Experimental Investigation on The Characterization of Solid Clay
Brick Masonry for Lateral Shear Strength Evaluation
Qaisar Ali1, Yasir Irfan Badrashi1, Naveed Ahmad1,2,*, Bashir Alam3, Shahzad Rehman3,
Farhat Ali Shah Banori3
1
Earthquake Engineering Center, UET, Peshawar, Pakistan.
ROSE School−IUSS Pavia, Pavia, Italy.
3
Department of Civil Engineering, UET, Peshawar, Pakistan.
Corresponding Author: anaveed@roseschool.it, +393463029255
2
Abstract
The aim of the paper was to carry out the mechanical characterization of solid fired clay brick masonry through
experimental investigation, essential for structural evaluation under lateral loads due to winds and earthquakes
within the context of design and assessment studies. The basic material properties of masonry including
compressive strength, diagonal tensile strength, shear strength, masonry bond strength, Young’s and shear
moduli are obtained through laboratory testing on masonry prisms (48 samples), triplets (96 samples) and
wallets (48 samples). Standard brick unit prevalent in Pakistan is considered, similar to units that can be found
also in neighboring countries like India, Iran and Bangladesh amongst others. Three types of mortar ─ cementsand, cement-sand-khaka and cement-khaka are used as bonding material for masonry assemblages. Khaka is
obtained as a byproduct of stone crushing process, employed in mortar preparation to produce relatively
workable and economical mortar. The effect of mix proportions of mortar is also investigated. Empirical
relationships are developed herein whereby basic mechanical properties of masonry are correlated with the
mortar strength, mortar type and mix proportions. An attempt is made to correlate mechanical properties
between each other and establish simplified relationships to help facilitate their use in future applications for
design and assessment of unreinforced masonry wall structures under wind and earthquake induced lateral
loading.
Keywords: shear, diagonal tensile strength, compression, elastic moduli, mortar, khaka, unreinforced brick
masonry.
1 Introduction
Masonry material is largely practiced for
construction of structures and infrastructures e.g.
buildings, bridges, retaining structures, etc., in most
of the underdeveloped and developing parts of the
world. It is due to the traditional construction
practices employed in these countries, motivated
also by the regional climatic conditions . Brick
masonry construction employing solid clay units
and cement-mortar can be found in many urban
exposure of Pakistan and so also in neighbouring
countries like India, Iran, Bangladesh among
others. Most of the structures in these urban
exposures are subjected to frequent lateral loads
due to heavy winds and earthquakes that
consequently induce shear stresses in the structural
walls. The behavior of masonry material under
lateral loading is dramatically different than its
counterpart materials - concrete and steel, due to
high non-homogeneity and composite nature of
masonry components. The different mechanical
properties of masonry units and mortar and their
interface makes the masonry system behavior
difficult to predict using simple hypotheses as
adopted for concrete and steel. The masonry
mechanical characterization can be best performed
through experimental investigations, which can
help facilitate development of analytical tools for
future applications.
Masonry structures are often composed of several
load bearing walls for carrying both gravity and
lateral loads. In building construction, when the
connection at wall intersections and at floor-to-wall
is achieved through proper means, with controlled
out-of-plane deflection of the floors, the building
primarily resist lateral loads by in-plane response
of walls (Magenes, 2006; Tomazevic, 1999). The
provision of reinforced concrete slab with deep
spandrels, presence of tie rods, ring beams at floor
levels and efficient floor-to-wall connections
favours the integrity of masonry walls. It enables
the structure respond in a box like action to lateral
loading with shear dominated damage in masonry
walls. Flexure rocking, that may result in toe
crushing of walls, is also a possible mechanism to
resist lateral loads (Magenes and Calvi, 1997;
Abrams, 2001, among others). Figure 1 shows
typical damages observed in masonry wall
buildings of the above characteristics during the
2005 Kashmir earthquake. Typical damages that
(A)
(C)
may occur in masonry infill of concrete structures
due to lateral in-plane forces observed during
earthquake are also shown. Local out-of-plane
collapse of wall is also evidenced in earthquakes
for deficient structures (D’Ayala and Paganini,
2011; Javed et al., 2008).
(B)
(A): Diagonal shear cracks in masonry building walls
observed during 2005 Kashmir earthquake. A building
with concrete floor slab, deep spandrels and walls with
lower vertical aspect ratio (height to thickness). Adopted
from Naseer et al. (2010).
(B): Toe crushing in masonry building walls observed
during 2005 Kashmir earthquake. A building with
concrete floor slab, deep spandrels and walls with high
vertical aspect ratio. Adopted from Javed et al. (2008).
(C): In-Plane shear cracks observed in masonry infill of
concrete structure damaged in 2005 Kashmir
earthquake. A building with reinforced concrete beams
and columns provided with concrete floor slab and
rigidly connected masonry infill. Adopted from Javed et
al. (2008).
Figure 1 Shear damages observed in load bearing walls of unreinforced masonry buildings and masonry infill of concrete buildings due to
earthquake induced lateral loads.
Many available analytical models can be used to
estimate the in-plane strength of masonry walls
(Abrams, 2001; CEN, 1994; FEMA, 2000;
Magenes and Calvi, 1997; Mann and Muller, 1982;
Tomazevic, 1999; Turnsek and Sheppard, 1980,
among others). Analytical models are also available
to estimate the strength of masonry infill panel
under lateral loads in concrete structures (Fardis
and Calvi, 1994; Kappos et al., 1998; Smyrou et
al., 2011, among others). All these models require
basic mechanical properties of masonry material to
obtain lateral in-plane strength. This fact makes the
experimental investigation on masonry materials
essential before the assessment of structures can be
performed within the context of existing stock
evaluation and design verification of new
construction schemes (Ahmad et al., 2010, 2011,
2012 among others).
This paper hence presents an experimental
investigation on solid clay fired-brick masonry
material for mechanical characterization. The
experimental work included laboratory tests under
monotonic loading on masonry prisms: for the
estimation of masonry compressive strength (fmc)
and elastic Young modulus (E), on triplets: for the
estimation of bond strength in shear: cohesion
parameter (c) and friction coefficient (µ) of MohrCoulomb model, and on wallets: for the estimation
of diagonal tension strength (ft) and shear modulus
(G), besides tests on constituent materials i.e. brick
units: for unit compression strength, water
absorption and initial rate of absorption and mortar:
for compression strength (fm).
The testing is performed using the standard testing
procedures: ASTM E-519-02 (2002) for wallet
tests, EN 1052-3 (2002) for triplet tests, ASTM C67-06 (2006) for masonry unit tests, ASTM
C109/C109M-08 (2008) for mortar compression
tests and ASTM C-1314-07 (2007) for masonry
compression tests. Three types of mortar are
considered; cement-sand mortar (CS), cementsand-khaka mortar (CSK), cement-khaka mortar
(CK). The mortars are considered with 12 various
mix proportions (four cases for each mortar type).
The motivation towards investigating masonry in
CSK and CK mortar is that they produce relatively
2 Experimental Investigation of Clay Fired
Brick Masonry
in most of the construction works are investigated.
Four cases for each mortar type are considered with
mix proportions of 1:4, 1:6, 1:8 and 1:10 for CS
and CK mortars; and 1:2:2, 1:3:3, 1:4:4 and 1:5:5
for CSK mortar. Gradation tests are performed on
both sand and khaka constituents, see Figure 2
which revealed a relatively fine graded aggregate
contents of khaka.
Gradation Profile of Sand & Khaka
100
Percent Cummulative passing
more workable and economical mortars for
masonry construction (Naeem et al., 1996); It is
essential to understand their impact on the
mechanical properties of masonry. Empirical
relationships are developed to relate the basic
mechanical properties of masonry with mortar
strength, mortar constituents and mix ratio. Also,
an attempt is made to correlate the mechanical
parameters with each other. These relationships can
provide a useful means for future applications in
the design and verification studies of masonry
construction.
2.1 Experimental Tests Program
80
Sand
Khaka
60
40
20
0
2.2 Tests on Masonry Constituents Material
2.2.1 Masonry Unit Tests Per ASTM C-67-06
The present study has focused on investigating
masonry of solid clay fired brick masonry units,
common in various parts of Pakistan, which can
also be found in other South Asian countries like
India, Iran, Bangladesh, among others. The tests on
brick units included water absorption test (on nine
samples), initial rate of absorption (IRA) test (on
five samples), compressive strength test (on nine
samples). The results of the experiments showed
unit water absorption of 19.3% (COV 4.23%); IRA
of 82.20 gm/min/30inch2 (COV 18.21%);
compressive strength of 16.91 Mpa (COV 22.89%).
The water absorption capacity which is less than
20% indicates a good quality of the unit. The IRA
of unit which is greater than 30gm/min/30inch2
indicates that it must be wetted well before
employing in the construction of masonry works.
2.2.2 Mortar Tests Per ASTM C109/C109M-08
Various types of mortars investigated in the present
study included CS, CSK and CK mortars. The
addition of khaka to the ordinary CS mortar
produces more workable and economical mortar for
brick masonry construction (Naeem et al., 1996).
Chemical analysis on khaka shows 95% of CaCo3
content (Naeem et al., 1996). In the present study,
the mix proportions of mortar constituents as found
4
16
28
40
52
Sieve No.
64
76
88
100
Figure 2 Gradation profile of sand and khaka constituent
employed for mortar preparation.
Mortar cubes of size 50mmx50mm were prepared
for the aforementioned mortar types and tested
after 28 days for compression strength. A total of
108 mortar cubes (nine samples for each mix
proportion) were tested. Figure 3 shows the mean
estimated compressive strength of each mortar
cubes (four cases for each mortar types).
Compressive Strength (MPa)
The experimental program for mechanical
characterization of masonry included tests on
masonry units, mortar, masonry prisms, masonry
triplets and masonry wallets. The tests are
performed at the Material Testing Laboratory of
Civil Engineering Department of UET Peshawar,
Pakistan. The following sections briefly elaborate
each of the tests.
30
CS
CK
CSK
25
20
15
10
5
0
1:4
1:6
1:8
1:10
1:4
1:6
1:8
1:10
1:2:2
1:3:3
1:4:4
1:5:5
Mortar Mix-Ratio
Figure 3 Mean compressive strength of mortar cubes, 28-days.
CS represents cement-sand mortar, CSK represents cementsand-khaka mortar and CK represents cement-khaka mortar.
Generally, the strength of mortar decreased with
increasing the mix-ratio. The experiments indicated
that the addition of khaka to ordinary mortar
increases the strength of mortar. On an average the
strength is increased by 72 percent for CK mortar
and 50 percent for CSK mortar.
2.3 Tests on Masonry Assemblages
2.3.1 Masonry Triplets Tests Per EN-1052-3
The triplet tests were performed on masonry
assemblages composed of three bricks using the
EN-1052-3 testing setup (Figure 4). The top and
bottom brick units were clamped whereas the
central unit was subjected to horizontal loading.
Two cases for pre-compression (250kg and 500kg)
were considered whereby the prism is loaded at the
top.
masonry: parameters employed in the MohrCoulomb shear strength model.
  c  
(1)
where τ represents the in-plane shear stress, c
represents the shear strength at zero precompression; µ represents the coefficient of
friction; σ represents the pre-compression stress on
the prism. A total of 96 prism samples (eight
samples prepared for each mix proportion of each
mortar type) were tested.
P
Elevation
Side View
Perspective view
Figure 4 Triplet test specimen and loading setup per EN-1052-3.
The testing provides estimates of the shear strength
(bond strength) and friction coefficient of the
CS
CK
CSK
0.3
0.25
0.2
0.15
0.1
0.05
0
1:4
1:6
1:8
1:10
1:4
1:6
1:8
1:10
1:2:2
1:3:3
1:4:4
(Masonry Bond Strength)
1.2
CS
shows the mean shear strength and CK
the
1
corresponding
friction coefficient observed CSK
for
each
mortar type. On average, the addition of khaka
0.8
to0.6 the ordinary mortar increased the strength by 40
percent for CK mortar type and 22 percent for CSK
0.4
mortar
type whereas the friction coefficient is
increased
by 20 percent for CK mortar type and 2
0.2
percent for CSK mortar type.
Figure 5
Friction Coefficient
Shear Strength (MPa)
0.4
0.35
0
1:5:5
1:4
1:6
1:8
1:10
Mortar Mix-Ratio
1:4
1:6
1:8
1:10
1:2:2
1:3:3
1:4:4
1:5:5
Mortar Mix-Ratio
CS
CK
CSK
0.3
0.25
0.2
0.15
0.1
0.05
0
1:4
1:6
1:8
1:10
1:4
1:6
1:8
1:10
1:2:2
1:3:3
1:4:4
1:5:5
CS
CK
CSK
1.2
Friction Coefficient
Shear Strength (MPa)
0.4
0.35
1
0.8
0.6
0.4
0.2
0
1:4
1:6
1:8
1:10
1:4
1:6
1:8
1:10
1:2:2
1:3:3
1:4:4
1:5:5
Mortar Mix-Ratio
Mortar Mix-Ratio
(Masonry Bond Strength)
(Friction Coefficient)
Figure 5 Observations made from the Triplet tests. From left to right: masonry bond strength (shear strength at zero pre-compression) and
friction coefficient. CS represents cement-sand mortar, CSK represents cement-sand-khaka mortar and CK represents cement-khaka mortar.
It is worth to mention that for the estimation of
lateral in-plane shear strength of wall a correction
factor is employed to the Mohr-Coulomb
parameters i.e. c & µ. It is due to the fact that these
parameters are obtained from tests at local level.
Their correction for strength evaluation of walls is
essential (Magenes and Calvi, 1997).
k
(2)
1


1  2 y

x





where k represents the correction factor; ∆x
represents the length of the brick unit, 230mm in
the present study; ∆y represents the height of the
brick unit, 70mm in the present study; µ represents
the friction coefficient. The new parameters can be
calculated then as follow: cnew = c×k & µnew = µ×k.
2.3.2 Masonry Wallets Tests Per ASTM E-519-2
Tests on masonry panels (wallets) of size
690mmx690mm with 230mm thickness were
prepared in English masonry bond pattern. Tests
were performed on panels for the estimation of
diagonal tension strength of masonry. The testing
setup was designed as per the ASTM E-519-2
recommendations (see Figure 6). Linear variable
displacement transducers (LVDTs) were installed,
both on each horizontal and vertical directions to
measure the mean horizontal and mean vertical
deformation of the specimen during loading.
present study to estimate the diagonal tensile
strength of tested wallets.
ft 
(3)
0.5P
t l1  l 2 
where ft represents the diagonal tensile strength; P
represents the peak vertical loading; t represents the
thickness of the specimen; l1 and l2 represent the
length of sides of the specimen. A total of 48 wallet
samples (four samples prepared for each mix
proportion of each mortar type) were tested.
Figure 6 Diagonal tension test setup per ASTM E-519-2.
Figure 7 reports the mean diagonal tensile strength
of tested masonry wallets for each mortar type. It
can be observed from the typical damage pattern
that the crack developed upon failure follows bed
and head joints of masonry. It is an indication that
the strength is largely contributed by the masonry
mortar and mortar-brick interface bond strength.
Thus, the use of various mortar types will affect the
tensile strength of masonry wallets.
This test setup is generally interpreted for diagonal
tensile strength evaluation based on the
consideration that the specimen is subjected to pure
shear, the specimen is cracked when the principal
stress at the center of the panel becomes equal to
the tensile strength of masonry (ASTM E519-02;
RILEM, 1994). However, it is urged based on
numerical and analytical studies that the specimen
in reality is not subjected to uniform and
homogenous state of stresses. Because of this the
specimen is not under pure shear (Brignola et al.,
2009; Frocht, 1931; Magenes et al., 2010).
On average the addition of khaka to the ordinary
mortar increases the diagonal tension strength by
110 percent for CK mortar type and 93 percent for
CSK mortar type.
Diagonal Tensile Strength (MPa)
The analytical formula recently proposed and
employed by Magenes et al. (2010) is used in the
2
CS
CK
CSK
1.5
1
0.5
0
1:4
1:6
1:8
1:10
1:4
1:6
1:8
1:10
1:2:2
1:3:3
1:4:4
1:5:5
Mortar Mix-Ratio
Figure 7 Diagonal Tension strength of masonry wallets. From left to right: typical damage mechanism of one of the representative samples
and mean estimates of masonry diagonal tensile strength for each mortar type. CS represents cement-sand mortar, CSK represents cementsand-khaka mortar and CK represents cement-khaka mortar.
The diagonal tension strength is also interpreted to
estimate the shear rigidity i.e. shear modulus, of
masonry material using the ASTM procedure,
which is employed and recommended for shear
modulus estimation (Magenes et al., 2010).
G


(4)
where
  0.707
P0.33Pmax
t l1  l 2 
 0.707
P0.05Pmax
t l1  l 2 
 V  H 
 V  H 


  
 
g
g

 0.33Pmax 
 0.05Pmax
where G represents the shear modulus; τ represents
the shear stress; γ represents the corresponding
shear strain; Pmax represents the peak vertical load
at failure; ∆V & ∆H represent the vertical and
horizontal deformation in the vertical and
horizontal LVDT’s, respectively; g represents the
gauge length of either of the LVDTs.
The above equation (4) is meant to obtain the shear
modulus as the slope of the shear stress-strain
curve between the two specified points when the
loading reaches 5 percent of the peak load and 33
percent of peak load i.e. the slope of stress-strain
curve between 5 percent and 33 percent of peak
load. Other parameters are defined earlier. Figure 8
reports the mean shear modulus of the masonry
wallets obtained for each mortar types.
Masonry Shear Modulus (MPa)
300
CS
CK
CSK
250
200
where fm (MPa) represents the compressive
strength of mortar, Additionally, constrained
regression analysis is performed whereby the
power of fm is kept 0.60 and 1.0, in order to
possibly further simplify the above equation.
150
100
c  0.0337 f m 0.60
(6)
c  0.014 f m
(7)
50
0
1:4
1:6
1:8
1:10
1:4
1:6
1:8
1:10
1:2:2
1:3:3
1:4:4
1:5:5
Mortar Mix-Ratio
On average, the addition of khaka to the ordinary
mortar increases the shear stiffness (shear modulus)
by 91 percent for CK mortar type and 90 percent
for CSK mortar type.
3 Simplified Empirical Relationships for
Masonry Mechanical Properties
The basic mechanical properties (masonry bond
strength and diagonal tensile strength) obtained
experimentally for each mortar types are correlated
with the mortar compressive strength to establish
simplified relationships for future applications.
Furthermore, correlation is performed between the
mechanical properties (bond strength and
coefficient of friction) and mortar types and mix
proportion.
Additionally, correlation is performed between
various mechanical properties (bond strength to
tension strength, compressive strength to tensile
strength, Young modulus to shear modulus) to
provide easy means for estimation and conversion
of masonry mechanical properties. These
relationships can be used for future applications
given either of the information on the mortar
strength or type and constituents.
3.1 Mortar Strength to Masonry Mechanical
Properties
3.1.1 Mortar Strength to Masonry Bond Strength
For each mortar type, the mean bond strength
obtained is correlated with the mean compressive
strength of mortar. Nonlinear regression analysis is
performed and empirical relationship is established
between mortar strength and masonry bond
strength through best fitting. The following
relationship is developed.
c  0.0326 f m 0.6633
(5)
Either of the above equation may be employed, for
most of the practical cases, to obtain the masonry
bond strength given the mortar compressive
strength. Figure 9 shows the experimentally obtained
data employed for correlating the bond strength to
mortar strength and possible best fitting through
regression (unconstrained and constrained)
analysis.
0.4
Masonry Shear Strength (MPa)
Figure 8 Shear modulus of the wallets obtained through
diagonal tension test on masonry wallets. CS represents cementsand mortar, CSK represents cement-sand-khaka mortar and CK
represents cement-khaka mortar.
Constraint Regression
c = 0.014fm
0.35
0.3
Unconstraint Regression
c = 0.0326f0.6633
m
0.25
0.2
0.15
Constraint Regression
c = 0.0337f0.60
m
0.1
0.05
0
0
5
10
15
20
25
30
35
Mortar Compressive Strenght (MPa)
Figure 9 Masonry bond strength (shear strength) to mortar
compression strength.
3.1.2 Mortar Strength to Masonry Diagonal
Tension Strength
For each mortar type, the mean masonry diagonal
tension strength is correlated with the mean
compressive strength of mortar. Nonlinear
regression analysis is performed and empirical
relationship is established between the mortar
compressive strength and diagonal tensile strength
through best fitting. The following relationship is
developed.
f t  0.11f m 0.8281
(8)
The above Equation 8 is found to provide higher
estimate of diagonal tension strength for CS mortar
type (see Figure 10). Thus additionally constraint
regression analysis is performed for CS mortar type
only whereby the power of mortar compression
strength fm is kept 0.80, in order to establish
relationship between CS mortar strength and
masonry diagonal tension strength.
f t  0.07 f m
For each mortar type, the mean masonry bond
strength and friction coefficient, parameters c & µ
employed in Equation (1), are correlated with the
mortar constituents proportion (mainly sand, khaka,
and sand-khaka). Linear regression analysis is
performed and empirical relationships are
established between the mortar constituents
proportion and shear strength parameters of
masonry. Each mortar type is considered
separately. The following relationships are
developed for c & µ of the Mohr-Coulomb strength
law for considered mortar types.
(9)
0.80
The above equation (8) may be employed for CK
and CSK mortar type to obtain the masonry
diagonal tensile strength given the mortar
compressive strength. Equation (9) can be
employed for masonry in case when CS mortar is
used in the construction work.
reports the experimentally obtained data
employed for correlating the masonry diagonal
tension strength to mortar compressive strength and
possible
best
fitting
through
regression
(unconstrained and constraint) analysis.
Figure 10
Diagonal Tensile Strength (MPa)
2
Bond Strength:
c  0.3344  0.0269 S ,
c  0.2806  0.0147 K ,
c  0.4268  0.0356 SK ,
CK and CSK Mortar
1.5
Friction Coefficient:
  0.31  0.03S ,
  0.80  0.04K ,
  0.17  0.05SK ,
Unconstraint Regression
ft = 0.11f0.8281
m
1
Constraint Regression
ft = 0.07f0.80
m
0
0
5
10
15
20
25
30
35
Mortar Compressive Strenght (MPa)
Figure 10 Masonry diagonal tension strength to mortar
compression strength. CS represents cement-sand mortar, CSK
represents cement-sand-khaka mortar and CK represents
cement-khaka mortar.
3.2 Mortar Type and Mix Proportion to
Masonry Mechanical Properties
3.2.1 Mortar Type and Mix Proportion to
Masonry Bond Strength and Friction
Coefficient
0.35
CSK Mortar
c = 0.4268-0.0356SK
0.3
(13)
(14)
(15)
CK – Mortar
CSK – Mortar
CK Mortar
c = 0.2806-0.0147K
0.25
0.2
0.15
CS Mortar
c = 0.3344-0.0269S
0.1
CS Mortar
 = 0.31+0.03S
0.8
Friction Coefficient
Masonry Shear Strength (MPa)
CS – Mortar
1
0.4
0.6
0.4
CSK Mortar
 = 0.17+0.05SK
0.2
0.05
0
CSK – Mortar
(10)
(11)
(12)
In the above equations, S represents the proportion
of sand for unit cement proportion in CS mortar; K
represents the proportion of khaka for unit cement
proportion in CK mortar; SK represents the
combined proportion of sand-khaka for unit cement
proportion in CSK mortar considering that sand
and khaka are employed in equal proportion. Figure
11 reports the experimentally obtained data
employed for correlating the masonry shear
strength parameters to mortar constituent for
considered mortar types and possible best fitting
through linear regression analysis. The horizontal
axis of the Figure 11 represents the proportion of
sand to cement for CS mortar; khaka to cement for
CK mortar and combined khaka-sand (added being
equally) proportion to cement for CSK mortar.
CS Mortar
0.5
CS – Mortar
CK – Mortar
2
4
6
8
10
Sand/Khaka/Sand-Khaka to Mortar Proportion
12
0
2
4
6
8
CK Mortar
 = 0.80-0.04K
10
12
Sand/Khaka/Sand-Khaka to Mortar Proportion
Figure 11 Masonry shear strength parameters to mortar types and mix proportion. From left to right: masonry bond strength and friction
coefficient employed in Mohr-Coulomb strength model. CS represents cement-sand mortar, CSK represents cement-sand-khaka mortar and
CK represents cement-khaka mortar.
The above equations may be employed to estimate
the masonry shear strength given the type of mortar
(i.e. mortar constituents), and mix proportion. It is
worth to mention that these parameters are obtained
at local level and will require to be modified by the
Mann and Muller (1982) correction factor k i.e.
Equation (2) before employing them in shear
strength evaluation of masonry wall (Magenes and
Calvi, 1997).
3.3 Correlating Masonry Mechanical Properties
3.3.1 Masonry Compressive Strength to Masonry
Diagonal Tension Strength
The above equation may be employed for most
practical cases to obtain the masonry shear
modulus given the masonry Young modulus. The
condition, E>1000 (MPa) given alongside the
equation is again essential to avoid any unrealistic
estimate of shear modulus.
report the experimentally obtained data
employed for correlating the masonry shear
modulus to masonry Young modulus and possible
best fitting through linear unconstraint regression
analysis. The figure also shows the code specified
relationships e.g. the EC6 specified like most of the
building codes, for masonry which in the present
case seems to provide a very higher estimate of the
shear modulus for a specified value of masonry
Young modulus.
Figure 13
The mean masonry compressive strength is
correlated with the mean masonry diagonal tensile
strength as elsewhere (Ali, 2006). Nonlinear
regression analysis is performed and an empirical
relationship is established between the masonry
compressive strength and diagonal tensile strength
through best fitting. The following relationship is
developed.
f mc  4.57 f t 0.30
where fmc represents the masonry compressive
strength. The model can be employed to estimate
the masonry compressive strength given the
masonry diagonal tensile strength and vise versa.
reports the experimentally obtained data
employed for correlating the masonry diagonal
tensile strength to masonry compressive strength
and possible best fitting through nonlinear
unconstrained regression analysis.
Masonry Compressive Strength (MPa)
Figure 12
8
1500
EC6 Specified
G = 0.40E
1000
500
0
Unconstraint Regression
G = 0.174E-137.21
0
500
1000
1500
2000
2500
3000
3500
Masonry Diagonal Strength (MPa)
Figure 13 Masonry Young modulus to shear modulus.
7
Unconstraint Regression
fmc = 4.57 f0.30
t
6
5
4 Conclusions
4
3
2
1
0
Masonry Compressive Strength (MPa)
(16)
0
0.5
1
1.5
2
Masonry Diagonal Strength (MPa)
Figure 12 Masonry diagonal tension strength to masonry
compression strength.
3.3.2 Masonry Young Modulus to Shear Modulus
For each mortar type used herein, the mean
masonry Young modulus is correlated with the
mean shear modulus of masonry, in order to
provide an easy means of converting elastic moduli
of masonry. Linear regression analysis is
performed and an empirical relationship is
established between the masonry Young modulus
and masonry shear modulus through best fitting.
The following relationship is developed.
G  0.174 E  137 .21 , E>1000 (MPa)
(17)
The
paper
presented
the
mechanical
characterization of solid fired clay brick masonry
through experimental investigation. Laboratory
tests were performed on 108 mortar cubes, 96
masonry prisms for triplet tests, 48 masonry prisms
for compression tests and 48 masonry wallets for
diagonal tension tests. The effect of various mortar
types (cement-sand CS, cement-khaka CK and
cement-sand-khaka CSK) and mix proportion on
the mechanical properties are investigated.
Simplified relationships are developed to relate the
mortar strength, mortar types and mix proportion
with the masonry basic mechanical properties. The
study provided tools essential within the context of
assessment and design verification of masonry
walls subjected to lateral loads. The relationships:
mortar type and mix proportion to masonry bond
strength and friction coefficient are first of its kind
and of a great importance for practical applications.
Masonry constructions common in Pakistan and
which can also be found in neighboring countries
(like India, Iran, Bangladesh among others) are
considered in the present study. The following
conclusions are drawn based on the experimental
study.


Given the mortar compression strength, the
basic mechanical properties of masonry can be
found as follow:
Bond Strength = 0.0326×Mortar Strength0.6633
Diagonal Tension Strength = 0.11×Mortar
Strength0.8281, for CK and CSK mortar
Diagonal Tension Strength = 0.07×Mortar
Strength0.80, for CS mortar
Masonry
Compression
Strength
=
4.57×Diagonal Tension Strength0.30
Masonry Young Modulus = 1790×Diagonal
Tension Strength0.30
Masonry Shear Modulus = 175.06× Diagonal
Tension Strength0.70

estimate for shear modulus for the considered
masonry type.
Given the mortar composition and mix ratio,
the basic mechanical properties of masonry for
Mohr-Coulomb relationship can be found as
follow:
Bond Strength:
c  0.3344  0.0269 S
for CS mortar
c  0.2806  0.0147 K
for CK mortar
c  0.4268  0.0356 SK
for CSK mortar
  0.80  0.04K
  0.17  0.05SK
Acknowledgements
The authors acknowledge the reviewers for kindly
providing constructive remarks which improved the
presentation of the research work significantly. The
first author gratefully acknowledges the support
and financial assistance provided by the University
of Engineering & Technology in the form of three
years of study leave. He also wishes to place on
record his gratitude to the Higher Education
Commission (HEC) of Pakistan for providing the
funds for this research under its Merit Scholarship
scheme for PhD studies in Science and
Technology.
REFERENCES
Friction Coefficient:
  0.31  0.03S
The research study revealed that mortars with
khaka either alone as the fine aggregate or in
combination with sand, provide relatively high
shear strength and stiffness as compared to
mortars with only sand as fine aggregate. The
positive aspects of use of khaka as a masonry
constituent are the good mechanical
characteristics besides being economical and
more workable in construction work.
for CS mortar
for CK mortar
for CSK mortar
where S represents the proportion of sand, K
represents the proportion of khaka and SK
represents the combined proportion of sandkhaka per unit cement.

Masonry bond strength, compression strength,
diagonal tension strength and elastic moduli
decreases with increasing the relatively
proportion of sand and khaka constituent in
mortar.

Masonry friction coefficient increases with
increasing the relatively proportion of sand and
khaka constituent in mortar for CS and CSK
mortar type whereas it decreases with
increasing the relatively proportion of khaka
constituent in mortar for CK mortar type.

The relationship between shear modulus and
Young modulus as specified by the Code
appears to provide an over-conservative
[1]. Abram, D.P. (2001). Performance-based
engineering concepts for unreinforced masonry
building structures. Progress in Structural
Engineering and Materials, 3(1), 48-56.
[2]. Ahmad, N., Crowley, H., Pinho, R. and Ali, Q.
(2010). Displacement-based earthquake loss
assessment of masonry buildings in Mansehra
city, Pakistan. Journal of Earthquake
Engineering; 14(S1), 1-37.
[3]. Ahmad, N., Ali, Q., Ashraf, M., Naeem, K. and
Alam, B. (2011). Seismic structural design
codes evolution in Pakistan and critical
investigation of masonry structures for seismic
design recommendations. International Journal
of Civil, Structural, Environmental and
Infrastructure Engineering Research and
Development; 1(1), 42-85.
[4]. Ahmad, N., Ali, Q., Ashraf, M., Naeem, A. and
Alam, B. (2012). Seismic performance
evaluation of reinforced plaster retrofitting
technique for low-rise block masonry
structures. International Journal of Earth
Sciences and Engineering, 5(2), 193-206.
[5]. Ali, M. (2006). To study the compressive
strength and Modulus of elasticity of local
brick masonry system. MSc Thesis, Civil
Engineering Department, UET, Peshawar,
Pakistan.
[6]. ASTM E-519-02 (2002). Standard test method
for diagonal tension (shear) in masonry
assemblages. American Society for Testing
and
Materials
International
(ASTM)
Committee, West Conshohocken, PA, USA.
[7]. ASTM C-67-06 (2006). Standard test methods
for sampling and testing brick and structural
clay tile. American Society for Testing and
Materials International (ASTM) Committee,
West Conshohocken, PA, USA.
[8]. ASTM C109/C109M-08 (2008). Standard test
method for compressive strength of hydraulic
cement mortars (using 2-in. or [50-mm] cube
specimens). American Society for Testing and
Materials International (ASTM) Committee,
West Conshohocken, PA, USA.
[9]. ASTM C-1314-07 (2007). Standard Test
Method for Compressive Strength of Masonry
Prisms. American Society for Testing and
Materials International (ASTM) Committee,
West Conshohocken, PA, USA.
[10]. Brignola A., Frumento S., Lagomarsino S.
and Podestà S. (2009). Identification of shear
parameters of masonry panels through the insitu diagonal compression test. International
Journal of Architectural Heritage, 3(1), 1-22.
[11]. CEN (1994). Eurocode 6: Design of masonry
structures-Part 1-1: General rules for
buildings. Rules for reinforced and
unreinforced masonry. ENV 1996-1-1,
Comité Européen de Normalisation (CEN),
Brussels, Belgium.
[12]. D’Ayala, D.F. and Paganoni, S. (2011).
Assessment and analysis of damage in
L’Aquila historic city center after 6th April
2009. Bulletin of Earthquake Engineering,
9(1), 81-104.
[13]. EN 1052-3 (2002). Methods of test for
masonry – Part 3: Determination of initial
shear strength. British Standards Institution
(BSI), London, UK.
[14]. Fardis, M.N., Calvi, G.M. (1994). Effects of
Infill on the Global Response of Reinforced
Concrete Frames. Proceedings of the Tenth
European
conference
on
Earthquake
Engineering, Vienna, Austria.
[15]. FEMA (2000). Pre-standard and commentary
for the seismic rehabilitation of buildings.
Federal Emergency Management Agency
(FEMA), Washington, DC, USA.
[16]. Frocht, M. (1931). Recent advances in
photoelasticity. Transactions of ASME, Ann
Arbor, 55, 135-153.
[17]. Javed, M., Naeem, A. and Magenes, G.
(2008). Performance of masonry structures
during earthquake - 2005 in Kashmir. Mehran
University Research Journal of Engineering &
Technology, 27(3), 271-282.
[18]. Kappos, A.J., Stylianidis, K.C., and
Michailidis, C.N. (1998). Analytical models
for brick masonry infilled r/c frames under
lateral loading, Journal of Earthquake
Engineering, 2(1), 59-87.
[19]. Magenes, G. (2006). Masonry building design
in seismic areas: recent experiences and
prospects from a European standpoint.
Proceedings of the First European Conference
on Earthquake Engineering and Seismology,
Keynote 9, Geneva, Switzerland.
[20]. Magenes, G., and Calvi, G.M. (1997). InPlane seismic response of brick masonry
walls. Earthquake Engineering and Structural
Dynamics, 26 (11), 1091-1112.
[21]. Magenes, G., Penna, A., Galasco, A. and
Rota,
M.
(2010).
Experimental
characterisation of stone masonry mechanical
properties. Proceedings of the Eight
International Masonry Conference, Dresden,
Germany.
[22]. Mann, W. and Muller, H. (1982). Failure of
shear-stressed masonry-An enlarge theory,
tests and application to shear walls.
Proceedings of the British Ceramic Society,
30, 223.
[23]. Naeem, et al. (1996). A Research Project on
Khaka”, Undergraduate research work at the
Civil Engineering Department, NWFP
University of Engineering and Technology,
Peshawar, Pakistan.
[24]. Naseer, A., Naeem, A., Hussain, Z. and Ali,
Q. (2010). Observed seismic behavior of
buildings in northern Pakistan during the 2005
Kashmir earthquake. Earthquake Spectra;
26(2): 425-449.
[25]. RILEM, T.C. (1994). Diagonal tensile
strength tests of small wall specimens, 1991.
In RILEM, Recommendations for the Testing
and Use of Constructions Materials, London,
England.
[26]. Smyrou, E., Blandon, C., Antoniou, S., Pinho,
R. and Crisafulli, F. (2011). Implementation
and verification of a masonry panel model for
nonlinear dynamic analysis of infilled RC
frames. Bulletin of Earthquake Engineering,
9(5), 1519-1534.
[27]. Tomazevic, M. (1999). Earthquake-resistant
design of masonry buildings-innovation in
structures and construction Vol. 1, Imperial
College Press, London, UK.
[28]. Turnsek, V. and Sheppard, P. (1980). The
shear and flexure resistance of masonry walls.
Proceedings of the International Research
Conference on Earthquake Engineering.
Skopje, Macedonia.