:Sl) 50.10 54.82 0.91 15.6 30.0 1.92** W9 (A:PG:Sl) 68.30 45.20 1.50 25.0* 48.0 --* The experimental test was stopped because the used LVDT reached its maximum value. ** The wall sliding was stopped due to the rapture of face shells.

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Figure (7.8): W4 (A:FG): Load-Displacement Curves for FE Models of Tested Walls (Test vs. FEM)

Figure (7.9): W5 (A:UG): Load-Displacement Curves for FE Models of Tested Walls (Test vs. FEM) 256

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Figure (7.10): W8 (A:UG:Sl): Load-Displacement Curves for FE Models of Tested Walls (Test vs. FEM)

Figure (7.11): W9 (A:PG:Sl): Load-Displacement Curves for FE Models of Tested Walls (Test vs. FEM) 257

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7.10. Parametric Study Using FE Models It can be seen from the verification stage in the previous section, that the FE-models capture the structural behavior of the tested walls specimens in a satisfactory way. Some parameters that are believed to affect the ultimate capacity and ductility of post-tension dry-stacked masonry walls, are the position of post-tension bars and the initial post-tension stress. The developed model will be used in this section to further investigate and evaluate these parameters. 7.10.1. Fully-Grouted Post-Tensioned Walls The position of post-tension bars and the initial post-tension stress were studied with the same parameters for the tested wall (A:FG) such as material properties, blocks dimensions and aspect ratio. Five additional wall specimens were added to extend results and study the effect of the two parameters on the behavior of dry-stacked fully-grouted shear walls as shown in Table (7.2) and Figure (7.12) shows the specimens configurations. Table (7.2): Extended Specimens Matrix for Grouted walls Specimen 1 2 3 4 5 6

A:FG A:FG-10% A:FG-20% A:FG-C A:FG-C-10% A:FG-C-20%

Post-Tension Ratio (% of f/m) 6.6 % 10.0 % 20.0 % 6.6 % 10.0 % 20.0 %

258

Bars location North + Center + South North + Center + South North + Center + South Only Center Only Center Only Center

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a) A:FG (6.6%)

b) A:FG-10%

c) A:FG-20%

d) A:FG-C (6.6%)

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e) A:FG-C-10%

f) A:FG-C-20%

Figure (7.12): Specimens Configurations for FE Models of Grouted Walls Table (7.3) summarized the ultimate load capacity and the ultimate displacement obtained from ABAQUS models. Figure (7.13) shows the load-displacement curves from FE analysis with respect to the loaddisplacement curve for experimentally fully-grouted post-tension tested wall W4 (A:FG), and Figure (7.14) presents comparison between the principle stress contours for all walls. Table (7.3): Lateral Loads and Displacement comparison for Grouted walls Specimen 1 2 3 4 5 6

A:FG (6.6%) A:FG-10% A:FG-20% A:FG-C (6.6%) A:FG-C-10% A:FG-C-20%

Ultimate Load (kN) (%) 80.25 100 119.93 149.4 232.50 289.7 81.30 101.3 121.62 151.6 236.21 294.3

260

Maximum Displacement (mm) (%) 48.0 100 40.0 83.3 28.0 58.3 55.0 114.6 42.0 87.5 34.0 70.8

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Figure (7.13): Predicated load-Displacement Curves for FE Models of Grouted Walls

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a) A:FG

b) A:FG-10%

c) A:FG-20%

d) A:FG-C

e) A:FG-C-10%

f) A:FG-C-20%

Figure (7.14): Principle Stress Contours for FE Models of Grouted Walls 262

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7.10.2. Un-Grouted Post-Tensioned Walls For the un-grouted post-tensioned shear walls, the position of post-tension bars and the initial post-tension stress were studied with the same parameters for the tested wall W5 (A:UG) such as material properties, blocks dimensions and aspect ratio. Five additional wall specimens were added to extend results and study the effect of the two parameters on the behavior of dry-stacked un-grouted shear walls as shown in Table (7.4) and Figure (7.15) shows the specimens configurations. Table (7.4): Extended Specimens Matrix for Un-Grouted Walls Specimen 1 2 3 4 5 6

A:UG A:UG-10% A:UG-20% A:UG-C A:UG-C-10% A:UG-C-20%

Post-Tension Ratio (% of f/m) 16.0 % 10.0 % 20.0 % 16.0 % 10.0 % 20.0 %

a) A:UG (16%)

Bars location North + South North + South North + South Center Center Center

b) A:UG-10% 263

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c) A:UG-20%

d) A:UG-C (16%)

e) A:UG-C-10%

f) A:UG-C-20%

Figure (7.15): Specimens Configurations for FE Models of Un-Grouted Walls Table (7.5) summarized the ultimate load capacity and the ultimate displacement obtained from ABAQUS models. Figure (7.16) shows the 264

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load-displacement curves from FE analysis with respect to the loaddisplacement curve for experimentally un-grouted post-tension tested wall W5 (A:UG), and Figure (7.17) presents comparison between the principle stress contours for all walls. Table (7.5): Lateral Loads and Displacement Comparison for Un-Grouted Walls Specimen 1 2 3 4 5 6

A:UG (16%) A:UG-10% A:UG-20% A:UG-C (16%) A:UG-C-10% A:UG-C-20%

Ultimate Load (kN) (%) 53.05 100 33.61 63.4 66.39 125.1 53.92 101.6 34.03 64.1 67.50 127.2

Maximum Displacement (mm) (%) 15.0 100 18.0 120.0 12.0 80.0 18.0 120.0 22.0 146.7 15.0 100.0

Figure (7.16): Predicated load-Displacement Curves for FE Models of Un-Grouted Walls

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a) A:UG

b) A:UG-10%

c) A:UG-20%

d) A:UG-C

e) A:UG-C-10%

f) A:FG-C-20%

Figure (7.17): Principle Stress Contours for FE Models of Grouted Walls 266

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7.10.3. Partially-Grouted Post-Tensioned Walls Two additional wall specimens were added to extend results and study the effect of the partially grouting the post-tension walls on the behavior of dry-stacked shear walls with sliding control as shown in Table (7.6) and Figure (7.18) shows the specimens configurations. Table (7.6): Extended Specimens Matrix for Walls with Sliding control Specimen

Grouting

1

A:UG-20%

Un-grouted

2

A:PG-1 course

Grouting of first course

3

A:PG-2 courses

Grouting of first and second courses

a) A:UG-20%

Post-Tension Ratio (% of f/m) 20.0 % 20.0 % 20.0 %

b) A:PG-1 course

267

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c) A:PG-2 courses Figure (7.18): Specimens Configurations for FE Models of PartiallyGrouted Walls Table (7.7) summarized the ultimate load capacity and the ultimate displacement obtained from ABAQUS models. Figure (7.19) shows the load-displacement curves from FE analysis, and Figure (7.20) presents comparison between the principle stress contours. Table (7.7): Lateral Loads and Displacement Comparison for Walls with Sliding control Specimen 1 2 3

A:UG-20% A:PG-1 course A:PG-2 courses

Ultimate Load (kN) (%) 66.39 100 85.42 128.7 93.80 141.3

268

Maximum Displacement (mm) (%) 12.0 100 16.0 133.3 18.0 150.0

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Figure (7.19): Predicated load-Displacement curves for FE Models of Partially- Grouted Walls

a) A:UG-PG-1 course

b) A:UG-PG-2 courses

Figure (7.20): Principle Stress Contours for FE Models of PartiallyGrouted Walls

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7.10.4. Partially-Grouted Post-Tensioned Walls with Sliding Control For the partially-grouted post-tensioned shear walls with sliding control, the position of post-tension bars and the initial post-tension stress were studied with the same parameters for the tested wall W9 (A:PG:Sl) such as material properties, blocks dimensions and aspect ratio. Eight additional wall specimens were added to extend results and study the effect of the two parameters on the behavior of dry-stacked shear walls with sliding control as shown in Table (7.8) and Figure (7.21) shows the specimens configurations. Table (7.8): Extended Specimens Matrix for Walls with Sliding control Specimen 1 2 3 4 5 6 7 8 9

A:PG:Sl A:PG:Sl-10% A:PG:Sl-15% A:PG:Sl-C A:PG:Sl-C-10% A:PG:Sl-C-15% A:PG:Sl-RL A:PG:Sl- RL-10% A:PG:Sl- RL-15%

Post-Tension Ratio (% of f/m) 20.0 % 10.0 % 15.0 % 20.0 % 10.0 % 15.0 % 20.0 % 10.0 % 15.0 %

270

Bars location North + Center + South North + Center + South North + Center + South Only Center Only Center Only Center North + South North + South North + South

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a) A:PG

b) A:PG-10%

c) A:PG-15%

d) A:PG-C

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e) A:PG-C-10%

f) A:PG-C-15%

h) A:PG-RL

i) A:PG-RL-10%

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j) A:PG-RL-15% Figure (7.21): Specimens Configurations for FE Models of PartiallyGrouted Walls with Sliding Control

Table (7.9) summarized the ultimate load capacity and the ultimate displacement obtained from ABAQUS models. Figure (7.22) shows the load-displacement curves from FE analysis with respect to the loaddisplacement curve for experimentally post-tension tested wall W9 (A:PG:Sl), and Figure (7.23) presents comparison between the principle stress contours for all walls.

273

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Table (7.9): Lateral Loads and Displacement Comparison for Walls with Sliding control Specimen 1 2 3 4 5 6 7 8 9

A:PG:Sl (20%) A:PG:Sl-10% A:PG:Sl-15% A:PG:Sl-C (20%) A:PG:Sl-C-10% A:PG:Sl-C-15% A:PG:Sl-RL (20%) A:PG:Sl- RL-10% A:PG:Sl- RL-15%

Ultimate Load (kN) (%) 58.20 100 29.35 50.4 43.92 75.5 81.18 139.5 40.58 69.7 60.88 104.6 56.55 97.2 28.27 48.6 42.80 73.5

Maximum Displacement (mm) (%) 38.0 100 48.0 126.3 42.0 110.5 28.0 73.7 44.0 115.8 35.0 92.1 38.0 100 48.0 126.3 42.0 110.5

Figure (7.22): Predicated load-Displacement curves for FE Models of Walls with Sliding control

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a) A:PG

b) A:PG-10%

c) A:PG-15%

d) A:PG-C

e) A:PG-C-10%

f) A:PG-C-15%

275

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h) A:PG-RL

i) A:PG-RL-10%

j) A:PG-RL-15% Figure (7.23): Principle Stress Contours for FE Models of Grouted Walls 7.11. Summary of Parametric Study The parametric study in the previous section shows clearly that: 1. For both grouted and un-grouted dry-stacked shear wall, the ultimate load capacity is directly proportional to the initial post-tension level. And the maximum displacement is inversely proportional to the initial post-tension level. 2. The concentration of post-tension force in the central cell did not affect the ultimate load capacity nor the failure mechanism of grouted and

276

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un-grouted walls but enlarge the maximum displacement by 13% and 22% in fully-grouted and un-grouted walls respectively. 3. The ductility of walls with sliding control could be 2.50 times the corresponding walls with the same post-tension and grouting conditions. 4. The ultimate load capacity of partially-grouted walls with sliding control directly proportional with the initial post-tension stress. 5. The usage of central bars changes the stress distribution along the cross section of base-isolated walls which change the failure mechanism from sliding to rocking and sliding, that change in failure mechanism can improve the ultimate load by 40%. 6. The grouting of first course can increase the ultimate load by 28.7%, and the grouting of two courses increases the ultimate load by 41.3% for the same post-tension level. 7. The finite element model was high estimate the displacement ductility comparing with the tested walls as a result of neglecting some crack development in thin face-shells of concrete blocks. It could be conclude that the improvement of geometry of blocks to enhance the failures in face-shells could improve the ductility of post-tension walls especially for base-isolated walls.

277

CHAPTER (8) SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS 7.1. Summary Masonry is one of the oldest construction materials. But there are several disadvantages of using masonry such as time consuming, need highly skilled laborers, the amount of mortar that is required to be mixed on-site and Shrinkage cracking due to mortar. Dry-stacking masonry is a suggested method to minimize some of these disadvantages. Dry-stacked masonry is manufactured as traditional brick work but without mortar joints. The dry-stack method makes construction significantly easier and thus reduces the need for skilled labor. However, dry-stack systems are not without their disadvantages such irregularities in the individual blocks and high initial settlement. Although the worldwide interest for the dry-stack masonry construction technique because of its attractive advantages, the lack of knowledge of loading and deformation behavior of dry-stacked masonry structures exists up to now in contrast to this of mortar layered brickwork. There are many available systems of interlocked mortar-less structures are already available in the local and worldwide markets. But these systems are based only on a small number of observations on the specific structures without gaining general information. Therefore, these systems are very restricted in design and application. The main objective of this research is to investigate the in-plane behavior of locally available dry-stacked masonry systems in Egypt, (i.e. Azar and Spar-lock systems) and comparing between these two systems and traditional masonry blocks system and study the feasibility of using locally available post-tension technique in dry-stacked masonry systems to 279

Chapter 8

Summary, Conclusions, and Recommendations

improve the in-plane performance and reduce the grout used in dry-stacked masonry constructions. To meet these objectives, experimental and analytical studies were conducted and documented in the thesis. In order to design the test program, properties of all used material were investigated then a pre-test analysis was carries out to predict the ultimate load carrying capacity and failure mechanism and choose how to construct sliding control to fulfill the design requirements. To assess the in-plane behavior of dry-stack shear walls, nine fullscale masonry shear walls were constructed and tested under in-plane cyclic loading. The specimens were constructed using three different concrete blocks, with different parameters such as grouting, reinforcement, post-tension and sliding control. The test results of each wall were presented in the form of crack patterns, load-drift angle curve, flexural strain at expected critical sections, panel drift angle and post-tension force - drift angle curves. Parametric study using finite element modeling was performed to cover those parameters which were not considered in the experimental study such as position of post-tension bars and its initial stress. 7.2. Conclusions The following conclusions were drawn from the experimental and analytical studies carried out in this research: (a) General Behavior 1. The dry-stacked Azar system behavior resembles the conventional masonry system and can be designed with the same formulas for grouted, un-grouted, reinforced, and post-tensioned walls.

280

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Summary, Conclusions, and Recommendations

2. Even the Spar-lock have special and better interlocking system than other dry-stack systems but it prevents the inclusion of horizontal reinforcement, thus leading to low ultimate load. 3. The Spar-lock system can be rearranged to allow horizontal reinforcement in the face shells which improves the ultimate load capacity by 17.90%, but the end blocks can’t be reinforced. 4. The use of post-tensioning with conventional and Azar walls can be an economical solution that can reduce the cost of the main reinforcement, grouting and skilled mason. The un-grouted post-tensioned drystacked masonry shear walls can resist more than 62.00% of the ultimate load capacity of the reinforced fully-grouted conventional walls. 5. The open/close movement of dry-stack joints could delay the crack propagation through the wall, the first crack would be observed at about 0.59% drift. 6. The sliding control improves the dry-sacked shear wall maximum drift up to 1.56% by allowing the wall to slide along the base. 7. For Azar and conventional block walls, the concentrated flexural rotation at wall footing was the main contribution of lateral displacement for reinforced and post-tension grouted walls, while the un-grouted post-tension walls had reasonable panel distortion contribution about 47% due to the open/close movement of dry-stack joints. The sliding control could enlarge the sliding contribution up to 35%. 8. The average residual displacements are 59% and 37% of the maximum displacements for conventionally reinforced and the post-tensioned walls respectively. The post-tensioning with sliding control could reduce the residual displacement in dry-stack walls to 10.9% of its overall drift. 281

Chapter 8

Summary, Conclusions, and Recommendations

9. Unexpected failures could be occurred due to stress concentration as a result of irregularities of individual dry-stack blocks. 10. The designing equations proposed by MSJC (2008) for reinforced and post-tensioned shear walls provides a good estimate for lateral load capacity with about 15% variation. The proposed formulas for posttension shear walls is given as following: 𝑎

𝑀𝑢 = (𝑓𝑝𝑠 𝐴𝑝𝑠 + 𝑓𝑦 𝐴𝑠 + 𝑃𝑢 ) (𝑑 − ) 2 Where, 𝑎 =

𝑓𝑝𝑠 𝐴𝑝𝑠 +𝑓𝑦 𝐴𝑠 +𝑃𝑢 /

0.80𝑓𝑚 𝑏

(b) Displacement Ductility 1. The displacement ductility (µ0.8∆) of reinforced shear walls were 5.88, 2.88 and 2.13 for conventional, Azar and Spar-lock walls respectively. 2. The displacement ductility (µ0.8∆) of post-tensioned walls had ranged between 2.34 and 3.92. 3. The sliding control could enhance the displacement ductility (µ 0.8∆) to reach more than 5.80. 4. Although the dry-stack walls had average half the displacement ductility at 20% degradation of load of the same conventional block walls, this displacement ductility could be improved using sliding control in post-tension dry-stack walls to be comparable to the conventional block walls. 5. The post-tension dry-stack walls with sliding control could maintain 80% of their ultimate lateral load capacity up to 2.51 times the drift angle at ultimate load. 6. The partially-grouted wall with sliding control A:RH:PG:P:Sl reached a drift limit of 1.0% with almost no strength degradation (in pull direction), which is the limit specified by the NBCC (2005) for Post-

282

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Summary, Conclusions, and Recommendations

disaster buildings, required to be fully operational after an earthquake event. 7. The tested walls results showed that the ASCE code is underestimate the ductility of post-tension walls by considering it as plain masonry shear walls with 1.5 R factor. The R factor could be assumed between 2.15 and 2.50 for the post-tensioned un-grouted shear walls and could be more than 2.83 if using sliding control with post-tension shear walls. 8. The un-grouted post-tensioned shear walls presented resulted in a high quality fragility function with median drifts of 0.30%, 0.58% and 1.14% corresponding to a dispersion of 0.26, 0.30 and 0.22 for predefined damage states DS1 – DS3, respectively. (c) Stiffness 1. Spar-lock had very low stiffness comparing with other wall systems; however, it could keep 46% of its initial stiffness up to 1% drift when other system lost more than 90% of its initial stiffness. 2. The initial stiffness of fully-grouted post-tension walls was almost 60% initial stiffness of the conventionally reinforced walls, and losses stiffness less gradually than reinforced walls. 3. The wall with sliding control lost its stiffness more gradually than other post-tension walls. 4. The elastic theory equation developed by Priestly and Hart (1989) provides a good estimate for stiffness of reinforced and post-tension walls with about 22% variation after scaling down the stiffness of reinforced walls by 0.3 as suggested by Hart et al (1988). The proposed formulas for reinforced and post-tensioned shear walls is given as following: 𝐾 = 0.3⁄ ℎ3 1.2ℎ (3𝐸 𝐼 + 𝐴𝐺 ) 𝑚 𝑒

(for reinforced walls)

𝑚

283

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Summary, Conclusions, and Recommendations

𝐾 = 1⁄ ℎ3 1.2ℎ (3𝐸 𝐼 + 𝐴𝐺 ) 𝑚 𝑒

(for post-tensioned walls)

𝑚

Where, 𝐼𝑒 = (

103 𝑓𝑦

+

𝑃 / 𝑓𝑚 𝑙𝑤 𝑏

) 𝐼𝑔

5. The elastic theory equation may be used to predict the stiffness of walls post-tensioned shear walls using the gross moment of inertia and gross section area, this method provides a fair estimate for stiffness of posttension walls with about 30% variation after scaling down the equation by 0.2 as follows: 𝐾 = 0.2⁄ ℎ3 1.2ℎ (3𝐸 𝐼 + 𝐴 𝐺 ) 𝑚 𝑔

𝑔 𝑚

(d) Energy Dissipation and Viscosity Damping 1. The energy dissipation of post-tensioned fully-grouted wall is equal twice the un-grouted wall, and almost 75% of the energy dissipated by the conventionally reinforced wall. 2. The open/close movement of dry-stack joints enable the Azar ungrouted post-tensioned walls to dissipate energy 2.5 times the conventional block walls, and even 35% more than the fully-grouted post-tension wall. And the sliding control could improve the energy dissipation of post-tension walls. 3. The viscous damping of conventionally reinforced walls ranged between 10% and 20%, where the fully-grouted post-tension wall had viscous damping between 7% and 12%. 4. The dry-stack (Azar and Spar-lock) un-grouted post-tension walls had increasing viscous damping with increased displacements. The average equivalent viscous damping ratio calculated at 0.5% drift and 1% drift for dry-stacked un-grouted post-tension walls was about 13% and 25%, respectively. This indicates that dry-stacked un-grouted 284

Chapter 8

Summary, Conclusions, and Recommendations

shear wall buildings can be expected to experience high levels of damping which would reduce the seismic demand. (e) Analytical Study 1. The proposed finite element models using Abaqus could capture the structural behavior of tested post-tension walls in satisfactory way. 2. For both grouted and un-grouted dry-stacked shear wall, the ultimate load capacity is directly proportional to the initial post-tension level. And the maximum displacement is inversely proportional to the initial post-tension level. 3. The concentration of post-tension force in the central cell did not affect the ultimate load capacity nor the failure mechanism of grouted and un-grouted walls but enlarge the maximum displacement by 13% and 22% in fully-grouted and un-grouted walls respectively. 4. The ductility of walls with sliding control could be 2.50 times the corresponding walls with the same post-tension and grouting conditions. 5. The ultimate load capacity of partially-grouted walls with sliding control directly proportional with the initial post-tension stress. 6. The usage of central bars changes the stress distribution along the cross section of base-isolated walls which change the failure mechanism from sliding to rocking and sliding, that change in failure mechanism can improve the ultimate load by 40%. 7. The grouting of first course can increase the ultimate load by 28.7%, and the grouting of two courses increases the ultimate load by 41.3% for the same post-tension level. 8. The finite element model was high estimate the displacement ductility comparing with the tested walls as a result of neglecting some crack development in thin face-shells of concrete blocks. It could be 285

Chapter 8

Summary, Conclusions, and Recommendations

conclude that the improvement of geometry of blocks to enhance the failures in face-shells could improve the ductility of post-tension walls especially for base-isolated walls. 7.3. Recommendations for Further Studies 1. In the current, study only the in-plane behavior of locally available dry-stack masonry shear walls was studies. Further studies are needed to investigate the out-of-plane behavior of locally available dry-stack masonry systems 2. Developing new block shape to minimize the effect of irregularities of blocks which could cause stress concentrations 3. Further studies are needed to improve the shear characterization of dry-stack shear walls. The usage of horizontal post-tensioning could be used

286

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References Priestly, M. J. N. and Park, R., (1987), “Strength and Ductility of Concrete Bridge Columns Under Seismic Loading,” ACI Structural Journal. Priestly, M. J. N. (1997), “Myths and Fallacies in Earthquake EngineeringConflicts between Design and Reality,” Concrete International, the Magazine of the American Concrete Institute. Priestly, M. J. N. (2000), “Performance Based Seismic Design,” Proceedings of 12th World Conference on Earthquake Engineering (12WCEE), Auckland, New Zealand. Rosenboom, O. A., and Kowalsky, M. J. (2004) “Reversed in-plane cyclic behavior of posttensioned clay brick masonry walls.” Journal of Structural Engineering, 130(5):787–798. Salah, M. S. (2010), “Post-Tensioned Masonry Shear Walls,” MSc. Thesis, Structural Engineering Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt. Schultz, A. E., Bean, J. R. and Drake, C. R. (2004), “Lateral Load Tests of Slender Post-Tensioned Masonry Walls,” Proceedings of the 13th International Brick and Block Masonry Conference, Amsterdam. Shedid, M. T., El-Dakhakhni, W. W. and Drysdale, R. G. (2009), “Behavior of fully grouted reinforced concrete masonry shear walls failing in flexure: Analysis,” ELSEVIER, Engineering Structures 31, 2032:2044. Shing P. B., Noland J. L., Spaeh H., and Klamerus E. (1986), “Response of Reinforced Masonry Story Height Walls to Fully Reversed In-Plane Loads,” Department of Civil Engineering, University of Colorado, Boulder.

297

References Shing P. B., Brunner J. D., and Lotfi H. R. (June 1993), “Analysis of Shear Strength of Reinforced Masonry Walls,” Proceedings of the Sixth North American Masonry Conference, Department of Civil and Architectural Engineering, Drexel University, Philadelphia, Pennsylvania. Shing P. B., Brunner J. D., and Lotfi H. R. (August 1993), “Evaluation of Shear Strength of Reinforced Masonry Walls,” The Masonry Society Journal. Shing P. B., and Hoskere V. S. (1990), “In-Plane Resistance of Reinforced Masonry Shear Walls,” Journal of Structural Engineering, Proceedings of ASCE, Vol 116, No. 3. Shing P. B., Klamerus E. W., Schuller M. P., and Noland J. L. (1988), “Behavior of Single-Story Reinforced Masonry Shear Walls Under In-plane Cyclic Lateral Loads,” Fourth Meeting of U.S.-Japan Joint Technical Coordination Committee on Masonry Research, San Diego. Shing P. B., Noland J. L., Klamerus E. W., and Spaeh H. (1989), “Inelastic Behavior of Concrete Masonry Shear Walls,” Journal of Structural Engineering, Proceedings of ASCE, Vol. 115, No. 9. Shing P. B., Schuller M., Hoskere V. S., and Carter E. (1990), “Flexural and Shear Response of Reinforced Masonry Shear Walls,” ACI Structural Journal. Spar-lock Technologies Inc. 2010. Spar-lock building system [online]. Available from http://sparlock.com/default.shtml [cited March 2012]. Tomazevic M. (1998), “Earthquake-Resistant Design of Masonry Buildings,” Covent Garden (London, UK): Imperial College Press. 298

References

UBC, Uniform Building Code (1997), Chapter 21-Masonry, The Masonry Society. Uzoegbo H. C., R. Senthivel and J. V. Ngowi (2007), “Load Capacity of Dry-Stack Masonry Walls”, TMS Journal, South Africa.

299

‫الملخص‬ ‫يعتبر الطوب من أقدم المواد االنش ا ااوييتب ويعتبر اا ا ااتوحاوو ل وقم وةومتوو لعمولت مدربت واالةتيو‬ ‫لاميوم ابيرة من المونت التي تخ ط بولموقع ومشا ا ااا ت شا ا ااروف االناموا بولم ون‬

‫ا ا اامن العديد من‬

‫العيوب ل مبوني الطوبب أةد االقتراةوم التي قد تق ل من عيوب مبوني الطوب هي البنوء بوا ااتخدام‬ ‫الوةدام المتداخ ت بدون مونتب تن ذ ةوايط المبوني من الوةدام المتداخ ت بدون مونت مثل الطريقت‬ ‫التق يديت ل بنوء لان بدون اا ااتخدام المونتب تا ااول هذي الطريقت مدا من عم يت االنش ااوء وبولتولي تق ل‬ ‫االةتيو ل عمولت المدربتب وال تخ وا طريقت البنوء بدون مونت من عيوب مثل عدم انتظوم الوةدام‬ ‫المنتمت والوبوط العولي بعد التن يذب‬ ‫بولرغم من االهتموم بطريقت البنوء بولوةدام المتداخ ت في أنةوء العولم لان هنوك نقص في‬ ‫المع وموم عن ا وك المبوني المن ذة بوذي الطريقت من ةيث األةمول والتشاحم مقورنت بولمبوني‬ ‫التق يديت المن ذة بولمونتب بول عل يتوفر ةوليو في الاوقين المة ي والعولمي العديد من أنظمت المبوني‬ ‫من الوةدام المتداخ ت بدون مونت‪ ،‬لان هذي األنظمت مبنيت ع ى عدد مةدود من المحةظوم ع ى‬ ‫مبوني مةددة دون ومود بيونوم عومتب لذلك تصمم وتن ذ هذي األنظمت بطرق متة ظتب‬ ‫أمريم هذي الدراات بغرض ااتاشون خواص ةوايط القص داخل الماتوى المن ذة من أنظمت‬ ‫مبوني الطوب من الوةدام المتداخ ت من اإلنتو المة ي (نظوم إزار ونظوم ابورلوك) ومقورنتوو بنظوم‬ ‫المبوني التق يديب‬ ‫اات زم تصميم البرنومج العم ي دراات خواص المواد الماتخدمت وعمل تصميم أولي ل ةوايط‬ ‫ل تنبؤ بقدرتوو ع ى تةمل األةمول المونبيت‪ ،‬واذلك اختيور الطريقت المنوابت لتن يذ عزل القوعدة لت بيت‬ ‫متط بوم التصميمب‬ ‫‪1‬‬

‫الملخص‬ ‫لدراات ا وك ةوايط القص من الوةدام المتداخ ت تم تن يذ واختبور عشرة ةوايط بةمل‬ ‫متارر داخل الماتوىب تم تن يذ العينوم بواتخدام ثحثت أنواع مخت ت من الب واوم األامنتيت‪ ،‬مع‬ ‫دراات تأثير بعض المتغيرام اولةقين والتا يح والشد الحةق وعزل القوعدةب تم عرض نتويج االختبور‬ ‫لال ةويط في صورة منةنى الةمل مع زاويت االنةران‪ ،‬ومنةنيوم االن عول عند المقوطع الةرمت‪،‬‬ ‫وتشال الةويط‪ ،‬ومنةنيوم قوى الشد الحةق مع زاويت االنةرانب‬ ‫تم امراء دراات تة ي يت بطريقت العنوصر المةددة لتغطيت العوامل التي لم ياع البرنومج‬ ‫العم ي درااتوو مثل تأثير أموان أايوف الشد الحةق وقيمتهب‬ ‫وقد أظورم نتويج البرنومج العم ي تشوبه ا وك نظوم إزار بنظوم مبوني الطوب التق يدي‪ ،‬في‬ ‫ةين انوورم ةوايط نظوم ابورلوك بطريقت قص ت ةتى بعد مةوولت اعودة ترتيبه وتا يةه أفقيوب امو‬ ‫أو ةم النتويج فوع يت ااتخدام الشد الحةق مع ةوايط المبوني من الوةدام المتداخ ت والمن ذة بدون‬ ‫ةقين والتي تةم م ‪ %62‬من قدرة الةوايط الما ةت وبواتخدام الةقين ا يوب امو اون ااتخدام عزل‬ ‫القوعدة م يدا في تةاين ممطوليت الةوايط بولوةدام المتداخ ت والمن ذة بولشد الحةقب‬ ‫وأظورم نتويج التة يل العددي أن قدرة تةمل الةوايط لألةمول المن ذة بولةقين وبدونه ع ى الاواء‬ ‫تتنواب طرديو مع ماتوى الشد الحةق المبديي من غير تأثير أموان أايوف الشد ع ى قدرتووب امو‬ ‫أو ح التة يل أن ااتخدام الةقين في المدموك األول فقط ل ةوايط يمانه زيودة قدرة تةم وو بنابت‬ ‫‪ %28‬وأن ةقن أول مدمواين يزيد القدرة بنابت ‪ %41‬وذلك لن س ماتوى الشد الحةقب واذلك‬ ‫تبين أن عزل القوعدة يق ل قدرة الةوايط لتةمل األةمول بةوالي ‪ %15‬ولان مع زيودة م ةوظت في‬ ‫ممطوليتووب واذلك بدراات الةوايط المن ذة بةقين مزيي مع عزل القوعدة تبين أن قدرتوو لتةمل‬ ‫األةمول تزيد بةوالي ‪ %40‬إذا ترازم أايوف الشد الحةق في منتصن الةويطب‬ ‫‪2‬‬

‫تعريف بمقدم الرسالة‬ ‫االام‬

‫‪ :‬مةمد اةيل مةمد فويز‬

‫توريخ الميحد‬

‫‪1982/1/8 :‬‬

‫مةل الميحد‬

‫‪ :‬الق يوبيت‬

‫آخر درمت مومعيت‬

‫‪ :‬موماتير الوندات اإلنشوييت‬

‫الموت المونةت‬

‫‪ :‬ا يت الوندات ‪ -‬مومعت عين شمس‬

‫توريخ المنح‬

‫‪ :‬ابتمبر ‪2009‬‬

‫الوظي ت الةوليت‬

‫‪ :‬مدرس ماوعد بقام الوندات اإلنشوييت‬ ‫ا يت الوندات ‪ -‬مومعت عين شمس‬

‫كليه الهندسه‬ ‫قسم الهندسة االنشائية‬ ‫رسالة دكتوراه‬ ‫اسم الطالب‬

‫‪ :‬محمد كحيل محمد فايز‬

‫عنوان الرسالة ‪ :‬سلوك حوائط المباني من الوحدات المتداخلة بدون مونة من اإلنتاج المحلي‬ ‫اسم الدرجة‬

‫‪ :‬دكتوراه الفلسفه فى الهندسة‬

‫لجنة االشراف‪:‬‬ ‫دكتور ‪ :‬هاني محمد الشافعي‬

‫أاتوذ ماوعد بقام الوندات اإلنشوييت‬ ‫ا يت الوندات ‪ -‬مومعت عين شمس‬

‫دكتور ‪ :‬أحمد رشاد محمد‬

‫مدرس بقام الوندات اإلنشوييت‬ ‫ا يت الوندات ‪ -‬مومعت عين شمس‬

‫دكتور ‪ :‬حسين أسامة عقيل‬

‫مدرس بقام الوندات اإلنشوييت‬ ‫ا يت الوندات ‪ -‬مومعت عين شمس‬

‫تاريخ البحث ‪............../............./......... :‬‬ ‫الدراسات العليا‪:‬‬ ‫ختم االجازة‪:‬‬

‫اجيزت الرسالة بتاريخ ‪............./............./......... :‬‬

‫موافقة مجلس الكلية ‪.........../............./......... :‬‬ ‫موافقة مجلس الجامعة ‪.........../............./......... :‬‬

‫القاهرة ‪)2015( -‬‬

‫الموافق ة على المنح‬ ‫كلية الهندسة‬ ‫قسم الهندسة االنشائية‬ ‫عنوان الرسالة‬

‫ا وك ةوايط المبوني من الوةدام المتداخ ت بدون مونت من اإلنتو المة ي‬ ‫اعداد‬ ‫محمد كحيل محمد فايز‬

‫لجنة الحكم‬ ‫االسم‬ ‫أستاذ دكتور ‪ :‬أحمد أحمد عبد الحميد‬

‫التوقيع‬ ‫بببببببببببببببببببببببببببب‬

‫أاتوذ و مدير معمل أبةوث المبوني ‪ -‬مومعت دراايل‬ ‫ڤحدلڤيو – الواليوم المتةدة األمريايت‬ ‫أستاذ دكتور ‪ :‬أحمد شريف عيسوي‬

‫بببببببببببببببببببببببببببب‬

‫أاتوذ المنشآم الخراونيت الما ةت ‪ -‬قام الوندات اإلنشوييت‬ ‫ا يت الوندات ‪ -‬مومعت عين شمس‬ ‫دكتور ‪ :‬هاني محمد الشافعي‬

‫بببببببببببببببببببببببببببب‬

‫أاتوذ ماوعد بقام الوندات اإلنشوييت‬ ‫ا يت الوندات ‪ -‬مومعت عين شمس‬ ‫(عن لمنت اإلشران)‬ ‫‪ 6‬مايو ‪2015‬‬

‫كليه الهندسة‬ ‫قسم‬

‫الهندسة االنشائية‬

‫ا وك ةوايط المبوني من الوةدام المتداخ ت بدون مونت من اإلنتو المة ي‬ ‫رسالة مقدمة للحصول على درجة دكتوراه الفلسفه فى الهندسة‬ ‫في الهندسة المدنية‬ ‫(الهندسة االنشائية)‬ ‫اعداد‬ ‫محمد كحيل محمد فايز‬ ‫حاصل على ماجستير فى العلوم الهندسية‬ ‫فى الهندسة المدنية‬ ‫(الهندسة االنشائية)‬ ‫كليه الهندسة‪ ،‬جامعة عين شمس‪ ،‬سنة ‪2009‬‬

‫المشرفون‬ ‫دكتور ‪ :‬هاني محمد الشافعي‬ ‫أستاذ مساعد بقسم الهندسة اإلنشائية‬ ‫كلية الهندسة – جامعة عين شمس‬ ‫دكتور ‪ :‬حسين أسامة عقيل‬ ‫مدرس بقسم الهندسة اإلنشائية‬ ‫كلية الهندسة – جامعة عين شمس‬

‫دكتور ‪ :‬أحمد رشاد محمد‬ ‫مدرس بقسم الهندسة اإلنشائية‬ ‫كلية الهندسة – جامعة عين شمس‬

‫‪2015‬‬