STUDIES ON MECHANICAL PROPERTIES OF BRICK MASONRY Peri Raghava Ravi Teja Department of Civil Engineering National Institute of Technology Rourkela Rourkela – 769 008, India Studies on Mechanical Properties of Brick Masonry Thesis submitted in partial fulfillment of the requirements for the degree of Master of Technology (Research) in Structural Engineering by Peri Raghava Ravi Teja (Roll No. 613CE1006) under the supervision of Dr. Pradip Sarkar and Dr. Robin Davis P. Department of Civil Engineering National Institute of Technology Rourkela Rourkela – 769 008, India August 2015 Dedicated to My Grandfather, Parents & Supervisors... Department of Civil Engineering National Institute of Technology Rourkela Rourkela-769 008 , Odisha , India. www.nitrkl.ac.in Certificate This is to certify that the work in the thesis entitled “Studies on Mechanical Properties of Brick Masonry” by Peri Raghava Ravi Teja, bearing Roll Number 613CE1006, is a record of an original research work carried out by him under our supervision and guidance in partial fulfillment of the requirements for the award of the degree of Master of Technology (Research) in Structural Engineering, Department of Civil Engineering. The content of this thesis, in full or in parts, has not been submitted to any other Institute or University for the award of any degree or diploma. Research Guides Rourkela-769008 Date: Prof. Pradip Sarkar Prof. Robin Davis P. Department of Civil Engineering Acknowledgement A research work requires the support of many people directly or indirectly. I would like to utilize this opportunity to convey my gratitude to all those people who have supported and blessed me during my research work. First and foremost I would like to thank my supervisors; Prof. Pradip Sarkar and Prof. Robin Davis P., for their constant support, encouragement and guidance throughout my research programme at NIT Rourkela. I would always cherish the moments I spent with my supervisors discussing about the research findings. They are the source of inspiration for me, their hard work, patience, time management and many other skills make them a true definition of a supervisor. I feel extremely proud and thank the almighty for making me their student. I could not ask for a better guide than them. I would like to thank Prof. S. K. Das and Prof. K. C. Biswal for the suggestions and interest they provided in my research work. I would like to thank my MSC members, faculty of civil engineering department and structural engineering laboratory staff of NIT Rourkela for their support. I wish to express my sincere gratitude to Prof. S. K. Sarangi, Director, NIT Rourkela for giving me the opportunities and facilities to carry out my research work. I would like to convey my heartfelt thanks to my friends and research scholars: Sharmili Routray, Subhashree Behera, Sambit Beura, Rupalika Dash, Pranab Kumar Ojha, Srikar Potnuru, Kirti Kanta Sahoo and Pratik Kumar Dhir for helping me in various ways to complete the research work. Above all, very special thanks to my family; I cannot express in words my gratitude to my Father, Mother and Sister for their continuous support, motivation, prayers and blessings because of which I am able to complete and present this thesis. Peri Raghava Ravi Teja Abstract Keywords: Brick masonry; water absorption; initial rate of absorption; compressive strength; variability; probability distribution function; shear bond strength Brick masonry, a composite of brick units bound together with mortar, is widely used for building construction in India. Burnt clay bricks are commonly used in construction of masonry structures since many years. But with growing environmental concern for conservation of natural resources and disposal of fly ash, bricks made with fly ash are emerging as a substitute to burnt clay bricks for construction of masonry structures. The behaviour of masonry structure is dependent on the properties of its constituents such as brick units and mortar separately and together as a unified mass. Brick properties vary largely from region to region as bricks are made with locally available raw materials with inherent randomness. Therefore, the analysis and design of brick masonry structures considering the mean values of material properties may underestimate or overestimate the structural capacity. In order to design a safer structure it is necessary to take in to consideration the randomness and variability of the material properties of brick masonry. This requires mathematical description of the variability in different material properties of brick masonry. The variability of mechanical properties related to steel and concrete is well researched, while the same for brick masonry has not received proper attention. The lack of data has led to ignorance of uncertainty in brick masonry while analysing structures. Under lateral loads, brick masonry is expected to undergo in-plane and out-of-plane forces. Resistance to out-of-plane forces in masonry structure is negligible and generally ignored in analysis and design. However, the in-plane forces which act parallel to the plane of wall is resisted by the bond between brick and mortar. Shear bond strength of masonry plays an important role in dealing with in-plane forces. The soaking of bricks prior to construction is very essential to achieve good shear bond strength. Bricks with higher initial rate of absorption must be pre-wetted prior to use in construction else they absorb more water from mortar inhibiting its hydration. But, the optimum duration of pre-wetting or the optimum moisture content of brick necessary to obtain higher shear bond strength is not available in published literatures. In present study, several experiments are carried out to determine mechanical properties such as initial rate of absorption, water absorption, dry density and compressive strength of brick units, compressive strength of mortar and masonry prism and shear bond strength of masonry triplet. Higher order analyses such as X-ray diffraction and field emission scanning electron microscopy are conducted to understand the morphological and microstructural differences in brick leading to variation in its compressive strength. Three different types of failure patterns such as vertical splitting, diagonal shear failure and crushing are identified for masonry prism under axial compression. The variability in the mechanical properties of brick masonry and its constituent materials is described using different probability distribution functions. Four two-parameter distribution functions namely normal, lognormal, gamma and Weibull distribution are chosen and their acceptability is evaluated using three goodness-of-fit tests such as Kolmogorov-Sminrov, Chi-square and log-likelihood test. All the distributions are found to be closely competing to fit the variability best. Lognormal is found to be common distribution function to best describe the variability for most of the mechanical properties studied. Weibull and gamma distributions are found to be most appropriate for other properties. However, in general, gamma distribution is found to be either the best or the next best distribution function to describe most of the mechanical properties studied. Therefore, lognormal or gamma distribution is recommended as the distribution function that best describe the variability of properties of brick masonry and its constituents. The morphological and microstructural analyses attributed the low and high strength in brick samples to the absence of certain chemical compounds and variation in surface texture. The presence of compounds of silica, aluminium, calcium, iron oxide and magnesium is observed to be helpful for bricks in attaining higher compressive strength. vi Simple mathematical equations are proposed to estimate the compressive strength of brick unit and masonry prism. The equations can be used for both clay and fly ash bricks. The proposed equations are validated by comparing the predicted value of the compressive strength with experimental value obtained from published literatures. The optimum moisture content in bricks at the time of construction to obtain higher shear bond strength is experimentally determined. It is observed from the failure pattern of triplets that shear bond failure depends on the strength of brick, mortar and their bond. IRA and moisture content of brick control the modes of failure indirectly through shear bond strength. vii Contents Certificate iii Acknowledgment iv Abstract v List of Figures xii List of Tables xvi Abbreviations xviii Notations xix 1 Introduction 1 1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Objectives of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Scope of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Organisation of the Thesis . . . . . . . . . . . . . . . . . . . . . . . 7 2 Literature Review 9 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Structural Properties of Brick Masonry 9 . . . . . . . . . . . . . . . 2.2.1 Clay Brick Masonry . . . . . . . . . . . . . . . . . . . . . . 10 2.2.2 Fly Ash Brick Masonry . . . . . . . . . . . . . . . . . . . . . 13 viii 2.3 Variability in Properties of Concrete . . . . . . . . . . . . . . . . . 16 2.4 Morphological and Microstructural Study on Clay and Fly Ash Bricks 19 2.5 Shear Bond Strength of Brick Masonry . . . . . . . . . . . . . . . . 22 2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3 Experimental Work 26 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2 Materials Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.3 3.4 3.2.1 Brick . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2.2 Sand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2.3 Cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Test Specimens Preparation . . . . . . . . . . . . . . . . . . . . . . 29 3.3.1 Brick Units . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3.2 Mortar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3.3 Masonry Assemblages Detailed Experimental Tests and Procedures . . . . . . . . . . . . . 33 3.4.1 3.4.2 3.5 . . . . . . . . . . . . . . . . . . . . . 31 Tests for Mechanical Properties . . . . . . . . . . . . . . . . 33 3.4.1.1 Initial Rate of Absorption . . . . . . . . . . . . . . 33 3.4.1.2 Water Absorption and Dry Density . . . . . . . . . 34 3.4.1.3 Compressive Strength . . . . . . . . . . . . . . . . 35 3.4.1.4 Shear Bond Strength . . . . . . . . . . . . . . . . . 35 Tests for Morphology and Microstructure . . . . . . . . . . . 36 3.4.2.1 X-ray Diffraction . . . . . . . . . . . . . . . . . . . 36 3.4.2.2 Field Emission Scanning Electron Microscopy . . . 36 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4 Variability and Analytical Study on the Properties of Bricks and its Masonry 39 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.2 Variability in Mechanical Properties of Bricks . . . . . . . . . . . . 40 4.2.1 Variation in different Properties of Brick Units . . . . . . . . 40 ix 4.3 Variation in IRA . . . . . . . . . . . . . . . . . . . 42 4.2.1.2 Variation in WA . . . . . . . . . . . . . . . . . . . 43 4.2.1.3 Variation in dry density . . . . . . . . . . . . . . . 44 4.2.1.4 Variation in compressive strength of brick units . . 45 4.2.2 Variation in Compressive Strength of Mortar 4.2.3 Variation in Compressive Strength of Masonry Prisms . . . . 47 4.2.4 Probability Distribution of Parameters . . . . . . . . . . . . 50 . . . . . . . . 45 4.2.4.1 IRA of Brick Units . . . . . . . . . . . . . . . . . 52 4.2.4.2 WA of Brick Units . . . . . . . . . . . . . . . . . . 52 4.2.4.3 Dry Density of Brick Units . . . . . . . . . . . . . 53 4.2.4.4 Compressive Strength of Brick Units . . . . . . . . 53 4.2.4.5 Compressive Strength of Mortar . . . . . . . . . . . 62 4.2.4.6 Compressive Strength of CB Prism . . . . . . . . . 62 4.2.4.7 Compressive Strength of FAB-I Prism . . . . . . . 67 4.2.4.8 Compressive Strength of FAB-II Prism . . . . . . . 67 Morphology and Microstructure of Bricks . . . . . . . . . . . . . . . 72 4.3.1 4.3.2 4.4 4.2.1.1 Interpretation from XRD Analysis . . . . . . . . . . . . . . . 72 4.3.1.1 XRD of Brick units . . . . . . . . . . . . . . . . . 72 4.3.1.2 XRD of different grades of Mortar . . . . . . . . . 75 Interpretation from FESEM Images . . . . . . . . . . . . . 77 Analytical Modelling of Brick Properties . . . . . . . . . . . . . . . 80 4.4.1 Modelling of Brick Compressive Strength . . . . . . . . . . . 80 4.4.2 Statistical inferences for Predicted Compressive Strength of Brick units . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.4.3 Estimation of Masonry Prism Compressive Strength . . . . . 90 4.5 Failure Pattern in Masonry Prism . . . . . . . . . . . . . . . . . . . 95 4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5 Shear Bond Strength of Brick Masonry 101 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.2 Lacunas in Past Researches . . . . . . . . . . . . . . . . . . . . . . 102 x 5.3 Salient Features of Present Study . . . . . . . . . . . . . . . . . . . 103 5.4 Specifications of the Experimental Work . . . . . . . . . . . . . . . 103 5.5 Discussion of Test Results . . . . . . . . . . . . . . . . . . . . . . . 105 5.6 Optimum Brick Moisture Content . . . . . . . . . . . . . . . . . . . 111 5.7 Bond Strength and Compressive Strength of Brick Masonry 5.8 Failure Patterns in Triplets . . . . . . . . . . . . . . . . . . . . . . . 116 5.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6 Summary and Conclusions . . . . 115 120 6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 6.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 6.3 Main Contribution of the Research . . . . . . . . . . . . . . . . . . 124 6.4 Scope for Future Work . . . . . . . . . . . . . . . . . . . . . . . . . 124 Appendices 126 A Introduction to Fly Ash Bricks 126 B Probability Distributions and Goodness-of-Fit Tests 136 C Correlation of Brick Properties 142 Bibliography 148 List of Figures 1.1 Multi storey building constructed using fly ash bricks . . . . . . . . 2 3.1 Typical burnt clay brick . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 Fly ash: (a) Source-I and (b) Source-II . . . . . . . . . . . . . . . . 28 3.3 FAB-I type fly ash brick . . . . . . . . . . . . . . . . . . . . . . . . 28 3.4 FAB-II type fly ash brick . . . . . . . . . . . . . . . . . . . . . . . . 29 3.5 CM1, CM2 and CM3 grade mortar cubes . . . . . . . . . . . . . . . 31 3.6 Typical stack-bonded masonry prism specimen . . . . . . . . . . . . 32 3.7 Typical stack bonded masonry triplet specimen . . . . . . . . . . . 33 3.8 Test setup for determining IRA . . . . . . . . . . . . . . . . . . . . 34 3.9 Compression test of (a) brick (b) mortar cube and (c) prism specimen 35 3.10 Test setup of shear bond strength test with triplet specimen . . . . 36 3.11 Multipurpose X-ray diffraction system (Rigaku ULTIMA IV) . . . . 37 3.12 FESEM (Nova Nano SEM/FEI ) . . . . . . . . . . . . . . . . . . . 37 4.1 Mean IRA values for three brick variants . . . . . . . . . . . . . . . 43 4.2 Mean WA values for three brick variants . . . . . . . . . . . . . . . 44 4.3 Mean dry density values for three brick variants . . . . . . . . . . . 45 4.4 Mean compressive strength values for three brick variants . . . . . . 46 4.5 Mean compressive strength for three mortar grades . . . . . . . . . 46 4.6 Mean compressive strength of the masonry prisms . . . . . . . . . . 49 4.7 Experimental and assumed cumulative probability distributions for IRA of brick units . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 xii 4.8 Experimental and assumed cumulative probability distributions for WA of brick units . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.9 Experimental and assumed cumulative probability distributions for dry density of brick units . . . . . . . . . . . . . . . . . . . . . . . . 60 4.10 Experimental and assumed cumulative probability distributions for compressive strength of brick units . . . . . . . . . . . . . . . . . . 61 4.11 Experimental and assumed cumulative probability distributions for compressive strength of three mortar grades . . . . . . . . . . . . . 64 4.12 Experimental and assumed cumulative probability distributions for for CB prism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.13 Experimental and assumed cumulative probability distributions for for FAB-I prism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.14 Experimental and assumed cumulative probability distributions for for FAB-II prism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.15 XRD pattern for CB (a) low strength (b) high strength . . . . . . 73 4.16 XRD pattern for FAB-I (a) low strength (b) high strength . . . . . 74 4.17 XRD pattern for FAB-II (a) low strength (b) high strength . . . . 75 4.18 XRD pattern for mortar of three grades (a) CM1 (b) CM2 (c) CM3 76 4.19 FESEM images of CB . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.20 FESEM images of FAB-I . . . . . . . . . . . . . . . . . . . . . . . . 79 4.21 FESEM images of FAB-II . . . . . . . . . . . . . . . . . . . . . . . 79 4.22 Variation of (a) IRA (b) WA (c) dry density with compressive strength for FAB-I . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.23 Correlation of (a) IRA (b) WA (c) dry density with compressive strength for FAB-I . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.24 Variation plot between actual and predicted compressive strength for FAB-I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.25 Predicted and assumed cumulative probability distributions for compressive strength of brick units . . . . . . . . . . . . . . . . . . 89 4.26 Experimental versus Estimated prism strength for CB . . . . . . . . 92 4.27 Experimental versus Estimated prism strength for FAB-I . . . . . . 92 xiii 4.28 Experimental versus Estimated prism strength for FAB-II . . . . . . 92 4.29 Vertical splitting failure in (a) CB (b) FAB-I and (c) FAB-II prisms 96 4.30 Fig. 4.30: Diagonal shear failure in (a) CB (b) FAB-I and (c) FAB-II prisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.31 Crushing failure in (a) CB (b) FAB-I and (c) FAB-II prisms . . . . 97 4.32 Failure due to crushing of brick . . . . . . . . . . . . . . . . . . . . 97 5.1 Triplet before shear bond strength test . . . . . . . . . . . . . . . . 106 5.2 Triplet after shear bond strength test . . . . . . . . . . . . . . . . . 106 5.3 Shear bond strength for Set-A triplets 5.4 Shear bond strength for Set-B triplets . . . . . . . . . . . . . . . . . 109 5.5 Shear bond strength for Set-C triplets . . . . . . . . . . . . . . . . . 110 5.6 Shear bond strength for Set-D triplets 5.7 Variation in shear bond strength with moisture content of CB at the . . . . . . . . . . . . . . . . 107 . . . . . . . . . . . . . . . . 111 time of construction (Saturation moisture content of CB = 16.69%) 112 5.8 Variation in shear bond strength with moisture content of FAB-I brick at the time of construction (Saturation moisture content of FAB-I = 16.80%) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.9 Variation in shear bond strength with moisture content of FAB-II brick at the time of construction (Saturation moisture content of FAB-II = 16.84%) . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.10 Relation between shear bond strength and compressive strength of masonry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 5.11 Failure within the brick-mortar interface (Type A) . . . . . . . . . . 117 5.12 Failure within the mortar joint (Type B) . . . . . . . . . . . . . . . 117 5.13 Fig. 5.13: Failure within the brick unit (Type C) . . . . . . . . . . 118 5.14 Combination of failure within the brick unit and mortar joint (Type D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 A.1 Various modes of utilization of fly ash [1] . . . . . . . . . . . . . . . 130 A.2 Batching of raw materials using wheel barrow . . . . . . . . . . . . 133 A.3 Mixing of raw materials in a mixer . . . . . . . . . . . . . . . . . . 134 xiv A.4 Moulding of bricks in a hydraulic press . . . . . . . . . . . . . . . . 135 A.5 Air curing of fly ash bricks . . . . . . . . . . . . . . . . . . . . . . . 135 B.1 KS test plot showing deviation between observed and hypothesizes CDF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 C.1 Variation of (a) IRA (b) WA (c) dry density with compressive strength for CB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 C.2 Variation of (a) IRA (b) WA (c) dry density with compressive strength for FAB-II . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 C.3 Correlation of (a) IRA (b) WA (c) dry density with compressive strength for CB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 C.4 Correlation of (a) IRA (b) WA (c) dry density with compressive strength for FAB-II . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 C.5 Variation plot between actual and predicted compressive strength for CB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 C.6 Variation plot between actual and predicted compressive strength for FAB-II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 List of Tables 3.1 Mix proportions and dimensions of brick specimens . . . . . . . . . 29 3.2 Designation and mix proportions of different grades of mortar . . . 30 3.3 Dimensions of masonry assemblages for three brick variants 4.1 Values of IRA, WA, dry density and compressive strength for brick . . . . 32 specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.2 Compressive strength (MPa) for three mortar grades . . . . . . . . 47 4.3 Compressive strength (MPa) for masonry prisms . . . . . . . . . . . 48 4.4 Estimated parameters of distributions, KS distances, CS and LK values for IRA(kg/m2 /min) of brick units . . . . . . . . . . . . . . . 54 4.5 Estimated parameters of distributions, KS distances, CS and LK values for WA(%) of brick units . . . . . . . . . . . . . . . . . . . . 55 4.6 Estimated parameters of distributions, KS distances, CS and LK values for dry density(kN/m3 ) of brick units . . . . . . . . . . . . . 56 4.7 Estimated parameters of distributions, KS distances, CS and LK values for compressive strength (MPa) of brick units . . . . . . . . . 57 4.8 Estimated parameters of distributions, KS distances, CS and LK values for compressive strength(MPa) of mortar . . . . . . . . . . . 63 4.9 Estimated parameters of distributions, KS distances, CS and LK values for compressive strength(MPa) of CB prism . . . . . . . . . . 65 4.10 Estimated parameters of distributions, KS distances, CS and LK values for compressive strength(MPa) of FAB-I prism . . . . . . . . 68 4.11 Estimated parameters of distributions, KS distances, CS and LK values for compressive strength(MPa) of FAB-II prism xvi . . . . . . . 70 4.12 Correlation coefficients (Cr ) among the properties of brick units . . 83 4.13 Coefficients for the equation to evaluate the brick strength . . . . . 85 4.14 Comparison of past experimental results with predicted compressive strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.15 Estimated parameters, KS Distances, CS and LK values for predicted compressive strength (MPa) of brick units . . . . . . . . 88 4.16 Comparison of distribution models for experimental and predicted compressive strength values of brick units . . . . . . . . . . . . . . . 90 4.17 Proposed equation for each of the three brick variant . . . . . . . . 91 4.18 Proposed equation for bricks based on its material . . . . . . . . . . 93 4.19 Comparision of past experimental results with predicted prism strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.20 Most appropriate statistical distribution functions for different mechanical properties of bricks . . . . . . . . . . . . . . . . . . . . . 99 4.21 Most appropriate statistical distribution functions for compressive strength of different grades of mortar . . . . . . . . . . . . . . . . . 99 4.22 Most appropriate statistical distribution functions for compressive strength of brick masonry . . . . . . . . . . . . . . . . . . . . . . . 99 5.1 Pre-wetting time (in minutes) for different sets of masonry triplets . 105 5.2 Mean shear bond strength (in MPa) for Set-A triplets . . . . . . . . 107 5.3 Mean shear bond strength (in MPa) for Set-B triplets . . . . . . . . 108 5.4 Mean shear bond strength (in MPa) for Set-C triplets . . . . . . . . 109 5.5 Mean shear bond strength (in MPa) for Set-D triplets . . . . . . . . 110 A.1 Chemical requirements of fly ash . . . . . . . . . . . . . . . . . . . 128 A.2 Physical requirements of fly ash . . . . . . . . . . . . . . . . . . . . 129 Abbreviations ASTM : American Society for Testing and Materials CB : Clay Brick CDF : Cumulative Distribution Function CM1 : Cement Mortar (with Cement to Sand ratio 1:6) CM2 : Cement Mortar (with Cement to Sand ratio 1:4.5) CM3 : Cement Mortar (with Cement to Sand ratio 1:3) COV : Coefficient of Variation CS : Chi-Square EDS : Energy Dispersive Spectroscopy FAB-I : Fly Ash Brick (with Fly Ash from Source-I) FAB-II : Fly Ash Brick (with Fly Ash from Source-II) FESEM : Field Emission Scanning Electron Microscopy IRA : Initial Rate of Absorption IS : Indian Standard KS : Kolmogorov-Sminrov LK : Log Likelihood PDF : Probability Density Function SD : Standard Deviation SEM : Scanning Electron Microscopy WA : Water Absorption XRD : X-Ray Diffraction xviii Notations English Symbols a : Constant coefficient to predict compressive stength of brick unit b : Constant coefficient of initial rate of absorption c : Constant coefficient of water absorption Cr : Correlation Coefficient d : Constant coefficient of dry density D : Dry density of the brick in kN/m3 fb : Compressive strength of brick in MPa f'b : Predicted compressive strength of brick in MPa fk : Predicted compressive strength of prism in MPa fm : Compressive strength of Mortar in MPa I : Initial rate of absorption in kg/m2 /min K : Constant coefficient to predict compressive stength of prism W : Water absorption in % Greek Symbols α : Power constant of compressive strength of brick β : Power constant of compressive strength of mortar χ : Moisture content of brick in % ν : Standard error of estimate xix Chapter 1 Introduction 1.1 Background and Motivation Housing is one of the basic requirements for human survival. Masonry is an inevitable component of housing. Among different types of masonries, brick masonry is one of the most widely used in our country and elsewhere because of low cost, easy availability of raw materials, good strength, easy construction with less supervision, good sound and heat insulation properties, and availability of manpower. Brick masonry is a composite material of systematic arrangement of brick units and mortar joints. The behaviour of masonry is dependent on the properties of its constituents such as brick units and mortar separately and together as a unified mass. Burnt clay bricks are widely used around the globe but in recent years many other varieties of bricks have been developed. Among them fly ash bricks has gained much popularity because of its numerous advantages over burnt clay bricks. A number of heavy engineering industries in our country are responsible for huge production of fly ash. It is found to be a challenge for the management to store the fly ash without polluting the environment. Around 143 thermal power stations consume nearly 500 million tons of coal and produce as much as 173 million tons of fly ash every year in our country [1]. One of the best ways for safe disposal of fly ash is to use in production of bricks. The government too 1 Chapter 1 Introduction emphasizes on the use of fly ash as building material in different construction fields. Of the total amount of fly ash utilized till 2014, around 13% is used in bricks production and this trend is expected to escalate up. Use of fly ash replacing clay in making bricks, saves vast acres of land from erosion. As fly ash bricks are hydraulic pressed, the use of fossil fuels for burning clay bricks is also eliminated thus reducing global warming. Apart from environmental benefits, fly ash bricks have structural advantages like low cost, high compressive strength, accuracy in shape and size, high strength to weight ratio, zero efflorescence and consumption of less mortar decreasing the overall cost of construction. Recently many multi storeyed buildings are constructed with fly ash brick masonry infill owing to good performance and low cost. With these benefits it is inevitable that fly ash bricks would soon replace clay bricks in building constructions. Fig. 1.1 presents a typical multi-storeyed framed building at Rourkela, India constructed using fly ash bricks as infill wall Figure 1.1: Multi storey building constructed using fly ash bricks A lot of research efforts on burnt clay bricks are reported in literatures while recently researchers have started giving attention to fly ash bricks because of its importance as building material. However, more research on this building material 2 Chapter 1 Introduction is required to cope with the recent changes coming in building design philosophy. Randomness and variability of material properties can considerably affect structural performance and safety [2]. In contradiction to reality, this phenomenon is usually neglected in conventional structural analysis and design that assume deterministic values of material properties. This assumption makes the analysis models less realistic and less satisfactory. With the advancement of computing facilities, the complex structural analyses including the probabilistic nature of the various parameters of the structure are not difficult and have become essential for its response against natural loads like earthquake, wind, etc. The probability distribution of various properties of building materials such as steel, concrete, bricks are needed to carry out probablistic analysis of a structure. There is hardly any literature available on the variability of mechanical properties of clay and fly ash bricks while the same is available for concrete and steel( [3] [4] [5]etc.). The variability in brick and mortar influences the overall strength of masonry which in turn affects the performance of masonry structure. The performance of brick masonry depends on its compressive strength as well as on the bond strength at brick mortar joint. However, the bond strength, especially for fly ash brick masonry, has got relatively less research attention. The bond strength is affected by brick properties such as initial rate of absorption, moisture content in bricks at the time of laying and mortar grade. Initial rate of absorption is often neglected by the design codes although it is an important factor for deciding strength of brick-mortar bond. The optimum moisture content in bricks at the time of laying with mortar to achieve good bond strength is not well documented. Brick properties vary largely from region to region as raw materials for brick production are locally available and do not come from the controlled industry environment. Therefore, it is obvious to have inherent variation in its properties that must be mathematically described in order to improve design standards of masonry structures reasonably. This has become the underlying motivation of the present study. 3 Chapter 1 1.2 Introduction Objectives of the Thesis Prior to defining the specific objectives of the present study, a detailed literature review was taken up. This is discussed in detail in Chapter 2 and briefly summarised here. Many literatures are available on experimental investigations of clay brick ( [6] [7] [8] [9] [10] [11] etc.) and fly ash brick ( [12] [13] [14] [15] etc.). Most of the papers for clay brick masonry focussed on the following mechanical properties: initial rate of absorption, water absorption, compressive strength and constitutive relation including elasticity modulus. With regards to fly ash brick, the literatures are mainly based on the study of environmental impact of fly ash bricks and devising various mix proportions of fly ash with other waste materials for production of good strength bricks. Some papers also focussed on different mechanical properties of fly ash bricks. The literature review shows that the mean values of different mechanical properties of brick masonry and its constituents are varying considerably from paper to paper. This may be due to the inherent variation in the structural and chemical properties of constituent materials. The mechanical properties of brick are highly uncertain and difficult to generalise. For reliability or sensitivity analysis of masonry structures these uncertainties must be transformed into a statistical distribution [16]. There is no published literature available which focuses on this aspect. Variations in the properties of bricks may arise from their morphological and microstructural differences. Some of the past literatures ( [17] [18] [19] [20] [21] etc.) were concerned with morphological analysis of both burnt clay bricks and fly ash bricks. However, the influence of chemical composition and microstructure on variation in different mechanical properties of brick is not reported by any of the previous studies. Shear failure of brick-mortar bond is one of the most common failure modes of the brick masonry. The shear bond strength depends on different properties of brick and mortar. Moisture level in bricks at the time of construction plays a vital role in achieving good bond strength. Most of the available literatures have reported the relation between shear bond strength and masonry compressive 4 Chapter 1 Introduction strength, shear bond enhancing parameters and shear bond strength of soil-cement blocks along with different types of mortar ( [22] [23] [24] [25] [26]). However, only few literatures ( [27] [28]) are available which studied the variations in tensile bond strength due to changes in the moisture level in clay bricks and soil-cement blocks. However, the same for shear bond strength of clay and fly ash brick masonry is not reported in previous literatures. Based on the above literature review, the salient objectives of the present study have been identified as follows: (i) To describe the variability in the mechanical properties of clay and fly ash brick masonry and its constituents (brick unit and mortar) (ii) To study the influence of chemical composition and microstructure of bricks on variation in its mechanical properties (iii) To study the effect of pre-wetting of bricks on the shear bond strength of brick masonry and to determine the optimum moisture content of brick to have higher shear bond strength of brick masonry. (iv) To propose analytical models for estimation of compressive strength of brick unit and brick masonry. 1.3 Scope of the Study The scope of the present study is listed as follows: (a) In the present study three brick variants are considered. Hand-moulded burnt clay bricks used in the present study are procured from a kiln near Rourkela, India. Two types of fly ash cement bricks are used in the study which differs on the basis of their composition and the source of fly ash used. These two varieties are widely used in construction of buildings in the regions surrounding Rourkela. 5 Chapter 1 Introduction (b) The bricks considered in the present study have non-modular size of approximately 235×110×75 mm. (c) Three different mixes of mortar are considered in the present study (Cement: Sand = 1:3, 2:9 and 1:6) and the mortar cube of size 70×70×70 mm is used. (d) Height/thickness ratio of masonry prism is kept between 2-5 as per Indian Standard IS-1905:1987 [29]. (e) The thickness of the mortar joint is maintained 8 to 10 mm for all masonry assemblages used in the present study. (f) Only two-parameter probability distribution functions are considered for the study. 1.4 Methodology The methodology to be followed in order to achieve the proposed objective is listed as follows: (a) Carry out extensive literature review, to establish the objectives of the research work. (b) Procure clay and fly ash bricks, prepare test specimens and perform different tests in the laboratory to evaluate the mechanical properties of brick units, mortar and masonry assemblages. (c) Analyse the variability in the mechanical properties of brick masonry and its constituents using different probability distribution functions and choose the appropriate distribution functions through goodness-of-fit test. (d) Perform higher order analyses such as X-ray diffraction (XRD) and field emission scanning electron microscopy (FESEM) to relate the morphology and microstructure of brick specimens to its mechanical properties. 6 Chapter 1 Introduction (e) Develop mathematical equations for predicting the compressive strength of brick units and masonry based on the experimental data set through regression analysis and validate the equations using the data from previous literature. (f) Conduct shear bond strength test on masonry triplets to study the effect of pre-wetting on the shear bond strength of masonry and arrive at optimum moisture content of brick from the experimental results. 1.5 Organisation of the Thesis This introductory chapter has presented the background, objective, scope and methodology of the present study. Chapter 2 starts with review of various literatures related to the structural properties of both burnt clay and fly ash brick masonry. Later this chapter reviews the literatures available on the study of microstructural and morphological variations in bricks and mortars. Finally it presents the review of the various studies carried in relation to shear bond strength of brick masonry. Chapter 3 describes the details of raw materials used, preparation of specimens, equipment used and procedures of experimental work carried out as part of the research. This includes the experiments to evaluate the different mechanical properties of masonry specimen such as initial rate of absorption (IRA), water absorption (WA), dry density, compressive strength and shear bond strength and higher order analyses such as XRD and FESEM. Chapter 4 presents the experimental results obtained as part of this research. The results are then analysed in context to variability of mechanical properties of masonry materials, morphology and microstructure of brick specimen, analytical modelling of compressive strength of brick unit and masonry prism and modes of failure observed for masonry prism under axial compression. Chapter 5 discusses the effect of moisture content in bricks during construction of masonry triplet on the shear bond strength. Variation in moisture content of bricks is achieved by soaking them in water for different duration. The influence 7 Chapter 1 Introduction of IRA on the shear bond strength is also presented in this chapter Finally, Chapter 6 presents a summary including salient features, significant conclusions from this study and the future scope of research in this area. 8 Chapter 2 Literature Review 2.1 Introduction A review of literature is carried out to identify the recent developments in the field of brick masonry and related areas. The literature review is done on a wide variety of topics but only the topics relevant to the objectives of the present study are presented in this chapter. This chapter is broadly divided into four segments. The first part of this chapter is devoted to the various researches related to the study of structural properties of both burnt clay and fly ash brick masonry. The second part deals with the variability in the properties of brick units, mortar and masonry prism. The third part is devoted to literature available on the study of microstructural and morphological variations in bricks and mortars. The fourth part reviews the various studies carried in relation to shear bond strength of brick masonry. 2.2 Structural Properties of Brick Masonry Structural properties (such as compressive strength, elastic modulus, dry density, water absorption, etc.) of brick unit, mortar and brick masonry are important parameters for design of masonry structures. Many literatures are available on 9 Chapter 2 Literature Review mechanical properties of clay brick whereas only few papers are found on the fly ash brick. This may be due to the fact that fly ash brick is recently developed building material. 2.2.1 Clay Brick Masonry McNary and Abrams (1985) [30] evaluated the strength and deformation of clay brick masonry under uniaxial compressive force. The constitutive relations of bricks and mortar were established by performing biaxial tension-compression tests on brick units and triaxial compression tests on mortar. The force-displacement relation for stack-bonded prisms was derived from a numerical model. The results were then compared with experimental values and a relation was established. The failure pattern of the masonry was also well recorded in the study. The mechanics governing the failure in a stack-bonded prism was analysed and explained. It was found from the analysis that mortar initiates the tensile stresses that cause tensile splitting of masonry prisms. The masonry prism strength was found to depend upon the strength of brick unit under biaxial tension-compression stresses. Naraine and Sinha (1992) [31] proposed a generalised approach to determine the interaction curve for brick masonry in cyclic and biaxial compression. The peak stresses were determined from many interaction curves and the corresponding strains were determined using empirical relations involving strain at the peak stress of envelope curve and principal stress ratio. The computed curves were found to be compared well with empirical curves obtained using experimental data. Crisafulli (1997) [32] in his research work focussed on the seismic behaviour of reinforced concrete structures with masonry infill. The properties of masonry and its constitutive materials were reviewed to understand the strength mechanism. Theoretical procedures were developed for rational evaluation of strength of masonry subjected to compressive and shear stresses. The response of infill walls under lateral loading was studied experimentally and the different modes 10 Chapter 2 Literature Review of failure were reviewed. The infill wall was also subjected to nonlinear cyclic loading and its response under such loading was studied. Analytical models were prepared on the basis of data obtained from experiments. A new design approach for the seismic design of structures with masonry infill was proposed. Totoev and Nichols (1997) [33] studied the dynamic modulus of elasticity of brick unit and masonry using longitudinal vibration test method and the ultrasonic pulse method and compared the value with the respective Youngs modulus obtained by quasi-static loading. Similar tests were also done for mortar cubes. The ratio of Youngs modulus to peak stress was derived for brick, prism and mortar. Gumaste et al. (2007) [6] studied the compressive strength and elasticity properties of wire-cut and table moulded bricks of India with different mortar grades. Different combinations of masonry prisms and wallets such as soft brick-strong mortar and strong brick-soft mortar were used for experimental study. Similarly, to study the size effect, different sizes of prisms and wallets with different bonding arrangement were tested. An empirical relationship for masonry prism compressive strength as a function of brick and mortar strength was derived for Indian context. Kaushik et al. (2007) [7] developed a uniaxial compressive stress-strain model for clay brick masonry. The compressive strength and elastic modulus of prisms was determined experimentally. An empirical equation for estimation of masonry prism compressive strength was developed as a function of compressive strength of brick units and mortar from regression analysis of experimental data. Analytical model for stress-strain curve of burnt clay brick masonry was developed. Pradhan et al. (2009) [9] developed nonlinear idealization of stress strain curve for different types of bricks and different grades of mortar using Power-Law-Process (PLP) fit model. For idealization, the curve below yield limit was assumed to 11 Chapter 2 Literature Review be linear where modulus of elasticity remains unchanged and the part above yield limit was assumed to be quadratic passing through yield point and ultimate point. The idealized stress strain curve obtained from PLP fit model was found to match the experimental curve closely. Costigan and Pavia (2009) [8] determined the compressive, flexural and bond strength of brick masonry with lime mortar. The behaviour of masonry constructed with hydraulic and non-hydraulic lime mortar was studied. The masonry wallets were subjected to lateral and vertical loads. The mechanical properties and modes of failures of each of the two type of lime mortar masonry was compared. It was reported that when masonry units were stiffer than mortar then the masonry compressive strength is not sensitive to bond strength variations. Two cases of failures were observed, vertical splitting when mortar is stiffer than brick and bond failure when brick is stiffer than mortar. Christy et al. (2012) [34] critically reviewed the various literatures that studied the in-plane shear behaviour of brick masonry. It was reported that, during earthquakes, severe in-plane and out-plane forces act on the masonry infill out of which in-plane force resist the action of earthquake to a large extent. Shear bond strength of masonry was reported to be the main source of resisting force for lateral loads. Hence, it was suggested that the parameters such as shear bond strength should be well analysed for designing of structure with infill in earthquake prone areas. The different construction methods and practices which could enhance the shear behaviour of masonry infill were reported. Palanisamy and Premalatha (2012) [10] evaluated experimentally the properties of brick masonry infill. The compressive strength tests were conducted on brick prisms with different mortar grades and the elastic modulus of prisms were calculated. The results of clay brick were compared with that of fly ash brick prisms. It was observed that fly ash brick masonry prisms show more strength and elastic modulus values as compared to clay brick masonry prism after 28 12 Chapter 2 Literature Review days of curing. Ravi et al. (2014) [11] reviewed the material behaviour of brick masonry by experimental and numerical investigations. Different material properties such as compressive strength, modulus of elasticity and stress-strain relationship was found for brick units, mortar cubes and masonry triplets. The constitutive relations were used to study the behaviour of masonry by performing finite element modelling in ANSYS. Macro and micro models of masonry triplets were developed for numerical study. The results from numerical investigations were compared with experimental results. Vimala and Kumarasamy (2014) [35] studied the strength of stabilised mud block masonry using different mortar proportions. The compressive strength was found in both wet state and dry state. It was found that the dry compressive strength of stabilised mud block and prism was higher than that of wet compressive strength. The dry and wet strength of prisms was found to increase with increase in mortar strength. 2.2.2 Fly Ash Brick Masonry Freidin and Erell (1995) [36] made bricks from coal fly ash and slag which were open air cured. It was found that such bricks could solidify when they were cured in open air eliminating the use of burning in kilns. Sodium silicate solution was used for mixing and binding the raw materials. The properties that were determined include compressive strength, water absorption, water uptake (initial rate of absorption) and volume mass. The water absorption of such bricks was found to be higher than usual, so hydrophobic additives such as Siloxane CS was added to the bricks while mixing the raw materials. Siloxane filled the pores to obstruct the capillary action, thus the water absorption of such bricks was greatly reduced. It was found that wet compressive strength of bricks increased with decrease in water intake capacity when hydrophobic additives were used. 13 Chapter 2 Literature Review Kumar (2002) [37] investigated the feasibility of fly ash-lime-gypsum bricks and hollow blocks which could be used for low cost housing projects. The properties of bricks such as water absorption, density, compressive strength and durability were tested. The effect of the curing type on the increase in strength of bricks was studied. It was observed that greater strength is achieved by hot water curing as compared to ordinary open air curing. Chindaprasirt et al. (2005) [38] replaced cement with Class F fly ash by 20% and40 % while mixing mortar and studied the properties of such mortar for their use as brick joints and plastering. Air entraining agent was added to the mortar to improve the workability. The properties such as compressive strength, flexural strength, water demand, water retention, flow, setting time, air content and relation between water to binder ratio were determined experimentally. The initial setting time of fly ash mortars was found to be extended. The strength of fly ash mortar was found to be increased. Liu et al. (2009) [39] conducted research on the environmental impact of using fly ash in building constructions as bricks and landfills. In the study Class C fly ash was used for making bricks. The fly ash bricks were found to meet the clay bricks in terms of structural properties. The brick samples were tested in laboratories to evaluate the chemical properties. It was found from these tests that the bricks absorb mercury from air making the ambient clean unlike other building materials. The radon gas (radioactive) emitted by fly ash bricks was found to be 50% of that from concrete. Leaching of pollutants from fly ash bricks in rain is negligible. Fly ash bricks were found to pass the toxicity characteristic leaching procedure test which makes them non-hazardous for use in landfilling. Keshava et al. (2010) [40] studied the strength efficiency of block masonry. The blocks were made with fly ash, marble dust, granite powder and cement. Different tests such as water absorption, compressive strength, and elastic 14 Chapter 2 Literature Review modulus were conducted on block units, mortar cubes and stack bonded brick prisms. It was observed that most of the prisms failed by vertical cracking. Permissible compressive stress of masonry was derived based on two approaches from Indian standard IS 3495:1992. Rushad et al. (2010) [12] investigated the properties such as water absorption and compressive strength of bricks made from fly ash, lime and local soil in different proportions. Hand moulded and pressure moulded fly ash bricks were used for experiments. It was found that bricks with fly ash and lime in the ratio 40:60 satisfied the requirements of Indian standard IS 3495:1992 with regard to both water absorption and compressive strength. Dhami et al. (2012) [41] used bacterial calcite in fly ash bricks to enhance the strength properties of fly ash bricks. Bacteria called bacillus megaterium was added to the mix which produced calcite in fly ash bricks. The calcite was found to be useful for filling the pores, increasing the compressive strength, reducing the water absorption and frost action. The durability of the bricks was thus reported to be enhanced. Scanning Electron Microscope (SEM) and X-Ray Diffraction (XRD) study confirmed the presence of calcite crystals on the surface of bricks. Christy et al. (2013) [13] found the compressive strength and elastic modulus of fly ash brick masonry prisms experimentally and compared the result with clay brick masonry prisms. Both reinforced and unreinforced masonry prisms were considered for the two brick types. An equation to determine the compressive strength of prism was proposed on the basis of compressive strength of brick units and mortar. Shakir et al. (2013) [14] studied the properties of bricks made using fly ash, quarry dust and billet scale mixed in different ratios. Non-conventional methods were used for production of bricks. The mechanical properties such as compressive strength, pulse velocity, initial rate of absorption and water 15 Chapter 2 Literature Review absorption of bricks and their durability were tested. The optimum ratio of the raw materials was arrived at on the basis of test results. It was suggested that these bricks could be used in place of traditional clay bricks. Vidhya et al. (2013) [15] experimentally studied the properties of bricks made from fly ash, pond ash, lime and gypsum in different mix proportions. The composition and microstructure of bricks were studied using XRD analysis and SEM images. From the experimental tests it was found that the bricks having higher percentage of pond ash showed increased compressive strength and reduced water absorption. From the review of literature for clay brick masonry it is observed that most of the papers focussed on the following mechanical properties: initial rate of absorption, water absorption, compressive strength and constitutive relation including elasticity modulus. With regards to fly ash bricks, the literatures are mainly based on the study of environmental impact of fly ash bricks and devising various mix proportions of fly ash with other waste materials for production of good strength bricks. Some papers also focussed on different mechanical properties of fly ash bricks. 2.3 Variability in Properties of Concrete The literature review presented in the previous section shows that the mean values of different mechanical properties of bricks are varying considerably from paper to paper. This may be due to the inherent variation in the structural and chemical properties of constituent materials. Therefore, the mechanical properties of brick are highly uncertain and difficult to generalise. For reliability or sensitivity analysis of masonry structures these uncertainties must be transformed into a statistical distribution. There is no published literature available which focuses on this aspect. The literature survey revealed, however, extensive research work on the statistical distribution of mechanical properties of another brittle material, 16 Chapter 2 concrete. Literature Review These research papers were reviewed to understand the statistical approach for describing uncertainty. This section presents the review of literature on variability in properties of concrete. Dayaratnam and Ranganathan (1976) [4] did the statistical analysis of variation in the compressive strength of concrete cubes of different grades collected over span of 10 years. It was observed that most of the concrete specimens followed normal distribution with one percent significance level. Chi-square test was used to find the suitable distribution. Oztemel and Sensoy (2004) [42] found the in-situ compressive strength of concrete and presented a mathematical model for the probability distribution. The study was aimed at developing a mathematical model for the probability distribution of in-situ concrete by carrying out compressive strength tests of concrete which helps in studying the behaviour and condition of concrete components in seismic evaluation. A lognormal probability distribution model was developed that best fits the in-situ compressive strength of concrete. This model was found to be useful for seismic fragility assessment of RC buildings. Silvestri et al. (2008) [43] identified the accurate probability distribution models for the compressive strength of concrete using statistical analysis of different models. The study reported that design of structures depends upon material strengths, which are highly uncertain. This uncertainty could deeply affect the performance of structures. In the study the variation in compressive strength of concrete cubes over a period of five years was analysed and a best fitted probability distribution model was found using statistical analysis. It was suggested that shifted lognormal best captures the variations in the compressive strength of concrete. Ait-Mokhtar et al. (2013) [44] experimentally investigated the variability in durability properties of concrete. The study was aimed to quantify the 17 Chapter 2 Literature Review variability in properties of concrete for predicting the service life of concrete structures by performance based probabilistic approach. The experimental study included testing of 40 sets of concrete specimens from two different construction sites for compressive strength and different durability properties. The experimental results were then used for estimating the variability by fitting the test data plot with suitable probability density functions. These probability density functions were used for probability based assessment of structures. Chen et al. (2013) [5] studied the variability of compressive strength of concrete cores obtained by core drilling. The experimental program consisted of testing the compressive strength of about 200 core specimens made from eight different mixes of concrete. The variation in the compressive strength was studied by fitting different probability models such as 2P and 3P Weibull, normal, lognormal, gamma distributions. The best fit model was decided by using validating techniques such as modified Kolmogorov-Smirnov, minimum Chi-square and maximum log-likelihood criterions. It was suggested that for some mixes 3P-Weibull and normal distribution was found as best fit while for other mixes 2P-Weibull was seemingly best fit model. The results obtained in the study were reported to be useful for analysis of RC members by reliability based techniques. Unanwa and Mahan (2014) [45] analysed statistically the variation in compressive strength of concrete used for California highway bridges. This paper presents the variation of concrete strength with age for different grades of concrete. It was found that the strength of concrete in bridge structures attain maximum strength within ten years of construction. Statistical tests were conducted to arrive at best fitting probability distribution. Traditionally normal distribution is used for statistical analysis of concrete due to its simplicity. However, recent studies reported that many other distributions (such as lognormal, gamma or Weibull distribution) describe the 18 Chapter 2 Literature Review variation in different properties of concrete better. The literatures studied here do not agree with a single probability distribution function to describe the variation in concrete properties. 2.4 Morphological and Microstructural Study on Clay and Fly Ash Bricks Variations in the properties of bricks may arise from their morphological and microstructural differences. Therefore, an effort has been made to review the literatures concerned with morphological and microstructural characteristics of brick with an objective to justify the variation. These literatures are briefly discussed in this section. Stutzman and Centeno (1995) [46] analysed the material properties of fly ash which could be used as an admixture in concrete. The objective of study was to understand the material properties of fly ash when used as admixture, which affects strength and durability of concrete. The programme of the study consisted of finding the kinetics of reaction of fly ash with concrete, microstructural study and simulation modelling. The experimental procedure consisted of casting mortar cylinders of 25 mm diameter of ratio 1:3 with partial replacement of cement with fly ash. The samples were then tested for microstructural and compositional studies. From SEM images it was observed that the calcium-silicate-hydrate (C-S-H) gel was formed on the mortar samples and the fine fly ash particles filled the porous surface of mortar. Some traces of unreacted fly ash and calcium hydroxide were present which shows that the pozzolanic reaction was incomplete even after 60 days of curing period. Livingston et al. (1998) [17] analysed the hand moulded clay bricks using X-ray diffraction data. This study delivered significant results with regard to durability of bricks. It was observed that durability of bricks is related to its 19 Chapter 2 Literature Review microstructure and mineralogy. The ratio of cristobalite to quartz in brick was found to be a reliable predictor of durability. The brick specimens from Germany and the United States (US) were tested and it was found that cristobalite was detected in US bricks but was absent in bricks from Germany even though they contain illite or mica. Thus, it was concluded from the X-ray diffraction analysis that cristobalite compound in US bricks is responsible for durability as feldspar is for Germany made bricks. This pointed out the importance of morphological and microstructural study of bricks to better understand its properties. Fatih and Umit (2001) [18] studied the utilization of fly ash in manufacture of bricks. It was reported that although huge amount of fly ash is produced but proper quality of it is not maintained which hinders its use in manufacture of bricks. The morphological (X-Ray diffraction) analysis was carried out on both fly ash and clay bricks to know the chemical components of both types of bricks. It was encouraged to use fly ash bricks instead of clay bricks because fly ash bricks are free from harmful chemical agents. Lingling et al. (2005) [19] studied the effect of clay replaced by fly ash in high volume ratio in fired clay bricks. The brick specimens were casted and fired at a high sintering temperature of 1050C, which was 50-100C more than the usual firing temperature. With the addition of fly ash the plasticity nature of clay decreased. The bricks with high replacement of clay by fly ash showed high compressive strength, low water absorption, no cracking due to lime and higher resistance to frost melting. Thus, it was suggested to use fly ash in manufacturing of bricks by replacement of clay. Karaman et al. (2006) [20] assessed the compressive strength of clay bricks using quantitative values of colour components. In this study, a relation was established between compressive strength of bricks, firing temperature and their colour component. Lightness and chromaticity parameters were used to adjudge the colour components. It was observed that with the increase in 20 Chapter 2 Literature Review firing temperature, the compressive strength of bricks increased with increase in colorimeter value up to 800C. For further increase in temperature and strength value, the colorimeter value observed to be decreased. The morphological study of clay bricks was also conducted. It was suggested that compressive strength of bricks can be predicted on the basis of colour values although not accurately. Kutchko and Kim (2006) [47] characterized Class F fly ashes from different sources using SEM and energy dispersive spectroscopy (EDS) analysis. The internal and surface structure of fly ash was considered for analysis. It was found that all the samples consisted of mainly amorphous alumino-silicate spheres and small amount of iron-rich spheres. Calcium was found to be associated with oxygen, sulphur or phosphorous, but not with silicon or aluminium. The elemental composition and texture of both alumina-silicate and calcium spheres were distinct. The EDS data was found to be in accordance with inductively coupled plasma optical emission spectrometry and XRD data. Oscar et al. (2012) [21] compared the mineralogical changes in fired clay bricks with changes in firing temperature by XRD and SEM analysis. It was observed that there were some compositional changes in the neoformed phases of the clays. Many mineral phases were identified in the fired clays with the reaction products including mullite, residual quartz, hematite, amorphous phase (glass generated by melting of feldspars and clays). It was observed that at high temperature the clays become darker because of the presence of goethite. It was found from SEM study that the vitreous texture of high temperature fired clay brick is because of alkaline glass and quartz which are formed from melting of free silica and alumina. The past studies were concerned with morphological analysis of both burnt clay bricks and fly ash bricks. The influence of chemical composition and microstructure on variation in different mechanical properties of brick is not reported by any of the previous studies. 21 Chapter 2 2.5 Literature Review Shear Bond Strength of Brick Masonry Shear failure of brick-mortar bond is one of the most common failure modes of the brick masonry. It is observed from past studies that poor bond strength results in failure originating from the brick mortar joint of the masonry wall. Therefore shear bond strength of brick masonry is very important parameter that needs special attention. This section presents the literature review conducted in this aspect. Hossain et al. (1997) [22] experimentally determined the in-situ deformation characteristics of bricks and mortar joints. Couplets with inclined bed joint were tested for shear bond strength by uniaxial loading. Failure for all the specimens was observed within the joint. Mean shear bond strength and nonlinear shear stress-strain behaviour were evaluated. Sarangapani et al. (2005) [23] studied the effect of brick-mortar bond strength on the compressive strength of masonry. The compressive strength, flexural bond strength and shear bond strength of the masonry made with local bricks and mortar was determined experimentally. In order to improve the bond strength of mortar, use of some bond-enhancing techniques like cement slurry and epoxy resin coating for lean mortars was suggested. It was observed that with the increase in flexural and shear bond strength, the compressive strength of masonry increased. Poor bond strength was observed responsible for the failure of prism along the brick-mortar joint. Similarly, high bond strength resulted in diagonal failure of masonry under compression. Therefore, the study highlighted the relation between bond strength, compressive strength and mode of failure in brick masonry. Reddy and Gupta (2006) [27] experimentally investigated the tensile bond strength of masonry constructed using soil-cement blocks and cement-soil mortars. The study was aimed to find the effect of different block properties (such as initial moisture content, cement content, strength and surface characteristics) 22 Chapter 2 Literature Review and mortar properties (such as workability and composition of cement-soil mortars) on the direct tensile strength of masonry couplets. It was observed that bond strength is affected by initial moisture content of blocks as partially saturated blocks provided good strength in comparison to completely dry or fully saturated blocks. Thus, this paper provides the importance of initial moisture content for achieving bond strength. Similarly, the higher bond strength was achieved with the increase in cement content on the block. It was found that cement-soil mortar achieved 15-20% higher bond strength in comparison to conventionally used cement mortar. Reddy et al. (2007) [24] studied the influence of shear bond strength on compressive strength of soil-cement block masonry. The methods to improve the shear bond strength of soil-cement block masonry was also suggested. The methods developed to improve the shear bond strength included making the bed surfaces texture of blocks rough, surface coatings and altering the frog size and area. It was experimentally observed that rough textured blocks and cement slurry coated blocks obtained higher shear bond strength. Similarly, no significant changes were observed in stress-strain and compressive strength properties of masonry with the change in shear bond strength when the masonry block unit modulus is greater than that of mortar. But, it was found that enhancing bond strength improves the compressive strength of soil-cement block masonry. Reddy and Vyas (2008) [25] focussed on the influence of bond strength on compressive strength and stress-strain characteristics of soil cement block masonry with cement lime mortar. It was found that the bond strength increased by three to four times with the application of surface coating and making the surface texture rough. In this study, three different cased of block masonry with different block to mortar elastic modulus ratio were considered. From the extensive experimental tests it was found that bond strength and compressive strength of masonry depend considerably on the block to mortar elastic modulus ratio. 23 Chapter 2 Literature Review Pavia and Hanley (2010) [28] investigated the bond strength of masonry with natural hydraulic lime mortar. The study aimed to correlate bond strength with mortar hydraulicity, water content, workability and water retention. The experimental programme included the determination of flexural bond strength by bond wrench test for different hydraulic strength lime mortars. It was suggested that water retention property of natural hydraulic lime mortar enables higher bond strength. Lumantarna et al. (2012) [26] performed experiments on existing masonry buildings (using lime mortar) constructed between 1800 and 1940. The in-situ samples were extracted from six heritage structures and compressive, bond wrench (flexural) and shear bond strength tests were performed on the samples. The experimental results indicated that the mortar compressive strength could be aptly related by flexural bond strength and bed-joint cohesion. The studies on bond strength of brick masonry under flexural, tensile and shear loading is discussed in this section. The bond strength of clay brick and soil cement block masonry is studied while fly ash brick masonry has not got the attention. It is reported that the brick mortar shear bond strength is dependent on various factors such as surface characteristics of bricks, property of mortar, etc. From critical review of past studies it is found that the variations in shear bond strength due to changes in the moisture level in bricks at the time of construction is studied only by a few researchers for clay bricks and soil-cement block masonry. However, the same for fly ash brick masonry is studied by none. 2.6 Summary This chapter presents the review of literature in four specific areas of brick masonry: (i) structural properties of burnt clay and fly ash brick masonry, (ii) variability in material properties, (iii) morphological and microstructural 24 Chapter 2 Literature Review variations in bricks and mortars and (iv) shear bond strength of brick masonry. Following are the important observation drawn out of the literature review which forms a base to set the objectives of this thesis: (a) The variation in the mean values of different mechanical properties of bricks as reported in various literatures could be attributed to the inherent variation in the properties of its constituent materials. This variation is probably the main cause for uncertainty in brick properties. The uncertainty must be addressed using a suitable statistical function which can be used as input parameter for reliability based analysis of masonry structures. However in absence of such study in past, variability in properties of brick and its masonry is often neglected in the analysis. Hence there is a need to understand and interpret the variability in the mechanical properties of brick and its masonry. (b) The variability in properties of bricks could be due to the differences in their morphology and microstructure. None of the available literature has been found to throw some light on this concept. Hence, the influence of chemical composition and microstructure on variation in different mechanical properties of brick need attention to justify the variability. (c) Shear failure of brick-mortar bond is one of the most common failure modes of the brick masonry. The shear bond strength is reported to depend on properties of brick, mortar and the surrounding condition. Moisture level in bricks at the time of construction plays a vital role in achieving good bond strength. Few literatures are available which studied the variations in tensile bond strength due to changes in the moisture level in clay bricks and soil-cement blocks. However, the same for shear bond strength of clay and fly ash brick masonry is not reported in previous literatures. 25 Chapter 3 Experimental Work 3.1 Introduction The present study is based on a series of experimental tests. The experimental work is aimed at determining the mechanical properties and morphology of the test specimens. The mechanical properties of masonry materials such as initial rate of absorption (IRA), water absorption (WA), dry density, compressive strength and shear bond strength are the interest areas of this thesis. Higher order analyses such as XRD and FESEM are conducted to understand the morphology and microstructure of brick and mortar. This chapter presents details about the experimental program undertaken. This includes description of the raw materials used, the preparation of specimens for conducting experimental work, equipment used and the experimental procedures. 3.2 Materials Used As part of experimental work, materials such as bricks, cement and sand are used to prepare the test specimens. In this study, brick is used both as test specimen and as a unit material for construction of masonry assemblages like prism and triplets. Similarly cement and sand is used for making of mortar. The specification of the all the materials are described as follows. 26 Chapter 3 3.2.1 Experimental Work Brick Brick is one of the primary materials used in this study. Three variants of brick are considered, out of which one is clay brick and other two are fly ash bricks. Burnt clay bricks used in the present study are procured from a kiln near Rourkela. The clay bricks used are of good quality and falls under the class designation of 7.5 as per Indian Standard IS 1077:1992 [48] classification. The clay bricks are hand-moulded and have non-modular size. Fig. 3.1 depicts a typical burnt clay brick used in the study. The bricks which are uniform in colour with sharp corners and smooth faces are selected for the study. Figure 3.1: Typical burnt clay brick Two types of fly ash cement bricks are used in the study which differs on the basis of their composition and the source of fly ash used. Fig. 3.2 shows two varieties of Class F fly ash considered: (a) grey coloured fly ash with high silica plus alumina which is collected from source-I and (b) brown coloured fly ash with silica plus alumina and significant amount of iron oxide which is collected from source-II. Both source I and II are coal based plants located at Rourkela, Odisha. The changes in the colour and properties of fly ash are probably because of variations in method of production of fly ash, loss of ignition and coal properties. The raw materials commonly used for making fly ash bricks and its entire manufacturing process are explained in Annexure A. The two variants of bricks 27 Chapter 3 Experimental Work Figure 3.2: Fly ash: (a) Source-I and (b) Source-II are chosen as those two varieties are widely used in construction of buildings in the regions surrounding Rourkela. The proportion of raw materials in both fly ash brick variants falls within the range usually followed elsewhere in the country (refer Section A.3.3 in Annexure A for detail). Figs. 3.3 and 3.4 show the two types of fly ash bricks used in the study. Figure 3.3: FAB-I type fly ash brick The composition and the dimensions of the bricks are presented in Table 3.1. The clay brick is designated as CB, fly ash brick specimens with fly ash from source I are designated as FAB-I and that from source II is designated as FAB-II. The physical properties of bricks such as compressive strength, water absorption, efflorescence, soundness etc. are tested conforming to Indian Standard IS 3495 (Part 1):1992 [49]. 28 Chapter 3 Experimental Work Figure 3.4: FAB-II type fly ash brick Table 3.1: Mix proportions and dimensions of brick specimens Designation 3.2.2 Mix Proportions Dimensions in mm (Fly Ash: Sand: Cement) (Length×Breadth×Height) CB Clay constituents 235×110×75 FAB-I 60:30:10 235×110×75 FAB-II 50:40:10 235×110×75 Sand The locally available river sand is used for making mortars conforming to the specifications of Indian Standard IS: 2116:1980 [50]. 3.2.3 Cement Portland Slag Cement of Konark brand is used in the present study for preparing mortar. 3.3 Test Specimens Preparation The specimens considered in the present study consist of brick units, mortar cubes and masonry assemblages. The masonry assemblages include four brick 29 Chapter 3 Experimental Work high stack bonded prisms and three brick high stack bonded triplets. The method of preparation of these specimens is explained below. 3.3.1 Brick Units Brick units of three variants are considered in the study as explained in the previous section. Around 1000 bricks of each type are procured for the tests out of which the required numbers of bricks are randomly selected. It is to be noted that care is taken to collect all the bricks in each of the above three categories from same batch of mix to avoid the variations arising out of change in mix proportions, mixing time, curing procedure, etc. from batch to batch. 3.3.2 Mortar Mortar is used as a binding material to combine brick units and together they form masonry. Mortar is a mixture of sand, a binder and water. The binder may be lime or cement, in this study, cement is used as the binder so the mortar is called cement mortar. Three grades of cement mortar are prepared by changing the ratios of cement and sand. The three mortar grades are designated as CM1, CM2 and CM3. Table 3.2 presents the designation, mix proportion and characteristic of the mortar. Table 3.2: Designation and mix proportions of different grades of mortar Designation Mix Proportions Characteristic (Cement:Sand) CM1 1:6 Weak Mortar CM2 1:4.5 Intermediate Mortar CM3 1:3 Strong Mortar To determine the strength and other properties of mortar, cubes of 70 mm dimension are casted in the laboratory. The batching of raw materials, mixing, casting of cubes and curing are done as per Indian Standard IS 2250:1981 [51]. 30 Chapter 3 Experimental Work While mixing due care is taken to maintain the water-cement ratio as 0.8 for CM1, 0.55 for CM2 and 0.45 for CM3 to achieve good workability and strength. All the test cubes are casted using same batch of mix, for each type of mortar, to avoid the variations arising out of change in mix proportions, mixing time, curing procedure, etc. The different grades of mortar cubes casted for experimental work are shown in Fig. 3.5. Figure 3.5: CM1, CM2 and CM3 grade mortar cubes 3.3.3 Masonry Assemblages Masonry assemblage is a unified mass of brick units bonded together with mortar joint. The masonry assemblages are of different types on the basis of height/thickness ratio, bond type etc. In this study masonry assemblages of two types are mainly used as discussed below. (i) Four brick high stack-bonded prisms for testing the compressive strength (ii) Three brick high stack-bonded triplets for testing the shear bond strength The masonry assemblages are constructed using three different grades of mortars and for all the three variants of bricks. The dimensions of the masonry assemblages for the three brick variants are given in Table 3.3. Prior to construction the bricks are pre-wetted for suitable period of time so that the hydration process in mortar is not affected by the absorption of water by bricks. The thickness of mortar joints is maintained at 8 to 10 mm. After construction is 31 Chapter 3 Experimental Work complete, the specimens are cured for 28 days by covering with wet burlap. The height-to-thickness ratio for four brick high prism is kept at 3 which fall in the range of 2 to 5 as mentioned in Indian Standard IS 1905:1987 [29]. The masonry specimens constructed for the experimental study are shown in Figs. 3.6-3.7. Table 3.3: Dimensions of masonry assemblages for three brick variants Brick Type Dimensions in mm (Length×Breadth×Height) Prism Triplet CB 235×110×330 235×110×245 FAB-I 235×110×330 235×110×245 FAB-II 235×110×330 235×110×245 Figure 3.6: Typical stack-bonded masonry prism specimen 32 Chapter 3 Experimental Work Figure 3.7: Typical stack bonded masonry triplet specimen 3.4 Detailed Experimental Tests and Procedures Several experimental tests are conducted to obtain different mechanical properties of brick units (such as IRA, WA, dry density and compressive strength) and masonry assemblages (compressive strength and shear bond strength). Also, XRD and FESEM analyses are conducted to study the microstructure and morphology of test specimens. This section presents the description of the relevant experiments in detail. 3.4.1 Tests for Mechanical Properties 3.4.1.1 Initial Rate of Absorption IRA test is essentially a measurement of the amount of water a unit brick absorbs when immersed in water at 3 mm depth for one minute. It is measured in kg/m2 /min or gm/30 in2 /min. The IRA value gives the in-hand knowledge about the absorptive capacity of bricks. The test is done as specified in ASTM C67-14 [52]. First, the bricks are oven dried for not less than 24 hours or until two consecutive readings show no variations in weight. Then the bricks are cooled for 4 hours or till the surface is not hot to touch. The testing tray is filled with 33 Chapter 3 Experimental Work water with its level kept at 3 mm above the supports. The dimension of the brick specimen is noted and its dry weight is determined. It is then placed on the supports and the water level is maintained by adding additional water when found necessary. After one minute the brick unit is taken out of testing tray, wiped with wet cloth and its weight is found. The gain in weight within one minute divided by its surface area gives the IRA value. The IRA test setup is shown in Fig. 3.8. Figure 3.8: Test setup for determining IRA 3.4.1.2 Water Absorption and Dry Density Water absorption is the measure of the amount of water the brick unit absorbs when placed in water for 24 hours. It is a commonly followed test and is conducted as per Indian Standard IS 3495:1992 [49]. The brick specimen is oven dried for not less than 24 hours or until two consecutive readings show no variations in weight. The dry weight of sample is found and it then immersed in water bath for 24 hours. Then the sample is taken out, wiped with wet cloth and its wet weight is found. The WA is calculated by dividing the gain in weight by dry weight of brick. The dry density of the brick is determined by dividing the dry weight of brick by its volume. 34 Chapter 3 3.4.1.3 Experimental Work Compressive Strength The strength of the specimen under compression is determined by testing in compression testing machine. In this study, specimens of brick units, mortar cubes and masonry prisms are tested under uniaxial monotonic compressive loading. The brick and prism specimens are tested with frog filled face towards loading surface between two plywood sheets (soft capping). The compression test of brick, mortar cube and prism are conducted as per specification in Indian Standards IS 3495:1992 [49], IS 2250:1981 [51] and ASTM C1314-14 [53] respectively as shown in Fig. 3.9. Figure 3.9: Compression test of (a) brick (b) mortar cube and (c) prism specimen 3.4.1.4 Shear Bond Strength The strength of the brick-mortar joint under shear force is determined by testing masonry triplets under direct shear loading. In this study the masonry triplet specimens are constructed as specified in earlier section. The specimen is placed in a compression testing machine or universal testing machine where loading is applied through a plunger. Two support blocks are provided under the two end bricks and loading is applied on the centre brick. The load at which the middle brick detaches from masonry is the failure load. The strength is calculated by 35 Chapter 3 Experimental Work dividing the load with twice the surface area of brick. Fig. 3.10 shows the test setup of shear bond strength test with triplet specimen. Figure 3.10: Test setup of shear bond strength test with triplet specimen 3.4.2 Tests for Morphology and Microstructure 3.4.2.1 X-ray Diffraction XRD is an analytic technique primarily used for phase identification of a crystalline material. By knowing the different phases of material, the unknown chemical compounds in a material can be determined. XRD is very useful for determining the various chemical compounds present that influence the properties of the specimen. In this study, XRD is performed for brick units and mortar specimens using Rigaku Japan ULTIMA-IV multipurpose X-ray diffraction system (Fig. 3.11). The specimens are grounded into a fine powder and then they are placed in a sample holder which is put in machine for testing. The testing is done with scanning range of 10◦ to 80◦ , scanning rate of 0.05 degree/sec and step size of 20/min. 3.4.2.2 Field Emission Scanning Electron Microscopy The surface structure of materials at molecular level is obtained by FESEM which provides ultra-high resolution microstructural characterization images of samples. 36 Chapter 3 Experimental Work Figure 3.11: Multipurpose X-ray diffraction system (Rigaku ULTIMA IV) In the present study, FESEM is conducted on brick and mortar samples using Nova Nano SEM/FEI model as shown in Fig. 3.12. Prior to testing, the specimens are coated with electrically conductive gold material to avoid the charging effect. The coated samples are placed on carbon tape attached to sample holder which is then fixed in the machine. The micrographs are taken at different magnification levels for clear view of the microstructure. Figure 3.12: FESEM (Nova Nano SEM/FEI ) 37 Chapter 3 3.5 Experimental Work Summary This chapter describes the details of raw materials used, preparation of specimens, equipment used and procedures of experimental work carried out as part of the research. Experiments are conducted to evaluate the different mechanical properties of masonry specimen such as IRA, WA, dry density, compressive strength and shear bond strength. Higher order analyses such as XRD and FESEM are conducted to understand the morphology and microstructure. 38 Chapter 4 Variability and Analytical Study on the Properties of Bricks and its Masonry 4.1 Introduction Analysis and design of any structure considering the mean values of material properties may underestimate or overestimate the structural capacity as most of the engineering materials pose randomness. Therefore, in order to design a safer structure it is necessary to take in to consideration the randomness and variability of the material properties. This requires mathematical description of the variability in different material properties. Although the variability of mechanical properties related to steel and concrete are reported in literature, brick masonry which is one of the most important building elements around the globe has not received necessary attention. The first part of the chapter presents the description of the variation of different mechanical properties of brick, mortar and brick masonry using different probability functions. A best fitted probability distribution function is derived by conducting various statistical tests. The second part, investigates the morphology and microstructure of the brick and mortar samples in order to obtain an insight 39 Chapter 4 Variability and Analytical Study of Brick Masonry of the cause of the uncertainty. The last part of this chapter is devoted to estimation of the compressive strength of brick unit and brick masonry. The compressive strength of brick is derived as a function of its different other properties (IRA, WA and dry density). Similarly, the compressive strength of brick masonry is derived as a function of brick and mortar compressive strength. This procedure will eliminate the destructive tests to obtain the compressive strength of brick and brick masonry. 4.2 Variability in Mechanical Properties of Bricks The statistical analysis conducted on the experimental test results obtained for different mechanical properties are presented in this section. The test specimens for determining the mechanical properties include brick units, mortar cubes and four brick high stack bonded masonry prism. The specifications for preparation of test specimens, different experiments and their procedures are explained in Chapter 3. The test results obtained for each test specimen type is explained in the following sections. 4.2.1 Variation in different Properties of Brick Units Several experimental tests are conducted on brick units to determine four mechanical properties such as IRA, WA, dry density and compressive strength. A total of 150 brick units comprising of 50 numbers each for CB, FAB-I, FAB-II are tested. The brick units of each variant collected randomly from a single-batch-made brick lot are tested. The values of each property obtained for all the 150 samples of the three brick variants along with mean, standard deviation and coefficient of variation (COV) are tabulated in Table 4.1. The variability in each of the properties of three types of bricks is discussed in the following sections. 40 Chapter 4 Variability and Analytical Study of Brick Masonry Table 4.1: Values of IRA, WA, dry density and compressive strength for brick specimens Sl. No. IRA(kg/m2 /min) Dry density (kN/m3 ) WA (%) † Compressive strength (MPa) CB FAB-I FAB-II CB FAB-I FAB-II CB FAB-I FAB-II CB FAB-I FAB-II 1 1.3 2.45 1.69 10.08 5.95 15.06 13.95 14.2 15.75 4.86 3.23 5.79 2 1.72 3.05 1.79 12.74 9.98 15.12 14.39 14.27 15.76 5.6 3.55 6.24 3 1.79 3.27 1.83 13.21 10.42 15.24 14.4 14.33 15.77 5.62 3.57 6.24 4 2.03 3.41 1.86 14.23 11.6 15.25 14.59 14.43 15.82 5.67 3.61 6.38 5 2.13 3.5 1.92 14.5 11.94 15.32 14.64 14.44 15.85 5.7 3.62 6.38 6 2.14 3.6 1.93 14.83 12.13 15.32 14.69 14.47 15.87 5.7 3.62 6.44 7 2.28 3.63 1.95 15.04 13.12 15.4 14.74 14.48 15.91 5.73 3.62 7.15 8 2.32 3.64 1.96 15.05 13.94 15.59 14.75 14.49 15.95 5.9 3.95 7.18 9 2.36 3.73 1.98 15.09 15.49 15.63 14.75 14.65 16 5.9 3.98 7.28 10 2.47 3.83 2.01 15.47 15.49 15.63 14.8 14.68 16.05 5.95 3.99 7.8 11 2.55 3.88 2.04 15.53 16.09 15.63 14.82 14.78 16.05 6.21 4.03 7.8 12 2.86 3.89 2.11 15.67 16.1 15.64 14.82 14.81 16.09 6.56 4.03 7.88 13 2.89 3.91 2.12 15.84 16.32 15.67 14.86 14.84 16.14 6.58 4.03 7.98 14 2.96 4.03 2.15 15.85 16.59 15.89 14.89 14.87 16.15 6.7 4.35 8.12 15 3.01 4.06 2.26 15.97 16.89 15.93 14.9 14.89 16.19 6.76 4.35 8.15 16 3.02 4.11 2.28 16.19 16.9 16.03 14.9 14.93 16.22 6.76 4.55 8.47 17 3.03 4.29 2.3 16.35 16.93 16.27 14.91 15 16.26 7.02 4.55 8.7 18 3.2 4.43 2.35 16.51 16.97 16.29 14.96 15.01 16.27 7.03 4.74 8.81 19 3.25 4.47 2.35 16.68 17.02 16.32 15.08 15.02 16.27 7.09 4.74 8.85 20 3.29 4.51 2.38 16.75 17.11 16.34 15.11 15.06 16.33 7.09 4.74 9.15 21 3.42 4.59 2.41 16.75 17.14 16.36 15.11 15.08 16.35 7.22 4.74 9.27 22 3.45 4.63 2.44 16.86 17.23 16.46 15.16 15.11 16.42 7.28 4.79 9.28 23 3.53 4.67 2.44 16.91 17.34 16.46 15.2 15.12 16.48 7.31 5.05 9.4 24 3.61 4.72 2.49 16.95 17.45 16.46 15.35 15.13 16.5 7.31 5.14 9.45 25 3.7 4.74 2.54 16.99 17.58 16.53 15.36 15.13 16.5 7.38 5.23 9.56 26 3.77 4.78 2.56 17 17.58 16.58 15.39 15.16 16.56 7.7 5.3 9.63 27 3.83 4.79 2.6 17.03 17.68 16.66 15.4 15.2 16.62 7.73 5.38 9.90 28 3.96 4.91 2.66 17.16 17.7 16.79 15.45 15.23 16.65 7.74 5.58 9.96 29 4.08 4.95 2.66 17.25 17.75 16.94 15.49 15.25 16.66 7.77 5.58 10.48 30 4.13 5.38 2.72 17.4 17.85 16.99 15.54 15.26 16.7 7.81 5.69 10.53 31 4.39 5.42 2.73 17.46 17.87 17.01 15.59 15.28 16.73 7.87 5.86 10.58 32 4.43 5.45 2.78 17.48 17.99 17.05 15.62 15.32 16.74 7.98 5.93 11.11 33 4.65 5.45 2.8 17.55 18.26 17.11 15.67 15.49 16.76 8.02 6.01 11.31 34 4.66 5.49 2.82 17.58 18.33 17.14 15.67 15.65 16.77 8.08 6.04 11.31 35 4.72 5.5 2.83 17.61 18.35 17.2 15.78 15.67 16.9 8.14 6.07 11.34 41 Chapter 4 IRA(kg/m2 /min) Sl. No. 1 Variability and Analytical Study of Brick Masonry Dry density (kN/m3 ) WA (%) † Compressive strength (MPa) CB FAB-I FAB-II CB FAB-I FAB-II CB FAB-I FAB-II CB FAB-I FAB-II 36 4.77 5.81 2.84 17.67 18.41 17.48 15.82 15.72 16.92 8.18 6.09 11.41 37 4.78 5.81 2.9 17.73 18.51 17.61 15.86 15.79 16.97 8.28 6.32 11.55 38 4.9 5.88 3.02 17.83 18.52 17.8 15.93 15.84 17.02 8.65 6.4 11.88 39 5.01 5.9 3.03 17.89 18.54 17.82 15.97 15.93 17.07 8.66 6.64 11.93 40 5.08 6.01 3.04 17.94 18.62 17.83 16.01 15.95 17.08 8.7 6.94 11.99 41 5.23 6.11 3.16 18.07 18.99 17.87 16.02 16.33 17.18 8.85 6.97 12 42 5.42 6.17 3.16 18.25 19.11 17.95 16.06 16.47 17.18 9.07 7.18 12.04 43 5.43 6.32 3.18 18.3 19.13 18.35 16.08 16.55 17.32 9.13 7.21 12.06 44 5.55 6.4 3.24 18.32 19.37 18.43 16.11 16.68 17.36 9.21 7.21 12.12 45 5.7 6.57 3.4 18.39 19.37 18.76 16.15 16.69 17.44 9.33 7.32 12.23 46 5.72 6.6 3.63 18.54 19.39 18.82 16.26 16.77 17.46 9.67 7.36 12.45 47 5.76 6.8 3.71 18.56 19.42 19.01 16.26 16.9 17.59 9.75 7.51 12.71 48 5.8 7.17 3.78 18.65 19.73 19.06 16.3 16.98 17.61 9.97 7.58 13.47 49 5.9 7.8 3.9 19.36 19.82 19.29 16.48 17.16 17.62 11.31 8.7 13.8 50 6.01 7.88 4.55 19.54 19.85 19.3 17.34 17.31 17.67 11.88 9.88 15.01 Mean 3.84 4.97 2.63 16.69 17.01 16.81 15.39 15.39 16.59 7.61 5.45 9.81 SD 1.3 1.24 0.62 1.75 2.87 1.21 0.66 0.83 0.57 1.49 1.49 2.26 COV 0.34 0.25 0.24 0.11 0.17 0.07 0.04 0.05 0.03 0.19 0.28 0.23 † Outliers are ignored while calculating mean 4.2.1.1 Variation in IRA IRA of bricks is an important property that influence the brick mortar joint. IRA identifies the absorptiveness of bricks; highly absorptive bricks absorb more water from mortar joint thus reducing the hydration in mortar. Therefore, pre-wetting is essential for highly absorptive bricks before laid with mortar for masonry wall construction as reported in many past literatures ( [54] [7] etc.). Similarly, low absorptive bricks tend to float on mortar, thereby reduce the bond strength. Thus, IRA gives an insight on the pre-wetting time needed and bond strength of brick masonry. It can be seen from the Table 4.1 that the IRA for the CB specimens used in this study is found to vary from 1.30 to 6.01 kg/m2 /min (with a COV of 0.34), that for FAB-I is found to vary from 2.45 to 7.88 kg/m2 /min (with a COV of 0.25) and similarly for FAB-II the values varied from 1.69 to 4.55 kg/m2 /min (with a COV of 0.24). According to Drysdale et al. (1994) [54], IRA values ranging from 42 Chapter 4 Variability and Analytical Study of Brick Masonry 0.25 to 1.5 kg/m2 /min provide good bond strength. If IRA is higher than 1.5 kg/m2 /min, brick units are highly absorptive and should be wetted prior to laying to achieve better bond strength. However, these IRA limits ( [54]) were derived on the basis of tests carried out on clay bricks. Basha and Kaushik (2014) [55] reported that the IRA values for fly ash brick varied from 3 to 7 kg/m2 /min with an average of 5.1 kg/m2 /min (COV of 0.19). It is also suggested that since, fly ash brick is newly emerging building material, the limits proposed for clay bricks may not be applicable to fly ash bricks. However, From Fig. 4.1 it could be understood that the mean value of IRA is found to be lowest in case of FAB-II whereas FAB-I has highest value among considered specimens. Mean IRA of CB lies between that of FAB-II and FAB-I. The COV in CB is higher than FAB-I and FAB-II which are nearly same. Figure 4.1: Mean IRA values for three brick variants 4.2.1.2 Variation in WA Like IRA, WA affect the bond strength and durability of brick masonry. In addition to that, higher value of WA causes cracks on plasters as well as damage to the wall finish. Table 4.1 shows that the WA for CB is ranged from 10.08% to 19.54% (with a COV of 0.11), for FAB-I from 5.95% to 19.85% (with a COV of 0.17) and similarly for FAB-II from 15.06% to 19.3% (with a COV of 0.07). This satisfies the criteria of maximum limit of 20% specified in Indian Standard 43 Chapter 4 Variability and Analytical Study of Brick Masonry IS 12894:2002 [56]. Similar results were presented in literature for clay bricks from south India ( [23]) and north India ( [7]) that shows the WA value varies from 11 to 18.36%. The WA value for fly ash bricks was reported ( [57] [58] [37] [55]) to vary from 12.5 to 37%. The mean values of WA are depicted in Fig. 4.2. It has been observed that the fly ash is highly water absorbent material so fly ash brick tends to have higher WA value [59]. This is probably the reason for higher WA in fly ash bricks than clay bricks. Moreover, the amount of fly ash is more in FAB-I as compared to FAB-II, hence, FAB-I has slightly higher mean WA value than FAB-II. It can be observed from Table 4.1 that the COV values associated with WA is lowest for FAB-II followed by CB and FAB-I. Figure 4.2: Mean WA values for three brick variants 4.2.1.3 Variation in dry density The dry density of CB is found to vary from 13.95 to 17.34 kN/m3 (with a COV of 0.04), for FAB-I it is 14.20 to 17.31 kN/m3 (with a COV of 0.05) and for FAB-II it is found to vary from 15.75 to 17.67 kN/m3 (with a COV of 0.03) as shown in Table 4.1. The mean dry density value of FAB-I and CB are found to be equal; dry density of FAB-II is slightly higher as shown in Fig. 4.3. However, the variation among FAB-II is least followed by CB and FAB-I. It is observed that FAB-II bricks have higher amount of sand and lower amount of fly ash as compared to FAB-I, hence its weight is slightly higher. It could be said that higher amount of fly ash 44 Chapter 4 Variability and Analytical Study of Brick Masonry in bricks makes the bricks lighter as dry density of FAB-I is lower than FAB-II. Figure 4.3: Mean dry density values for three brick variants 4.2.1.4 Variation in compressive strength of brick units As seen from Table 4.1, the compressive strength value for CB is found to vary from 4.86 to 11.88 MPa (with a COV of 0.19), for FAB-I the values ranged from 3.23 to 9.88 MPa (with a COV of 0.28) and similarly, the compressive strength of FAB-II varied from 5.79 to 15.01 MPa (with a COV of 0.23). The compressive strength of clay brick (CB) and fly ash brick specimens (FAB-I and FAB-II) is found to be in good agreement with the studies carried out by many past researchers ( [55] [7] [23] [37] [57]) in which the values reported to vary from 4.3 to 8.0 MPa for fly ash bricks and 3.2 to 18.0 MPa for clay bricks. It is observed from Fig. 4.4 that the mean compressive strength of FAB-II bricks is highest followed by CB and then by FAB-I. 4.2.2 Variation in Compressive Strength of Mortar A total of 60 cubes comprising of 20 for each mortar grade: CM1, CM2 and CM3 are tested for determination of compressive strength. The compressive strength values along with mean, standard deviation and COV is presented in Table 4.2. Higher amount of cement increases the strength of mortar. CM1 is a weak mortar, CM2 is intermediate mortar and CM3 is strong mortar in terms of their 45 Chapter 4 Variability and Analytical Study of Brick Masonry Figure 4.4: Mean compressive strength values for three brick variants Figure 4.5: Mean compressive strength for three mortar grades compressive strength. It could be observed from Table 4.2 that the compressive strength value for CM1 is found to vary from 5.61 to 8.61 MPa (with a COV of 0.15), for CM2 the values ranged from 8.21 to 14.01 MPa (with a COV of 0.14) and similarly, the compressive strength of CM3 varied from 18.02 to 30.03 MPa (with a COV of 0.14). It is understood from Fig. 4.5 that the mean compressive strength of CM3 is highest followed by CM2, and CM1 has lowest strength. The COV values are nearly equal for all grades. The COV value for compressive strength of mortar is much less than that for bricks because mortar cubes are prepared in laboratory with a higher percentage of cement which produced in controlled environment. 46 Chapter 4 Variability and Analytical Study of Brick Masonry Table 4.2: Compressive strength (MPa) for three mortar grades 4.2.3 Sl. No. CM1 CM2 CM3 1 5.61 8.21 18.02 2 5.81 9.01 19.02 4 6.01 10.01 20.02 5 6.01 10.01 20.02 6 6.01 10.01 20.02 7 6.01 10.22 20.02 8 6.01 10.72 21.02 9 6.21 11.01 22.02 10 7.01 11.01 22.02 11 7.01 11.29 22.02 12 7.01 11.61 22.22 13 7.21 11.67 23.02 14 8.01 11.71 24.02 15 8.01 12.01 24.02 16 8.01 12.01 24.02 17 8.01 13.01 26.03 18 8.21 13.01 26.03 19 8.41 14.01 28.23 20 8.61 14.01 30.03 Mean 6.96 11.18 22.54 SD 1.03 1.60 3.19 COV 0.15 0.14 0.14 Variation in Compressive Strength of Masonry Prisms Four brick high stack-bonded masonry prisms are constructed using three brick variants and three mortar grades. Twelve prisms of CB and FAB-I brick type 47 Chapter 4 Variability and Analytical Study of Brick Masonry and six prism of FAB-II for each mortar grade are tested resulting to total of 90 prisms. The individual prism compressive strength for each type is presented in Table 4.3. Fig. 4.6 presents a bar chart diagram for mean compressive strength of prism. Table 4.3: Compressive strength (MPa) for masonry prisms Brick Type CB FAB-I FAB-II Mortar CM1 CM2 CM3 CM1 CM2 CM3 CM1 CM2 CM3 1 1.49 2.33 3 1.36 2.3 2.91 1.55 3.49 4.65 2 1.56 2.35 3.2 1.45 2.46 3.1 1.94 3.49 5.04 3 1.57 2.81 3.33 1.55 2.6 3.3 1.94 3.88 5.04 4 1.63 2.84 3.4 1.55 2.67 3.49 2.71 3.88 5.23 5 1.74 2.9 3.52 1.71 2.71 3.61 2.71 4.27 5.43 6 1.94 3.05 3.71 1.74 2.8 3.72 3.49 5.04 5.62 7 2.33 3.1 3.96 1.94 2.91 3.88 - - - 8 2.35 3.1 4.07 1.98 3.02 3.92 - - - 9 2.78 3.1 4.27 2.1 3.1 4.05 - - - 10 2.91 3.15 4.3 2.13 3.1 4.18 - - - 11 3.1 3.49 4.58 2.27 3.3 4.46 - - - 12 3.88 3.88 4.65 2.52 3.49 4.46 - - - Mean 2.27 3.01 3.83 1.86 2.87 3.76 2.39 4.01 5.17 SD 0.76 0.43 0.55 0.36 0.35 0.5 0.71 0.58 0.34 COV 0.33 0.14 0.14 0.19 0.12 0.13 0.3 0.15 0.06 It could be witnessed from Table 4.3 that the compressive strength in clay brick prisms varies from 1.49 to 3.88 MPa for CB-CM1 prism (with a COV of 0.33), 2.33 to 3.88 MPa for CB-CM2 prism (with a COV of 0.14) and 3.00 to 4.65 MPa for CB-CM3 prism (with a COV of 0.14). The compressive strength for first variety of fly ash bricks varies from 1.36 to 2.25 MPa for FAB-I-CM1 prism (with a COV of 0.19), 2.30 to 3.49 MPa for FAB-I-CM2 prism (with a COV of 0.12) and 48 Chapter 4 Variability and Analytical Study of Brick Masonry Figure 4.6: Mean compressive strength of the masonry prisms 2.91 to 4.46 MPa for FAB-I-CM1 prism (with a COV of 0.13). Similarly the compressive strength for second variety of fly ash bricks ranges from 1.55 to 3.49 MPa for FAB-II-CM1 prism (with a COV of 0.30), 3.49 to 5.04 MPa for FAB-II-CM2 prism (with a COV of 0.15) and 4.65 to 5.62 MPa for FAB-II-CM3 prism (with a COV of 0.06). From these data the following observations can be drawn. (i) From Table 4.3 and Fig. 4.6, it is evident that with the increase in grade of mortar the prism compressive strength increases irrespective of the brick type. This proves the fact that rich mortar performs better than weak mortar in imparting strength to masonry. (ii) The compressive strength of prism made using FAB-II is highest followed by CB and least by FAB-I. It is to be noted that FAB-II brick unit has highest mean strength followed by CB and least by FAB-I. The similar trend is followed for all mortar grades which signify that high strength of brick unit is also responsible for increasing the compressive strength of masonry. (iii) It is always perceived that the strength of brick-mortar masonry would lie in between individual strength of brick unit and mortar as it is a composite of both. But the results presented here show that this notion is not correct. 49 Chapter 4 Variability and Analytical Study of Brick Masonry Masonry prism fails early and has compressive strength lesser than that of brick unit and mortar because of its slenderness. (iv) The COV in prism compressive strength is more for all type of brick prisms made of CM1 than that of other two mortar grades. COV is found to be nearly equal in case of prisms made of CM2 and CM3. In overall, COV of compressive strength of fly ash brick prisms is less than clay brick prisms. This may be due to the fact that fly ash brick being made from pozzolanic material (fly ash) reacts better with mortar and forms good bond and reduces the variation in masonry of fly ash bricks. 4.2.4 Probability Distribution of Parameters The present study focus on the representation of variability of mechanical properties such as IRA, WA, dry density and compressive strength of brick units, mortar and masonry prism using probability distribution models. The best fit standard probability distribution models are verified using goodness-of-fit tests. The two parameter distribution models considered are normal, lognormal, gamma and Weibull distribution. The best-fit probability distribution model is captured by performing statistical goodness-of-fit tests such as Kolmogorov-Smirnov (KS), Chi-square (CS) and Log-likelihood (LK) tests. The characteristics of each distribution and goodness-of-fit test are explained in Appendix B. The best fit distribution model is selected on the basis of minimum KS distance, minimum CS and maximum LK values. Moreover, all the experimental values are positive hence, it is reasonable to analyse the data by using different non-negative probability functions. Followings are the step by step procedure adopted to perform the analysis on the experimental data to evaluate the variability using probability distribution. The steps are outlined based on several literatures ( [60] [61] [43] [5]) (a) The study of variability in mechanical properties of bricks, mortar and masonry prism is taken as an event of interest. 50 Chapter 4 Variability and Analytical Study of Brick Masonry (b) The test data obtained from several experiments are considered as random variables that represent the event. (c) The probability distribution of the random variables is unknown. So a probability distribution is assumed to be representing the event of random variables. (d) The parameters of the assumed probability distribution is estimated for determining the probability density function (PDF) or cumulative distribution function (CDF). For e.g. mean and standard deviation are the two parameters for normal distribution. (e) The closeness between PDF or CDF of assumed probability distribution and the same for observed test data is compared. (f) The acceptance or rejection of the assumed distribution is judged by performing goodness-of-fit tests. If the assumed distribution fits closely with observed data then the distribution is accepted otherwise some other distribution is checked. (g) The procedure is followed until the distribution model fitting best to the observed data is found. In this study a probability distribution model is considered to be best fit if it satisfies all the following criteria: (a) It should have passed confidence test at 5% significance level (for KS and CS test) otherwise the hypothesis is rejected. (b) The KS distance and CS value should have to be minimum among the four distributions (c) The LK value should be maximum among the four distributions. It is to be noted that Chi-square value may not be always reliable ( [5]). Chi-square test result depends upon the way in which data is divided into bins. 51 Chapter 4 Variability and Analytical Study of Brick Masonry Moreover, the binning of data delivers optimum results only when large random variables are included. This is also the reason for not performing CS test for mortar and masonry prism in this study, as their sample size is less. In present study, the closest fit distribution for most cases is decided from KS distance and LK values even if Chi-square does not indicate minimum value. However, in cases where a single model meets the criteria of all tests as mentioned above, then that model is selected as best fit. In many cases the goodness-of-fit test values differ by a small margin that indicates that all distributions closely compete to fit the variability in the properties best. It is to be noted that the CS value of only those distributions are shown which have been accepted at 5% significance interval. The statistical inference for each property is described in following sections. 4.2.4.1 IRA of Brick Units Table 4.4 shows estimated parameters (shape and scale) of distributions, KS distances, CS and LK values for IRA of each brick variants. CS values for CB and FAB-I bricks have not been shown as they do not meet the 5% significance criteria. On the basis of minimum KS distance and maximum LK value criteria, Weibull distribution is found to be the closest fit to the distribution obtained from experimental data for CB brick variant. For FAB-I and FAB-II, lognormal distribution perform slightly better than gamma distribution to represent the best fit in the goodness-of-fit tests. The probability distributions obtained from experiments and the assumed cumulative probability distribution models for IRA are compared for each brick variants and presented in Figs. 4.7(a) - 4.7(c) respectively. 4.2.4.2 WA of Brick Units The estimated parameters (shape and scale) of distributions, KS distances, CS and LK values for WA of each brick variants are shown Table 4.5. For CB and FAB-I, Weibull distribution is found to be the best fitted model as per 52 Chapter 4 Variability and Analytical Study of Brick Masonry the goodness-of-fit tests and all other models show large deviation from the experimental results. While for FAB-II, lognormal distribution is found to be best fit. A comparison of the probability distributions obtained from experiments and the assumed cumulative probability distribution models for WA are shown in Figs. 4.8(a) - 4.8(c) for three brick variants. 4.2.4.3 Dry Density of Brick Units The estimated parameters (shape and scale) of selected distributions, KS distances, CS and LK values for WA of each brick variants are shown Table 4.6. Table 4.6 show that all three goodness-of-fit tests are not in agreement with a single distribution for CB. However, gamma or lognormal distributions can be considered based on KS distance and LK value criteria. For FAB-I and FAB-II, lognormal is the best fitted model which satisfies all the three tests. A graphical depiction of comparison of the probability distributions obtained from experiments and the assumed cumulative probability distribution models for dry density for each brick variants (CB, FAB-I and FAB-II) are shown in Figs. 4.9(a)- 4.9(c). 4.2.4.4 Compressive Strength of Brick Units Table 4.7 presents the estimated parameters (shape and scale) of distributions, KS distances, CS and LK values for compressive strength for each brick variants. This table show that all three criteria (KS, CS and LK) are not in agreement with a single distribution for CB and FAB-I. However, based on KS distance and LK value, lognormal is found to be the closest fit model for these two brick variants. For FAB-II, Weibull distribution is found to be the best fitted model as it meets all the three validating criteria of maximum LK, minimum CS and KS values. Figs. 4.10(a), (b) and (c) show comparison of the probability distributions obtained from experiments and the assumed cumulative probability distribution models for compressive strength for each brick variants, CB, FAB-I and FAB-II respectively. 53 Chapter 4 Variability and Analytical Study of Brick Masonry Table 4.4: Estimated parameters of distributions, KS distances, CS and LK values for IRA(kg/m2 /min) of brick units Brick Type Distribution Shape Scale KS CS LK Normal 3.840 1.301 0.073 - -83.615 Lognormal 0.376 3.604 0.092 - -85.587 Gamma 7.983 0.481 0.090 - -84.130 Weibull 3.361 4.289 0.073 - -82.809 Normal 4.968 1.242 0.097 - -81.268 Lognormal 0.254 4.816 0.068 - -87.830 Gamma 16.242 0.306 0.065 - -88.308 Weibull 4.345 5.449 0.105 - -91.464 Normal 2.626 0.619 0.084 1.364 -46.426 Lognormal 0.227 2.560 0.061 1.103 -43.239 Gamma 19.621 0.134 0.062 1.202 -43.937 Weibull 2.871 4.335 0.105 1.499 -48.568 CB FAB-I FAB-II 54 Chapter 4 Variability and Analytical Study of Brick Masonry Table 4.5: Estimated parameters of distributions, KS distances, CS and LK values for WA(%) of brick units Brick Type Distribution Shape Scale KS CS LK Normal 16.692 1.749 0.117 2.285 -98.388 Lognormal 0.116 16.593 0.139 4.809 -103.048 Gamma 81.978 0.204 0.132 3.604 -101.328 Weibull 12.901 17.394 0.061 0.527 -93.085 Normal 16.796 2.869 0.213 - -123.151 Lognormal 0.219 16.478 0.246 - -134.493 Gamma 25.654 0.655 0.238 - -130.232 Weibull 8.945 17.816 0.162 4.788 -115.659 Normal 16.814 1.210 0.097 2.353 -79.963 Lognormal 0.071 16.777 0.091 1.673 -79.170 Gamma 200.919 0.084 0.093 1.855 -79.402 Weibull 14.166 17.392 0.125 7.714 -84.150 CB FAB-I FAB-II 55 Chapter 4 Variability and Analytical Study of Brick Masonry Table 4.6: Estimated parameters of distributions, KS distances, CS and LK values for dry density(kN/m3 ) of brick units Brick Type Distribution Shape Scale KS CS LK Normal 15.388 0.660 0.105 - -49.693 Lognormal 0.043 15.379 0.104 - -49.366 Gamma 558.675 0.028 0.095 - -49.490 Weibull 15.709 22.505 0.093 - -55.184 Normal 15.396 0.827 0.177 3.342 -60.942 Lognormal 0.053 15.379 0.167 2.977 -60.013 Gamma 362.193 0.043 0.169 3.034 -60.302 Weibull 15.806 17.999 0.205 - -66.990 Normal 16.591 0.566 0.095 - -41.942 Lognormal 0.034 16.577 0.092 - -41.692 Gamma 883.794 0.019 0.109 - -41.813 Weibull 16.868 30.582 0.113 - -45.635 CB FAB-I FAB-II 56 Chapter 4 Variability and Analytical Study of Brick Masonry Table 4.7: Estimated parameters of distributions, KS distances, CS and LK values for compressive strength (MPa) of brick units Brick Type Distribution Shape Scale KS CS LK Normal 7.608 1.497 0.071 3.889 -90.621 Lognormal 0.194 7.471 0.079 5.461 -89.004 Gamma 27.146 0.280 0.078 5.059 -89.258 Weibull 5.225 8.227 0.099 3.317 -93.125 Normal 5.451 1.497 0.111 1.669 -90.612 Lognormal 0.269 5.259 0.099 2.068 -87.830 Gamma 14.142 0.385 0.099 2.019 -88.308 Weibull 3.851 6.016 0.100 0.989 -91.464 Normal 9.81 2.265 0.086 2.551 -111.324 Lognormal 0.240 9.545 0.100 2.457 -111.908 Gamma 18.401 0.533 0.099 2.593 -111.386 Weibull 4.901 10.702 0.071 2.302 -111.379 CB FAB-I FAB-II 57 Chapter 4 Variability and Analytical Study of Brick Masonry (a) CB (b) FAB-I (c) FAB-II Figure 4.7: Experimental and assumed cumulative probability distributions for IRA of brick units 58 Chapter 4 Variability and Analytical Study of Brick Masonry (a) CB (b) FAB-I (c) FAB-II Figure 4.8: Experimental and assumed cumulative probability distributions for WA of brick units 59 Chapter 4 Variability and Analytical Study of Brick Masonry (a) CB (b) FAB-I (c) FAB-II Figure 4.9: Experimental and assumed cumulative probability distributions for dry density of brick units 60 Chapter 4 Variability and Analytical Study of Brick Masonry (a) CB (b) FAB-I (c) FAB-II Figure 4.10: Experimental and assumed cumulative probability distributions for compressive strength of brick units 61 Chapter 4 4.2.4.5 Variability and Analytical Study of Brick Masonry Compressive Strength of Mortar Table 4.8 presents the estimated parameters (shape and scale) of distributions, KS distances and LK values for compressive strength for each grade of mortar. CS test is not conducted owing to less sample size of random variables. For CM1 mortar grade, the KS distance and LK value are nearly same for all distributions except Weibull. So considering the criteria, lognormal which has minimum KS distance (almost same as normal) and maximum LK value is considered to be the best fit distribution model. For CM2, gamma distribution is the best fit model because it meets all the requirements of the criteria. Similarly for CM3 mortar grade, lognormal is the distribution that best captures the variability on the basis of minimum KS distance and maximum LK criteria. Figs. 4.11(a), 4.11(b) and 4.11(c) show comparison of the probability distributions obtained from experiments and the assumed cumulative probability distribution models for compressive strength for each mortar grade, CM1, CM2 and CM3 respectively. 4.2.4.6 Compressive Strength of CB Prism Table 4.9 presents the estimated parameters (shape and scale) of distributions, KS distances and LK values of compressive strength for CB prism with different grades of mortar. For CB-CM1 combination prism, the KS distance of lognormal and Weibull is nearly same and minimum but the LK value of lognormal distribution is maximum. So lognormal is considered to be the best fit distribution for this case. For CB-CM2 type of prism, the KS distance of lognormal and gamma is nearly equal whereas LK value of gamma distribution is maximum. Hence gamma distribution is best fit for this combination of masonry. The lognormal distribution has the minimum KS distance and its LK value is almost close to gamma which has maximum value for CB-CM3 combination prism. Therefore, lognormal distribution is taken as the best fit distribution representing this type of prism. The probability distributions obtained from experiments and the assumed cumulative probability distribution models for CB prism with each mortar grade: CM1, CM2 and CM3 are shown in Fig. 4.12(a), 4.12(b) and 4.12(c) respectively. 62 Chapter 4 Variability and Analytical Study of Brick Masonry Table 4.8: Estimated parameters of distributions, KS distances, CS and LK values for compressive strength(MPa) of mortar Brick Type Distribution Shape Scale KS LK Normal 6.960 1.026 0.223 -28.387 Lognormal 0.147 6.889 0.224 -28.067 Gamma 48.993 0.142 0.230 -28.129 Weibull 7.403 7.737 0.272 -29.902 Normal 11.178 1.595 0.101 -37.219 Lognormal 0.145 11.068 0.086 -37.278 Gamma 51.082 0.219 0.085 -37.192 Weibull 7.842 11.859 0.132 -37.721 Normal 22.542 3.191 0.141 -51.086 Lognormal 0.137 22.338 0.138 -50.234 Gamma 55.176 0.409 0.144 -50.460 Weibull 7.158 23.948 0.159 -52.722 CB FAB-I FAB-I 63 Chapter 4 Variability and Analytical Study of Brick Masonry (a) CM1 (b) CM2 (c) CM3 Figure 4.11: Experimental and assumed cumulative probability distributions for compressive strength of three mortar grades 64 Chapter 4 Variability and Analytical Study of Brick Masonry Table 4.9: Estimated parameters of distributions, KS distances, CS and LK values for compressive strength(MPa) of CB prism Brick Type Distribution Shape Scale KS LK Normal 2.270 0.760 0.173 -13.242 Lognormal 0.319 2.166 0.167 -12.108 Gamma 10.56 0.215 0.181 -12.352 Weibull 3.309 2.536 0.165 -13.170 Normal 3.010 0.430 0.203 -6.334 Lognormal 0.144 2.980 0.183 -6.331 Gamma 53.659 0.0561 0.185 -6.273 Weibull 7.668 3.189 0.236 -6.877 Normal 3.830 0.550 0.131 -9.403 Lognormal 0.145 3.79 0.115 -9.394 Gamma 52.104 0.0736 0.130 -9.353 Weibull 8.209 4.065 0.153 -9.499 CB FAB-I FAB-II 65 Chapter 4 Variability and Analytical Study of Brick Masonry (a) CB-CM1 (b) CB-CM2 (c) CB-CM3 Figure 4.12: Experimental and assumed cumulative probability distributions for for CB prism 66 Chapter 4 4.2.4.7 Variability and Analytical Study of Brick Masonry Compressive Strength of FAB-I Prism The estimated parameters (shape and scale) of distributions, KS distances and LK values for compressive strength of FAB-I prism with each grade of mortar are presented in Table 4.10. For FAB-I-CM1 prism combination, lognormal distribution is the best fit model satisfying the criteria of minimum KS distance and maximum LK value. The KS distance and LK value of Weibull distribution for FAB-I-CM2 combination deviates from other three models. Lognormal is found to be the best fit distribution model for FAB-I-CM2 as its KS distance is minimum and LK value is almost close to maximum value. For FAB-I-CM3 masonry prism Weibull distribution is the best fit while others show large deviation from the criteria. A comparison of the probability distributions obtained from experiments and the assumed cumulative probability distribution models for masonry prism combination of FAB-I with each mortar grade: CM1, CM2 and CM3 are shown in Figs. 4.13(a), 4.13(b) and 4.13(c) respectively. 4.2.4.8 Compressive Strength of FAB-II Prism Table 4.11 presents the estimated parameters (shape and scale) of distributions, KS distances and LK values for compressive strength for FAB-II prism with each grade of mortar. For FAB-II-CM1 prism combination, KS distance of lognormal is minimum whereas LK value is close to gamma distribution which is maximum. So, lognormal is considered to be close fit for this combination of masonry prism. For FAB-II-CM2 type of prism, lognormal is the best fit model while other distributions deviate from criteria. Similarly for FAB-II-CM3 combination of masonry prism, KS distance of lognormal is minimum whereas the LK values of all the models vary by small margin with Weibull has the maximum value. Hence, lognormal is taken as close fit to describe the variability in the compressive strength of FAB-II-CM2 masonry. A comparison of the probability distributions obtained from experiments and the assumed cumulative probability distribution models for masonry prism combination of FAB-II with each mortar grade: CM1, CM2 and CM3 are shown in Figs. 4.14(a), 4.14(b) and 4.14(c) respectively. 67 Chapter 4 Variability and Analytical Study of Brick Masonry Table 4.10: Estimated parameters of distributions, KS distances, CS and LK values for compressive strength(MPa) of FAB-I prism Brick Type Distribution Shape Scale KS LK Normal 1.860 0.360 0.138 -4.168 Lognormal 0.192 1.827 0.137 -3.949 Gamma 29.819 0.062 0.148 -3.957 Weibull 5.885 2.003 0.146 -4.445 Normal 2.870 0.350 0.095 -3.876 Lognormal 0.122 2.852 0.081 -3.856 Gamma 73.836 0.039 0.092 -3.821 Weibull 9.357 3.0218 0.114 -4.228 Normal 3.760 0.500 0.079 -8.203 Lognormal 0.136 3.725 0.094 -8.384 Gamma 59.974 0.063 0.084 -8.279 Weibull 9.092 3.966 0.078 -8.129 CB FAB-I FAB-II 68 Chapter 4 Variability and Analytical Study of Brick Masonry (a) FAB-I-CM1 (b) FAB-I-CM2 (c) FAB-I-CM3 Figure 4.13: Experimental and assumed cumulative probability distributions for for FAB-I prism 69 Chapter 4 Variability and Analytical Study of Brick Masonry Table 4.11: Estimated parameters of distributions, KS distances, CS and LK values for compressive strength(MPa) of FAB-II prism Brick Type Distribution Shape Scale KS LK Normal 2.390 0.710 0.238 -5.965 Lognormal 0.297 2.304 0.219 -5.739 Gamma 13.781 0.173 0.245 -5.724 Weibull 4.020 2.639 0.249 -5.935 Normal 4.010 0.580 0.254 -4.783 Lognormal 0.139 3.975 0.238 -4.452 Gamma 60.456 0.066 0.251 -4.505 Weibull 7.357 4.253 0.269 -5.289 Normal 5.170 0.340 0.148 -1.540 Lognormal 0.066 5.159 0.136 -1.581 Gamma 274.387 0.0188 0.141 -1.521 Weibull 19.124 5.313 0.193 -1.508 CB FAB-I FAB-II 70 Chapter 4 Variability and Analytical Study of Brick Masonry (a) FAB-I-CM1 (b) FAB-I-CM2 (c) FAB-I-CM3 Figure 4.14: Experimental and assumed cumulative probability distributions for for FAB-II prism 71 Chapter 4 4.3 Variability and Analytical Study of Brick Masonry Morphology and Microstructure of Bricks In this section, the morphological and microstructural study of brick specimens based on XRD and FESEM tests is presented. The tests are conducted as per the procedure explained in Section 3.4.2 of Chapter 3. The samples for the test are collected from the broken bricks specimens of low and high compressive strength. The attempt has been made to justify the variation in compressive strength of brick through its morphology and microstructure. 4.3.1 Interpretation from XRD Analysis XRD analysis is conducted for the brick units of all three variants and mortar specimens of three mortar grades. The samples are selected from the brick specimens which showed maximum and minimum compressive strength among the range of specimens tested. This analysis is useful in understanding the unknown chemical compounds present in a material. The procedure is explained in Section 3.4.2.1 of Chapter 3. The chemical properties responsible for differences in compressive strength of bricks specimens are studied from the analysis. It is observed that absence or presence of some chemical compounds affect the strength of brick greatly. Similar analysis is also conducted on representative specimens of three grades of mortar. These are discussed in succeeding sections in detail. 4.3.1.1 XRD of Brick units It is known that good bricks should have a composition that includes chemical compounds of silica, alumina, lime (calcium), oxides of iron and magnesium [62]. The presence of such compounds is verified from XRD patterns. Fig. 4.15 presents the XRD pattern of low and high compressive strength CB specimens. It can be seen that both low and high strength bricks have absence of calcium compounds. In low strength brick, only peaks of silicon oxide and iron oxide are present while high strength brick has small intensity peaks of magnesium and aluminium along with intensified peaks of silicon and iron oxide. The absence 72 Chapter 4 Variability and Analytical Study of Brick Masonry of aluminium and magnesium compounds may be the reason for loss of strength in bricks. (a) (b) Figure 4.15: XRD pattern for CB (a) low strength (b) high strength The XRD pattern of low and high strength FAB-I bricks is shown in Fig. 4.16. It indicates that low strength brick has peaks of silicon oxide and calcite. High strength brick has peaks of quartz which is a form of silicon oxide, calcium carbonate and berlinite which is an aluminium compound. Absence of traces of berlinite (aluminium) is probably the reason for low strength in this brick variant. From the XRD pattern for FAB-II bricks shown in Fig. 4.17 it is found that low strength brick has peaks of silicon oxide, hematite (form of iron oxide), magnesium 73 Chapter 4 Variability and Analytical Study of Brick Masonry (a) (b) Figure 4.16: XRD pattern for FAB-I (a) low strength (b) high strength calcite and copper sulphate. High strength brick has peaks of quartz, potassium calcium phosphate, magnesium calcite, iron oxide and berlinite. Except berlinite all other compounds are present in both low and high strength brick. The absence of berlinite (aluminium phosphorous oxide), a compound of aluminium, may be the reason for low strength in this brick variant. In clay brick specimens CB, absence of peaks of magnesium, aluminium resulted in low strength. For both fly ash brick specimens FAB-I and II, the absence of strong peak of element aluminium (berlinite) found to be the main factor for reduction in strength. It can be concluded from the XRD patterns 74 Chapter 4 Variability and Analytical Study of Brick Masonry (a) (b) Figure 4.17: XRD pattern for FAB-II (a) low strength (b) high strength that the presence of compounds of silica, aluminium, calcium, oxides of iron and magnesium are important in imparting strength to bricks. 4.3.1.2 XRD of different grades of Mortar Fig. 4.18 presents the XRD peaks for CM1, CM2 and CM3 mortar grades. CM1 has peaks of quartz, aluminium chromium and magnesium calcite. CM2 has peaks of quartz, aluminium oxide and calcium carbonate. The peaks of quartz, calcite magnesian and aluminium silicon phosphate are present in CM3. From the patterns it is found that all three mortar specimens contain peaks of 75 Chapter 4 Variability and Analytical Study of Brick Masonry (a) (b) (c) Figure 4.18: XRD pattern for mortar of three grades (a) CM1 (b) CM2 (c) CM3 76 Chapter 4 Variability and Analytical Study of Brick Masonry important elements such as silica, aluminium, calcium and magnesium. However, the intensity of peaks of silica and calcium compounds increases from CM1 (weak mortar) to CM3 (strong mortar). The increased intensity of peaks justifies the rise in strength of mortar from CM1 to CM3. 4.3.2 Interpretation from FESEM Images FESEM images illustrate the surface microstructure of the specimens. The microstructural study is helpful in identifying the shape of the crystals and their quantity, pores, etc. The procedure for obtaining the images is followed as discussed in Section 3.4.2.2 of Chapter 3. Huge variations in the mechanical properties are observed as shown in Section 4.2 although all the bricks used in the study are made from single batch of mix. Hence, the significance of this test is to detect the textural changes in brick specimen which may have influence on the variations in its properties. Small samples of brick specimens showing high and low compressive strength are selected for this test. The interpretation is done on FESEM images obtained at a magnification of 10,000 times for CB, FAB-I and FAB-II bricks. Figs. 4.19(a) and 4.19(b) show the images for CB type brick samples having low strength and high strength respectively. The image of CB having high strength depicts a void free vitreous or glassy texture surface. While that of low strength looks more like a rough textured surface which is porous. It can be interpreted that high strength CB is likely to undergo high temperatures and as a result of which the silica present in clay in the form of quartz melts and forms a void free glassy textured surface. The voids in high strength CB are less because the molten quartz fills the pores; this can be observed from the FESEM images for CB. When bricks are burnt at low temperatures the melting of the quartz is not complete and this can be attributed to the reason behind the low strength in brick. It can be said that to achieve good strength in clay bricks, all the bricks should be uniformly burnt at a suitable high temperature to activate the melting process of quartz and its fusion with other elements. This interpretation is well supported by Oscar et 77 Chapter 4 Variability and Analytical Study of Brick Masonry al. (2012) [21]. Figs. 4.20 and 4.21 show the images for FAB-I and FAB-II samples. It is evident from Figs. 4.20(b) and 4.21(b) that both the high strength brick samples consist of large amount of fibre or needle like crystals embedded on some irregular crystalline gel like surface. The needle like crystals are calcium based compounds and the irregular crystalline surface is formed as a product of silica based compounds. The fibres or needle like crystals probably act as good interlocking system which helps in imparting the strength to bricks. Figs. 4.20(a) and 4.21 (a) for low strength FAB-I and FAB-II bricks show that the fibres or needles are absent in first case or not fully developed and present in small quantity in second case respectively. This gives the idea that calcium compounds are not fully formed in low strength bricks for which the bricks lack good bonding leading to low strength. The fibres help in good interlocking between them and result in higher strengths. The fibres are surrounded by strongly bonded silicate crystals (Fig. 4.21(b)) in FAB-II whereas they are not strongly supported in silicate crystals in FAB-I. This may be the reason for the higher strength of FAB-II compared to FAB-I. The glassy textured surface of clay bricks helps in less water absorption which is why CB has less mean water absorption values as compared to FAB-I and FAB-II. Also, the strength of FAB-II is more than CB probably due to presence of fibres which imparts strength by good interlocking. The fibres are absent in CB due to absence of calcium compound as shown in XRD pattern for CB. The interpretation is well supported by the XRD analysis of samples. 78 Chapter 4 Variability and Analytical Study of Brick Masonry (a) Low strength (b) High strength Figure 4.19: FESEM images of CB (a) Low strength (b) High strength Figure 4.20: FESEM images of FAB-I (a) Low strength (b) High strength Figure 4.21: FESEM images of FAB-II 79 Chapter 4 4.4 Variability and Analytical Study of Brick Masonry Analytical Modelling of Brick Properties The determination of compressive strength of any material needs large testing machines. Some non-destructive tests such as ultra-sound pulse velocity measurement, rebound hammer tests etc., have been developed, which can determine the strength of material such as concrete. However it is not always feasible to use them at construction site as it increases overall cost and time. In this study simple mathematical equations are proposed which can predict the strength of brick and masonry with little error. The model is useful for quality controlling of bricks, mortar and ultimately masonry at construction site. The model could give first-hand knowledge on strength and quality of brick units without the need of any large testing equipment. The mathematical models proposed for predicting the strength of masonry and its units are explained in further sections. 4.4.1 Modelling of Brick Compressive Strength The compressive strength of brick units influences the overall strength of masonry in many ways. Hence, it must be determined before the bricks are used for construction purposes. But usually it is neglected at site because of lack of instruments. The equation developed in this research would be very useful in such situations. The mathematical model proposed in this research is derived based on simple mechanical properties such as IRA, WA and dry density of bricks. These properties can be easily determined at site with help of a weighing machine. Hence this equation is considered to be very useful for predicting the strength of brick and ultimately its quality. The following steps are taken for deriving the equation. (a) Large numbers of bricks (nearly 50 bricks of each type) are tested for obtaining the mechanical properties: IRA, WA, dry density and compressive strength of each brick unit in the laboratory. (b) From the experimental data a regular pattern of variation among the properties for all brick variants is observed. Similar pattern of variation of IRA, WA, and dry density with compressive strength is observed for all three 80 Chapter 4 Variability and Analytical Study of Brick Masonry brick variants. The pattern for FAB-I is shown in Fig. 4.22. Similar plots for CB and FAB-II are available in Appendix-C. (c) Correlation coefficient among the parameters is determined which confirmed that IRA, WA and dry density of brick influence its corresponding compressive strength. This implies that compressive strength can be determined when these parameters are given as input. (d) On the basis of this correlation, a mathematical equation is developed which takes IRA, WA and dry density of brick as input and delivers compressive strength as output. (e) The equation is developed by conducting multi-linear regression of large size of experimental values. In this study, three such equations are proposed for each variant of brick. (f) The R-square value is also found to be in good range validating the effectiveness of the model. The equation will be very useful because compressive strength of brick can be found with simple non-destructive tests that can be done quickly at site and without any sophisticated instruments. From Fig. 4.22, it could be observed that the compressive strength is maximum at those points where IRA and WA are minimum for every brick unit. Similarly, the maximum point of dry density is followed with maximum point of compressive strength. This provides the information that there is inverse relation of compressive strength with IRA and WA and direct relation with dry density. Hence a correlation exists between the properties. The four mechanical properties for each of 50 brick samples are determined experimentally. The correlation coefficient values of the properties of three brick variants are reported in Table 4.12. The correlation plots of IRA, WA and dry density with compressive strength for FAB-I is shown in Fig.4.23. Similar plots for the effect of IRA, WA and dry density with compressive strength for other two brick variant (CB and FAB-II) are presented in Appendix-C. 81 Chapter 4 Variability and Analytical Study of Brick Masonry (a) (b) (c) Figure 4.22: Variation of (a) IRA (b) WA (c) dry density with compressive strength for FAB-I 82 Chapter 4 Variability and Analytical Study of Brick Masonry Table 4.12: Correlation coefficients (Cr ) among the properties of brick units Sl. No. Correlation between CB FAB-I FAB-II 1 IRA- Compressive Strength -0.11 -0.67 -0.76 2 WA- Compressive Strength -0.67 -0.68 -0.76 3 Dry Density- Compressive Strength 0.55 0.84 0.81 4 IRA-WA 0.31 0.57 0.60 5 IRA- Dry Density -0.21 -0.71 -0.56 6 WA- Dry density -0.36 -0.76 -0.74 From Table 4.12 and Fig. 4.23, it is observed that IRA and WA has negative correlation with compressive strength. That means with the decrease in IRA and WA the compressive strength of brick increases. Dry density has a positive correlation with compressive strength which implies that increase in dry density influence the increase in compressive strength. This unique correlation of different properties with compressive strength encouraged to develop an equation that can predict the strength of brick units. The general form of the proposed mathematical equations is as follows: f'b = a + bI + cW + dD (4.1) Where, a, b, c and d are the constant coefficients, f'b is the predicted compressive strength of brick in MPa, I is the IRA of brick expressed in kg/m2 /min, W is the WA of brick expressed in percentage and D is the dry density of brick in kN/m3 . The equation takes into account the correlation because of which the coefficient of IRA and WA is negative while coefficient of dry density is positive. IRA and WA effect reduces the strength whereas dry density increases the strength. Table 4.13 presents the values of the coefficients for the three brick variants. Fig. 4.24 depicts the plot between experimental and predicted compressive strength values for FAB-I bricks. The plot shows that the equation performs well in predicting the strength. However small error may be possible but taking the large variation in bricks properties into consideration the error is negligible. 83 Chapter 4 Variability and Analytical Study of Brick Masonry (a) (b) (c) Figure 4.23: Correlation of (a) IRA (b) WA (c) dry density with compressive strength for FAB-I 84 Chapter 4 Variability and Analytical Study of Brick Masonry Table 4.13: Coefficients for the equation to evaluate the brick strength Brick type a b c d CB 4.568 -0.338 -0.391 0.705 FAB-I -7.239 -0.294 -0.046 0.953 FAB-II -9.387 -0.322 1.696 -1.382 Similar plots for CB and FAB-II are available in Appendix-C ; Figure 4.24: Variation plot between actual and predicted compressive strength for FAB-I The validation of the Eq. 4.1 is done by comparing the predicted value of the compressive strength with experimental value obtained from different literatures. Table 4.14 presents the comparison of the predicted compressive strength of brick unit and the experimental values reported in past studies with the percentage error in prediction put in parenthesis. From Table 4.14, it is understood that the error percentage in prediction of compressive strength of clay bricks is very high which indicates that the proposed equation is not suitable for clay bricks of other regions. The primary constituent of clay bricks is clay, the properties of which vary across regions. Hence it can be said that the prediction of compressive strength of clay bricks on the basis of its mechanical properties using a single equation is not a feasible option. Therefore 85 Chapter 4 Variability and Analytical Study of Brick Masonry many such empirical equations may be developed for different regions. It can be observed from Table 4.14 that for higher value of IRA, the predicted values shows less error when they are derived from Eq. 4.1 using coefficients of FAB-I. Similarly, for lower value of IRA, predicted values derived using coefficients of FAB-II shows less error. This is true for all the cases of fly ash bricks. Hence it can be said that the Eq. 4.1 using coefficients of FAB-I can suitably be used in cases where the IRA value is higher (>3 kg/m2 /min). Similarly Eq. 4.1 using FAB-II coefficients can be used when IRA value of brick is lower (<3 kg/m2 /min). It is to be noted that the IRA of FAB-I bricks is highest and that of FAB-II is lowest among the three variants used for deriving the coefficients of Eq. 4.1 (ref. Section 4.2.1 of Chapter 4). 4.4.2 Statistical inferences for Predicted Compressive Strength of Brick units The estimated parameters (shape and scale) of distributions, KS distances, CS and LK values for predicted compressive strength of each brick variants are shown Table 4.15. For CB brick, the KS distance of both normal and gamma distribution is equal and minimum and LK value of lognormal distribution is maximum although the value of gamma distribution is nearly equal. The CS value for Weibull is not shown because it is rejected at 5% significance level as per the criteria. Hence, the minimum CS value is shown by normal distribution. However ignoring CS value, gamma distribution can be considered as best fit because it meets the minimum KS distance and maximum LK criteria and lognormal distribution can be the next closest fit. For FAB-I, minimum KS distance is shown by lognormal distribution while gamma distribution is very close to the minimum KS distance and its LK value is also maximum. Minimum CS value is shown by normal distribution followed by gamma distribution. Hence, gamma distribution is considered as best fit and lognormal distribution can be the next closest fit. For FAB-II, minimum KS distance is shown by normal distribution but lognormal and Weibull distribution are also close to it. Similarly, minimum CS value is shown by 86 Chapter 4 Variability and Analytical Study of Brick Masonry Table 4.14: Comparison of past experimental results with predicted compressive strength Data Brick IRA (kg/ WA Dry Density Source Type Present Clay m2 /min) (%) 3.84 16.69 4.97 16.79 fb† (MPa) (kN/m3 ) (MPa) CB* 15.39 7.6 7.6 - - (0.3) - - - 5.19 4.46 (4.77) (18.17) - 7.02 9.72 - (28.44) (0.92) 17.47 - - (31.9) - - 10.92 - - (50.1) - - 9.48 - - (75.6) - - 13.07 - - (129.3) - - 11.80 - - (43.3) - - - 5.08 3.79 - (10.9) (33.5) - 7.36 8.57 - (2.5) (19.4) - 7.32 9.07 - (19.6) (0.3) - 4.82 2.48 - (9.1) (53.2) study Present Fly ash 0 fb† 15.39 5.45 study Present Fly ash 2.63 16.81 16.59 9.81 study [63] [64] [64] [65] [7] [55] [13] [64] [64] 2 Clay Clay Clay Clay Clay Fly ash Fly ash Fly ash Fly ash 0.2 2.7 4.4 1.52 1.9 5.1 6.3 1.6 4.4 5 13.4 15 10.1 12.3 18.3 11 25.4 24.4 21.18 17.74 17.4 18.4 18 15.39 17.8 17 15.2 21.9 5.4 5.7 20.8 5.7 7.18 9.1 5.3 0 † fb is the experimental value of brick compressive strength and fb is the brick compressive strength predicted using Eq. 4.1 3 25.65 FAB-I* FAB-II* * calculated with corresponding coefficients 87 Chapter 4 Variability and Analytical Study of Brick Masonry lognormal distribution and Weibull distribution shows the maximum LK value. Hence, Weibull distribution can be considered as the best fit distribution model for describing the variability in predicted compressive strength of FAB-II bricks. A comparison of the probability distributions obtained from experiments and the assumed cumulative probability distribution models for predicted compressive strength of each brick variants, CB, FAB-I and FAB-II are shown in Figs. 4.25(a), 4.25(b) and 4.25(c) respectively. Table 4.15: Estimated parameters, KS Distances, CS and LK values for predicted compressive strength (MPa) of brick units Brick Type Distribution Shape Scale KS CS LK Normal 7.571 0.925 0.060 0.404 -66.561 Lognormal 0.122 7.516 0.071 1.090 -66.053 Gamma 68.924 0.109 0.063 0.847 -66.099 Weibull 7.984 8.317 0.208 - -70.006 Normal 5.326 1.104 0.082 0.059 -75.397 Lognormal 0.210 5.214 0.059 0.389 -75.007 Gamma 23.572 0.226 0.066 0.208 -74.863 Weibull 5.306 5.776 0.086 0.610 -76.288 Normal 9.720 1.930 0.050 2.627 -103.363 Lognormal 0.213 9.516 0.070 2.299 -105.834 Gamma 23.843 0.408 0.060 2.361 -104.650 Weibull 5.818 10.494 0.060 3.189 -103.088 CB FAB-I FAB-II Table 4.16 presents the comparison of the obtained appropriate probability distribution model for experimental and predicted compressive strength of brick units. From the table it is evident that the equations proposed in this study are valid and predict the most appropriate values of compressive strength with simple calculations and without any need of heavy testing instruments 88 Chapter 4 Variability and Analytical Study of Brick Masonry (a) CB (b) FAB-I (c) FAB-II Figure 4.25: Predicted and assumed cumulative probability distributions for compressive strength of brick units 89 Chapter 4 Variability and Analytical Study of Brick Masonry Table 4.16: Comparison of distribution models for experimental and predicted compressive strength values of brick units Distribution Model for Compressive Strength 4.4.3 Brick Type Experimental Predicted CB Lognormal Gamma/Lognormal FAB-I Lognormal Gamma/Lognormal FAB-II Weibull Weibull Estimation of Masonry Prism Compressive Strength Masonry prism compressive strength is a fundamental property which is used in designing of structures with brick masonry. However in situations when the data is not available or it is not feasible to conduct experiments, simple mathematical equation could be useful. In the present study, a simple mathematical equation is proposed that can predict the prism compressive strength. The equation is based on two input parameters: compressive strength of brick unit and mortar. The general form of the equation for prism strength is taken from Eurocode 6 (CEN 2005a) [66] as follows: fk = K fαb fβm (4.2) Where, K, α and β are constants, fb and fm are the compressive strength of brick unit and mortar in MPa. The constants K, α and β are determined from unconstrained regression analysis of above Eq. 4.2 using least square fit method. The constants depend upon the brick and mortar strength. The bricks used in present study have less strength than mortar. So the prism made with such combination is termed as soft brick-strong mortar prism. The constants as derived separately for three brick variants with their equations are shown in Table 4.17. The value of constant α is less than β for all brick variants. This shows that the influence of mortar strength is more than the influence of brick strength for soft brick-strong mortar masonry prism as justified in past studies ( [55]). But for strong brick-weak mortar combination of prism the value of α is 90 Chapter 4 Variability and Analytical Study of Brick Masonry found to be more than β in past literatures ( [66] [23] [7]). The equation very well takes into consideration the brick and mortar strength which affect the prism strength. The coefficient of determination (R2 ) and standard error of estimate value (ν), which gives idea about the scatter of actual data from the estimated data, are also shown in Table 4.17. The R2 and ν values are calculated as per formula presented by Wesolowsky, 1976 [67] and Wonnacott and Wonnacott, 1972 [68] respectively. A value of R2 close to unity indicates a good fit and that close to zero indicates a poor fit. Similarly, it is desirable that ν is minimum, implying that the scatter in the data about the estimated value is a minimum. Table 4.17: Proposed equation for each of the three brick variant Brick Type Equation (fk ) K α β R2 ν CB 0.43 0.58fb0.29 fm 0.58 0.29 0.43 0.91 0.27 FAB-I 0.56 0.43fb0.29 fm 0.43 0.29 0.56 0.94 0.26 FAB-II 0.58 0.61fb0.15 fm 0.61 0.15 0.58 0.86 0.51 The estimated prism strength is calculated using each equation for three brick variants. The predicted values show good correlation with the experimental values which indicates the viability of the equations. Figs. 4.26 - 4.28 depict the correlation between experimental and estimated prism strength for CB, FAB-I and FAB-II respectively. The equations would be very useful for estimating the masonry strength without conducting any experiments on brick masonry. Three equations for three brick variants are not always convenient to use. It is not a good option to have as many equations as brick variants as there are many types of bricks available for construction. Although different types of bricks have different shapes and sizes, their chief ingredient is commonly clay or pozzolanic material like fly ash. Therefore, an effort have been given to develop a simpler equation to predict the compressive strength of brick masonry. The constant K which is discussed earlier depends upon the material property of bricks as well as mortar joint thickness. The Eurocode 6 (2005) [66] has proposed the value of K to be between 0.4 and 0.6 for different types of bricks and thickness of mortar joint. 91 Chapter 4 Variability and Analytical Study of Brick Masonry Figure 4.26: Experimental versus Estimated prism strength for CB Figure 4.27: Experimental versus Estimated prism strength for FAB-I Figure 4.28: Experimental versus Estimated prism strength for FAB-II 92 Chapter 4 Variability and Analytical Study of Brick Masonry The other constants α, β mainly represent the relative strength of brick and mortar in the masonry. Eurocode 6 [66] proposed the values of constant α and β as 0.7 and 0.3 respectively irrespective of brick variant. These values signify that more importance is given to brick strength than mortar strength as the bricks in Europe generally have higher strength than mortar. A similar approach is considered in the present study where the value of constant K is varied for different brick type but the values of other two constants are kept same for all brick variant. In this study thickness of mortar joint is kept constant between 8-10 mm for all prisms. So the K value is developed based solely on the material property of bricks. Eq. 4.3 presents the generalised equation developed to predict the masonry strength. It can be observed from the equation that the value of α is lesser than β as the bricks have lower strength than mortar in the present study. 0.55 fk = K f0.35 fm b (4.3) Where K is 0.37 for clay bricks and 0.41 for fly ash bricks. Table 4.18 presents the R2 and ν of predicted strength of prism for three brick variants. Because of generalization of data the error percentage found is little higher than that for individual equations shown in Table 4.17. A small change in the values of K is observed in comparison with the previous values. This generalised equation is computationally simple to be used in practice. Table 4.18: Proposed equation for bricks based on its material Brick Type Equation (fk ) K α β R2 ν CB 0.55 0.37fb0.35 fm 0.37 0.35 0.55 0.86 0.34 FAB-I 0.55 0.41fb0.35 fm 0.41 0.35 0.55 0.93 0.27 FAB-II 0.55 0.41fb0.35 fm 0.41 0.35 0.55 0.86 0.51 Proposed generalised equation (Eq. 4.3) to estimate the compressive strength of clay and fly ash brick masonry is validated by experimental data obtained from different literatures ( [69] [6] [7] [40] [13] [55]). The comparison of experimental 93 Chapter 4 Variability and Analytical Study of Brick Masonry results obtained from past studies with predicted values are presented in Table 4.19. The percentage of error is shown in parenthesis. It can be observed from the table that the equations proposed in this thesis for clay brick (K = 0.37) and fly ash brick (K = 0.41) perform better (error range of 1% to 40%) with the corresponding results when the brick compressive strength is lower than that of mortar. This is because the equations in present study are derived for weak brick-strong mortar combination. Similarly large error in prediction is encountered when the equations are used for bricks having higher compressive strength than mortar. Hence, the current generalised equations can be used for clay brick and fly ash brick masonry with bricks having lower strength than mortar. Table 4.19: Comparision of past experimental results with predicted prism strength Source Brick fb fm Type Experimental Predicted Strength (MPa) Strength (MPa) K = 0.37 K = 0.41 [69] Clay 13.1 6.1 5.4 2.5 (54.4) - [6] Clay 5.7 6.6 1.3 1.9 (47.8) - [6] Clay 23 6.6 6.7 3.1 (53.3) - [7] Clay 20.6 3.1 4.1 2.0 (51.4) - [7] Clay 20.6 20.8 7.5 5.7 (24.6) - [40] Clay 5.8 8.0 1.6 2.2 (34.3) - [13] Fly ash 3.3 5.5 1.7 - 1.6 (6.5) [13] Fly ash 7.2 8.5 3.0 - 2.7 (11.5) [55] Fly ash 5.7 6.9 3.1 - 2.2 (29.6) [55] Fly ash 5.7 17.3 3.9 - 3.6 (7.3) [55] Fly ash 5.7 21.6 4.6 - 4.1 (11.2) 94 Chapter 4 4.5 Variability and Analytical Study of Brick Masonry Failure Pattern in Masonry Prism Masonry is a composite involving two materials having different properties. The strength of masonry depends on the properties of its constituent materials. Masonry is weak in tension and is expected to take the compressive loads. Under compression, the mortar in the joint expands laterally more than the brick. But the expansion is restricted at the brick-mortar interface by bricks because of the bond between them. Therefore shear stresses formed at the brick-mortar interface develop internal stresses which results in tri-axial compression in mortar and bi-axial tension coupled with axial compression in bricks. In this state of stress mortar initiates the vertical splitting in masonry causing its failure ( [30] [70] [54]). The above mentioned stress mechanism is valid for strong bricks and relatively softer mortar. In the present study, the case is quite opposite. The prisms considered in the present study is a combination of soft brick and stronger mortar. So in this case brick expands laterally under axial compression but is confined due to mortar. Hence, bricks are in tri-axial compression and mortar is in bi-axial tension coupled with axial compression. Therefore, in the present case, bricks initiate the failure by vertical splitting in prisms. The following three types of failure patterns are observed in the study: (i) Vertical splitting failure Fig. 4.29 presents the vertical splitting failure in masonry prisms of different brick variants. The vertical splitting failure in masonry is caused by the soft brick-strong mortar combination. This is the predominant failure observed in most samples of the present study. Especially the prisms constructed using CM3 mortar grade failed by this pattern. The splitting originates in the central region of masonry and spreads to corners. The gap is wider at middle and narrow at corners. (ii) Diagonal shear failure Fig. 4.30 depicts the shear failure in masonry prisms along the diagonal. This type of failure is one of the most common failures observed next to vertical 95 Chapter 4 Variability and Analytical Study of Brick Masonry splitting failure. Diagonal shear failure is observed in prisms constructed using CM2 (intermediate) and CM1 (weak) mortar grade. The pattern of diagonal shear failure depends on the relative strength of brick and mortar. In case of CB and FAB-I prisms, the bricks have much low strength than mortar so, the diagonal failure occurs through crushing of bricks. Whereas in case of FAB-II prisms, the bricks strength is close to mortar strength or even higher, the failure occurs through crushing of mortar along the mortar joint as shown in Fig. 4.30(c). (a) (b) (c) Figure 4.29: Vertical splitting failure in (a) CB (b) FAB-I and (c) FAB-II prisms (a) (b) (c) Figure 4.30: Fig. 4.30: Diagonal shear failure in (a) CB (b) FAB-I and (c) FAB-II prisms 96 Chapter 4 Variability and Analytical Study of Brick Masonry (iii) Crushing failure Fig. 4.31 shows the crushing failure in prisms of different brick variants. This type of failure is observed in some of the specimens constructed with CM3 (strong) mortar grade. When the brick strength is much lesser than the mortar strength then the crushing of bricks occurs due to compression force. It is observed that the crushing of bricks originates from the mortar joint. (a) (b) (c) Figure 4.31: Crushing failure in (a) CB (b) FAB-I and (c) FAB-II prisms Figure 4.32: Failure due to crushing of brick 97 Chapter 4 Variability and Analytical Study of Brick Masonry Some of the FAB-I prisms are observed to fail through crushing of bricks. Since FAB-I has relatively lower strength (compared to CB and FAB-II) the brick crushes and fails under compression while the bond is still intact as shown in Fig. 4.32. Low strength bricks fail through this mode early without utilising the full strength of brick-mortar bond resulting a lower masonry strength. 4.6 Summary This chapter presents the experimental results and analysis of the results in following four aspects: (i) variability of mechanical properties of brick unit, mortar and brick masonry, (ii) morphology and microstructure of brick specimen, (iii) analytical modelling of compressive strength of brick unit and masonry prism and (iv) modes of failure observed for masonry prism under axial compression. The variability of mechanical properties of brick unit, mortar and brick masonry are described using four different two-parameter probability distribution functions. Most appropriate statistical distribution functions for mechanical properties are arrived based on the results of goodness-of-fit tests and other necessary criteria. Tables 4.20, 4.21 and 4.22 present the most appropriate distribution for brick unit, mortar and brick masonry respectively. These tables shows that lognormal is the most common distribution function to describe the variability of different mechanical properties of masonry materials. Weibull and gamma distributions are found to be most appropriate for some of the properties. However, in general, gamma distribution is found to be either the best or the next best distribution function to describe most of the mechanical properties studied. Therefore, lognormal or gamma distribution is recommended as the distribution function that best describe the variability of properties of brick masonry and its constituents. The next part of the chapter presents morphology and microstructure of brick specimens based on XRD and FESEM tests. XRD results show that the presence of silica, aluminium, calcium, oxides of iron and magnesium are important in 98 Chapter 4 Variability and Analytical Study of Brick Masonry imparting strength to bricks. FESEM results justifies the differences between bricks with low and high compressive strength based on microstructure. Table 4.20: Most appropriate statistical distribution functions for different mechanical properties of bricks Brick Type IRA WA Dry density Compressive Strength CB Weibull Weibull Lognormal Lognormal FAB-I Lognormal Weibull Lognormal Lognormal FAB-II Lognormal Lognormal Lognormal Weibull Table 4.21: Most appropriate statistical distribution functions for compressive strength of different grades of mortar Mortar Grade CM1 CM2 CM3 Compressive Strength Lognormal Gamma Lognormal Table 4.22: Most appropriate statistical distribution functions for compressive strength of brick masonry Fitted Distribution CM1 CM2 CM3 CB Lognormal Gamma Lognormal FAB-I Lognormal Lognormal Weibull FAB-II Lognormal Lognormal Lognormal Mathematical equations are proposed in this chapter to predict the strength of brick and masonry without destructive experiments. Mechanical properties such as IRA, WA and dry density of bricks are used to predict the strength of brick units whereas the strength of masonry prism is derived based on strength of brick unit and mortar. The validation of the proposed equations is done by comparing the predicted value of the compressive strength with experimental value obtained 99 Chapter 4 Variability and Analytical Study of Brick Masonry from different literatures. The generalised equation for masonry prism can be used for brick masonry with bricks having lower strength than mortar. Finally this chapter presents the failure patterns of masonry prism under axial compression observed in the study. Three different types of failure patterns such as vertical splitting, diagonal shear failure and crushing are identified. 100 Chapter 5 Shear Bond Strength of Brick Masonry 5.1 Introduction Under lateral loads, a masonry wall has to resist both in-plane and out-of-plane forces. Resistance to out-of-plane forces in masonry structure is negligible and generally ignored in analysis and design. However, the in-plane forces which act parallel to the plane of wall is resisted by the bond between brick and mortar. Shear bond strength of masonry plays an important role in dealing with in-plane forces. The bond strength is developed by formation of mechanical key through absorption of cement from mortar by brick. In this chapter the shear bond strength of both burnt clay and fly ash bricks is studied with varying different parameters such as moisture content of bricks, pre-wetting time, mortar grades, etc. The study helps in understanding the influence of these parameters on bond strength of masonry. The failure patterns obtained from experimental tests which give an insight of the weak zones initiating failure are also discussed. The results are compared among considered brick variants. 101 Chapter 5 5.2 Shear Bond Strength of Brick Masonry Lacunas in Past Researches Shear bond strength is a measure of the strength of brick-mortar joint under in-plane shear loading. Many past researches were conducted on the characterization of bond strength of brick masonry under flexure, shear, tension and compression. The relation between bond strength and the corresponding compressive strength of the masonry assemblages was studied by Sarangapani et al. (2005) [23]. Similar study was conducted by Reddy and Vyas (2008) [25] in which the influence of bond strength on the stress strain characteristics of masonry was established. This study ( [25]) revealed that poor bond strength causes the failure of brick mortar joint of masonry under compression. Several studies ( [23] [27] [24]) were conducted on enhancing the flexural, tensile and shear bond strength of masonry by changing the brick and mortar properties. The mortar strength was increased by replacing the cement mortar with lime or soil-cement mortar. Similarly, the brick properties were improved by making the texture of bed surface of brick as rough, altering the size and shape of the frogs, applying special surface coatings, etc. Although many brick properties were taken into consideration for enhancement of bond strength, the effect of water retentivity of mortar or the initial rate of absorption of brick units on bond strength got little attention. Samarsinghe and Lawrence (1992) [71] conducted shear bond tests on triplets constructed with masonry units that were pre-wetted and obtained higher bond strength as compared to those constructed with dry brick units. Sinha (1967) [72] and Reddy and Gupta (2006) [27] have considered the effect of pre-wetting time of bricks on tensile bond strength. Pavia and Hanley (2010) [28] studied the influence of hydraulicity, water content, workability and water retention of lime mortar to achieve higher flexural bond strength. All the past studies on the bond strength of brick masonry are conducted on burnt clay bricks or soil-cement blocks; fly ash cement bricks found no scope. Although wetting of bricks prior to construction is recommended, the effect of moisture content in bricks on shear bond strength of brick masonry or pre-wetting time required to achieve the maximum bond strength is not emphasized. The importance of the present research lies in performing the 102 Chapter 5 Shear Bond Strength of Brick Masonry necessary tests to fill the voids in the past studies as mentioned. 5.3 Salient Features of Present Study The present research work considers both burnt clay brick and fly ash cement bricks for investigating the shear bond strength of brick masonry. The effect of moisture content of the bricks at the time of laying on bond strength is studied by varying the pre-wetting time. The importance of IRA is established from the test results. The following methodology is adopted for achieving the objective: (a) Masonry triplets are constructed using the all three brick variants: CB, FAB-I and FAB-II. (b) Three different grades of cement mortar are used for construction of the triplets: CM1, CM2 and CM3. (c) Four sets of specimens with each set having triplets constructed using three brick variants and three mortar grades are studied. (d) Each of the four set of specimens differ with other on the basis of moisture content maintained in bricks by pre-wetting. (e) The influence of IRA and pre-wetting time on shear bond strength is established. 5.4 Specifications of the Experimental Work The experimental work involves the construction of triplets which are then tested for shear bond strength. The details of various materials used with their properties and procedure for construction of masonry triplets are explained in Chapter 3. The triplets are prepared using CB, FAB-I and FAB-II type of bricks with CM1, CM2, CM3 grades of mortar. The pre-wetting time is the important criteria of this test on the basis of which the triplets are divided into four sets 103 Chapter 5 Shear Bond Strength of Brick Masonry (named as A, B, C and D) depending on the moisture content (χ) in the bricks expressed as percentage of saturation moisture content. Saturation moisture content is defined as the maximum amount of water that can be contained in a brick, when all pore spaces are filled with water; it is expressed as the percentage of the dry weight of the brick. The pre-wetting time for the four sets of masonry triplets are presented in Table 5.1. The pre-wetting time is decided depending on saturation level of brick units, IRA and the moisture content(χ) needed in each set. The specifications for each set are explained as follow. Set-A (χ = 25%): It consists of triplets in which the brick units are not pre-wetted which is the usual practice followed at construction site. The brick units are brought from a brick lot which are neither completely dry nor soaked in water before, are directly laid on mortar for construction of specimens. During casting the moisture level in bricks is found to be around 20%-25% of the saturation moisture content. The shear bond strength test on Set A triplets would be useful in recreating the site conditions for masonry and thus help in quantifying the loss in strength because of no soaking. Pre-wetting is not given importance at construction site which affect the bond strength largely. The results could very well be interpreted for generalising the influence of IRA on bond strength. Set-B (χ = 50%): The moisture level of the brick units in Set B triplets is maintained at 50% of saturation moisture content. The brick units are pre-wetted for different durations to obtain that moisture level corresponding to their saturation moisture level. It is reported by Sarangapani et al. (2005) [23] that the soaking time should be chosen so that a water-cement ratio of 0.4 in mortar is maintained even after one hour contact with bricks. So when rich mortar grades (with more quantity of cement) are used such as CM2 and CM3 having water-cement ratio 0.6 and 0.5 respectively, the brick units are soaked for more time. Hence, the soaking time of bricks is increased by two minutes(for CB and FAB-II) and five minutes(for FAB-I) when higher grade of mortar is used as 104 Chapter 5 Shear Bond Strength of Brick Masonry shown in Table 5.1. Set-C (χ = 75%): The moisture level of the brick units in this set is maintained at 75% of saturation moisture content. The moisture level is obtained by soaking each brick variant at different time limits. Similarly the soaking time of all the three brick variants is increased for CM2 and CM3 mortar. Set-D (χ = 100%): In this set, the moisture level in bricks is maintained at 100% of the saturation moisture content. In this set, the brick units are used for construction of triplets in fully saturated state. The effect of complete saturation of brick units on bond strength is determined. Table 5.1: Pre-wetting time (in minutes) for different sets of masonry triplets Set of Triplets A Mortar Grade All Bricks CB FAB-I FAB-II CB CM1 0 5 10 5 10 15 10 1440 CM2 0 7 15 7 12 20 12 1440 CM3 0 10 20 10 15 25 15 1440 5.5 B C D FAB-I FAB-II All Bricks Discussion of Test Results Three triplets are constructed using each mortar grade and each brick variant resulting to 27 numbers of triplets under each set for three brick variants. Therefore a total number of 108 triplet samples are tested to determine the shear bond strength of both burnt clay and fly ash bricks under various moisture contents and soaking time. The test setup for the test is shown in Fig. 3.10 of Chapter 3. Fig. 5.1 and Fig. 5.2 show the triplet prior and after the test. 105 Chapter 5 Shear Bond Strength of Brick Masonry Figure 5.1: Triplet before shear bond strength test Figure 5.2: Triplet after shear bond strength test Results for Set-A The triplets of Set A are constructed without any pre-wetting. The moisture content for all bricks at the time of laying with mortar is found to be nearly 20%-25%. This moisture is probably absorbed by bricks from atmosphere when kept in open place. The test results signify the shear bond strength of triplets when the bricks are not soaked which is the common practice at construction sites. The results obtained can be correlated with bond strength of masonry in actual site conditions. Table 5.2 presents the mean shear bond strength values for triplets constructed with three brick type and using three mortar grades. Fig.5.3 shows the graphical interpretation of test results. The shear bond strength values of triplets with CM3 mortar is highest, followed 106 Chapter 5 Shear Bond Strength of Brick Masonry Table 5.2: Mean shear bond strength (in MPa) for Set-A triplets Mortar Ratio CB FAB-I FAB-II CM1 0.082 0.075 0.092 CM2 0.097 0.088 0.111 CM3 0.127 0.118 0.140 Figure 5.3: Shear bond strength for Set-A triplets by CM2 and is least for CM1 mortar. CM3 (strong mortar) has higher amount of cement as compared with CM1 (weak mortar), and CM2 (intermediate mortar) lies in between the two. This proves the fact that the higher cement content in mortar provides good bond strength. The shear bond strength varies from 0.082 MPa to 0.127 MPa for CB, 0.075 MPa to 0.118 MPa and 0.092 MPa to 0.140 MPa for FAB-II for different mortar grade. From the values it is observed that triplet made using FAB-I shows lowest strength with that for FAB-II is highest and CB has intermediate strength. This is because the IRA value of FAB-I is highest followed by CB, and FAB-II has lowest IRA among the three considered brick types. The brick units are not pre-wetted in this set, so when the bricks are laid with mortar the brick having higher IRA value absorbs more water from mortar. This causes the decrease in water content of mortar and reduces the water-cement ratio to below 0.4. 107 Chapter 5 Shear Bond Strength of Brick Masonry Reduction in water-cement ratio hampers the hydration of cement thus causing huge loss in strength. FAB-II has lowest IRA among the three, so it absorbs relatively less water and allows better hydration of cement although not complete as it is also not pre-wetted. There is nearly 23% loss in bond strength for FAB-I (higher IRA) in comparison to FAB-II (lower IRA). This justifies the fact that bricks with higher IRA value must be soaked prior to use. Higher the IRA, higher must be the soaking time. Results for Set-B The moisture content in the bricks used for constructing triplets of Set-B is maintained at 50% of their saturation moisture content through pre-wetting. Bricks are soaked for different duration based on IRA value and mortar grade as mentioned in Table 5.1. The result obtained implies the shear bond strength of masonry when the bricks have 50% moisture. The mean shear bond strength values for Set-B are presented in Table 5.3 and shown graphically in Fig. 5.4. Table 5.3: Mean shear bond strength (in MPa) for Set-B triplets Mortar Ratio CB FAB-I FAB-II CM1 0.111 0.112 0.118 CM2 0.129 0.133 0.150 CM3 0.162 0.171 0.180 The increase in bond strength with grade of mortar is evident from the figure. The bond strength values of CB used triplets vary from 0.111 MPa to 0.162 MPa. The same for FAB-I range from 0.112 MPa to 0.171 MPa and for FAB-II it varies from 0.118 MPa to 0.180 MPa. It can be observed that shear bond strength for Set-B is more than Set-A for all categories due to the increase in moisture content of bricks. The shear bond strength value of CB is lowest and among fly ash bricks, FAB-II performs better than FAB-I. The performance of fly ash bricks is better than clay bricks because fly ash is pozzolanic material which reacts better with cement to form strong bond than clay. 108 Chapter 5 Shear Bond Strength of Brick Masonry Figure 5.4: Shear bond strength for Set-B triplets Results for Set-C The moisture level of bricks used for making triplets under Set-C is maintained at 75% of their saturation moisture content value. The soaking time for the bricks is presented in Table 5.1. The result obtained signifies the shear bond strength of masonry when the bricks have 75% moisture in them while laid with mortar. The mean shear bond strength values for Set-C are presented in Table 5.4 and shown graphically in Fig. 5.5. Table 5.4: Mean shear bond strength (in MPa) for Set-C triplets Mortar Ratio CB FAB-I FAB-II CM1 0.118 0.129 0.133 CM2 0.162 0.168 0.182 CM3 0.204 0.232 0.249 There is increase in bond strength of triplets with grade of mortar as observed from the figure. The bond strength values of CB used triplets vary from 0.118 MPa to 0.204 MPa. The same for FAB-I range from 0.129 MPa to 0.232 MPa and for FAB-II it varies from 0.133 MPa to 0.249 MPa. As compared with Set-A and Set-B, the shear bond strength of the triplets of this set (Set-C) increases 109 Chapter 5 Shear Bond Strength of Brick Masonry Figure 5.5: Shear bond strength for Set-C triplets significantly with increase in moisture content of bricks. The bond strength exhibited by fly ash bricks is more than clay bricks for same mortar grade and soaking time. Results for Set-D The triplets of Set-D are constructed with bricks that are soaked in water for 24 hours to achieve 100% moisture content. The result obtained signifies the shear bond strength of masonry in which the bricks are completely saturated when laid with mortar. The mean shear bond strength values for Set-D are presented in Table 5.5 and shown graphically in Fig. 5.6 Table 5.5: Mean shear bond strength (in MPa) for Set-D triplets Mortar Ratio CB FAB-I FAB-II CM1 0.065 0.068 0.070 CM2 0.078 0.082 0.085 CM3 0.085 0.092 0.097 The shear bond strength for CB used triplets varies from 0.065 MPa to 0.085 MPa and for FAB-I it range from 0.068 MPa to 0.092 MPa. The same for FAB-II vary from 0.07 MPa to 0.097 MPa. The similar trend of fly ash bricks achieving 110 Chapter 5 Shear Bond Strength of Brick Masonry Figure 5.6: Shear bond strength for Set-D triplets higher bond strength than clay bricks is observed in this set too. There is a reduction in the strength values for this set as compared with Set A, B and C. This is because the pores in bricks are filled with water as bricks are completely saturated that means the tendency to absorb water from mortar is blocked. This forms a situation where brick floats on mortar. This results in complete lapse of mechanical bonding between the brick surface and mortar causing great reduction of bond strength. 5.6 Optimum Brick Moisture Content The optimum moisture content of bricks for which higher shear bond strength is achieved based on the experimental results is discussed in this section. The variation of shear bond strength with increase in moisture content of CB triplets is shown in Fig. 5.7 for various mortar grades. The shear bond strength is found to be more for triplets made with mortar having higher amount of cement. The bond strength plot follows a rising trend up to third point after which it starts decreasing. There are four points in the plot signifying each of four sets of triplet specimens A, B, C and D. The strength is 0.082 MPa for CM1, 0.097 MPa for CM2 and 0.127 MPa for CM3 grade mortar, when the moisture content of brick is 4.16% or 25% of its saturated moisture content (Set-A). The strength 111 Chapter 5 Shear Bond Strength of Brick Masonry Figure 5.7: Variation in shear bond strength with moisture content of CB at the time of construction (Saturation moisture content of CB = 16.69%) increases by 30% to 35% with the increase in moisture content of brick by 25% of saturation moisture content making the overall moisture content equal to 8.34% (Set-B). This is true for all three mortar grades considered. When the moisture content of brick is further increased by 25% which is now 75% of the saturation moisture content, the value of shear bond strength reaches up to 0.118 MPa for CM1, 0.162 MPa for CM2 and 0.204 MPa for CM3 grade mortar (Set-C). From this point the reduction in strength starts with increase in moisture content and becomes lowest when moisture content is 16.69% which is 100% of saturation level (Set-D). This implies that there loss in bond strength when the bricks used are completely saturated for the reason as explained in previous section. From the Fig. 5.7 it could be understood that highest shear bond strength is achieved by CB triplets when the moisture content is 12.52% or 75% of the saturation moisture content. So it is concluded that at 75% of saturation moisture content is the optimum moisture content value for CB masonry at which shear bond strength will be maximum. Completely dry bricks or fully saturated bricks do not provide good bond strength to the masonry. So bricks with higher IRA must be pre-wetted up to 75% of their saturation moisture content limit prior to construction. The variation in shear bond strength with increase in moisture content of FAB-I 112 Chapter 5 Shear Bond Strength of Brick Masonry brick follows a similar trend as observed for CB brick and is shown in Fig. 5.8. The escalating pattern of shear bond strength with increase in moisture content of FAB-I is followed up to the point where the moisture content is 12.58% or around 75% of the saturation moisture content. After this point the strength decreases with rise in moisture content. Figure 5.8: Variation in shear bond strength with moisture content of FAB-I brick at the time of construction (Saturation moisture content of FAB-I = 16.80%) The relationship between the shear bond strength and moisture content of the brick during construction of triplet for FAB-II is found to be similar to that that CB and FAB-I as shown in Fig. 5.9. The optimum moisture content of FAB-II at which highest shear bond strength is obtained for all mortar grades is found to be 12.67% which is 75% of the saturation moisture content. Following are the important observations drawn based on the experimental results obtained for CB, FAB-I and FAB-II triplets with different mortar grades (CM1, CM2 and CM3): (a) Completely dry brick does not yield good bond strength in brick masonry. Dry bricks having high IRA tend to absorb most of the water from mortar hampering its hydration process causing loss in mortar strength which reduces the bond strength. 113 Chapter 5 Shear Bond Strength of Brick Masonry Figure 5.9: Variation in shear bond strength with moisture content of FAB-II brick at the time of construction (Saturation moisture content of FAB-II = 16.84%) (b) Similarly saturated bricks abstain from absorbing any water from mortar which is crucial because through absorption cement enters the pores of brick and forms a mechanical key which helps in achieving higher bond strength. Saturated bricks are likely to float on mortar without any bonding with it. This situation leads to a bond strength lesser than that with complete dry bricks. (c) The optimum moisture content for all the three brick variants and mortar grades is found to be around 75% of the saturation moisture content. That means the bricks should be soaked until they gain weight equivalent to optimum moisture content prior to be used for construction of masonry. By this, bricks can absorb optimum amount of water from mortar to form the mechanical key and mortar can develop good strength through adequate hydration which finally results in good bond between the two. 114 Chapter 5 5.7 Shear Bond Strength of Brick Masonry Bond Strength and Compressive Strength of Brick Masonry The mean values of shear bond strength obtained at optimum moisture content is correlated with the corresponding mean compressive strength of masonry prism constructed using the three brick variants and three mortar grades as shown in Fig. 5.10. Details of the prism compressive strength results are discussed in Chapter 4 of this thesis. It is observed from Fig. 5.10 that shear bond strength has a direct influence on the compressive strength of masonry as proved in earlier studies ( [23] [24] etc.). It could be seen that with the increase in brick-mortar shear bond strength, the compressive strength of masonry increases proportionally. Steep increase in strength is observed in masonry with FAB-II bricks which have higher compressive strength than CB and FAB-I. Hence shear bond strength is an important parameter deciding the compressive strength of masonry. Figure 5.10: Relation between shear bond strength and compressive strength of masonry 115 Chapter 5 5.8 Shear Bond Strength of Brick Masonry Failure Patterns in Triplets The failure patterns of triplets tested for shear bond strength is classified into following types by past researchers ( [23] [27] [28] [26]). • Type A: When failure occurs at brick-mortar interface • Type B: Failure within the mortar joint • Type C: Failure within brick unit • Type D: A combination of failure within the brick unit and mortar joint The type of failure depends upon the relative strength of brick, mortar and the bond between them which together resist the shear force. All the above four types of failure modes are observed in the present study. This section discusses failure modes observed and investigates the reason of such failures. (a) Failure at brick-mortar interface (Type A) This is the predominant type of failure observed among many triplet specimens of all sets, brick variants and mortar grades. The failure at brick mortar interface is shown in Fig. 5.11. This type of failure occurs because of weak bonding between the brick and mortar joint. Most of the triplet specimens constructed with CM1 and CM2 mortars show such type of failure pattern as less amount of cement in such mortar affect the bond strength. (b) Failure within the mortar joint (Type B) This type of failure is observed in some of the specimens of Set-A triplets constructed using CB and FAB-I with CM1 mortar. CB and FAB-I have comparatively higher IRA and when used without pre-wetting they absorb water from mortar affecting the hydration process of cement and thus reducing its strength. This makes the mortar in contact with brick to develop good bond but central part of mortar is weak. Thus failure originates from weak central region and affects the interface bond. The failure pattern is shown in Fig. 5.12. 116 Chapter 5 Shear Bond Strength of Brick Masonry Figure 5.11: Failure within the brick-mortar interface (Type A) Figure 5.12: Failure within the mortar joint (Type B) (c) Failure within the brick unit (Type C) Failure pattern of this type is found in triplets constructed with relatively weak brick and strong mortar. Most of the FAB-I (weak brick) constructed with CM3 (strong mortar) failed by this pattern. Strong mortar makes the interfacial bond strong with brick and if the brick strength is less than the combined bond and mortar strength then failure occurs within the brick. Fig. 5.13 shows Type C failure pattern. 117 Chapter 5 Shear Bond Strength of Brick Masonry (d) Combination of failure within the brick unit and mortar joint (Type D) This type of failure is observed in triplets of Set-C where good bond strength is obtained. In this failure type, a portion of brick surface sticks to the mortar joint or vice-versa. When brick unit, mortar and their interfacial bond are strong, a failure occurs combining all the three. Fig. 5.14 depicts the failure where a portion of brick sticks to mortar. Figure 5.13: Fig. 5.13: Failure within the brick unit (Type C) Figure 5.14: Combination of failure within the brick unit and mortar joint (Type D) 118 Chapter 5 5.9 Shear Bond Strength of Brick Masonry Summary The chapter deals with studying the influence of moisture content in bricks during construction of masonry triplet on the shear bond strength. The variation in moisture content in bricks is achieved by soaking them in water for required time. The test is performed on triplets constructed with different type of bricks (CB, FAB-I and FAB-II) and mortar grades (CM1, CM2 and CM3). The following concluding remarks are drawn from this chapter: (i) Shear bond strength of brick masonry is influenced by the IRA of bricks when they are not soaked prior to construction. Higher the IRA of brick lower will be the bond strength. (ii) The amount of cement in mortar impacts the bond strength of masonry. Strong mortar (CM3) is found to be performing better than weak mortar (CM1). (iii) The variation in the moisture content of bricks greatly alters the shear bond strength of masonry. (iv) It is found that highest shear bond strength is obtained when the moisture content in bricks is 75% of their saturation moisture content. This is observed for all the three brick variants and all grades of mortar. (v) Shear bond failure pattern depends on the strength of brick, mortar and their bond. IRA and moisture content of brick control the modes of failure indirectly through shear bond strength. 119 Chapter 6 Summary and Conclusions 6.1 Summary The primary objectives of this research were identified as follows: (i) To describe the variability in the mechanical properties of clay and fly ash brick masonry (ii) To model the compressive strength of brick unit and brick masonry (iii) To determine the optimum pre-wetting of bricks to have higher shear bond strength of brick masonry. The above mentioned objectives are fixed after conducting a detailed review of the literatures available on properties of clay and fly ash brick masonry is carried out. The review of literatures paved the path to identify the voids in past studies related to brick masonry. All the literatures which benefitted this research work are explained in Chapter 2 of this thesis under various sections. A number of experimental tests are conducted on specimens of brick masonry and its constituents to determine properties such as initial rate of absorption (IRA), water absorption (WA), dry density, compressive strength and shear bond strength. Higher order analyses such as XRD and field emission scanning electron microscope (FESEM) are also conducted to understand the morphology 120 Chapter 6 Summary and Conclusions and microstructure of brick specimens. Three brick variants (CB, FAB-I and FAB-II) and three mortar grades (CM1, CM2 and CM3) are used in the present study for preparation of test specimens. The experimental plan, details of raw materials used, preparation of test specimens, equipment used and procedures of experimental work carried out are explained in Chapter 3. Chapter 4 of this thesis describes the variability in the properties of brick masonry using various probability distribution functions. Four different two-parameter probability distribution functions are used. The validity of the probability distributions is evaluated from three goodness-of-fit tests namely Kolmogorov-Sminrov, Chi-square and Log-likelihood Test. Certain criteria are followed based on which the best fit probability distribution is selected. This chapter also identifies the influence of morphology and microstructure on properties of bricks. A relation between the mechanical properties is established and equations are proposed to predict the compressive strength of brick and brick masonry. The failure patterns of masonry prism under axial compression observed in the study are discussed. The influence of moisture content in brick at the time of construction and IRA on shear bond strength determined experimentally is presented in Chapter 5. The variation in moisture content in bricks is achieved by soaking them in water for required time. The test is performed on triplets constructed with different type of bricks (CB, FAB-I and FAB-II) and mortar grades (CM1, CM2 and CM3). 6.2 Conclusions The variability in the properties of brick masonry has not received the attention of researchers as observed from the literature review. Similarly the influence of the moisture content in bricks on shear bond strength of clay and fly ash brick masonry is not adequately studied. Hence a detailed study is carried out as part of this research work to overcome the shortcomings. The following conclusions are drawn from the present research: 121 Chapter 6 Summary and Conclusions (i) Lognormal is found to be common distribution function to describe the variability of different mechanical properties of masonry materials. Weibull and gamma distributions are found to be most appropriate for some of the properties. However, in general, gamma distribution is found to be either the best or the next best distribution function to describe most of the mechanical properties studied. Therefore, lognormal or gamma distribution is recommended as the distribution function that best describe the variability of properties of brick masonry and its constituents. (ii) The presence of compounds of aluminium and magnesium along with silica and iron oxide is observed to be helpful for clay bricks in attaining higher compressive strength. Similarly, the absence of berlinite, an aluminium based compound is found to be the reason for low strength of fly ash bricks (FAB-I and FAB-II) as evident from the XRD analysis. (iii) The FESEM images on microstructure of clay brick samples of low and high strength CB specimen revealed glassy or vitreous type of texture resulting from melting of quartz at high temperature is found in high strength CB whereas the texture of low strength CB specimen is rough, porous and less vitreous because of lack of burning at suitable high temperature. This proves that suitable high temperature and uniform burning is needed for clay brick to achieve higher strength. (iv) The microstructural study of high and low strength samples of fly ash brick (FAB-I and FAB-II) specimens revealed the presence of fibre or needle like structure (calcium compounds) embedded on a gel like surface (silica compound) for high strength bricks. While the low strength FAB-I possess unreacted calcium compounds on its surface without any fibres and low strength FAB-II depicted small fibres. This gives an insight that fibres or needle shaped structures impart good strength to fly ash bricks signifying the full formation of calcium based compound. (v) A relation between IRA, WA, dry density and compressive strength of 122 Chapter 6 Summary and Conclusions brick units is established. On the basis of which empirical equations for determining the compressive strength of brick is proposed. This equation will allow a quick calculation of brick compressive strength at construction site without the necessity of any sophisticated instruments. The validation of the proposed equations is done by comparing the predicted value of the compressive strength with experimental value obtained from different literatures. (vi) The estimation of masonry compressive strength based on brick unit and mortar compressive strength is proposed in form of equation. This equations can be used for clay brick and fly ash brick masonry with bricks having lower strength than mortar. The validation of the proposed equations is done by comparing the predicted value of the compressive strength with experimental value obtained from different literatures. (vii) The influence of IRA on shear bond strength is determined experimentally. It proves the fact, that higher the IRA lower will be the brick mortar bond strength. Hence, bricks having higher IRA must be soaked for more time prior to construction of masonry. (viii) The effect of moisture content in brick at the time of construction on shear bond strength is confirmed through experimental tests. Masonry triplets having 75% of the saturation moisture content of bricks performed better. This implies that an optimum moisture content of 75% of the saturation moisture content in bricks result in higher shear bond strength of masonry. (ix) The shear bond strength of masonry is observed to increase with increase in grade of mortar irrespective of the brick variants. (x) It is observed from the failure pattern of triplets that shear bond failure depends on the strength of brick, mortar and their bond. IRA and moisture content of brick, control the modes of failure indirectly through shear bond strength. 123 Chapter 6 6.3 Summary and Conclusions Main Contribution of the Research The following enlisted are the main contributions of this thesis: (i) A statistical approach to the description of the variation in the mechanical properties of clay and fly ash brick masonry and its constituents is established for the first time. This could be used in probability based analysis of structures involving brick masonry. (ii) Simple mathematical equation is proposed for estimation of the compressive strength of brick from corresponding IRA, WA and dry density properties. This approach is implemented for the first time to predict the brick compressive strength. The equation eliminates the use of heavy testing equipment and could be best used at construction sites to quickly predict the quality and compressive strength of brick units. (iii) In past studies different equations are proposed to predict the compressive strength of the brick masonry prism for stronger brick and weaker mortar combination. This study proposes an alternative equation based on weaker brick and stronger mortar combination. (iv) The effect of moisture content on the tensile bond strength of brick masonry is studied in previous literature. The same for shear bond strength is studied by none. The optimum moisture content needed in clay and fly ash bricks at the time construction to achieve higher shear bond strength is suggested. 6.4 Scope for Future Work The present study can be extended to include the variability on the deformation and ductility properties of brick units and brick masonry. This study will help to establish a statistically significant model for nonlinear stress-strain behaviour of fly ash brick. 124 Chapter 6 Summary and Conclusions There are many different varieties of masonry units such as concrete hollow blocks, aerated autoclaved block, etc. used in recent constructions. A proper description of variability of their mechanical properties will be necessary for the probability based analysis of such structures. The present study can be extended to include these masonry units. Equations to estimate the shear bond strength of masonry can be developed by conducting large scale laboratory tests on masonry triplets. Further, the effect of pre-wetting time on the compressive strength of masonry prism can be studied. 125 Appendix A Introduction to Fly Ash Bricks A.1 Introduction India is one of the most rapidly developing countries in the world. To match the pace of the development, the country must meet its infrastructural needs. This has led the booming of the construction sector which in turn increased the demand for electricity and put pressure on the utilisation of natural resources. Nearly 63% of the power requirements are met from coal-based thermal power plants. Around 143 thermal power stations consume nearly 500 million tons of coal and produce as much as 173 million tons of fly ash every year (CEA, 2014 report) [1]. The storage of fly ash is in itself a herculean task as it needs to be transported away from populated areas and stored in specially assigned places. The storage of fly ash consumes vast acres of land and it needs lot of water to be spayed to keep it wet as in dry state it gets mixed with air and could pollute air causing severe breathing problems. So, the safe disposal of fly ash is a big problem for the management. Traditionally used fired clay bricks are one of the most important building materials acting as a backbone for the construction industry. Fired clay bricks have been used since Indus valley civilization. The clay bricks are fired in kilns at high temperatures with coal and other biomass as fuel. Nearly 24 million tons of coal is used for burning at kilns and 42 million tons of carbon dioxide is emitted through this process. The smoke from brick kilns is also the main reason 126 Appendix A for increase in air pollution. This trend of creating pollution only increases with increase in demand for bricks from construction industry. Apart from this, the clay bricks require good clayey soil as its main ingredient, in this process the top fertile soil is consumed which could otherwise be used for agricultural purposes. Every year, around 350 million tons of top soil is consumed solely for making clay bricks (PSCST report, 2010) [73]. The ever increasing deposits of fly ash from coal based plants, consumption of natural resources such as top soil for making bricks and the traditional process of making bricks only escalate the carbon foot print in atmosphere causing health hazards and finally global warming. These problems paved way for creation of a green building material. It is called as fly ash brick or green brick as it is made up of waste materials such as fly ash and requires no burning, which is the solution for all the above mentioned problems. A.2 Fly Ash Fly ash is a fine powder residue produced by the burning of coal which is used as pulverised fuel for generation of electricity in thermal power plants. Solidified fly ash is collected from electro static precipitator (ESP) or filter bags and is separated from flue gases. The ash that falls at the bottom of boiler is called bottom ash. The collected fly ash is then transported either in dry or wet state and stored in specially constructed ash ponds or dykes. The fly ash is waste material from the thermal power plants and its storage is very problematic as discussed in previous section. The property of fly ash varies considerably depending upon the type and quality of coal from which it is produced, burning process of coal etc. The fly ash mostly consist substantial amount of silicon dioxide, aluminium oxide and calcium oxide apart from several heavy metals. On the basis of chemical compounds present in the fly ash, it is classified broadly into two types: Class F and Class C as per ASTM C-618. The physical and chemical requirements of fly ash are prescribed in Indian Standard IS: 3812-1981. 127 Appendix A (a) Class F: The burning of bituminous and anthracite coal produces Class F fly ash. This fly ash contains less than 20% of calcium oxide (CaO), so it requires a cement agent such as lime, Gypsum or Portland cement to react with glassy silica and alumina to produce cementing compounds. In India, most of the coal deposits are of anthracite or bituminous type. So, the fly ash produced from these coal sources are of Class F type. (b) Class C: It is produced by the burning of lignite or sub-bituminous coal. Class C contains more than 20% of calcium oxide (CaO), so it has self-cementing property and gets harder and stronger in presence of water. The chemical and physical requirements of Class F and Class C fly ash as per ASTM C-618 and IS: 3812-1981 are reported in TableA.1 and A.2. Table A.1: Chemical requirements of fly ash Sl. No. 1 Chemical Characteristics Requirements (in percent by mass) Class F Class C Silicon dioxide, Aluminium oxide and Iron oxide 70 50 SiO2 + Al2 O3 + Fe2 O3 , min 2 Silicon dioxide SiO2 , min 35 20 3 Reactive silica, min 20 20 4 Magnesium oxide MgO, max 5.0 5.0 5 Total sulphur as sulphur trioxide SO3 , max 3.0 3.0 6 Available alkalis as sodium oxide Na2 O, max 1.5 1.5 7 Total chlorides, max 0.05 0.05 8 Loss on ignition, max 5.0 5.0 The cause of concern is the storage of fly ash as it consumes land as well as pollutes the environment. The awareness about its uses is created, thus promoting 128 Appendix A Table A.2: Physical requirements of fly ash Sl. No. Physical Characteristics 1 Fineness- Specific surface in m2 /kg by Blaine’s permeability method, min 2 34 Lime reactivity- Average compressive strength in N/mm2 , min 4 320 Particles retained on 45 micron IS sieve (wet sieving) in percent, max 3 Requirements (Class C & F) 20 Compressive strength at 28 days in N/mm2 , min Not less than 80 percent of the stength of plain cement mortar cubes 5 Soundness by autoclave testExpansion of specimen in percent, max 0.8 the utilization of fly ash as raw material in various sectors. The present utilization of fly ash must be increased to meet its output; the utilization of fly ash during year 2013-14 is shown in Fig. A.1. From the figure it is evident that major portion of the fly ash is used by the cement manufacturing industries, while minimum is utilized in concrete. The overall production of fly ash stands at 173 million tons out of this only 99.30 million tons is utilized. That means only 57.63% of fly ash generated is used for various purposes. This is proves that still nearly 33% is left unused every year. Realising this, the government has passed resolution to make the use of fly ash compulsory for all construction purposes in around 100km radius of coal based plants. Fly ash in majority can be utilized in making bricks, as bricks are the integral part of every type of construction. The use of fly ash in bricks has gained momentum after its properties being proven superior to fired clay bricks. The succeeding section discusses about the bricks made up of fly ash and its manufacturing process in detail. 129 Appendix A Figure A.1: Various modes of utilization of fly ash [1] A.3 Fly Ash Bricks Fly ash brick is a recent entrant to the class of bricks that is primarily made of fly ash which is abundantly produced from different coal based plants, lime or cement and sand. These bricks can be used in all construction fields where fired clay bricks are used. It has numerous advantages over clay bricks including its superior quality to clay bricks, eco-friendly nature and most importantly helps in good utilization of large quantities of fly ash, reducing the consumption of top layer of soil. The advantages of fly ash bricks are listed in the following section. A.3.1 Advantages and disadvantages of Fly Ash Brick On comparison to fired clay bricks, fly ash bricks hold superiority because of the following advantages it possesses. (i) Fly ash bricks have high compressive strength as compared to certain clay bricks. (ii) As main raw material, fly ash is freely available, only the transportation and production cost decide the price of fly ash bricks. So they are available at low cost than clay bricks. 130 Appendix A (iii) For large constructions, the bricks can be made at the site itself with the help of portable hydraulic-pressing machine. This helps in the breakage of bricks during transportation. (iv) Mostly fly ash bricks are machine made so they maintain high dimensional accuracy. Uniform bricks reduce the consumption of mortar, which is used for covering joints and plaster, by 50%. (v) They have high strength to weight ratio and efflorescence is nearly absent. (vi) Fly ash bricks are hydraulic-pressed and air cured, eliminating the use of burning by fossil fuels. This reduces the consumption of coal and helps in lessening air pollution. (vii) Fly ash bricks absorb mercury and carbon dioxide from air reducing global warming [39]. Fly ash bricks have a few disadvantages which could be overlooked taking into consideration its tremendous environment friendly properties. The disadvantages are listed below as following. (a) Its mechanical strength is low if correct amount of lime, gypsum, marble waste or cement is not added, especially for bricks made using class F fly ash. (b) Improper curing may lead to less strength and also affect the durability of the bricks. A.3.2 Types of Fly Ash Brick On basis of raw materials used for manufacture of bricks, fly ash bricks are of following types: (a) Fly ash cement bricks or fly ash cement-gypsum bricks (b) Fly ash lime-gypsum bricks (c) High fly ash content bricks by mineral polymerisation 131 Appendix A (d) Burnt clay fly ash bricks (e) High ash content burnt clay fly ash bricks (f) Flux bonded burnt clay fly ash bricks Of the above mentioned type of bricks, first two types are most widely used for making bricks. In this thesis fly ash cement bricks is taken into consideration. A.3.3 Raw materials and their composition In the present study fly ash cement bricks are considered because they are widely used in construction purposes. The raw materials and their proportion are very essential for making good quality bricks and must be controlled at site. The raw material used for making fly ash bricks are: (a) Fly ash: Fly ash conforming to the physical and chemical requirements as specified in Indian Standard IS: 3812 (Part 1)-2003 is required for good quality bricks. The fly ash must be stored properly at site to avoid excess ingress of moisture and is usually covered. The fly ash is transported to mixer by closed tankers, trolleys or barrows. (b) Cement: Ordinary Portland Cement (OPC) of 43 or 53 grade is generally used for manufacturing of fly ash cement bricks and gypsum-lime is used for bricks made without cement. (c) Sand: The locally available sand preferably river sand is used and it must confirm to the requirements specified in Indian Standard IS: 383:1970. Very fine or coarse quality of sand is usually avoided in the process. The sand at site is usually covered during rainy season to protect from ingress of moisture. The following composition is usually followed by fly ash cement brick manufacturers all over the country (NTPC, Report). [74] • Fly ash: 50-60% 132 Appendix A • Sand: 30-40% • Cement: 8-10% The composition is carefully observed as slight variations may cause large deviations in the strength values of produced bricks. A.3.4 Manufacturing Process The fly ash bricks are manufactured using a semi-automatic hydraulic press machine, which is portable and can easily set up near the construction site. The entire manufacturing process is very simple as compared to clay bricks and takes less time. The process is divided into following steps. A.3.4.1 Batching The raw materials such as fly ash, sand and cement are brought to the mixer using wheel barrows or pull carts or by any other means. The batching is done either by weight or by volume whichever is suited. Due care is to be taken while batching to follow the prescribed composition. The batching at site is shown in Fig.A.2 Figure A.2: Batching of raw materials using wheel barrow 133 Appendix A A.3.4.2 Mixing All the raw materials are put in the pan mixer and are thoroughly mixed so as to obtain a uniform mix. The mixer capacity is usually 300kg which can produce 90-120 bricks. Fly ash is added first to the mixer followed by sand and cement. The ingredients are first dry mixed properly and then required quantity of water is added and wet mixed for assigned time. Care is taken while mixing to prevent the formation of lumps. After proper mixing of materials is done, the mix is transported to hydraulic-press using a conveyer belt. The typical arrangement of pan mixer and conveyer belt is shown in Fig. A.3 Figure A.3: Mixing of raw materials in a mixer A.3.4.3 Moulding of Bricks The semi-dry homogenous mix is fed to hydraulic press through conveyor belt or manually. The mix is filled in moulds which are pressed at a load of 1000 kg/cm2 . The moulded bricks are placed on wooden pallets in four to five layers. These bricks are then transferred to separate place for curing. The hydraulic press machine is shown in Fig.A.4 A.3.4.4 Curing The moulded bricks are placed on wooden pallets and are moved to separate place for curing. The bricks are first air dried for 1-2 days then they are placed in stacks 134 Appendix A Figure A.4: Moulding of bricks in a hydraulic press and are water cured for 15-20 days by sprinkling or spraying of water. After the curing process is over the bricks are transported to building site for use. The curing of bricks in stacks is shown in Fig. A.5 Figure A.5: Air curing of fly ash bricks 135 Appendix B Probability Distributions and Goodness-of-Fit Tests B.1 Introduction Different two parameter probability functions are adopted in Chapter 4 of this thesis for description of the variation in different mechanical properties of brick, mortar and brick masonry. Best fitted probability distribution function is arrived through different goodness-of-fit tests. The probability distribution functions considered are normal, lognormal, gamma and Weibull. The goodness-of-fit test includes Kolmogorov-Smirnov (KS), Log-likelihood (LK) and minimum Chi-square criterion (CS). This section describes selected probability distribution functions and the goodness-of-fit tests briefly. B.2 B.2.1 Probability Distributions Normal Distribution Normal distribution (also known as Gaussian distribution) is one of the most commonly used continuous type of distribution. It is a special case of binomial distribution and is suitably applicable for large data. Normal distribution is a 136 Appendix B two-parameter probability distribution function that consists of mean (µ) and standard deviation (σ) as its parameters. This distribution is applicable in situations where the random variable is dependent on several other independent variables. The probability density function (PDF) of the normal distribution is given by Eq. B.1 1 −(x − µ)2 √ N (x; µ, σ) = exp σ2 σ 2π (B.1) The cumulative distribution function (CDF) of the normal distribution is given by Eq. B.2 1 N (x; µ, σ) = √ σ 2π Z x −∞ −(t − µ)2 dt 2σ 2 (B.2) Where x, µ and σ are random variable, mean and standard deviation respectively. The normal distribution is symmetric and unimodal about the mean. The curve has maximum value at x = µ and point of inflexion at x = µ ± σ. The PDF of normal distribution range from -∞ to +∞ while the CDF is from 0 to 1 which is used in goodness-of-fit tests. Because of simplicity, many researchers prefer considering normal distribution than other distributions. This distribution could be used for both positive and negative outcomes. However engineering properties such as compressive strength or weight is always positive in that case the range of normal distribution can be truncated to the requirement and called as truncated normal distribution. B.2.2 Lognormal Distribution Lognormal distribution is similar to normal distribution and both are interrelated to each other. This distribution can be appropriately used when the outcomes are non-negatives. In such cases the data is skewed and not symmetrical like normal 137 Appendix B distribution. It is a two-parameter distribution having mean (µ) and variance (σ) as its parameters. If a variate X is such that log(X) is normally distributed, then the distribution of X is said to be lognormal. The range of lognormal distribution is from 0 to +∞. Lognormal distribution finds its application in many engineering fields because it captures the non-negative values. The PDF of the lognormal distribution is given by Eq. B.3 L(x; µ, σ) = 1 −(log x − µ)2 √ exp 2σ 2 σx( 2π) (B.3) when x ≥ 0 otherwise 0 The CDF of the lognormal distribution is given by Eq. B.4 L(x; µ, σ) = B.2.3 1 √ σx( 2π) Z x exp 0 −(log x − µ)2 2σ 2 dt t (B.4) Gamma Distribution Gamma distribution (also known as Erlang distribution) is used to model data which is only positive and is derived from gamma function. It is a two-parameter distribution with positive parameters σ and λ. The mean (µ) and variance (σ 2 ) of gamma distribution are given in Eq. B.5 µ= α λ σ2 = α λ2 (B.5) where α and λ are called as shape and scale factors respectively The PDF of the gamma distribution is given by Eq. B.6 G(x; α, λ) = λα e−λx when x ≥ 0 otherwise 0 138 x(α−1) (α − 1)! (B.6) Appendix B The CDF of the gamma distribution is given by Eq. B.7 1 N (x; µ, σ) = α λ Γ(α) Z x α−1 t −t e λ dt (B.7) 0 By changing the shape and scale parameters of gamma distribution, curves with different shapes can be generated fitting to the outcome. This makes gamma distribution reliable and flexible. Many distributions such as normal, exponential and chi-square can be derived from shape and scale parameters of gamma distribution. B.2.4 Weibull Distribution Weibull distribution is one of the versatile and widely used distributions. The application of Weibull involves reliability and life testing such as to model the time of failure or life of a component. This distribution has two parameters α and β which are its shape and scale parameter respectively. The distribution can also have another parameter depending on its location called as location parameter (γ). The PDF of the Weibull distribution is given by Eq. B.8 −x α α α−1 ( β ) W (x; α, β) = α x e β (B.8) when x ≥ 0 otherwise 0 The CDF of the Weibull distribution is given by Eq. B.9 Z W (x; α, β) = x −t β ) βα−β tβ−1 e α dt 0 139 ( (B.9) Appendix B B.3 B.3.1 Goodness-of-Fit Tests Kolmogorov-Sminrov Test Kolmogorov-Sminrov (KS) test is based on the statistic that measures the deviation of the observed cumulative distribution from the hypothesized cumulative distribution function as shown in Fig. B.1. The main advantage of KS test is that it can be performed on less number of samples. It utilizes the unaltered and unaggregated form of data, as binning or lumping of data is not necessary. The only disadvantage of KS test is that it is valid only for continuous distributions. Figure B.1: KS test plot showing deviation between observed and hypothesizes CDF B.3.2 Chi-square Test Chi-square (CS) test measures the difference between the frequencies of observed samples and hypothesized samples. CS test is essentially a large sample test and yields better results if sample size is more than 50. In this test the data is divided in to a number of bins and the frequencies are derived. These frequencies are compared with the frequencies from the hypothesized distribution. Then the chi-square value is calculated from the sum of deviations between the frequencies. A significance level is assumed and the critical chi-square value is obtained from 140 Appendix B the chi-square distribution table. If the observed chi-square value is less than critical chi-square at assumed significance level then the hypothesis is accepted else it is rejected. The main disadvantage of CS test is that it involves dumping of data into bins for calculating the frequency which is influenced by the change in bins. B.3.3 Log-likelihood Test Log-likelihood (LK) test is used to measure the goodness-of-fit of two models. The test is based on log-likelihood ratio that expresses the number of times the data of one model is more likely than other. In this study the log-likelihood values are determined from MATLAB which returns negative log-likelihood values. 141 Appendix C Correlation of Brick Properties Section 4.4.1 of Chapter 4 of this thesis derives mathematical models to predict compressive strength of brick units as a function of different mechanical properties such as IRA, WA and dry density of bricks. The results of all the three brick variants follow a similar trend and the results of one of them (FAB-I) are presented in Chapter 4. The results for remaining two brick variants (CB and FAB-II) are presented in this section. 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