STUDIES ON MECHANICAL PROPERTIES OF BRICK MASONRY Peri Raghava Ravi Teja

STUDIES ON MECHANICAL PROPERTIES OF BRICK MASONRY Peri Raghava Ravi Teja
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
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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
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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.
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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.
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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
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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
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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.
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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.
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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.
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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
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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.
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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.
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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.
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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. The discussions presented in Chapter 4 for FAB-I are
valid for the results presented here.
142
Appendix C
(a)
(b)
(c)
Figure C.1: Variation of (a) IRA (b) WA (c) dry density with compressive
strength for CB
143
Appendix C
(a)
(b)
(c)
Figure C.2: Variation of (a) IRA (b) WA (c) dry density with compressive
strength for FAB-II
144
Appendix C
(a)
(b)
(c)
Figure C.3: Correlation of (a) IRA (b) WA (c) dry density with compressive
strength for CB
145
Appendix C
(a)
(b)
(c)
Figure C.4: Correlation of (a) IRA (b) WA (c) dry density with compressive
strength for FAB-II
146
Appendix C
Figure C.5: Variation plot between actual and predicted compressive strength
for CB
Figure C.6: Variation plot between actual and predicted compressive strength
for FAB-II
147
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