out-of-plane seismic performance of unreinforced masonry ... · out-of-plane seismic performance of...

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).

mailto:[email protected]




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(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.


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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


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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,


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(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.


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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.


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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


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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


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)


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


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


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)



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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.


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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,


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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.

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