Download Experimental Seismic Performance Evaluation of Unreinforced Brick

Experimental Seismic Performance
Evaluation of Unreinforced Brick
Masonry Buildings
Khan Shahzada,a) Akhtar Naeem Khan,b) Amr S. Elnashai,c)
Mohammad Ashraf,d) Muhammad Javed,d) Amjad Naseer,d)
and Bashir Alamd)
This paper presents an experimental study on the performance of a full-scale
unreinforced brick masonry (URM) building system tested under quasi-static loading at the Earthquake Engineering Centre, University of Engineering and Technology in Peshawar, Pakistan. The configuration and materials used in the single-story
URM building are typical of those found in the northern areas of Pakistan affected
by the 2005 Kashmir earthquake. This study is a part of ongoing research for the
earthquake impact assessment of the city of Abbottabad. Combined shear and flexural behavior was observed during the test. The experimental data was analyzed
and is presented in the form of force-deformation hysteresis loops and envelope
curves. Based on the measured data, different performance levels have been established. The measured response of the test structure is also compared to the estimated
response obtained using three capacity evaluation procedures and the two are found
to be in good agreement. [DOI: 10.1193/1.4000073]
INTRODUCTION
A devastating earthquake of magnitude 7.6 on the Richter scale struck the northern parts
of Pakistan and Kashmir on 8 October 2005. More than 73,000 people lost their lives, 80,000
were injured, and 3.5 million were left homeless (ADB/WB 2005). Most of the casualties
were the direct result of both partial or full building collapses in one of five districts located in
the Khyber Pakhtunkhwa province (formerly known as the Northwest Frontier province, or
NWFP) and Kashmir region (including Mansehra, Battagram, Abbottabad, Shangla, and
Kohistan). The reconnaissance survey reports indicated that a majority of the unreinforced
buildings, including those made of stone masonry, brick masonry, and concrete block
masonry, were either partially or completely damaged (Durrani et al. 2005).
Severe earthquakes are relatively infrequent compared to other types of natural disaster,
but they have the potential to be extremely destructive. It is not possible to prevent such
disasters, but the losses can be mitigated. The Himalayan region is considered to have
a)
Ph.D. student, Department of Civil Engineering, University of Engineering and Technology, Peshawar, Pakistan
Professor, Department of Civil Engineering, University of Engineering and Technology, Peshawar, Pakistan
c)
Professor, Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign,
United States
d)
Assistant Professor, Department of Civil Engineering, University of Engineering and Technology, Peshawar,
Pakistan.
b)
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Earthquake Spectra, Volume 28, No. 3, pages 1269–1290, August 2012; © 2012, Earthquake Engineering Research Institute
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SHAHZADA ET AL.
the potential to produce earthquakes of magnitude 8.0 and greater once every 100 years
(Chin and Scawthorn 2003). In recent history, several moderate earthquakes (i.e., Mw 5.0
to Mw 5.5) have struck the northern parts of Pakistan. These earthquakes show that the
north of Pakistan is a seismically active area.
Modern seismic codes can improve new and existing buildings through the evaluation of
their dynamic response and mechanical performance. Improper design and detailing can make
buildings vulnerable to earthquakes. The enormous losses inflicted by the Kashmir earthquake were mainly due to the fact that in the absence of a seismic code, buildings were either
non-engineered or designed for gravity loads only (Javed et al. 2008, Naseer et al. 2010).
Since Pakistan lies in a seismically active region of the world and most of its buildings are
vulnerable to earthquakes, a detailed study and seismic risk assessment is required. In order to
perform an investigation of the existing buildings in the affected area, a pilot project was
jointly undertaken by the Department of Civil Engineering at the University of Engineering
and Technology in Peshawar, Pakistan and the Mid-America Earthquake Center at the
University of Illinois at Urbana-Champaign. The project included a building stock survey,
a hazard assessment, and a fragility assessment of the existing buildings in the city of
Abbottabad and was based on field surveys and experimental and numerical studies.
This paper presents an experimental study, conducted as part of the research project mentioned above, on the seismic performance evaluation of unreinforced masonry buildings
(URM) in the study area. Several experimental studies have been carried out worldwide
on URM elements. For instance, studies on isolated shear walls and piers have been
done by Epperson and Abrams (1989), Abrams and Shah (1992), Magenes and Calvi
(1992), Anthoine et al. (1995), Manzouri et al. (1995), Tomazevic et al. (1996), Craig
et al. (2002), Franklin et al. (2003). In addition, Simsir et al. (2002) studied out-of-plane
walls. In Pakistan, some work has been done on the behavior of URM isolated piers by
Javed (2009), Naseer et al. (2010), and Ashraf (2010), and a full-scale one-room masonry
building was tested by Ali (2004) through underground explosion loading. However, only a
few researchers have investigated full-scale URM building systems (e.g., Magenes et al.
1995, Costley and Abrams 1996, Paquette and Bruneau 2003, Yi 2004, and Yi et al. 2006).
Because of differences in material properties and building geometry, the previous
research work on URM buildings in other parts of the world cannot be used to develop fragility curves and estimate the risk for buildings in Pakistan. Furthermore, the indigenous
research is limited to isolated piers; therefore it was decided to test a typical URM building
under quasi-static reverse cyclic loading to ascertain its seismic response parameters.
EXPERIMENTAL PROGRAM
The building stock survey of the city of Abbottabad indicates that 73% of the stock is
non-engineered URM buildings, out of which 78% are made with burnt clay bricks with
reinforced concrete rigid diaphragms. To predict the actual response of the existing
URM buildings in the area, a typical model building was selected and constructed at the
Earthquake Engineering Centre of the Department of Civil Engineering, University of Engineering and Technology in Peshawar (Figure 1). The test specimen was built with construction materials commonly used in the study area.
EXPERIMENTAL SEISMIC PERFORMANCE EVALUATION OF UNREINFORCED BRICK MASONRY BUILDINGS
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Figure 1. Unreinforced brick masonry test structure.
The height of the URM structure selected was one story, replicating an internal room
within a building. The size and configuration of the test structure was based on the field
practice and testing facility. Figure 2 shows a detailed drawing of the building. The sizes
of the openings and piers in the in-plane walls were selected according to the pier aspect
Figure 2. Details of unreinforced brick masonry test structure.
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SHAHZADA ET AL.
ratios and wall density ratios of the unreinforced brick masonry buildings in the city of
Abbottabad. A window was provided in one of the out-of-plane walls in order to reduce
the flange effect on one side.
The walls were constructed with 9-inch-thick brick masonry in an English bond pattern
(with alternate courses of stretchers and headers), which is commonly practiced in the study
area. Reinforced concrete lintel beams, 6 in. high and 9 in. wide were provided above all
openings. Lintel beams were reinforced with four 12-in. diameter longitudinal bars and
3/8-in. diameter stirrups spaced at 6 in. on center. The reinforced concrete roof slab
was 6 in. thick and reinforced with 12-in. diameter bars spaced at 9 in. center-to-center
in both directions. To simulate vertical precompression from the adjacent parts of the building, 13.5 in. walls were provided all around the slab over the center line of the walls. To
simulate dead load from the roof treatment, a 10-inch-thick layer of sand was provided on
top of the roof. The model was constructed on a 7.5-inch-thick reinforced concrete footing
that was secured to the strong floor.
The materials used in the construction of the test structure are given in Table 1. The
compressive strength and modulus of elasticity of the masonry are based on tests conducted on masonry prisms measuring 16 in. long by 16 in. high by 9 in. thick, according
to ASTM International’s C1314 – 11a Standard Test Method for Compressive Strength of
Masonry Prisms, as shown in Figure 3. Diagonal tensile strength was calculated from
diagonal compression tests on masonry prisms measuring 27 in. long by 27 in. high
by 9 in. thick, as shown in Figure 4. The diagonal strength of the masonry was very
low, which was probably due to the weak bond established between the mortar and
brick because a high initial rate of absorption. The compressive strength of the mortar
was determined according to ASTM International’s C-109/109M 11b Standard Test
Method for Compressive Strength of Hydraulic Cement Mortars. The cement-to-sand
ratio of 1:6 (one part cement to six parts sand) was based on observations from the
field survey of Abbottabad.
TEST SETUP AND PROCEDURE
The lateral load was applied using a hydraulic jack attached to the strong wall and
was provided with swivel (moment hinges) at each end to release the moment, as shown
Table 1.
fb
f mo
fm
f tu
Em
γm
Material properties
Masonry unit compressive strength, psi
Compressive strength of mortar, psi
Water absorption of bricks, %
Initial rate of absorption, g/min/30 in.2
Masonry compressive strength, psi
Masonry diagonal tensile strength, psi
Elastic modulus of masonry, ksi
Specific weight of masonry material, pcf
1803
733
23.0
91.7
438
7.3
178
93.3
EXPERIMENTAL SEISMIC PERFORMANCE EVALUATION OF UNREINFORCED BRICK MASONRY BUILDINGS
Figure 3. Compressive strength test of masonry prism.
Figure 4. Diagonal compression test of masonry specimen.
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SHAHZADA ET AL.
Figure 5. Test setup.
in Figure 5. The jack was attached to the roof slab with two loading shoes on the east and west
sides that were connected to each other by four lightly prestressed bolts. The capacity of the
loading system was approximately 45 kips, which was greater than the estimated capacity of
the building. The horizontal load was measured with a load cell of 112 kips capacity. The base
of the test structure was bolted tightly to the strong floor.
Twelve linear variable displacement transformers (LVDTs) were used to record the
displacement at various locations, as shown in Figure 6. The displacement capacity of
these transducers was 50 mm. Displacement Transducer 01 was used to record in-plane
displacement at the middle-center of the slab and served as the control gauge. Gauges
02–05 were installed to record the torsional rotation of the structure. The horizontal deflection
at the top of each pier was recorded with Gauges 06–10. Gauges 11 and 12 were used to
measure the possible vertical movement produced due to global rocking of the structure.
All the gauges were installed on steel reference frames and connected to the walls with flexible wires. The load cells and displacement transducers were connected with a static data
acquisition system, UCAM-70, which has a maximum data scanning speed of 20 channels
per second.
The test structure was subjected to increasing reverse displacement cycles at the roof
level. Each displacement cycle was repeated three times, as shown in Figure 7. During
and after each displacement cycle, the test building was thoroughly checked and marked,
and the cracks produced were photographed. The test was stopped when the peak load started
decreasing with the increasing displacement cycles.
EXPERIMENTAL SEISMIC PERFORMANCE EVALUATION OF UNREINFORCED BRICK MASONRY BUILDINGS
1275
Figure 6. Instrumentation of the test structure.
0.8
Displacement (inch)
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
Figure 7. Displacement pattern.
RESULTS AND DISCUSSION
DAMAGE MECHANISM
The damage states of the test structure at different story drift levels are shown in
Figures 8–11. Detailed descriptions of the damage patterns at different story drift levels
are given in Table 2.
Cracking started at the beginning of the test, indicating that masonry buildings behave
nonlinearly even at very low drift ratios. Since the lateral load was resisted mainly by the
in-plane walls (the north and south walls), these suffered more damage in comparison to the
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SHAHZADA ET AL.
Figure 8. Crack propagation in walls of full-scale URM structure at 0.18% story drift.
Figure 9. Crack propagation in walls of full-scale URM structure at 0.30% drift.
EXPERIMENTAL SEISMIC PERFORMANCE EVALUATION OF UNREINFORCED BRICK MASONRY BUILDINGS
1277
Figure 10. Crack propagation in walls of full-scale URM structure at 0.36% story drift.
Figure 11. Final damage pattern of the test structure.
out-of-plane walls. The behavior of the structure as a whole may be characterized as a combination of shear and flexure. Vertical cracks, mostly following the mortar bed and head
joints, were also observed. These were produced by vertical stress and increased as a result
of overturning moments. It was noted that cracks developed at the interface of the mortar and
bricks due to the weak bond between the two.
Pier P1 on the north wall developed vertical compression and flexural rocking cracks,
while flexural, shear, and vertical cracks were observed in Pier P2 on the same wall. Typical
diagonal shear cracks, originating from the opening corners and propagating toward the outer
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Table 2.
Story
Drift (%)
0.18
0.30
0.36
0.42
SHAHZADA ET AL.
Damage propagation
Damage Description
Stepped shear cracks were observed at the left
and right bottom corners of sill wall of the
southeast in-plane wall. Small vertical and
horizontal cracks were also noted.
The existing cracks widened and new cracks
were observed. Stepped shear cracks were
noticed in the spandrel wall above Pier P1.
Horizontal and horizontal-cum-vertical cracks
were also noticed in the out-of-plane wall.
Horizontal-cum-vertical cracks were observed
in Pier P4. Stepped shear and horizontal cracks
were noted in the southeast out-of-plane wall.
A horizontal crack was also noted in the
northwest out-of-plane wall.
Vertical and horizontal cracks were noticed
in Pier P1. Vertical cracks were also observed
in Pier P2. Stepped shear cracks were noted in
Pier P5. The existing cracks in the out-of-plane
wall widened and new cracks appeared.
Stepped shear cracks, vertical, and horizontal
cracks were observed in the southeast
out-of-plane wall.
Governing
Failure Mode
Referenced
Figures
Rocking
Figure 8
Rocking and
vertical splitting
Figure 9
Rocking and
vertical splitting
Figure 10
Global/local
rocking and shear
Figure 11
corners, were observed in the south wall. These cracks were produced due to rocking and the
stress concentration at the opening corners. Some vertical compression cracks were also
observed in Piers P3 and P5. Pier P4, the central one on the south wall, first rocked and
then developed diagonal shear cracks at a higher drift ratio. Besides flexural cracks developed
in out-of-plane walls, some vertical cracks were also observed at the intersection of the south
wall with the east and west walls. These cracks developed because of the poor connections
between the two orthogonal walls.
Similar crack patterns were observed in unreinforced brick masonry buildings damaged
during the Kashmir earthquake (Javed et al. 2008, Naseer et al. 2010), as shown in Figures 12
and 13.
FORCE-DEFORMATION BEHAVIOR
The force-deformation behavior of the test structure is given in Figure 14 in the form of
force-deflection hysteresis loops and envelope curves. Story drift is expressed as a ratio of the
lateral story displacement to the story height at the load level. As a sign convention, displacement and the corresponding load recorded during the westward movement of the jack were
called positive displacements/loads and vice versa. The envelope curves were obtained by
EXPERIMENTAL SEISMIC PERFORMANCE EVALUATION OF UNREINFORCED BRICK MASONRY BUILDINGS
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Figure 12. Rocking failure of masonry piers in 2005 Kashmir earthquake (Javed 2008).
Figure 13. Diagonal cracks produced at opening of a building in 2005 Kashmir earthquake
(Javed 2008).
joining the points corresponding to peak load in the positive and negative direction of each
displacement cycle. The shape of the loops represents predominantly shear behavior, which
was nonlinear from the beginning of test. The stiffness degraded with increasing displacement cycles and became almost zero at a story drift of 0.20%. The structure reached its peak
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SHAHZADA ET AL.
30
25
20
10
0
-0.5 -0.4 -0.3 -0.2 -0.1 0
-10
0.1
0.2
0.3
0.4
0.5
Lateral Load, kips.
Lateral Load, kips.
30
20
15
Positive Loading
10
Negative Loading
5
Average
-20
0
-30
Story Drift (%)
0
0.1
0.2
0.3
0.4
0.5
Story Drift (%)
Figure 14. Force-deflection hysteresis response of full-scale unreinforced brick masonry building: (a) Hysteresis loops and (b) envelope curves.
resistance at a story drift of 0.23%, after which strength degradation started at a slow rate. The
strength was degraded by 5% of the peak load at a story drift of 0.41% and the test was
stopped at this point. The structure could have been tested further, but instead it was retrofitted and retested.
FLANGE EFFECT
Behavior in the positive and negative load directions was expected to be asymmetric due
to the provision of a window in one of the out-of-plane walls. However, this was not the case.
Instead, the positive and negative envelope curves followed almost the same path. This may
have been because the effective flange width was less than the actual flange width, resulting
in the same flange effect in both directions.
SPANDREL DEFORMATION
Figure 15 shows the difference between the displacements recorded at story level and at
pier-top level, with the variation in story drift for each of five piers.
For Piers P1 and P2 of the north wall, the difference varied linearly up to a story drift of
0.15%, at which point the test structure yielded. This difference could have been due to the
global rocking and deformation produced in the spandrel. As described later, the effect of
global rocking was negligible before the test structure yielded (0.15% drift); this difference
could have been due to deformation in the spandrels. Beyond a story drift of 0.15%, rocking
seems to have been the main reason for the difference, because it was more in the positive
direction for P1 and in the negative direction for P2. Similar variations were also noted in the
deformation pattern of Piers P3 and P5, the two end piers of south wall. However the difference in displacement of Pier P4, the middle pier, was very small in both directions because
the global rocking effect was minimal in the middle. Some permanent residual deformation
was also noticed in the positive direction of Pier P5 of the south wall.
EXPERIMENTAL SEISMIC PERFORMANCE EVALUATION OF UNREINFORCED BRICK MASONRY BUILDINGS
20
20
15
10
5
-0.5
-0.3
0
-0.1 -5
0.1
0.3
0.5
-10
Difference (in x 100)
Difference (in x 100)
15
Pier P1
Pier P2
-0.5
0
-0.1 -5
-0.3
0.5
-20
Story Drift (%)
20
20
15
15
Difference (in x 100)
Difference (in x 100)
0.3
-15
Story Drift (%)
10
5
0
-0.3
0.1
-10
-20
-0.5
10
5
-15
Pier P3
1281
-0.1 -5
0.1
0.3
0.5
-10
Pier P4
10
5
0
-0.5
-0.3
-0.1 -5
0.1
0.3
0.5
-10
-15
-15
-20
-20
Story Drift (%)
Story Drift (%)
20
Difference (in x 100)
15
Pier P5
10
5
0
-0.6
-0.4
-0.2
-5 0
0.2
0.4
0.6
-10
-15
-20
Story Drift (%)
Figure 15. Relationship of building story displacement to displacement at the top of each pier.
TORSIONAL EFFECTS
During the design stage of the model, an attempt was made to keep the lateral stiffness of
both in-plane walls the same in order to avoid any torsional movement. To record any
possible torsional effects two out-of-plane gauges (Gauges 4 and 5) were installed. The diaphragm rotation was calculated as the sum of the displacement recorded by these gauges
divided by the distance between gauges, as shown in Figure 16. The variation of diaphragm
rotation with story drift is also shown in Figure 16. The maximum rotation was 0.001 radians
ð0.06°Þ, which is negligible. The rotation was smaller in the positive direction than in the
negative load direction. The reason for this difference could have been imperfections in the
masonry materials or different lateral stiffness in the out-of-plane walls.
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SHAHZADA ET AL.
Figure 16. Effect of torsion produced in the form of diaphragm rotation.
GLOBAL ROCKING
The global rocking of the test structure was measured by installing two displacement
transducers (Displacement Transducers 11 and 12) to record the vertical displacement at
the west and east sides of the building, as shown in Figure 6. The vertical displacements
were practically zero until a story drift of 0.15% in both the positive and negative directions,
indicating that global rocking started after 0.15% story drift (see Figure 17). At a story drift of
0.40%, a maximum of 0.08 in. of vertical displacement was recorded on both the west and
east sides.
HYSTERETIC DAMPING
The variation of hysteretic damping expressed as equivalent viscous damping with story
drift is shown in Figure 18. Equivalent viscous damping is calculated as the ratio of dissipated
energy ðE d Þ and input energy ðE inp Þ in accordance with Equation 1.
ξeq ¼
EQ-TARGET;temp:intralink-;e1;41;305
Ed
2πE inp
(1)
Vertical Displacement (inch)
0.1
0.05
0
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
-0.05
West Side
East Side
-0.1
Story Drift (%)
Figure 17. Global rocking of test structure: Variation of vertical displacement with story drift.
EXPERIMENTAL SEISMIC PERFORMANCE EVALUATION OF UNREINFORCED BRICK MASONRY BUILDINGS
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Equivalent Viscous Damping (%)
8
6
4
2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Story Drift (%)
Figure 18. Equivalent viscous damping of full-scale unreinforced masonry building.
The dissipated energy, which is equal to the area enclosed by the hysteresis loop, is a
direct function of cracks produced in the specimen. The damping remains practically constant
within the range of testing, with an average value of 6.7%. A slight increase in the damping
was noticed beyond a story drift of 0.15%. Studies performed on isolated piers (Javed 2009,
Ashraf 2010) found similar results for hysteretic damping.
BILINEAR IDEALIZATION
The average force-deflection envelope curve is idealized to be a bilinear, elasto-plastic
curve using the equal energy principle, as shown in Figure 19. The ultimate state is defined as
the point where the lateral strength is dropped by 20%. Since the ultimate state is not known,
from the existing trend it is assumed to have occurred at a drift of 0.50%. The three
30
Lateral Load, kips.
25
LS
20
CP
IO
15
10
5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Story Drift (%)
Figure 19. Force-deflection envelope and idealized bilinear curve of full-scale unreinforced
masonry building.
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SHAHZADA ET AL.
parameters—lateral stiffness, yield strength, and ultimate story drift—defining the bilinear
elasto-plastic curve, are 421.3 kips/in., 22.2 kips, and 0.50%, respectively.
Displacement ductility ðμD Þ is defined as the ratio of ultimate drift to yield drift. The yield and
ultimate story drifts for the test structure were 0.04% and 0.50%, respectively. The displacement
ductility is thus 0.50/0.04 = 12.5. The response modification factor (R) and displacement amplification factor ðCd Þ, as defined from the equal energy principle, are given by:
pffiffiffiffiffiffiffiffiffiffiffiffiffi
R ¼ 2μ − 1
(2)
EQ-TARGET;temp:intralink-;e2;41;561
μ
C d ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi
2μ − 1
(3)
EQ-TARGET;temp:intralink-;e3;41;531
The response modification factor and displacement amplification factor as calculated
from Equations 2 and 3 are 4.90 and 2.60, respectively. According to Eurocode 8, the
recommended response modification factor for unreinforced brick masonry buildings
is 1.50 (CEN 1995). The high values for deformation capacity could be due to the
following:
1.
The high deformation capacity of an unreinforced building is due to the rocking and
sliding of the structure and its components (i.e., masonry piers), rather than the ductility of its materials.
The quasi-static test, which is conducted at a lower strain rate, is considered to be
conservative for stiffness and strength but not for deformation capacity. The deformation capacity of a structure with shear critical piers tested under cyclic loading is
greater than that under dynamic loading. However, the effects of strain rate are less
significant for rocking critical structures.
2.
PERFORMANCE LEVELS
Three performance levels mentioned in the American Society of Civil Engineers’ (ASCE)
standard ASCE/SEI 41-06—immediate occupancy (IO), life safety (LS), and collapse prevention (CP)—are presented in the form of story drift and the corresponding base shear coefficient
(the ratio of the lateral load to the total weight of the test structure) in Table 3 (ASCE 2006). The
total weight of the building was calculated to be 75.1 kips. The drift corresponding to the yield
point on the elasto-plastic curve is taken as the IO performance level up to which there is no
permanent deformation or strength degradation. The CP performance level is taken as the
ultimate drift at which the lateral strength dropped by 20%, and drift corresponding to LS is
taken as 75% of CP level, as recommended in the ASCE standard.
Table 3.
Building performance levels
Performance Levels
Story Drift (%)
Base Shear Coefficient
IO
LS
CP
0.04
0.38
0.50
0.22
0.31
0.26
EXPERIMENTAL SEISMIC PERFORMANCE EVALUATION OF UNREINFORCED BRICK MASONRY BUILDINGS
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MEASURED RESPONSE VERSUS ESTIMATED RESPONSE
The measured response of the test structure was compared with its estimated response
based on:
1.
2.
3.
ASCE/SEI 41-06
The Magenes and Calvi Model (Magenes and Calvi 1997)
The Lang Model (Lang 2002)
All of the five piers (Figure 20) were assumed to be fixed at both ends because of the rigid
footing at the base secured to a strong floor, and the deep spandrel and rigid diaphragm at the
top. Flange effect was considered in the estimation of the elastic stiffness of each pier. However, global rocking (overturning moment) and flange effect were not considered in the lateral strength calculation. The material properties given in Table 1 were used for the analysis.
The shear modulus was taken to be 40% of the elastic modulus. The model proposed by
Magenes and Calvi doesn’t consider the estimation of elastic stiffness. The other two models,
however, use the mechanics-based approach, considering both flexural and shear deformations, to estimate the elastic stiffness of piers. In the present analysis the lateral stiffness of the
structure is calculated as the sum of the values for stiffness of the individual piers corrected
for height, as given in Equation 4.
kb ¼
n
X
EQ-TARGET;temp:intralink-;e4;62;409
i¼1
kpi
H pi
Hw
(4)
Where kb and H w are the lateral stiffness and height of the horizontal load level, respectively,
and kpi and H pi are the lateral stiffness and height of ith pier, respectively.
The ultimate pier drift is converted to wall drift using the equation (Equation 5) originally
proposed by Lang (2002) and adopted by Javed (2009).
Figure 20. Definition of piers for estimating lateral response of model.
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SHAHZADA ET AL.
δuw
EQ-TARGET;temp:intralink-;e5;41;640
H p δup
¼ 1þ
− 1 δyw
H b δyp
(5)
Where δup and δyp are the ultimate and yield drifts of the pier, respectively, δuw and δyw are the
ultimate and yield drifts of the wall, respectively, and H p and H w are the heights of the pier
and wall respectively. The height of the wall is equal to the distance from the base to the
horizontal load level. δyw is assumed to be equal to δyp . The diaphragm is assumed to be rigid
and connected to the wall such that the displacements at the top of walls are equal.
ASCE STANDARD
Three failure modes—rocking, bed-joint sliding shear, and toe crushing—are considered
in ASCE’s standard for URM piers. In this standard, the lateral strength is estimated as the
lowest strength calculated from equations Equations 7-3, 7-4, and 7-5. Further, rocking is
considered to be a deformation control action, while bed-joint sliding shear and toe crushing
are considered to be force-control actions. A complete force-deformation curve for a URM
pier is defined in Figure 7-1(b) of the standard. The deformation capacities d (corresponding
to peak strength) and e (corresponding to a 40% degradation in lateral strength) are given in
Table 7-4 of the standard. Points B and C of the curve are assumed to have the same strength,
while points C and D have the same drift.
MAGENES AND CALVI MODEL
Magenes and Calvi proposed the following three equations to estimate the lateral strength
as the minimum strength corresponding to toe crushing ðV tc Þ, shear sliding ðV sl Þ, and diagonal tension failure ðV dt Þ of URM piers:
L2p t p p
p
1−
V tc ¼ ψ
(6)
Hp 2
0.85f ’m
EQ-TARGET;temp:intralink-;e6;41;342
V sl ¼ μP
(7)
EQ-TARGET;temp:intralink-;e7;41;287
V dt
EQ-TARGET;temp:intralink-;e8;41;253
f tu Lp t
¼
b
rffiffiffiffiffiffiffiffiffiffiffiffiffiffi
p
1þ ;
f tu
b¼
Hp
; 1.0 ≤ b ≤ 1.5
Lp
(8)
Where ψ is the boundary condition factor, taken to be 2 when the pier is fixed at both ends
and 1 when the pier is fixed on one end and free to rotate on the other; p is the vertical stress
on the pier; f ’ m is the compressive strength of the masonry; Lp , H p , and t p are the length,
height, and thickness of the pier, respectively; μ represents the sliding coefficient of the
masonry joints; P is the vertical load on the pier; and f tu is the diagonal tensile strength
of the masonry. Equation 6, above, is equivalent to Equation 7-5 of the ASCE standard
except for the factor 0.85, which is 0.70 in the standard.
Magenes and Calvi considered toe crushing as the ultimate result of rocking and recommended a limiting drift value of 1.0% for rocking mode and 0.50% for the other two shear
failure modes.
EXPERIMENTAL SEISMIC PERFORMANCE EVALUATION OF UNREINFORCED BRICK MASONRY BUILDINGS
1287
LANG MODEL
Lang (2002) proposed a different approach for the estimation of lateral load capacity of a
URM building based on a theory of elasticity. The lateral load capacity, which violates
neither the stress nor the sliding criteria, is:
Vm ¼
EQ-TARGET;temp:intralink-;e9;62;586
f my ·lw ·t·N· tan ϕ
N þ N·ðtan ϕÞ2 þ 2·f my ·t·ho · tan ϕ
(9)
Where f my is the compressive strength of masonry parallel to the bed joints, taken as 30% of
the compressive strength of the masonry perpendicular to bed joints; ϕ is the angle of the
internal friction of the masonry; lw , t, and ho are the length, thickness, and height to the point
of inflection (equal to half the height of the pier in the present case) of the pier, respectively;
and N is the total vertical load on the pier.
The ultimate drift of the pier is taken to be 0.80%, which is modified for vertical stress
and pier aspect ratio according to the equation given below:
8
hp ∕lw < 0.5
< 0.8ð0.8 − 0.25σ n Þ
0.5 < hp ∕lw < 1.5
(10)
δu ¼ ð0.8 − 0.25σ n Þ
:
1.2ð0.8 − 0.25σ n Þ
hp ∕lw > 0.5
EQ-TARGET;temp:intralink-;e10;62;456
where σ n is the vertical stress in MPa, and hp is the height of pier. An upper limit on pier
ductility—the ratio of ultimate drift to yield drift of the pier—is set at 12.
COMPARISON
The measured and estimated lateral stiffness, lateral strength, and ultimate drift of the test
structure are shown in Table 4. The estimated stiffness is greater than the measured stiffness
by 10%. The reason for this difference is that the measured stiffness is based on the secant
Table 4.
Measured vs. estimated force-deformation characteristics
Force-Deformation Stiffness, Strength, Ultimate
Parameters
kips/in.
kips
Drift, (%)
Measured
Response
421.3
23.9
0.50
ASCE Standard
462.4
16.4
0.31
-
16.7
0.26
462.4
16.3
0.14
Magenes and
Calvi
Lang
Failure Mode
Mixed shear-rocking failure mode with global
rocking. Piers toward ends (P1, P2, P3, P5)
showed some vertical cracks, P4 showed
rocking mode toward the test end
Piers P1, P3, P4, and P5 failed due to rocking
while P2 showed a bed-joint shear sliding
failure mode
Piers P1 and P4 failed due to toe crushing, and
P2, P3, and P5 showed diagonal shear sliding
The lateral load corresponds to a condition
where the maximum stresses and sliding occur
simultaneously
1288
SHAHZADA ET AL.
stiffness while the estimated stiffness is the initial elastic stiffness, which should be greater
than the secant stiffness because of the nonlinear behavior. Other researchers have defined
factors to calculate the effective stiffness of a pier from its elastic stiffness; for example, Javed
(2009) used a factor of 0.75 and Lang (2002) defined a range from 0.50–0.70. In the current
study the factor comes out to be 0.90, which is quite high when compared with the values
provided by previous researchers.
The estimated lateral strengths from all three methods match each other but are 46% less
than the measured strength. This significant difference is due to the effects of the overturning
moment and flange behavior, which are neglected in the estimated strength. Thus the overturning moment and flange behavior have a significant effect on lateral strength. However,
strength, as defined by ASCE 41, is in the lower bounds for force-based actions and in the
expected range for displacement-based actions. They are not intended to represent actual
strengths because of uncertainty and safety. The actual strength will certainly be higher
than the estimated strength.
All three models conservatively estimate the ultimate drift of the test structure. Global
rocking, which was neglected in the estimated response, is the main reason for the difference
in the measured and estimated deformation capacities. Furthermore, rocking is a stable
mechanism that may have a very high deflection capacity but the models limit the deflection
capacity to avoid any associated failure. The ultimate drift from the model proposed by the
Lang Model is relatively low because of the limit imposed on the ductility of the pier.
CONCLUDING REMARKS
A full-scale unreinforced brick masonry building was tested under reverse cyclic quasistatic loading to evaluate the seismic performance of a typical brick masonry building in
northern Pakistan. The measured response was compared with the estimated response
using methodologies proposed by various researchers around the world. The following conclusions can be made:
•
•
•
•
The properties of the materials used in the construction of unreinforced brick
masonry buildings in Pakistan, namely the initial rate of absorption (IRA) of the
bricks and the compressive strength of the mortar, are different from those commonly used in other parts of the world. The IRA is very high (91.7 g/min/
30in.2) which results in a very weak bond between the bricks and mortar and, consequently, low diagonal tensile strength (7.3 psi) and compressive strength (438 psi).
The damage pattern of the test structure was a combination of shear and flexural
cracks. However, the predominant failure mode was shear. High compressive stresses developed at the two ends of the in-plane walls due to overturning moments,
resulting in vertical splitting at the wall corners.
The test structure has a very large deformation capacity, resulting in a high ductility
factor (12.5), response modification factor (4.9), and displacement amplification factor (2.6), which is due to global rocking of the test structure. The results, however,
could not be generalized for other URM buildings with different configurations.
The equivalent viscous damping (6.0%) and the effective stiffness (90% of the analytical elastic stiffness) of the test structure are almost similar to those of other URM
buildings tested worldwide.
EXPERIMENTAL SEISMIC PERFORMANCE EVALUATION OF UNREINFORCED BRICK MASONRY BUILDINGS
•
1289
Any of the three models—the ASCE standard, the Magenes and Calvi Model, or the
Lang Model—can be used for the lateral load capacity evaluation of URM buildings
constructed in northern Pakistan. The models conservatively estimate the lateral
strength (70% of the actual strength) and deformation capacity. The difference is
due to the neglected contribution of the flange effect and global rocking, and
the inherent safety margins in code values.
ACKNOWLEDGEMENTS
The authors are grateful to the Higher Education Commission of Pakistan for providing
financial support under the International Linkages of Pakistani Universities with Foreign
Universities project. The University of Engineering and Technology in Peshawar provided
support through access to their testing facilities. Valuable comments and suggestions were
made by Professor D. P. Abrams, University of Illinois at Urbana-Champaign. These contributions are highly appreciated. The authors are grateful to the reviewers for their precious
suggestions and comments, which have enhanced the quality of the paper. The first author is
grateful to the Mid-America Earthquake Center, at the University of Illinois at Urbana-Champaign for hosting him as a visiting scholar.
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(Received 29 September 2010; accepted 27 September 2011)