Experimental Investigation on The Characterization of Solid Clay Brick Masonry for Lateral Shear Strength Evaluation

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29 Νοε 2013 (πριν από 3 χρόνια και 4 μήνες)

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Experimental Investigation on The
Characterization
of

Solid

Clay
Brick
Masonry

for Lateral
Shear
Strength Evaluation



Qai
sar Ali
1
, Yasir Irfan Badrashi
1
,

Naveed Ahmad
1,2
,
*
,
Bashir Alam
3
,
Shahzad Rehman
3
,
Farhat Ali Shah Banori
3



1
Earthqu
a
ke Engineering C
enter,
UET
, Peshawar, Pakistan
.

2
ROSE School

IUSS Pavia, Pavia, Italy.

3
Department of Civil Engineering,
UET
, Peshawar, Pakistan
.


Corresponding Author:
anaveed@roseschool.it
, +393463029255




A
bstract

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 wind
s

and earthquakes
within the context of

design and
assessment studies
. The basic material properties
of masonry including
compressi
ve

strength, diagonal tensi
le
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)
.
St
andard brick unit prevalent in Pakistan

is considered, similar to

units
that
can be found
also in
neighboring countries like
India, Iran and Bangladesh
among
st

others
.

Three
type
s of mortar



cement
-
sand,
cement
-
sand
-
khaka

and cement
-
khaka
are used as bo
nd
ing material

for masonry assemblages.

Khaka is
obtained
as a byproduct of
stone crushing process
, employed in mortar preparation to produce
relative
ly

workable and economical mortar
.

The effect of mix proportion
s

of mortar is also investigated.
Empirical
r
elationships are developed herein whereby
basic
mechanical properties of masonry are correlated with the
mortar strength
,

mortar

type and
mix proportion
s
. An attempt is made to
correlate
mechanical properties
between each other and establish simplified
rel
ationships to help facilitate the
ir

use in future applications for
design and assessment of
unreinforced
masonry
wall structure
s

under wind

and earthquake
induced
lateral
loading.








K
eywords
:
shear, diagonal tensile strength, compression, elasti
c moduli, mortar, kh
aka, 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
part
s

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
exp
osure

of

Pakistan

and so also in
neighbouring
countries like India, Iran, Bangladesh

among
others
.

Most of the structures in these urban
exposure
s

are subjected to
frequent
lateral loads
due to heavy winds and earthquakes that
consequently
induce shear str
esses 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 mech
anical
properties of masonry units and mortar and their
interface makes the masonr
y
system
behavior
difficult to predict using simple hypothes
e
s
as
adopted for concrete and steel
.
T
he masonry
mechanical characterization
can be best

performed
through
experi
mental investigatio
n
s
, 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, w
hen 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

l
ateral loads by in
-
plane response
of walls (Magenes, 2006
; Tomazevic, 1999
). The
p
rovision 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
enabl
es
the structure respond in a box like action to lateral
load
ing 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 load
s

(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
may occur in masonry infill of concrete structures
due to lateral in
-
plane forces observed during
ear
thquake
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
)
.




(A)



(B)


(C)


(A): Diagonal shear cracks in masonry building walls
observe
d 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 Kas
hmir 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 unreinforc
ed masonry buildings
and masonry infill of concrete buildings
due to
earthquake induced lateral loads.


Many
available
analytical model
s

can be used to
estimate the in
-
plane strength of masonry walls
(
Abrams, 2001; CEN, 1994; FEMA, 2000;
Magenes and Calv
i, 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 load
s

in concrete structures (
Fardis
and Calvi, 1994; Kappos et
al., 1998
;
Smyrou

et
al., 2011
, among others
)
.
All these

models

r
equire
basic mechanical properties of masonry material to
obtain lateral in
-
p
lane strength
. This fact
makes the
experimental investigation on masonry material
s

essential before

the
assessment of structures can be
pe
rformed
within the context of existing stock

evaluation

and
design

verif
ication of new
constru
ction schemes

(Ahmad et
al., 2010, 2011,
2012

among others)
.









Th
is

p
aper
hence
presents

an

experimental
investigation
on solid clay fired
-
brick masonry
material for mechanical characteriz
ation. The
experimental work included laboratory tests

under
monotonic

loading

on mas
o
nry prisms
:
for the
estimation of

masonry compressive strength
(f
mc
)
and elastic Young modulus

(E)
,
on
triplets
:
for the
estimation of bond strength in shear: cohesion
parameter
(c)
and friction coefficient

(µ)

of Mohr
-
Coulomb model
, and
on
wallets
:
for th
e estimation
of diagon
al tension strength (f
t
) and
shear modulus

(G)
, besides tests on constituent mat
erial
s

i.e.
bri
ck
units: for unit compression strength, water
absorption and initial rate of absorption

and mortar
:
for compression strength (f
m
)
.


The
te
st
ing

is performed using the
standard testing
procedures:
ASTM

E
-
519
-
02 (2002)
for wallet
tests
,
EN 1052
-
3 (2002)

for triplet tests
, ASTM C
-
67
-
06

(
2006
) for masonry unit test
s
,
ASTM
C109/C109M
-
08 (2008) for mortar compression
test
s and
ASTM C
-
1314
-
07 (2007
)
for masonry
compression tests
.

Th
ree types of mortar are
considered; cement
-
sand mortar (CS), cement
-
sand
-
khaka mortar (CSK), cement
-
khaka mortar
(CK). The mortars are considered with 12 various
mix proportion
s

(four cases for each mortar type).
The moti
vation towards investigating masonry in
CSK and CK mortar is that t
hey

produce relatively
Gradation Profile of Sand & Khaka
0
20
40
60
80
100
4
16
28
40
52
64
76
88
100
Sieve No.
Percent Cummulative passing
Sand
Khaka
more workable and economical mortar
s

for
masonry construction

(Naeem et al., 1996)
; It is
essential to understand
t
heir

impact on the
mechanical properties of masonr
y
.

Empirical
relationships are developed to relate the basic
mechanical properties of
masonry with mortar
strength,
mortar constituent
s

and mix ratio
. Also,
an attempt is made to correlate the mechanical
parameters with each other. These relationship
s can
provide a useful means for future applications in
the design and verification studies of masonry
construction
.






2

Experimental Investigation of Clay Fired
Brick Masonry


2.1

Experimental Tests Program


The experimental program
for mechanical
charact
erization
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.




2.2

Tests on Masonry Constituents

Material


2.2.1

Masonry Unit Tests Per
ASTM C
-
67
-
06


The
present study
has focused on
investigat
ing

masonry of
solid
clay
fired brick

masonry unit
s
,
common in various parts of Pakistan
,

wh
ich can
also
be found in other South Asia
n

countries like
India, Iran, Bangladesh, among others
. The tests on
brick unit
s

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
experiment
s

showed
unit water absorption of 19.3%

(
COV 4.23%
)
; IRA
of 82.2
0

gm/min/30inch
2

(
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/30inch
2

indicates that it mus
t be wetted well before
employing
in the construction of masonry works.






2.2.2

Mortar

Tests Per
ASTM C109
/C109M
-
08


Various types of mortar
s

investiga
ted
in
t
he present
study

included
CS
,

CSK

and

CK
mortars
.

The
addition of khaka to the ordinary
CS
mort
ar
produces more workable and economic
al
mortar for
brick masonry construction

(Naeem

et al.,
1996)
.

C
hemical analysis on khaka shows

95% of CaCo
3

conten
t

(Naeem
et al.,
1996).
In t
he present study
,

the mix proportion
s

of mortar
constituents

as
found
in most of the construction works

are investigated
.
Four cases for each mortar type

are

considered with
mix proportion
s

of 1:4, 1:6, 1:8 and 1:10 for CS
and C
K mortar
s
;

and

1:2:2, 1:3:3, 1:4:4 and 1:5:5
for CSK mortar.

Gradation test
s are

performed on
both sand and khaka constituent
s
, see
Figure
2

which revealed
a relatively fine graded aggregate
content
s

of khaka.



Figure
2

Gradation profile of sand and khaka constituent
employed for mortar preparation.


Mortar cubes

of
size
50mm
x
50mm
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).


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
0
5
10
15
20
25
30
Mortar Mix-Ratio
Compressive Strength (MPa)


CS
CK
CSK

Figure
3

Mean c
o
mpressive strength of mortar cubes, 28
-
days.

CS represents cement
-
sand mortar, CSK represents cement
-
sand
-
khaka mortar and CK represents cement
-
khaka mortar.


Generally, the strength of mortar decreased with
increasing the mix
-
ratio.
The experiments ind
icate
d

that the addition of khaka to ordinary mortar
increases the strength of mortar. On an average the
strength is increased by 72 percent

for C
K mortar
and 50 percent for C
S
K 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 t
o horizontal loading.

Two cases for pre
-
compression (250kg and 500kg)
Perspective view
Elevation
Side View
P

were
consi
dered whereby the prism is loaded
at

the
top.




Figure
4

Triplet t
est specimen and loading setup per EN
-
1052
-
3.


The testing provides estimates of t
he shear strength
(bond strength) and friction coefficient of the
masonry: parameters employed in the Mohr
-
Coulomb shear strength model.






c

(1)

where τ represents the in
-
plane shear stress, c
represents the shear strength at zero pre
-
compression; 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 e
ach mix proportion of each
mortar type) were tested.



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
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Mortar Mix-Ratio
Shear Strength (MPa)


CS
CK
CSK

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
0
0.2
0.4
0.6
0.8
1
1.2
Mortar Mix-Ratio
Friction Coefficient


CS
CK
CSK

(Masonry Bond Strength)

(Friction
Coefficient)

Figure

5

shows the
mean shear strength
and the
corre
sponding friction coefficient

o
bserved for
ea
ch mortar type
.
On average
,

the addition of khaka
to the ordin
ary mortar increased

the strength by 40
percent for CK mortar type and 22 percent for CSK

mortar type

whereas the friction coefficient is
increased by 20 percent for CK mortar type and

2

percent for CSK mortar type
.


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
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Mortar Mix-Ratio
Shear Strength (MPa)


CS
CK
CSK

(Masonry Bond Strength)

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
0
0.2
0.4
0.6
0.8
1
1.2
Mortar Mix-Ratio
Friction Coefficient


CS
CK
CSK

(Friction
Coefficient)

Figure

5

Observations made from the
Triplet test
s.

From left to right:
masonry bond strength (shear strength at zero

pre
-
compression) and
friction coefficient.

CS represents cement
-
sand mortar, CSK represents cement
-
s
and
-
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).















x
y
2
1
1
k

(2
)


where k represents the correction factor; ∆
x
represents

the length of the bri
ck unit,
230mm
in
the present study; ∆
y
represents

the height of the
brick unit,
70mm i
n the present study;

µ represents
the friction coefficient. The new parameters can be
calculated
then
as follow: c
new

= c×k & µ
new

= µ×k.


2.3.2

Masonry Wallets Tests Per AS
TM 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
.



Figure
6

Diagonal tension test setup per ASTM E
-
519
-
2.


This test setup is generally interpreted for diagonal
tensile strength evaluation based on the
consideration that the specimen is su
bjected 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 speci
men
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)
.




The analytical formula recently proposed and
employed by Mag
enes et al. (2010) is used in the
present study to estimate the diagonal tensile
strength of tested wallets.




2
1
t
l
l
t
P
5
.
0
f



(3)


where f
t
represents the diagonal tensile strength
; P
represents
th
e peak vertical loading; t

represents
the

thickne
ss of the specimen; l
1
and l
2
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
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 con
tributed by the masonry
mortar

and mortar
-
brick interface bond strength
.

Thus, the use of various mortar type
s

will affect the
tensi
le

strength of masonry wallets.



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.


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
0
0.5
1
1.5
2
Mortar Mix-Ratio
Diagonal Tensile Strength (MPa)


CS
CK
CSK

Figure
7

Diagonal Tension
strength of
masonry wallets
.

From left to right:
typical damage mechanism
of one of the
representative samples

and mean

estimate
s

of masonry
diagonal tensile
strength for each mortar type.

CS represents cement
-
sand mortar, CSK represents cement
-
sand
-
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

where

(
4
)





2
1
P
05
.
0
2
1
P
33
.
0
l
l
t
P
707
.
0
l
l
t
P
707
.
0
max
max








max
max
P
05
.
0
P
33
.
0
g
H
V
g
H
V





























where
G represents the shear modulus;
τ represents
the shear stress
;

γ represents
the
corresponding
shear strain;

P
max

represents the peak vertical load
at failure
;
∆V

& ∆H represent

the vertical

and
horizontal
deformation in the vertical and
horizonta
l LVDT’s, respectively; g represents the
gauge length of
either of the
LVDT
s
.


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 earlie
r.
Figure
8

reports the mean shear modulus of the m
asonry
wallets obtained for each mortar types.


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
0
50
100
150
200
250
300
Mortar Mix-Ratio
Masonry Shear Modulus (MPa)


CS
CK
CSK

Figure
8

Shear modulus of the wallets obtained through
diagonal tension test on masonry wallets.

CS represents cement
-
sand mortar, CSK represents cement
-
sand
-
khaka mortar and CK
r
epresents cement
-
khaka mortar.


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
Mason
ry Mechanical Properties


The
basic mechanical properties

(masonry bond
strength and diagonal tensi
le

strength)

obtained
experimental
ly for each mortar types are correlated
with the mortar compressive strength to establish
simplified relationships for futu
re applications.

Furthermore, correlation is performed between the
mechanical properties (bond strength and
coefficient of friction) and mortar type
s

and mix
proportion.



Additionally, correlation is performed between
various mechanical properties (bond
strength to
tension strength, compressive strength to tensi
le

strength, Young modulus to shear modulus) to
provide easy mean
s

for estimation and conversion
of masonry mechanical properties
. These
relationships can be used for future applications
given eith
er of the information

on the mortar
strength or type

and constituent
s
.





3.1

Mortar Strength to Masonry Mechanical
Properties


3.1.1

Mortar
S
trength
to

Masonry Bond Strength




For each mortar type, the
mean
bond strength
obtained is correlated with the mean co
mpressive
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.


6633
.
0
m
f
0326
.
0
c


(5
)


where f
m

(MPa)
represents the compressive
strength of mortar,

Additionally, constrained
regression analysis is performed whereby the
power of f
m

is kept 0.60

and 1.0
, in order to
possibly further simplify the above equation.


60
.
0
m
f
0337
.
0
c


(6
)



m
f
014
.
0
c


(7
)


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 obtain
ed
data employed for correlating the bond strength to
mortar strength and possible best fitting through
regression (unconstrain
ed

and constrain
ed
)
analysis.






0
5
10
15
20
25
30
35
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Mortar Compressive Strenght (MPa)
Masonry Shear Strength (MPa)
Constraint Regression
Unconstraint Regression
Constraint Regression
c = 0.014f
m
c = 0.0326f
m
0.6633
c = 0.0337f
m
0.60

Figure
9

Masonry bond strength (shear strength) to mortar
compr
ession 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.


8281
.
0
m
t
f
11
.
0
f


(8
)


The above Equation 8 is found to provide higher
estimate
of dia
gonal tension strength for CS mortar
type

(see
Figure
10
)
. Thus additiona
lly
constraint
r
egression analysis is performed
for CS mortar type
only
whereby the power of
mortar compression
strength
f
m

is kept 0.80
,
in
order to
establish
relationship between CS mortar strength and
masonry diagonal tension strength
.


80
.
0
m
t
f
07
.
0
f


(9
)


T
he

above equation
(8)
may be employed
for CK
and CSK mortar type
to obtain the masonry
diagonal tensile
strength given the mo
rtar
compressive strength.

Equation
(
9
)

can be
employed for masonry

in case when CS mortar is
used in the construction work.


Figure
10

reports
the experimentally obtained data
employed for
correlating the masonry
diagonal
tensio
n strength to mortar compressive strength and
possible best fitting through regression
(unconstrain
ed

and constraint
) analysis.


0
5
10
15
20
25
30
35
0
0.5
1
1.5
2
Diagonal Tensile Strength (MPa)
Mortar Compressive Strenght (MPa)
Unconstraint Regression
f
t
= 0.11f
m
0.8281
CS Mortar
Constraint Regression
f
t
= 0.07f
m
0.80
CK and CSK Mortar

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




For ea
ch mortar type, the mean masonry
bond
strength and friction coefficient
,
parameters c & µ
employed in Equation
(
1)
,
are
correlated with the
mortar

constituents
proportion
(mai
nly sand, khaka,
and sand
-
khaka)
.
L
inear regression analysis is
performed and emp
irical relationship
s are
established between the mortar
constituents
proportion
and

shear strength

parameters
of
masonry. Each mortar

type is considered
separately.
The
following relationship
s are
developed

for c & µ of the Mohr
-
Coulomb strength
law for co
nsidered mortar types.



Bond Strength:

S
0269
.
0
3344
.
0
c


,


CS


Mortar


(10
)

K
0147
.
0
2806
.
0
c


,
C
K


Mortar

(11
)

SK
0356
.
0
4268
.
0
c


,
CSK


Mortar

(12
)


Friction Coefficient:

S
03
.
0
31
.
0



,

CS


Mortar


(13
)

K
04
.
0
80
.
0



,

C
K



Mortar

(14
)

SK
05
.
0
17
.
0



,

CS
K



Mortar

(1
5
)


In the above equations,
S represents the proportion
of sand for unit cement proportion in CS mortar
;

K

represents

the proportion of khaka f
or 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 experimen
tally 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 proportio
n 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.

2
4
6
8
10
12
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Sand/Khaka/Sand-Khaka to Mortar Proportion
Masonry Shear Strength (MPa)
CSK Mortar
c = 0.4268-0.0356SK
CS Mortar
c = 0.3344-0.0269S
CK Mortar
c = 0.2806-0.0147K

2
4
6
8
10
12
0
0.2
0.4
0.6
0.8
1
Sand/Khaka/Sand-Khaka to Mortar Proportion
Friction Coefficient
CK Mortar

= 0.80-0.04K
CSK Mortar

= 0.17+0.05SK

= 0.31+0.03S
CS Mortar

Figure
11

Masonry
shear strength parameters
to mortar

types and mix proport
ion.

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 ma
y 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 Mul
ler (1
982) 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



T
he
mean masonry
compressive strength
is
correlated with the mean
masonry diagonal tensile
strength

as elsewhere (Ali, 2006)
. Nonl
inear
regression analysis is performed and an empirical
relationship is established between the masonry
compressive strength and d
iagonal tensile strength
through best fitting. The following relationship is
developed.


30
.
0
t
mc
f
57
.
4
f


(16
)


w
here

f
mc

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.


Figure
12

report
s
the experimentally obtained data
employed for correlating the masonry
diagonal
tensile strength
to masonry
compressive strength
and possible best fitting throug
h
nonlinear

unconstrain
ed

regression analysis.


0
0.5
1
1.5
2
0
1
2
3
4
5
6
7
8
Masonry Diagonal Strength (MPa)
Masonry Compressive Strength (MPa)
Unconstraint Regression
f
mc
= 4.57 f
t
0.30


Figure
12

Masonry diagonal tension strength to

masonry
compression strength.


3.3.2

M
asonry Young Modulus to Shear Modulus


For each mortar type

used herein
, the mean
masonry Young modu
lus
is correlated with the
mean
shear modulus of masonry, in order to
provide
an easy mean
s

of conver
ting elastic moduli
of masonry.
L
inear 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.


21
.
137
E
174
.
0
G


,

E>1000 (MPa
)

(17
)


The above equation may be employed
for most
practical cases
to obtain the masonry
shear
modulus
given the
masonry Young mod
ulus
. The
condition
,

E>1000
(MPa
) given alongside
the
equation is
again
essential to avoid any unrealistic
estimate of shear modulus.


Figure
13

report

the experimentally obtained data
emplo
yed for correlating the masonry shear
mo
dulus
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 s
eems to provide a very higher estimate of the
shear modulus for a specified value of masonry
Young modulus.



0
500
1000
1500
2000
2500
3000
3500
0
500
1000
1500
Masonry Diagonal Strength (MPa)
Masonry Compressive Strength (MPa)
EC6 Specified
G = 0.40E
Unconstraint Regression
G = 0.174E-137.21

Figure
13

Masonry
Young modulus to shear modulus
.


4

Conclusions


The paper present
ed
the mechanical
characterizatio
n of solid fired clay brick masonry
through experimental investigation
. L
aboratory

tests were performed on
108 mortar cubes, 96
masonry prisms

for
t
riplet
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 mechanic
al properties are investigated.




S
implified relationships are
developed to relate the
mortar strength,
mortar types and mix prop
ortion
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.

T
he 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.
M
asonry construction
s

common in Pakistan and
which can
also be
found in neighboring countries
(like India, Iran, Bangladesh among others) are
cons
idered 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 Strength
0.6633


Dia
gonal Tension Strength

= 0.11×Mortar
Strength
0.8281
,
for CK and CSK mortar


Diagonal Tension Strength = 0.07×Mortar
Strength
0.80
,
for CS mortar

Masonry Compression Strength =
4.57×Diagonal Tension Strength
0.30


Masonry Young Modulus
= 1790
×Diagonal
Tension

Strength
0.30


Masonry Shear Modulus = 175.06×

Diagonal
Tension Strength
0.70




Given the mortar composition and mix ratio,
the basic mechanical properties of masonry for
Mohr
-
Coulomb relationship can be found as
follow:


Bond Strength:

S
0269
.
0
3344
.
0
c



for
CS m
ortar


K
0147
.
0
2806
.
0
c



for CK mortar


SK
0356
.
0
4268
.
0
c




for CSK mortar


Friction Coefficient:

S
03
.
0
31
.
0




for CS mortar

K
04
.
0
80
.
0




for
CK

mortar

SK
05
.
0
17
.
0




for CS
K

mortar


where
S represents the proportion of sand
,

K

represents

the proportion of khaka and SK
represents the combined proportion of sand
-
khaka per unit cement
.




Masonry bond strength
,
compression strength,
diagonal tension strength and
elastic moduli
decrease
s

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 typ
e 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
estimate for she
ar modulus

for the considered
masonry type
.




The research study revealed that mortars with
k
haka 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.



Acknowledgements


The au
thors acknowledge the reviewers
for kindly
pr
oviding
constructive remarks which improved the
presentation

of the research work s
ignificantly
.
The
first a
uthor
gratefully
acknowledge
s 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.


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