15th International Brick and Block
Masonry Conference
Florianópolis – Brazil – 2012
OUT-OF-PLANE SEISMIC PERFORMANCE OF UNREINFORCED
MASONRY WALLS RETROFITTED USING POST-TENSIONING
Ismail, Najif1; Schultz, Arturo E.
2; Ingham, Jason M.
3
1 PhD Student, University of Auckland, Dept. of Civil and Environmental Engg., [email protected]
2 PhD, Prof., University of Minnesota, Dept. of Civil Engg., [email protected]
2 PhD, Assoc. Prof., University of Auckland, Dept. of Civil and Environmental Engg., [email protected]
The development of equations for a post-tensioning seismic retrofit design of URM walls is
discussed and a summary of out-of-plane flexural testing is reported. A total of five (05) full
scale unreinforced masonry (URM) walls, of which one was tested as-built and four were
seismically retrofitted using post-tensioning, were structurally tested using an out-of-plane air
bag rig. The out-of-plane loaded test walls had two different wall configurations that were
representative of prevalent seismically deficient URM walls and were constructed using
salvaged clay bricks and an ASTM type O mortar. Varying levels of post-tensioning were
applied to the test walls using a single mechanically restrained sheathed and greased strand,
inserted into a cavity at the centre of each test wall. Several aspects pertaining to the seismic
behaviour of post-tensioned URM walls were investigated, including damage patterns, force-
displacement behaviour, tendon stress variation, hysteretic energy dissipation, toughness, and
initial stiffness. Finally, measured response was compared to calculated values and the
proposed design equations were validated.
Keywords: seismic, performance, masonry, retrofitting, post-tensioning
INTRODUCTION
The majority of fatalities caused by earthquakes in the last one hundred years have resulted
from the collapse of unreinforced masonry (URM) buildings (Coburn and Spence 1992). Poor
seismic performance of URM buildings was also observed in recent earthquakes such as the
2005 M7.6 Pakistan earthquake (Bothara and Hicisyilmaz 2008), the 2008 M7.9 Sichuan
earthquake (Zhao et al. 2009), the 2009 M5.8 L'Aquila earthquake (Kaplan et al. 2010) and
the 2010 M7.1 Darfield earthquake (Dizhur et al. 2010). These experiences have highlighted
the vulnerability of URM buildings to damage in the event of a large earthquake, arising from
their high seismic mass and limited ductility. The two options available to alleviate the risk
posed by these earthquake prone buildings are either demolition, or the implementation of
seismic retrofit to improve earthquake response. But important concerns associated with
heritage preservation make demolition of these historic URM buildings undesirable, resulting
in their seismic retrofit being preferred. One technique to improve the seismic performance of
unreinforced masonry (URM) walls is to apply vertical unbonded post-tensioning, which had
been investigated and reported previously in several research studies (such as Al-Manaseer &
Neis 1987, Bean Popehn et al. 2008, Ganz and Shaw 1997, Rosenboom & Kowalsky 2004).
15th International Brick and Block
Masonry Conference
Florianópolis – Brazil – 2012
(a) Coring operation (b) External post-tensioning
Figure 1: Post-tensioning retrofit techniques
Research and codification of post-tensioned masonry originated from Switzerland and the
United Kingdom, and over the last two decades significant research and development has led
to multiple design code drafts (such as MSJC 2005, NZS 2004). The performance of post-
tensioned URM walls depends upon the initial post-tensioning force, tendon type and spacing,
restraint conditions, and confinement. Post-tensioning can either be bonded when tendons are
fully restrained, by grouting the cavity, or left unbonded by leaving cavities unfilled. Lateral
restraint of post-tensioning tendons is important when considering second-order effects.
Because unbonded post-tensioning is reversible to some extent and has minimal impact on the
architectural fabric of a building, the technique is deemed to be a desirable retrofit solution for
URM buildings having important heritage value and is considered in this testing program. The
unbonded post-tensioning retrofit is applied either by placing post-tensioning tendons inside
cored cavities located at the centreline of the wall or by placing post-tensioning tendons
externally at discrete locations. The external unbonded post-tensioning involves using pairs of
external tendons, discretely located at the wall corners or next to buttresses such that
architectural impacts can be minimized. Figure 1(a) shows a photograph of the coring
operation being performed in Auckland on a heritage URM building and Figure 1(b) shows
discretely localised post-tensioned strands in a retrofitted URM building located in
Christchurch, New Zealand.
During large earthquakes URM walls may be subjected to out-of-plane lateral loading and
vertical compression due to self weight and overburden loads. Out-of-plane lateral loading
creates bending and because of their low tensile strength, URM walls are prone to damage
(Ewing and Kariotis 1981, Rutherford and Chekene 1990). The out-of-plane seismic
performance of URM walls retrofitted using unbonded post-tensioning was investigated by
structurally testing five full scale slender URM walls that were constructed using salvaged
bricks and a mortar composition closely replicating historic URM building construction. Post-
tensioning tendons were placed inside cavities, which are typically cored in retrofit
applications but in this testing program were achieved by placing flexible conduits while the
test walls were constructed. The selected wall configurations, test boundary conditions,
material characteristics, and post-tensioning process used in this testing represented typical
seismically retrofitted post-tensioned URM walls and enabled the development of a post-
tensioning seismic retrofit design procedure.
15th International Brick and Block
Masonry Conference
Florianópolis – Brazil – 2012
N +P
e
t
vo
e
n
P +N +0.5We t
Stress Profile
e
h
bw
w
w
b
h /2
N +P +Pt e
P +P+N +0.5We t
Stress Profile
f'm
d
b
h /2e
w
w
a
wb (a) Bilinear approximation (b) Wall loads (c) Wall displacements
Figure 2: Forces, stresses, displacements and bilinear idealisation
ANALYTICAL MODELLING
The failure mode of out-of-plane loaded URM walls, having sufficient diaphragm anchorage,
is characterised by one or several large horizontal cracks at or near mid-height of the wall,
which form when the flexural strength of the wall is exceeded and the wall starts to rock about
the mid height crack/cracks. A bi-linear elastic behaviour was observed in testing performed
previously (Ismail et al. 2011), given that tendon stress did not exceed the specified elastic
limit. Therefore, a bi-linear response was adopted (refer Figure 2a) to interpret the seismic
behaviour of post-tensioned masonry walls, where Mc = first cracking flexural strength and
Mn = nominal flexural strength. A force based design procedure is presented in the following
section, with two flexural capacities of post-tensioned walls corresponding to cracking and
nominal strength being estimated. Stiffness characteristics are influenced by the dynamic
properties of the wall and are typically quantified by evaluating the mid-height displacement,
which may be determined using Equation 3. Figure 2b shows a URM wall retrofitted using
post-tensioning that is subject to a uniform out-of-plane lateral pressure vo*, representing
lateral force generated due to an earthquake. The wall, having pin-to-pin height he and
thickness t, is post-tensioned by a centrally locating tendon at an effective depth d from the
extreme compression fibre. The effective post-tensioning force is Pe, Nt is the overburden
weight, and Ww is the wall self weight.
FIRST CRACKING STRENGTH At first cracking, stress on the tension face of the wall reaches the masonry modulus of
rupture, fr, and the corresponding moment capacity, Mc, can be evaluated by considering the
equilibrium of forces as,
(1)
where fm = pre-compression stress applied; fr = masonry modulus of rupture; fse = effective
tendon stress; Aps = tendon cross-sectional area; lw = wall length; bw = wall thickness; and
Nt = overburden weight; and Ww = self weight of the wall. The effective prestress, fse, is
defined as the post-tensioning stress after all losses, and can be presented by Equation 2,
(2)
where fpsi = initial tendon stress; Ppsi = initial applied force; and Eps = steel elastic modulus.
-80 -60 -40 -20 0 20 40 60 80
-30
-20
-10
0
10
20
30
Displacement (mm)
Tota
l F
orc
e (
kN
)
-4 -3 -2 -1 0 1 2 3 4
-15
-10
-5
0
5
10
15
Drift (%)
Analo
gous M
om
ent (k
Nm
)
Post-tensioned Wall
M
Mn
c
Bilinear Response
15th International Brick and Block
Masonry Conference
Florianópolis – Brazil – 2012
Table 1: Post-tensioning loss parameters Masonry ksh kcr kr
Type (µε) (µε/MPa) Bar Strand
Clay Brick 0 10 0.04 0.03
CMU 65 36 0.04 0.03
Where ksh = masonry shrinkage loss parameter; kcr = masonry creep loss parameter; kr = tendon relaxation loss parameter; and
CMU = concrete masonry unit
The parameters ksh, kc, and kr were established for clay brick and concrete masonry from
MSJC (2005) suggested values and further verified by experimental work performed by Ganz
(1993) and Laursen et al. (2006). Table 1 presents the recommended values for these
parameters. The displacement of the wall at the cracking moment, c, is computed using beam
theory. While the section remains elastic, the displacement can be computed as,
(3)
where Em = masonry elastic modulus and Ig = wall gross moment of inertia. The calculated
displacement value is used to estimate the initial stiffness of post-tensioned walls. It should be
noted that the displacement, c, is based on uncracked section properties and hence the gross
wall moment of inertia Ig is used for wall stiffness calculations.
NOMINAL FLEXURAL STRENGTH At nominal strength the compression stress distribution at the mid-height crack location
becomes non-uniform, which is typically approximated by an equivalent rectangular
compression stress block idealisation (refer Figure 2c). The equivalent stress block has a
depth of αf’m and width a, where α is a constant and typically has a value of 0.85 and f’m is
the compression strength of masonry. The effective depth is d and distance of neutral axis
from extreme compression fibre is c. Predicting the seismic response of a post-tensioned
URM wall at the nominal strength limit state is a diligent task and requires accurate
estimation of maximum useable masonry strain at the extreme compression fibre, εmu, and
increased tendon stress, fps. It was found in an experimental investigation on URM materials
that due to the higher deformability of prevalent weak lime mortar used in historic URM
construction, the strain values observed at nominal strength were inflated and much higher
than that typically defined for URM i.e., 0.0035 (MSJC 2005). But to keep the wall
displacement to a safe limit, the nominal strength for clay brick post-tensioned masonry walls
is defined herein as the point when the wall out-of-plane drift reaches 3% i.e., θ = 0.03 (refer
Figure 2c) and the corresponding masonry strain value is termed the maximum useable
masonry strain. Figure 2c shows a post-tensioned URM wall that is assumed to rock about the
neutral axis, where the post-tensioning tendon, having a 1% specified nominal yield strength
fpy and a modulus of elasticity Eps, has been post-tensioned with an effective tendon stress fse.
The tendon stress at nominal strength increases due to tendon elongation. If εs is the tendon
strain due to tendon elongation, then the increased tendon stress at nominal strength, fps, can
be calculated using Equation 4.
(4)
If the unbonded length of the tendon is equal to the height of the wall and the rotation value is
small, then the tendon strain, εs, can be estimated as,
15th International Brick and Block
Masonry Conference
Florianópolis – Brazil – 2012
(5)
where a maximum drift of 3% is stipulated. The maximum tendon stress should be taken as
the smaller of 0.85fpy or 0.7fpu, and as 0.7fpu is generally the smaller of these two calculated
values, a maximum tendon stress of 0.7fpu is stipulated herein. Substituting Equation 5 and
values for constants α and β of 0.85 for both (typical in flexural design) into Equation 4
yields,
(6)
An equation similar to Equation 6 has been investigated by Bean Popehn and Schultz (2010)
in a recent research study using a data set from 127 finite element analyses and 66
experimental wall tests and was found to predict tendon stress better than current design
expressions. Similarly, based on the equilibrium of forces at nominal strength (refer to Figure
2c) Equation 7 is developed for the evaluation of nominal strength of post-tensioned URM
walls.
(7)
A flexural strength reduction factor of ɸ = 0.85 shall be used for retrofit design and the
resulting reduced nominal moment capacity ɸMn shall be greater than or equal to the required
moment capacity, M*, calculated as,
(8)
where vo* is the design out-of-plane lateral pressure, lw is the effective wall length for one
post-tensioning strand and can be adopted as equal to the centre to centre tendon spacing, and
he is the effective height of the wall and is dependent upon the end constraints. Simple
supports at ends of the walls provide no rotational restraint so that he = 1.0h. Vertically
spanning face-loaded URM walls are known to remain linearly elastic until cracking initiates,
after which upper and lower segments rotate about the hinge that forms at wall mid-height
(Bean Popehn et al. 2008, Ismail et al. 2011). Therefore, simply supported boundary
conditions were used in the test setup.
MATERIAL PROPERTIES
Test walls were constructed following a common masonry bond pattern, with one header
course after every three stretcher courses, by an experienced brick layer under supervision.
Salvaged solid clay bricks (220 mm × 110 mm × 90 mm in size) were laid with roughly
15 mm thick mortar courses. Average URM material properties were determined by material
testing consistent with standardised procedures (AS/NZS 2003, ASTM 2002, ASTM 2003,
ASTM 2004), typically in sets of three. Masonry compressive strength f’m was determined by
testing three brick high prisms (refer Figure 3a), and mortar compressive strength f’j was
determined by testing 50 mm square cubes subjected to compression loading. Brick
compressive strength f’b was established by testing half brick specimens. Masonry cohesion C
and coefficient of friction µf were investigated by bed joint shear testing of 6 three bricks high
prisms that were subjected to varying magnitudes of axial compression applied using external
post-tensioned high strength bars (refer Figure 3b). Table 2 reports results of the material
testing.
15th International Brick and Block
Masonry Conference
Florianópolis – Brazil – 2012
Table 2: Masonry Material Properties Property f’b f’j f’m fr C µf
MPa MPa MPa MPa MPa Ratio
Value 21.4 1.4 8.7 0.08 0.1 0.46
COV 23% 8% 3% 66% - -
where f’b = brick compressive strength; f’j = mortar compressive strength; f’m = masonry compressive strength;
fr = tensile strength of masonry; C = mortar cohesion; and µf = coefficient of internal friction
(a) Compression testing (b) Shear test
Figure 3: Photographs of material testing
Currently, two main types of post-tensioning tendons are prevalent, which are threaded steel
bars and sheathed greased seven wire strands (referred to as strands herein). Threaded steel
bars are typically used for straight post-tensioning over short distances and have relatively
lower tensile strength than strands. Threaded mild steel bars are post-tensioned by using a
hydraulic jack which is removed after tightening of the nut that clasps the post-tensioning bar,
and strands are post-tensioned using an electronically operated hydraulic jack and the taut
strand is clasped by wedge interlocking at live end anchorages. The greased coating of strands
enables high corrosion resistance and lower frictional losses, which makes them an ideal
choice for unbonded post-tensioning application. The added advantage of high corrosion
resistance facilitates the use of unbonded strands for external post-tensioning applications by
locating strands at discrete locations, typically at corners of flanged or buttressed walls. A
sheathed greased seven wire strand was used to apply post-tensioning to test walls, which has
a nominal specified tensile strength, fpy, of 1680 MPa and a nominal specified ultimate tensile
strength, fpu, of 1860 MPa.
TEST WALL DETAILS
Test wall details are specified in Table 3, with four test walls (ABO-01, PTS-02, 03 and 04)
having the same height, and test wall PTS-05 being 4.1 m high. The selected wall
configurations were representative of the most prevalent storey heights found in historic URM
buildings and the level of pre-compression applied to the wall was representative of typical
stress levels, where stresses would be attributed to both overburden compression due to upper
storeys and compression due to post-tensioning. As maximum stresses develop at mid-height
(hinge zone) when slender vertically spanning URM walls are subjected to out-of-plane
seismic excitations, a single prestress tendon with bearing plates is adequate to produce the
required stresses in the hinge zone by distributing axial compression stress at an angle of 45°
from the anchorage and into the wall.
15th International Brick and Block
Masonry Conference
Florianópolis – Brazil – 2012
Table 3: Wall dimensions and properties Wall he
(mm)
lw
(mm)
bw
(mm)
Pe
(kN)
fse
(MPa)
Ww
(kN)
fm
(MPa)
f’m
(MPa)
fm/f’m
(ratio)
ABO-01 3670 1170 220 - - 17.9 0.035 6.5 0.005
PTO-02 3670 1170 220 50 506 17.9 0.229 6.5 0.035
PTO-03 3670 1170 220 70 709 17.9 0.307 6.5 0.047
PTO-04 3670 1170 220 100 1013 17.9 0.423 6.5 0.065
PTO-05 4100 1170 220 100 1013 19.5 0.426 6.5 0.066
where he = wall height; lw = wall length; bw = wall thickness; Pe = effective post-tensioning force; fse = effective
post-tensioning tendon stress; Ww = wall self weight; fm = initial pre-compression applied; and f’m = masonry
compression strength.
All test walls were prestressed using one post-tensioned tendon (strand) inserted at the centre
of the wall, and steel bearing plates were used to avoid localized masonry crushing. A flexible
conduit with an inside diameter of 25 mm was installed during construction to provide a wall
cavity and bricks were accordingly chiselled to accommodate the conduit. As there was no
bond between masonry and tendon, the conduit encased tendon behaved as if it was placed in
a cored cavity. An electronically controlled hydraulic jack was used to apply the initial post-
tensioning force immediately before testing and the taut strand was clasped by wedge
interlocking.
TESTING DETAILS
Testing was performed using an air bag rig as
shown in Figure 4. Air bags were used to
apply a uniformly distributed pseudo-static
load, emulating a lateral seismic load
generated in the out-of-plane direction. The
backing frames were placed over two pairs of
smooth greased steel plates having negligible
friction, such that the backing frame self
weight did not impair the test results. The
rigid reaction frame acted as a backing and
also supported the top of the wall, creating
boundary conditions that were comparable to
those when a post-tensioned wall is
connected to a floor or ceiling diaphragm.
For all post-tensioned walls a load cell was
located between the tendon anchorage and
the top of the wall, to record the force in the
post-tensioning tendon. One linear variable
differential transducer (LVDT) was located
at wall mid-height to determine lateral
displacement and four S shape 2 volt load
cells were used to determine the force applied by air bags. A displacement controlled loading
history was applied by inflating and deflating the air bags alternatively. Each cycle was
repeated twice and displacement was increased gradually as a function of drift values up to a
maximum of 4%.
Figure 4: Out-of-plane test setup
Rea
ctio
n
Fra
me
Backin
g
Fra
me
To A
ir C
om
pre
sso
r
Air B
ag
Strong Floor
Load Cell
LVDT
Hydraulic Jack
Str
on
g W
all
Rea
ctio
n
Fra
me
15th International Brick and Block
Masonry Conference
Florianópolis – Brazil – 2012
TEST RESULTS
A single large crack at or near mid-height was observed in all tests except PTO-05, which
failed prematurely in shear at a location above the airbag, which was attributed to a very low
modulus of rupture and is not likely to happen for actual boundary conditions. Therefore, for
further analysis PTO-05 was neglected. Distributed flexural cracking was not observed in the
testing and upon increasing the applied lateral load, the horizontal crack started to widen.
None of the test walls reached their maximum strength, which would result from either tendon
yielding or after reaching an instability displacement at mid-height.
(a) Force-displacement response for PTO-02
(b) Tendon stress history for PTO-02
(c) Force-displacement response for PTO-03
(d) Tendon stress history for PTO-03
(e) Force-displacement response for PTO-04
(f) Tendon stress history for PTO-04
(g) Force-displacement response for PTO-05
(h) Tendon stress history for PTO-05
Figure 5: Force-displacement responses and tendon stress histories
-80 -60 -40 -20 0 20 40 60 80-30
-20
-10
0
10
20
30
Displacement (mm)
Late
ral F
orc
e (
kN
)
-4 -3 -2 -1 0 1 2 3 4
-15
-10
-5
0
5
10
15
Drift (%)
Analo
gous M
om
ent (k
Nm
)
ABO-01
PTO-02Wall Height = 3760 mmPosttensioning Force = 50 kN
M
nM
c
-80 -60 -40 -20 0 20 40 60 8040
60
80
100
120
140
Displacement (mm)
Tendon F
orc
e (
kN
)
-4 -3 -2 -1 0 1 2 3 4
404
606
808
1010
1212
1414
Drift (%)
Tendon S
tress (
MP
a)
Wall Height = 3760 mmPosttensioning Force = 50 kN
Predicted Tendon Stress
-80 -60 -40 -20 0 20 40 60 80-30
-20
-10
0
10
20
30
Displacement (mm)
Late
ral F
orc
e (
kN
)
-4 -3 -2 -1 0 1 2 3 4
-15
-10
-5
0
5
10
15
Drift (%)
Analo
gous M
om
ent (k
Nm
)
ABO-01
PTO-03Wall Height = 3760 mmPosttensioning Force = 70 kN
nM
Mc
-80 -60 -40 -20 0 20 40 60 8040
60
80
100
120
140
Displacement (mm)
Tendon F
orc
e (
kN
)
-4 -3 -2 -1 0 1 2 3 4
404
606
808
1010
1212
1414
Drift (%)
Tendon S
tress (
MP
a)
Wall Height = 3760 mmPosttensioning Force = 70 kN
Predicted Tendon Stress
-80 -60 -40 -20 0 20 40 60 80-30
-20
-10
0
10
20
30
Displacement (mm)
Late
ral F
orc
e (
kN
)
-4 -3 -2 -1 0 1 2 3 4
-15
-10
-5
0
5
10
15
Drift (%)
Analo
gous M
om
ent (k
Nm
)
ABO-01
PTO-04Wall Height = 3760 mmPosttensioning Force = 100 kN
nM
cM
-80 -60 -40 -20 0 20 40 60 8040
60
80
100
120
140
Displacement (mm)
Tendon F
orc
e (
kN
)
-4 -3 -2 -1 0 1 2 3 4
404
606
808
1010
1212
1414
Drift (%)
Tendon S
tress (
MP
a)
Wall Height = 3760 mmPosttensioning Force = 100 kN Predicted Tendon Stress
-80 -60 -40 -20 0 20 40 60 80
-20
-10
0
10
20
Displacement (mm)
Late
ral F
orc
e (
kN
)
-4 -3 -2 -1 0 1 2 3 4
-15
-10
-5
0
5
10
15
Drift (%)
Analo
gous M
om
ent (k
Nm
)
ABO-01
PTO-05Wall Height = 4100 mmPosttensioning Force = 100 kN
nM
Mc
-80 -60 -40 -20 0 20 40 60 8040
60
80
100
120
Displacement (mm)
Tendon F
orc
e (
kN
)
-4 -3 -2 -1 0 1 2 3 4
404
606
808
1010
1212
Drift (%)
Tendon S
tress (
MP
a)
Wall Height = 4100 mmPosttensioning Force = 100 kN
15th International Brick and Block
Masonry Conference
Florianópolis – Brazil – 2012
FORCE-DISPLACEMENT RESPONSE
Figure 5a, 5c, 5e and 5g show the measured force-displacement histories, which were plotted
with analogous moment and drift values on a secondary axis to allow comparison between the
results of test walls having different heights. Measured lateral force at nominal strength was
compared to calculated strength and plotted on force-displacement histories, which show
good agreement between the calculated and measured strength values. The results of as-built
tested wall were also plotted (red dotted line) with each measured force-displacement curve to
investigate the seismic improvement due to a post-tensioning retrofit. A ductile and nonlinear
elastic behaviour was observed in walls PTO-02, PTO-03 and PTO-04, with strand stress not
exceeding the specified elastic limit and the wall returning to its original position. This
nonlinear elastic behaviour was attributed to the self centering behaviour of post-tensioned
masonry. The behaviour of post-tensioned walls PTO-02, PTO-03 and PTO-04 was similar to
that observed in one-directional cyclic testing previously performed and reported in Ismail et
al. (2011). Positively sloped post cracking behaviour was observed for all test walls, attributed
to the prestressing strand not exceeding its elastic limit even at large displacement values. The
measured force-displacement hysteretic curves at small displacements show that a mid-height
displacement occurred with little or no lateral force measured, which is possibly due to a gap
that occurred on both sides of test walls (between the backing frame and the wall), to inflate
and deflate air bags and allowing the wall to displace in the direction. A comparison of the
force-displacement histories indicated that the nominal out-of-plane flexural strength is
directly dependent on applied post-tensioning force magnitude, with post-tensioned test walls
exhibiting larger flexural capacity and less sensitivity to cracking than as-built wall, AB0-01.
TENDON STRESS
Bending of the wall generates deformation between the tendon anchorages at the top and
bottom of the wall, which elongates the tendon and increases the tendon tensile stress.
Measured tendon stress was plotted against the lateral displacement at mid-height in Figures
5b, 5d, 5f and 5h, with the strand stress increasing linearly without exceeding specified elastic
limits. Predicted tendon stress at nominal strength was also shown in the plots, which is
reasonably accurate when compared to measured tendon stress at nominal strength. Minor
stress loss was observed following the conclusion of testing to large displacement excursions.
In order for retrofitted walls to exhibit ductile behaviour, the restoring force provided by the
tendon must be maintained and design must ensure that the increased tendon stress does not
exceed the tendon yield strength.
Table 4:Test results and comparison with calculated values Wall Vc
kN
Vn
kN
Mc
kN.m
Mn
kN.m
V’c
kN
V’n
kN
Vc/V’c
ratio
Vn/V’n
ratio
%
T
kPa
K’i
N/mm
Ieff/Ig
ratio
ABO-01 2.8 2.8 1.3 1.3 3.3 6.7 0.86 0.42 22 185 179 0.05
PTO-02 6.1 17.5 2.9 8.2 6.7 21.1 0.92 0.83 13 405 454 0.13
PTO-03 7.6 21.5 3.6 10.1 9.0 26.8 0.84 0.80 15 705 1192 0.34
PTO-04 9.6 27.4 4.5 12.869 21.0 31.0 0.46 0.88 16 960 3134 0.89
PTO-05 8.9 25.0 4.5 12.8 17.8 22.0 0.50 1.14 - - - -
where Mc = calculated first cracking strength; Vc = calculated first cracking lateral force; Mn = calculated
nominal flexural strength; Vn = calculated nominal strength lateral force; V’c = measured first cracking lateral
force; V’n= measured maximum lateral force; = Equivalent viscous damping; T = wall toughness;
Ki = calculated initial wall stiffness; and K’i = measured initial wall stiffness.
15th International Brick and Block
Masonry Conference
Florianópolis – Brazil – 2012
HYSTERETIC ENERGY DISSIPATION
Hysteretic energy dissipated in each cycle was calculated by integrating the area enclosed
between the loading and unloading curve of each excursion (half loading cycle). It was
established from the results that the post-tensioning seismic retrofit increased the wall
capacity to withstand higher energy demand, with more energy dissipated in large
displacement excursions than in small displacement excursions. In seismic design of
structures energy dissipation characteristics are crucial and are typically quantified by
toughness, T. Therefore, a toughness value for each test wall was calculated by dividing the
maximum cumulative hysteretic energy by the volume of URM in the test wall.
EQUIVALENT VISCOUS DAMPING
Equivalent viscous damping was calculated from experimental results using the hysteretic
model first presented by Jacobsen (1930) and later used by Rosenboom and Kowalsky (2004)
for the calculation of equivalent viscous damping from pseudo-static in-plane cyclic testing.
For each excursion (push loading cycle) a damping value was calculated using Equation 9,
where ξ = Equivalent viscous damping; A1 = Area between loading and unloading curve; and
A2 = Area of rectangle surrounding the loop.
(9)
For numerical comparison the equivalent viscous damping calculated for the fourth cycle is
reported in Table 4. The calculated value for test wall ABO-01 was the highest and that for
PTO-04 was the least, with the damping values observed being close to code (NZS 2004)
recommended value of 15%. Initial stiffness is used in the strength based design methods, and
therefore the initial stiffness of the walls, Ki, was also calculated and is reported in Table 4.
Predicted Vs Measured Response
Table 4 presents a summary of the statistical comparison performed. First cracking strength,
Mc, nominal strength, Mn, and tendon stress at nominal strength, fps, were calculated using the
equations discussed earlier and ratios of these calculated to measured values were compared
statistically. The statistical comparison resulted in an overall mean ratio of 0.76, with a
coefficient of variation of 39%. However, the calculated cracking moment was found to be
conservative and result in smaller values. Finally, initial wall stiffness calculated based on
gross moment of inertia, Ki, was compared to measured initial wall stiffness, K’i, to determine
the ratio of effective moment of inertia, Ieff, to gross moment of inertia, Ig, and the ratios were
reported in Table 4.
SUMMARY AND CONCLUSIONS
Based on the observations of previously performed testing and the principles of structural
mechanics, equations were developed for a post-tensioning seismic retrofit design and the
developed design equations were investigated by comparing predicted response to the results
of structural testing performed on a total of five URM walls, with one wall tested as-built and
four walls being seismically retrofitted using different magnitude of post-tensioning. Several
characteristics pertaining to their out-of-plane seismic behaviour were also investigated and
reported. In order for test walls to represent a typical historic URM wall, historic URM
construction was imitated by using salvaged clay bricks and a hydraulic cement mortar,
having strength and stiffness characteristics similar to that found in typical historic URM
buildings. Masonry material properties were determined using standardised test methods,
15th International Brick and Block
Masonry Conference
Florianópolis – Brazil – 2012
typically in sets of three, which were used later to predict the response of the test walls. A
uniformly distributed out-of-plane cyclic loading was applied using a set of multiple air bags,
emulating seismic forces generated due to wall self weight. The key findings of the
experimental program are:
1. A single horizontal crack at or near mid-height was observed in all tests, confirming
that the boundary conditions used in response prediction are appropriate i.e., have no
rotational restraint at top and bottom of the wall. The post-tensioned out-of-plane
loaded URM walls failed with a displacement controlled rocking mode.
2. A bi-linear elastic behaviour was observed for test walls that were post-tensioned
using strands, where strand stress did not exceed the tensile yield strength. It was also
established that a post-tensioning retrofit design should ensure that the tendon stress
will not exceed the tendon yield strength.
3. Structural performance of URM walls was improved after retrofitting using post-
tensioning, with the flexural strength of post-tensioned URM walls ranging from
316% to 465% of that from an as-built tested wall.
4. Flexural capacities of all test walls were calculated and compared to experimental
results and a mean ratio of calculated/measured values was found to be 0.76 (COV
39%). It was inferred from statistical comparison that the proposed equations provided
good prediction for the structural performance of post-tensioned URM walls.
ACKNOWLEDGEMENTS
This research was conducted with financial support from the New Zealand Foundation for
Research, Science and Technology and from Reid Construction Systems. The Higher
Education Commission of Pakistan provided funding for the doctoral studies of the first
author. The authors thank Derek Lawley and Terry Seagrave for assisting with the
experimental program.
REFERENCES
Al-Manaseer, A.A., and Neis, V.V. (1987). “Load tests on post-tensioned masonry wall
panels,” ACI Structural Journal, 84(3), 467-472.
Bean Popehn, J.R., Schultz, A.E., Lu, M., Stolarski, H.K., and Ojard, N.J. (2008). "Influence
of transverse loading on the stability of slender unreinforced masonry walls," Engineering
Structures, 30(10), 2830-2839.
Bean Popehn, J.R., and Schultz, A.E. (2010). "Design provisions for post-tensioned masonry
walls loaded out-of-plane," The Masonry Society Journal, 28(2), 9-26.
Bothara J.K. and Hicisyilmaz K.M.O. (2008). “General observations of building behaviour
during the 8th October 2005 Pakistan earthquake,” Bulletin of the New Zealand Society for
Earthquake Engineering, 41(4), 209-33.
Coburn, A and Spence, R. (1992). “Earthquake Protection”. Willey New York.
Dizhur, D., Ismail, N., Knox, C., Lumantarna, R. and Ingham, J. M. (2010). “Performance of
unreinforced and retrofitted masonry buildings during the 2010 Darfield earthquake,” Bulletin
of the New Zealand Society for Earthquake Engineering, 43(4), 321-339.
15th International Brick and Block
Masonry Conference
Florianópolis – Brazil – 2012
Ewing, R. D, and Kariotis, J. C. (1981). "Methodology for mitigation of seismic hazards in
existing unreinforced masonry buildings: Wall testing, out-of-plane,” Topical Report Number
04, A joint venture of Agbabian Associates, S.B. Barnes and Associates and Kariotis and
Associates (ABK), El Segundo, CA.
Ganz, H.R. (1993). “Post-tensioning masonry structures,” VSL Intl. Ltd., Berne, Switzerland.
Ganz, H.R., and Shaw, G. (1997), “Stressing masonry’s future”. Civil Engineering (New
York), 67(1), 42-45.
Ismail, N., Lazzarini, D.L., Laursen, P.T., and Ingham, J.M. (2011). “Seismic performance of
face loaded unreinforced masonry walls retrofitted using post-tensioning,” Australian Journal
of Structural Engineering, (accepted for publication).
Jacobsen, L.S. (1930). “Steady force vibrations as influenced by damping,” ASME Trans.,
52(1), 1969-1990.
Kaplan, H., Bilgin, H., Yilmaz, S., Binici, H., and Aztas, A. (2010). “Structural damages of
L'Aquila (Italy) earthquake,” Natural Hazards and Earth System Science, 10(3), 499-507.
Laursen, P.T., Wight, G.D., and Ingham, J.M. (2006). "Assessing creep and shrinkage losses
in post-tensioned concrete masonry," ACI Materials Journal, 103(6), 427-435.
MSJC. (2005). “ACI 530-05/ASCE 5-05/TMS 402-05 Building code requirements for
masonry structures and specification for masonry structures”. The Masonry Standards Joint
Committee, United States.
NZS. (2004). “NZS 4230: 2004 Design of reinforced concrete masonry structures”. Standards
New Zealand, Wellington, New Zealand.
Rosenboom, O.A., and Kowalsky, M.J. (2004). "Reversed in-plane cyclic behavior of post-
tensioned clay brick masonry walls," Journal of Structural Engineering, 130(5), 787-798.
Rutherford and Chekene. (1990). "Seismic retrofitting alternatives for San Francisco's
unreinforced masonry buildings: Estimates of construction cost and seismic damage for the
San Francisco Department of City Planning," Rutherford and Chekene Consulting Engineers,
San Francisco CA.
Zhao, T., Zhang, X., and Tian, Z. (2009). “Analysis of earthquake damage to masonry school
buildings in Wenchuan earthquake,” World Information on Earthquake Engineering, 25(3),
150-158.