Download Seismic vulnerability of the Himalayan half-dressed rubble

Nat. Hazards Earth Syst. Sci., 12, 3441–3454, 2012
www.nat-hazards-earth-syst-sci.net/12/3441/2012/
doi:10.5194/nhess-12-3441-2012
© Author(s) 2012. CC Attribution 3.0 License.
Natural Hazards
and Earth
System Sciences
Seismic vulnerability of the Himalayan half-dressed rubble stone
masonry structures, experimental and analytical studies
N. Ahmad1,2 , Q. Ali2 , M. Ashraf3 , B. Alam3 , and A. Naeem3
1 ROSE
School-IUSS Pavia, Pavia, Italy
Engineering Center, University of Engineering & Technology (UET), Peshawar, Pakistan
3 Civil Engineering Department, University of Engineering & Technology (UET), Peshawar, Pakistan
2 Earthquake
Correspondence to: N. Ahmad ([email protected])
Received: 27 April 2012 – Revised: 10 July 2012 – Accepted: 9 October 2012 – Published: 21 November 2012
Abstract. Half-Dressed rubble stone (DS) masonry structures as found in the Himalayan region are investigated using experimental and analytical studies. The experimental
study included a shake table test on a one-third scaled structural model, a representative of DS masonry structure employed for public critical facilities, e.g. school buildings,
offices, health care units, etc. The aim of the experimental study was to understand the damage mechanism of the
model, develop damage scale towards deformation-based assessment and retrieve the lateral force-deformation response
of the model besides its elastic dynamic properties, i.e. fundamental vibration period and elastic damping. The analytical study included fragility analysis of building prototypes using a fully probabilistic nonlinear dynamic method.
The prototypes are designed as SDOF systems assigned
with lateral, force-deformation constitutive law (obtained experimentally). Uncertainties in the constitutive law, i.e. lateral stiffness, strength and deformation limits, are considered through random Monte Carlo simulation. Fifty prototype buildings are analyzed using a suite of ten natural accelerograms and an incremental dynamic analysis technique.
Fragility and vulnerability functions are derived for the damageability assessment of structures, economic loss and casualty estimation during an earthquake given the ground shaking intensity, essential within the context of risk assessment
of existing stock aiming towards risk mitigation and disaster
risk reduction.
1
Introduction
Mountainous regions in the Himalayan largely employ stone
masonry in building constructions, either as load-bearing
walls or as an infill in timber framing structures. For example, in Pakistan stone masonry is used in construction in 40 to
80 percent of sub-administrative units (Tehsil) of the state of
Khyber Pakhtoonkhwa and Punjab (Maqsood and Schwarz,
2008). This is due to the fact that stone material is abundantly
available in northern parts of Pakistan. Low-cost and lowskilled labour may be employed for construction work that
consequently results in overall economical schemes.
Stone masonry buildings in the Himalayan region consist
of two-wythe, load-bearing walls (Fig. 1). The void between
the wythes is left empty or filled with small stones. For rural constructions, i.e. residential buildings, bearing walls are
built in rubble stone masonry in which undressed stone units
are laid randomly in mud mortar or simply placed in dry
form, whereas half-dressed stone units laid in cement mortar
are employed for urban constructions, i.e. public buildings.
The buildings are provided with wooden floors in case of rural constructions, whereas reinforced concrete slab floors and
roofs are used in the case of urban constructions (Ali and Mohammad, 2006; Gupta et al., 2008). The public buildings are
also provided with a lightly reinforced roof band (ring beam)
at the top of the walls.
Stone masonry buildings, having thick walls provided with
heavy roofing, perform excellently in protecting the inside of
the building from the extremity of the outside temperature
and humidity, a characteristic essential in most of the Himalayan region. However, due to the low quality of construction, this structure type has performed very poorly in recent
Published by Copernicus Publications on behalf of the European Geosciences Union.
2008). The public buildings are provided
that represent critical facilities like sch
also
roof band
offices,
healthstructures
care units, e
3442 with aN.lightly
Ahmad et reinforced
al.: Seismic vulnerability
of the Himalayanbuildings,
half-dressed rubble
stone masonry
are constructed of load bearing walls b
(ring beam) at the top of the walls.
in the Governor’s estate in Darjeeling were damaged during
in half-dressed stone masonry in cem
the recent 2011 Sikkim earthquake in India. Typical damages
with
reinforced
concr
observed inmortar
Darjeelingprovided
public buildings
included
separation
at wall junctions
and
in-plane
shear
failure
(EERI,
2012).
slab floors and roofing. In the recent 20
The complex seismic behavior of this construction type renKashmir
ab
ders its modeling
timid forearthquake
analytical studies.unfortunately
Thus, experimental investigations
essential to calibrate
19,000 arechildren
died engineering
because of
tools and help develop simplified hypotheses for seismic
collapse
of school
buildings
of
analysis and
vulnerability assessment
of the considered
construction type.
mentioned characteristics (EERI, 200
This study presents research carried out on the seismic
state of
geodynamic
assessmentThe
of DScurrent
masonry structures
employed
for public setting
buildings (schools,
offices, health
units, etc.).
the region
hascareshown
toIt isbepartcapable
of the research program focusing on the seismic vulnerabilFigure
1
Cross-section
of
the
typical
stone
masonry
Fig. 1. Cross-section of the typical stone masonry load-bearing
trigger further future large earthquakes
load
practiced
Himalayan.
From ity assessment of typical building types in the Himalayan rewalls bearing
practiced in walls
the Himalayan
region.in
From
left to right: halftowards
mitigation
and disaster
risk reducor risk
even
greater
than
magnitude
dressed
wall employed
for publicmasonry
buildings (in-wall gion aimingto
left
to coursed
right:masonry
half-dressed
coursed
tion
in
the
region
(Ali
et
al.,
2012).
Fragility
and
vulnerabilvestigated in the present study) and undressed random masonry wall
(Avouac
et by
al.,means2006;
Bilham,
200
employed
for public buildings (investigated in the ity functions
are derived herein
of analytical
and
employed for rural residential buildings.
present study) and undressed random masonry wall experimental
investigations.
The presentessential
study provides eswhich
makes
to asse
sential input for risk assessment of the considered DS maemployed for rural residential buildings.
communicate and consequently mitig
sonry structures aiming towards risk mitigation (pre-event
and past earthquakes (e.g., Ali and Mohammad, 2006; Bothphase) andthe
disaster
riskof
reduction
(post-eventvulnerable
phase) in the stock.
risk
the existing
ara and Brzev,
2011; Guptabuildings
et al., 2008; Kaushik
et al., 2006;
Stone
masonry
having
thick Himalayan region in general and northern Pakistan in particMurty, 2003; Naseer et al., 2010; Rai and Murthy, 2006,).
walls
provided with heavy roofing perform ular.
Figure 2 reports an office building
The poor performance of stone masonry buildings have also
been observedin
in other
parts of thethe
worldinside
(Adanur, 2010;
excellent
protecting
of the
Mansehra
City
of Pakistan
that w
2 Experimental
investigation
of half-dressed
stone
Akkar et al., 2011; Gulkan et al., 1992; Ingham and Griffith,
building
from
the
extremity
of
the
outside
masonry
model by means
of dynamic shake
table test
moderately
damaged
in 2005
Kashmir M
2011; Spence, 2007a).
temperature
and humidity,
characteristic
Earthquakes observations
may provide a
significant
qualita7.6objective
earthquake.
Typical
2.1 Aim and
of the dynamic
test damages observ
tive information on the earthquake resistance and vulneraessential
in
most
of
the
Himalayan
region.
in the building are also described. This c
bility of stone masonry buildings common in the Himalayan
Earthquake observations in the Himalayan region have
However,
due
to
the
low
quality
of
region. However, there is very limited quantitative informareported
with
of VII-VIII
shown verywas
complex
behavior of
ruble intensity
masonry structures,
tion available to help this
derive analytical
fragility and
vulnera-has including in-plane shear cracking, damage to walls from roof
construction
structure
type
MMI scale (Javed et al., 2008). Sim
bility functions for half-dressed stone DS masonry in urban
thrust, delamination of stone units, damage to building corperformed
very
poorly
in
recent
and
past
structures found in the Himalayan region. It is very essential
type bulging,
of collapse
dressed
stone
maso
ners, out-of-plane
of walls
and totalDS
colto
investigate
this
construction
type,
as
most
of
the
public
earthquakes (Ali and Mohammad, 2006; lapse of structures
(EERI,found
2012; Javed
al.,Governor’s
2008; Naseer
buildings
in etthe
estate
buildings that represent critical facilities like school buildet al., 2010). This fact makes the analytical modeling of rubBothara
and
Brzev,
2011;
Gupta
et
al.,
ings, offices, health care units, etc., are constructed of loadDarjeeling
damaged
during
ble stone masonry
structureswere
less confident
for seismic
anal- the rec
bearing walls
built in half-dressed
stone masonry
in cement
2008;
Kaushik
et al., 2006;
Murty,
2003; ysis, which2011
makes the
experimental
investigation in
essential.
Sikkim
earthquake
India. Typi
mortar and are provided with reinforced concrete slab floors
The
aim
of
the
dynamic
test
was
to
retrieve
the
elastic
dyNaseer
et Inal.,
Rai
and earthquake,
Murthy,about
2006, namic properties
and roofing.
the 2010;
recent 2005
Kashmir
damages
observed
Darjeeling
pub
(i.e. fundamental
vibrationin
period
and elas19 000 children
unfortunately
because
of the collapse of tic viscous damping) of the building, understand the damage
among
others).
The died
poor
performance
buildings included separation at w
of school buildings of the mentioned characteristics (EERI,
mechanism
of the model, obtain lateral force-deformation restone
buildings
been
2006). Themasonry
current state of geodynamic
settingshave
in the region
and limits
in-plane
shear failure (EE
sponse and junctions
deduce performance
for deformation-based
has shown to also
be capable
of triggering
further
observed
in other
parts
of future
the large
world assessment2012).
of the building
model.
These
properties
will be
The complex seismic
behavior
earthquakes up to or even greater than a magnitude 8 (Avouac
employed
later
for
analytical
modeling
and
fragility
analysis
(Adanur,
2010;
Akkar
et
al.,
2011;
Gulkan
et al., 2006; Bilham, 2004), which makes it essential to asthisengineering
construction
using simplified
tools. type renders its modell
communicate
consequently
mitigate
the risk of2011;
the
etsess,al.,
1992; and
Ingham
and
Griffith,
timid for analytical studies. Th
existing vulnerable stock.
2.2 Model description
Spence,
2007a).
experimental investigations are essentia
Figure 2 reports an office building in Mansehra City of
Pakistan that was moderately damaged in the 2005 KashThe DS masonry structure investigated herein is a represencalibrate engineering tools and h
mir Mw = 7.6 earthquake. Typical damages observed in the
tative model of public buildings, e.g. school buildings, ofEarthquakes
observations
may
provide
develop
simplified
hypotheses
building are also described. This city was reported with an
fice buildings,
health care
units, etc., common
in the north-for seism
significant
qualitative
on the ern areas ofanalysis
intensity of VII–VIII
on the MMI information
scale (Javed et al., 2008).
Pakistan. Theand
modelvulnerability
is designed respecting
the
assessment
Similar types of dressed stone DS masonry buildings found
similitude requirements for a reduced scaled Simple Model
earthquake resistance and vulnerability of
the considered construction type.
stone
masonry
buildings
common
in
the
Nat. Hazards Earth Syst. Sci., 12, 3441–3454, 2012
www.nat-hazards-earth-syst-sci.net/12/3441/2012/
Himalayan. However, there is very limited
This study presents research carried out
quantitative information available to help
the seismic assessment of DS maso
375
OUT SIDE
375
IN SID E
THE ROOM
N. Ahmad et al.: Seismic vulnerability of the Himalayan half-dressed rubble stone masonry structures
3443
Page 1/1
Minor diagonal shear cracks
observed in load-bearing
walls.
Horizontal
large
cracks
developed between the floor
and walls.
Separation of paint coating is
observed in slab and walls.
Delamination of wall is
observed whereby stone units
fell out of walls.
Description: A two-story office building situated in
Mansehra City, Pakistan. It was subjected to the 2005
Kashmir earthquake Mw 7.6 at a distance of about 40 km
from seismic source.
Fig. 2. A moderately damaged half-dressed stone DS masonry structure. From left to right: view of the building and description of the
observed main damages in the building.
(Tomazevic, 2000; Ali et al., 2012). A scale factor of 3 is used
to reduce the dimensions of the model, whereas a scale factor of 1 is used for scaling the mechanical properties (stressstrain constitutive law) of materials (stone units, mortar, masonry, concrete, steel).
Table 1 reports the characteristics of the simple model and
similitude requirements for model-to-prototype conversion
of quantities. Figure 3 shows details of the building model
tested at the Earthquake Engineering Center of UET Peshawar.
2.3
2.3.1
Testing program
the model. Figure 4 provides details on the instrumentation
of building model.
2.3.2
Characteristics of input excitation
The North–South component of the Kobe 1995 record is used
for the dynamic excitation of the model. The acceleration
record is modified to respect the prototype to model similitude requirements (Tomazevic, 2000). The time duration and
predominant period of the record was reduced by 3. It resulted in a compressed acceleration time history with peak
ground acceleration (PGA) of 0.83 g, predominant period of
0.12 s and total duration of 10 s.
Model setup and instrumentation
2.3.3
The structure model was built on a strong concrete pad which
was firmly connected to the shake table by means of bolts.
The model was tested in the weaker direction. Three accelerometers were installed on the model: two at the base to
record the input excitation and one at the roof level to record
the response acceleration of the model. Four displacement
transducers were installed to record the displacement time
history of the model: two at the base of the model and two at
the roof level. The difference of the top and bottom transducers will provide an estimate of the relative lateral deformation
of the model. All the gauges were connected to a data acquisition system where the data (acceleration and displacement
time history) were recorded at a time step of 0.005 s. Cameras were installed to continuously monitor the behavior of
Testing scheme
The model was subjected to dynamic excitation in three
phases. The input excitations were designed accordingly to
push the structure from elastic to inelastic to collapse state,
thereby enabling the monitoring of the complete response of
the model. The first phase included a low amplitude, 5 percent scaled record excitation of the model, having a PGA of
0.04 g. This phase was mainly included to retrieve the dynamic characteristics, i.e. fundamental vibration period and
viscous damping, of the model. For the second and third
run, the record was scaled up in 5 percent increments in
the excitation amplitude resulting in a PGA of 0.083 g and
0.20 g, respectively. The model was completely collapsed
in the last run. The test video can be viewed online at the
Copernicus Publications
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Table 1. Characteristics of the simple test model and similitude requirements for quantities conversion
of The Tested
Model of the HimalayanSimilitude
Requirements
formasonry
Simple Model
N. Characteristics
Ahmad et al.: Seismic
vulnerability
half-dressed
rubble stone
structures
3444
Physical Quantity
Prototype Building
Model
Building for quantities
Table 1. Characteristics
of the simple test model1/3
andScaled
similitude
requirements
conversion.
Scale Factor
3.00
Length
Load bearing walls: 450mm thick Load bearing walls: 150mm thick
Characteristics
of
The
Tested
Model
Similitude
Requirements
two wythes coursed half-dressed two wythes coursed half-dressed
Stress, Strengthfor Simple Model1.00
stone masonry.
stone masonry.
1.00
Strain
1/3Cement-sand
Scaled modelmortar
building
Prototype
building mortar with Mortar:
Physical quantity Scale factor
Mortar:
Cement-sand
with 4
Load-bearing
walls:
150
mm
thick
Load-bearing
walls:
450
mm
thick
4 MPa compressive strength.
MPa compressive strength.
1.00
Specific
Mass
Length
3.00
two wythes
half-dressed
two wythes
coursed
half-dressed
Concrete:
Normal
concrete
with stone
Concrete:
Normalcoursed
concrete
with stone Stress, Strength
1.00 3.00
Displacement
masonry.
masonry. strength of 17 MPa.
compressive
compressive
strength of 17 MPa.
1.00
Mortar: Cement-sand mortar with Mortar: Cement-sand mortar with Strain
Force
Horizontal Band: 150mm thick Horizontal Band: 50mm thick beam
Specific Mass
1.00 9.00
4 MPa compressive strength.
4 MPa compressive strength.
beam lightly reinforced with 4 10 lightly reinforced with 4 3
Displacement
3.00 3.00
Concrete: Normal concrete with com- Concrete: Normal concrete with
Time
longitudinal bars tied with 1 3 longitudinal bars tied with 1 1
Force
9.00
strength of 17 MPa.
pressive strength of 17 MPa.
stirrup
provided at 150mm center- stirrupcompressive
provided at 50mm center-toFrequency
Time
3.00 0.33
Horizontal
Band:
50
mm
thick
beam
Horizontal
Band:
150
mm
thick
beam
to-center distance.
center distance.
Frequency
0.33 1.00
lightly reinforced with 4–10 longitudi- lightly reinforced with 4–3 longitudinal Velocity
Roof:
150mm
thick
reinforced
Roof:
50mm
thick
reinforced
Velocity
1.00
nal bars tied with 1–3 stirrup provided bars tied with 1–1 stirrup provided at
concrete slab.
concrete slab.
Acceleration
0.33 0.33
Acceleration
50 mm center-to-center distance.
at 150 mm center-to-center distance.
Roof: 150 mm thick reinforced concrete
slab.
Roof: 50 mm thick reinforced concrete
slab.
5" [127.00mm]
5' [1524.00mm]
6" [152.40mm]
3' [914.40]
W
SINGLE ROOM STONE
MESONARY
MODEL
W
6" [152.40mm]
D
5" [127.00mm]
4' [1219.20mm]
4" [101.60mm]
6" [152.40mm]
6" [152.40mm]
4" [101.60mm]
(1/3 Scaled DS Masonry Structures Model)
(Plan View)
2" [50.80mm]
1' [304.80]
WINDOW
1' [304.80]
1'-212" [368.30]
Concrete Pad
1'-6" [457.20]
3' [914.40mm]
1'-6" [457.20]
3' [914.40mm]
4" [101.60mm]
3" [76.20]
WINDOW
1'-6" [457.20]
1'-6" [457.20]
3" [76.20]
2" [50.80mm]
Concrete Pad
4" [101.60mm]
(Front and Back Elevation View)
Fig. 3. Geometric details of the structural model tested at the Earthquake Engineering Center of UET Peshawar.
Nat. Hazards Earth Syst. Sci., 12, 3441–3454, 2012
www.nat-hazards-earth-syst-sci.net/12/3441/2012/
N. Ahmad et al.: Seismic vulnerability of the Himalayan half-dressed rubble stone masonry structures
YouTube videos database maintained by EERI Institute of
USA (http://www.youtube.com/watch?v=r8JDj-DFzJs).
2.4
2.4.1
Observed behavior and damage mechanism
Global performance under input excitation
The first test run at PGA of 0.04 g did not cause any appreciable damage in the model. The building behaved primarily
in a boxlike manner. A horizontal crack was developed between the walls and ring beam during the second test run at
PGA of 0.08 g. Slight cracks were also developed in the inplane and out-of-plane walls. The building collapsed during
the third test run at PGA of 0.20 g.
2.4.2
Observed main damages
During the last test cracks developed in the in-plane and
out-of-plane walls, which widened largely with increased
shaking intensity. Damage in the in-plane walls included diagonal, horizontal and inclined pattern cracks. Horizontal
and inclined cracks developed in the out-of-plane walls. The
widening of cracks and separation of roof from walls upon
increased shaking intensity led to extensive damage in the
in-plane walls, delamination of stone units from the out-ofplane walls, damage to corners and consequent stone falling,
out-of-plane collapse of walls and complete collapse of the
building model. The observed behavior of the model in the
initial stages were comparable with the observed damages in
the recent 2005 Kashmir earthquake for public buildings (see
Fig. 2).
2.4.3
Observed global damage mechanism and
comparison with EMS-98 scale
The behavior of the model was closely monitored during the
last run to deduce damage states of the buildings and develop
a damage scale towards performance-based assessment of the
building for future applications. Figure 5 reports the global
damage states of the building observed during the test with
increased shaking level. The observed damage states are also
compared with the EMS-98: European Macroseismic Scale
(Grunthal et al., 1998) for masonry buildings. It is a standard
scale adopted in Europe for masonry building damage rating
within the context of post-earthquake screening, vulnerability and fragility analysis. It is observed that the two scales
are comparable for DS1 and DS2 damage states. However,
the EMS-98 damage scale seems more conservative for DS3
and DS4 limit states, i.e. the extent of building damage specified by the EMS-98 scale is more than the observed damages in the considered building. The observed damage, particularly of the floor, is different than the EMS-98 specified
damage pattern. The floor for the considered building failed
in an abrupt manner upon the complete damage and spalling
of load-bearing walls, which is due to the rigid nature of the
floor and its monolithic connection with the walls. This type
www.nat-hazards-earth-syst-sci.net/12/3441/2012/
3445
of roof collapse was also observed during the 2005 Kashmir earthquake for block masonry buildings with monolithic
RCC roof slab (Bothara and Brzev, 2011). Generally, the typical roof used for European masonry buildings is composed
of timber, roof trusses braced with timber, covered with an
iron sheet (in some cases) and roof tiles. For these types of
buildings, the tiles from the roof detach in a progressing manner during earthquakes, unlike the rigid RCC slab employed
for the considered buildings.
2.4.4
Damage mechanism of component walls
The behavior of individual component walls, i.e. in-plane
walls and out-of-plane walls, were also closely monitored
with increased shaking level, in order to fully understand
the seismic response of each component wall. Figure 6 reports the damage mechanism and cracking propagation for
each component wall. It can be observed that the response
of rubble masonry structure is very complex, which is due to
the random nature of rubble masonry and rough construction
work.
For example, one of the piers (with similar characteristics)
of the in-plane wall developed diagonal shear mechanism,
whereas the other pier developed sliding and rocking mechanism, with progressing disintegration of piers. Such complex behavior, which is due to the random nature of masonry,
cannot be simulated with available numerical tools and thus
presents a challenge for computing tools for seismic behavior assessment of rubble stone masonry buildings. This fact
also point to the importance of experimental investigation of
rubble masonry buildings for understanding the seismic behavior and evaluating the seismic performance.
2.4.5
Dynamic characteristics of the building model:
walls
The low amplitude input excitation (PGA 0.04 g) was primarily meant to help retrieve the elastic dynamic properties of the model, including fundamental vibration period
T0 and damping coefficient ζ . Both the vibration period T0
and damping were obtained from the response acceleration
time history (Fig. 7). The period is obtained using the basic
definition of period of an oscillating body (i.e. the time required for a complete oscillation). An average value of 0.07 s
is obtained for the vibration period. The decay function for
the time history of the response acceleration as proposed by
Chopra (2003) is used to calculate the model damping
A1
1
Ln
,
(1)
ζ=
2nπ
An
where ζ represents elastic damping coefficient; A1 represents the peak amplitude of response acceleration at reference point 1; An represents the peak amplitude of response
acceleration at reference point after n cycles; and n represents the number of cycles between the peaks. The model
Nat. Hazards Earth Syst. Sci., 12, 3441–3454, 2012
3446
online at the YouTube videos database
Characteristics of Input Excitation: The
maintained by EERI Institute of USA
north-south component of the Kobe 1995
(http://www.youtube.com/watch?v=r8JDjrecord is used for the dynamic excitation
DFzJs&feature=plcp&context=C45c7e56VDvjVQa1PpcFMfBU
of theN.model.
acceleration
record isof the Himalayan
0O_Ox2aFLz4o5w8JWsi84jR0y4ZEw%3D).
AhmadThe
et al.:
Seismic vulnerability
half-dressed rubble stone masonry structures
D4,D2
W
A3
SINGLE ROOM STONE
MESONARY
MODEL
A1
A2
W
D
Instrument Type
Designation
D3,D1
Accelerometer
A1
A2
Displacement Transducer
A3
D1
D2
D3
D4
Figure 4 Testing setup and instrumentation details of the building model tested on shake table at the Earthquake
Engineering
Center
of Peshawar.
Fig. 4. Testing
setup and
instrumentation
details of the building model tested on shake table at the Earthquake Engineering Center of
Peshawar.
gives an estimate of 4.008 % for damping using the positive
peaks and 5.404 % using the negative peaks. On average a
damping value of 4.71 % is computed, which may be approximated as 5 % for the building model.
3
3.1
Fragility assessment of half-dressed stone DS
masonry structures
Seismic assessment framework
Many available techniques may be employed to derive the
fragility functions of structures (Borzi et al., 2008; Calvi et
al., 2006; Crowley, 2004; Coburn and Spence, 2002; D’Ayala
et al., 1997; Erberik, 2008; Kappos and Panagopoulos, 2010;
Porter et al., 2007; Rota et al., 2010, among others). The
present study included a fully probabilistic, nonlinear, dynamic reliability-based method (NDRM) recently developed
by Ahmad (2011) for the seismic performance evaluation and
fragility analysis of considered structure, as employed recently for other structure types (Ahmad et al., 2012a, b). This
method is found to provide reasonable estimates of building
damageability when compared with earthquake observations
in Pakistan (Ahmad et al., 2012c).
The NDRM is a probabilistic method for calculating the
damage exceedance probability of structures for a specified
ground motion. The method of incremental dynamic analysis (IDA) proposed by Vamvatsikos and Cornell (2002) was
used to derive the structure response curve that correlates the
shaking intensity with the drift demand. The method incorporates total uncertainties in the drift demand. The drift demand on structure is convolved then with the structure drift
capacity for a specified limit state to obtain the exceedance
probability of target limit state at a given shaking level. It is
Nat. Hazards Earth Syst. Sci., 12, 3441–3454, 2012
carried out for all the intensity levels to allow the derivation
of fragility functions.
3.2
Mathematical modeling
Other available, more or less sophisticated modeling techniques may be calibrated for global seismic analysis of masonry buildings (Magenes and Fontana, 1998; Galasco et al.,
2002; Kappos et al., 2002). However, these methods cannot be confidently extended for seismic response evaluation
of rubble masonry buildings due to its complex behavior as
observed during the experimental investigation. The present
study included single degree of freedom (SDOF) mathematical model for seismic analysis. The SDOF system is assigned
with observing the global lateral force-deformation response
of the building simulating the lateral stiffness, strength and
deformation capacity of the tested building model. Thus,
fully respecting the fundamental response parameters importance for global dynamic seismic analysis and response evaluation of buildings (Elnashai and Di-Sarno, 2008).
The SDOF system is assigned with lateral forcedeformation constitutive law, which is derived from the observed response of the model, i.e. the peak drift and the corresponding base shear observed during each test run. The
model is assigned with the mass of the building model,
which is adjusted to achieve the fundamental vibration period (T0 0.07 s) of the model as observed during the test. The
model is assigned with 5 % elastic viscous damping, as observed during the low amplitude test. For dynamic seismic
analysis, the Rayleigh damping model with tangent stiffness proportionality is used in the present study. The system of nonlinear equations in the analysis is solved using the KrylovNewton algorithm (Scott and Fenves, 2010)
and the average acceleration Newmark time-stepping method
www.nat-hazards-earth-syst-sci.net/12/3441/2012/
N. Ahmad et al.: Seismic vulnerability of the Himalayan half-dressed rubble stone masonry structures
3447
Damage Description and Comparison with EMS Damage Scale
Present Study
EMS-98
Damage States
Grade–1: DS1
Slight diagonal cracks are initiated in walls
parallel to excitation direction.
Horizontal cracks initiated at the opening base
corner of walls parallel to excitation, likely to
forming short pier.
Horizontal cracks initiated between walls and
roof.
Vertical cracks initiated at the end of walls
parallel to excitation direction, likely to form
failure plane for detachment of walls
perpendicular to excitations i.e. face loaded
walls.
Horizontal cracks initiated in the face loaded
walls at mid-height and top of wall.
Inclined cracks initiated in the face loaded
walls, likely to form a wedge for out-of-plane
failure.
Grade–2: DS2
Diagonal cracking increased in walls parallel
to excitation direction.
Horizontal cracks developed at the opening
base and top corners of walls parallel to
excitation, short pier is formed.
Horizontal cracks fully developed between
walls and roof.
Inclined cracks developed at the end of walls
parallel to excitation direction, failure plane for
detachment of face loaded wall is developed.
Horizontal cracks fully developed in the face
loaded walls at mid-height and top of wall.
Inclined cracks developed in the face loaded
walls, a wedge for out-of-plane failure is
formed.
Grade–3: DS3
Diagonal cracking widened significantly in
walls parallel to excitation direction.
Horizontal cracks developed at the opening
base and top corners of walls parallel to
excitation, short pier is formed to slide and
rock.
Horizontal cracks fully developed between
walls and roof.
Inclined cracks fully developed at the end of
walls parallel to excitation direction,
detachment of face loaded wall is likely to
occur.
Horizontal cracks fully developed in the face
loaded walls at mid-height and top of wall. Top
wall portion is likely to rock.
Inclined and horizontal cracks developed in the
face loaded walls, a wedge is likely to separate.
Grade–4: DS4
Diagonal cracking widened extensively in
walls parallel to excitation direction.
Horizontal cracks fully formed at the opening
base and top corners of walls parallel to
excitation, short pier is responding through inplane sliding and rocking.
The face loaded wall fully detached from walls
parallel to excitation direction, separating a
wing from transverse walls. The face loaded
wall fully developed horizontal crack at the
top, base and mid-height, forming three pivot
points for rocking.
A wedge like portion started falling in out-ofplane direction from the face loaded walls.
The structure is at the verge of total collapse.
Negligible to slight damage,
No structural damage, slight nonstructural damage.
Hair-line cracks in very few
walls.
Fall of small pieces of plaster
only.
Fall of loose stones from upper
parts of buildings in very few
cases.
Remarks: comparable damage
state.
Moderate damage,
Slight
structural
damage,
moderate non-structural damage.
Cracks in many walls.
Fall of fairly large pieces of
plaster.
Partial collapse of chimneys.
Remarks: comparable damage
state.
Substantial to heavy damage,
Moderate structural damage,
heavy non-structural damage.
Large and extensive cracks in
most walls.
Roof tiles detach. Chimneys
fracture at the roof line; failure of
individual
non-structural
elements
(Partitions,
Gable
Walls)
Remarks: conservative damage
state.
Very heavy damage,
Heavy structural damage,
Very
heavy
non-structural
damage.
Serious failure of walls; partial
structural failure of roofs and
floors.
Remarks: conservative damage
state.
Figure 5. Global damage mechanism of half-dressed stone DS masonry building model retrieved through
shake tableof
test
and comparison
withmasonry
the EMS-98
(Grunthal
et al., 1998)
damage
scale.shake
Fromtable
left test
to and comparFig. 5. Global dynamic
damage mechanism
half-dressed
stone DS
building
model retrieved
through
dynamic
right: observed
damage
label
andleft
description
observed
and EMS
damage
scale.
ison with the EMS-98
(Grunthal
et al.,state,
1998)damage
damagestate
scale.
From
to right: of
observed
damage
state,
damage
state label and description of
observed and EMS damage scale.
www.nat-hazards-earth-syst-sci.net/12/3441/2012/
Nat. Hazards Earth Syst. Sci., 12, 3441–3454, 2012
3448
N. Ahmad et al.: Seismic vulnerability of the Himalayan half-dressed rubble stone masonry structures
0.06
0.02
Response Acceleration(g)
Response Acceleration(g)
Response Acceleration(g)
Right Pier (Diagonal Shear Damages)
Transverse Wall (Out-of-Plane Delamination
and Collapse)
Left Pier (Shear Sliding and Rocking)
Response Acceleration(g)
For example, one of the piers (with similar
0.015
Building Model
0.04
Free Vibration
characteristics) of in-plane wall developed
0.01
diagonal shear
0.02 mechanism whereas the
0.005
other pier developed sliding and rocking
0
mechanism, 0
with
progressing
disintegration of piers. Such complex
-0.005
-0.02
behavior, which is due to the random
-0.01
nature of masonry,
cannot be simulated
-0.04
-0.015
with available numerical tools and thus
3 Cy
-0.06
-0.02
presents a challenge
for
computing
tools
40
42
44
46
48
50
47
for seismic behavior assessment
of rubble
Time(sec)
(Response
stone masonry buildings.
This Acceleration)
fact also
0.06
7. Dynamic characterization
of building model under 0.04g inp
point toFigure
the0.02
importance
of experimental
3 Cycles in and
0.21 Secs
response
acceleration
freebuildings
vibration time history processed for the
0.015
Building Model investigation
of
rubble
masonry
0.04
(47.05,0.0078g)
and elastic damping
coefficient.
Free Vibration
for understanding
the seismic behavior and
0.01
(47.26,0.0037g)
evaluating
the seismic performance.
0.02
drift dem
3 Fragility
Assessment of Half0.005
total unce
Dressed
Stone
DS
Masonry
0
0
DynamicStructures
Characteristics
of The Building
drift dem
Model: Walls:
-0.005 The low amplitude input
then with
-0.02
excitation
0.04g)
was primarily
(47.23,0.0036g)
specified
-0.01
3.1 (PGA
Seismic
Assessment
Framework
meant to help retrieve
the elastic dynamic
(47.015,0.01g)
-0.04
exceedanc
-0.015
properties
includingmay be
3the
Cycles inmodel
0.215 Secs
at a given
Manyof available
techniques
-0.06
-0.02vibration period T0 and
fundamental
40
42
44
46
48
50
47
47.1
47.2
47.3
47.4
47.5
for all th
employed to derive the fragility functions
damping coefficient ζ. Both Time(sec)
the vibration
Time(sec)
derivation
of structures (Borzi et al., 2008; Calvi et
period T0 and damping
were Model
obtained
(Response Acceleration)
(Building
Freefrom
Vibration)
al., 2006; Crowley,
2004;
Coburn and
Figure 7. Dynamic characterization of building model
under 0.04gacceleration
input excitation.
From
left to right: model
the response
time
history
2002;
D’Ayala
et model
al.,
1997;
Fig.
7.Spence,
Dynamic
of building
under
0.04 g in- 3.2 Math
response acceleration and free vibration time history
processed
for characterization
the
estimation
of
building
vibration
period
(Figure
7).
The
period
is obtained
using
put
excitation.
From
top
to
bottom:
model
response
acceleration
and
Erberik,
2008;
Kappos
and
Panagopoulos,
and elastic damping coefficient.
the free
basic
definition
ofprocessed
periodforof
an
vibration
time
history
the
estimation
of
building
2010;
Porter
et
2007;
Rota et
Other ava
oscillating
body
(i.e.elastic
theal.,
time
required
foral., 2010,
periodothers).
and
damping
coefficient.
drift
demand.
The
method
incorporates
3 Fragility Assessment of Half- vibration
among
The
present
study
included
modelling
a complete oscillation). An average value
total
uncertainties
in nonlinear
the drift demand.
The
Dressed
Stone
DS
Masonry
a
fully
probabilistic
dynamic
for globa
of 0.07 sec is obtained for vibration period.
drift
demand
on
structure
is
convolved
Structures
reliability-based
method
(NDRM)
recently
The(Chopra,
decay function
forγ the
time
ofA time step equal buildings
2003) with
= 0.5
and history
β = 0.25.
then
with
the
structure
drift
capacity
for a
developed
by
Ahmad
(2011)
for the
the toresponse
acceleration
proposed
by record
the sampling
size of theasground
motion
is consid- Galasco e
specified
limit
state
to
obtain
3.1 Seismic Assessment Framework
seismic
evaluation
and the
However,
Chopra
(2003)
isperformance
used to calculate
the
ered in
the analysis.
exceedance
probability
of
target
limit
state
fragility
analysis
of
considered
structure,
modelUncertainties
damping: that may be observed when considering a confidentl
recently
for
other
evaluation
a given
shaking
level.
It is structure
carried
out
Many available techniques may be groupasofatemployed
buildings
the
characteristics
are incorpo⎞ same
⎛of
1
A
Ln ⎜⎜ 1et⎟⎟ al., 2012a, 2012b).
ζ = (Ahmad
(1)
This
for
all
the
intensity
levels
to
allow
the
employed to derive the fragility functions ratedtypes
in the 2constitutive
nπ ⎝ A n ⎠ law through Monte Carlo simula- due to its
method
is found
to
provide
reasonable
tions.
In
this
regard,
SDOF
systems
were generated, during the
of fifty
fragility
functions.
of structures (Borzi et al., 2008; Calvi where
et
ζ derivation
represents
elastic
damping
which
are
assigned
with
random
constitutive
Uncertain- present s
estimate
building damageability
when
al., 2006; Crowley, 2004; Coburn and
the peak law.
coefficient;
A1 ofrepresents
ties
in
the
lateral
stiffness,
strength
and
deformation
compared
with earthquake
observations
in limits freedom (
Spence, 2002; D’Ayala et al., 1997;
3.2
Modelling
amplitude
of Mathematical
response
acceleration
at
are
modeled
considering
lognormal
distribution.
The
exper- seismic a
Pakistan
(Ahmad
et al., 2012c).
Erberik, 2008; Kappos and Panagopoulos,
reference
point 1;
A represents
the peak
imentally obtained nmechanical properties are considered as assigned
2010; Porter et al., 2007; Rota et al., 2010,
available acceleration
less or more atsophisticated
amplitude Other
of response
the median
estimate.
A
logarithmic standard
deviation
of force-defo
The
NDRM
istechniques
a probabilistic
for
among others). The present study included
modelling
may method
be calibrated
reference
point
after
n
cycles;
n represents
0.25 calculating
is considered tothe
modeldamage
variability in
the
peak
strength,
exceedance
simulating
the whereas
number
ofglobal
cycles
between
the peaks.
a fully probabilistic nonlinear dynamic
for
seismic
analysis
of is
masonry
0.50
logarithmic
standard
deviation
considered
probability
of
structures
for
a
specified
and defo
The
model
gives
estimate
of
4.008%
for
reliability-based method (NDRM) recently to model
buildings
and Fontana,
variability(Magenes
in the deformation
limits. The1998;
ratios of
ground
motion.
The
method
of
incremental
damping
using
the
positive
peaks
and
developed by Ahmad (2011) for the the lateral
Galasco
et al.,
2002;
2002). lat- building m
force (i.e.,
limit
stateKappos
force to et
theal.,
maximum
dynamic
analysis
(IDA)
proposed
by be to fundamen
5.404%
using
negative
peaks.
Figure 6.seismic
Local damage
mechanism of half-dressed
performance
evaluation and
However,
these limits
methods
cannot
eral force)
andthe
deformation
(i.e.,On
limit
state drift
Vamvatsikos
and
Cornell
(2002)
was
used
stone damage
DSfragility
masonry
wallsofobserved
during
average
damping
of 4.71%
Fig. 6. Local
mechanism
half-dressed
stoneshake
DS masonry
analysis
of considered
structure,
extended
for seismic
response as importanc
the firstaconfidently
drift
limit) ofvalue
the constitutive
lawisare considered
table
test.
From
top
to
bottom:
damages
observed
to evaluation
derive
the structure
response
curve
that
computed
which
may
be approximated
as
walls observed during
shake table test.
From topfor
to bottom:
observed
experimentally.
The uncertainty
in the
stiffnesses analysis
asand
employed
recently
otherdamages
structure
of
rubble
masonry
buildings
in in
in-plane
out-of-plane
walls.
observed
in-plane
and
out-of-plane
walls.
correlates
the
shaking
intensity
with
the
5%
for
the
building
model.
are
considered
then
accordingly.
Figure
8
reports
the lateral buildings
types (Ahmad et al., 2012a, 2012b). This
due to its complex behavior as observed
Damage Pattern with Increasing Shaking Intensity
law obtained
experimentally.
method is found to provide reasonable force-deformation
during theconstitutive
experimental
investigation.
The
estimate of building damageability when
present study included single degree of
earthquake
observations
in
freedom
(SDOF) mathematical model for
Nat. Hazards compared
Earth Syst. with
Sci., 12,
3441–3454,
2012
www.nat-hazards-earth-syst-sci.net/12/3441/2012/
Pakistan (Ahmad et al., 2012c).
seismic analysis. The SDOF system is
assigned with the observed global lateral
The NDRM is a probabilistic method for
force-deformation response of the building
Base Shear Coefficient
Normalized
when
f the
ed in
variability that
in the
Uncertainties
maydeformation
be observedlimits.
whenThe assigned to each of the fifty SDOF systems
ratios of athe
lateral
(i.e. limit
considering
group
of force
buildings
of thestate are also shown in Figure 8.
force
to the maximum
lateral force)in and
same
characteristics,
are incorporated
N. Ahmad et al.: Seismic vulnerability of the Himalayan half-dressed rubble stone masonry structures
3449
deformation limits (i.e. limit state drift to
2
the0.2first drift limit) of the constitutive law Table 2. Damage
scale considered for fragility
Medianfunctions derivation.
BSC = BSCmax
Random Simulation
are considered as observed
experimentally.
θ(%) = 0.50
Limit States (LS) versus Damage State (DS)
Drift Limits
1.5
The
0.15 uncertainty in the stiffnesses are
LS1: Damage level Grade-1 DS1 will be attained. θ1 = 0.7θy
consideredBSC then
accordingly. Figure 8 LS2: Damage level Grade-2 DS2 will be attained. θ2 = 1.5θy
= 0.80BSCmax
θ(%) = 0.16
Damage1 level Grade-3 DS3 will be attained. θ3 = 0.5 θy + θu
reports
the lateral force-deformation LS3:
0.1
LS4: Damage level Grade-4 DS4 will be attained. θ4 = θu
constitutive law obtained experimentally.
where θi represents the mean target drift limit states; θy represents the idealized yield
The
simulated constitutive laws drift limit derived
0.5 from the possible bi-linearization of lateral force-deformation
0.05 randomly
BSC = 0.33BSCmax
response of model; θu represents the ultimate drift limits. A mean value of 0.16 % is
θ(%) = 0.02
assigned to each of the fifty SDOF systems considered for θy and 0.60 % for θu . A logarithmic standard deviation of 0.20 is
considered for each of the drift limit sates.
are also
shown in Figure 8.
0
0
Base Shear Coefficient
n the
inear
using
and
erage
pping
and β
pling
rd is
0.03ki
-0.10ki
0.16ki
ki
0
0.2
0.4
0.6
0.8
1
0
0.5
1
1.5
2
2.5
3
Peak Normalized Drift(%)
3.4 Fragility functions
(Randomly Generated, Fifty Simulations)
2
Figure 8 Lateral
force-deformation
constitutive
law
of
DS
masonry
structures.
From using
left totheright:
constitutive
Each
SDOF
system
is analyzed
selected
ground
Median
motions
scaled
to
multiple
PGA
levels.
The
drift
demand
law obtained experimentally and randomly
generated
for
SDOF
mechanical
model.
The
lateral
force
in
thefor
later
Random Simulation
each
record
and
target
PGA
is
obtained
for
all
the
SDOF
syscase is normalized
by the peak lateral strength.
1.5
tems. The drift demand is correlated with the corresponding
ground motion intensity to derive response curves for each
natural
accelerograms
are record.
obtained
from
3.3 Selection
and
Scaling
of
SDOF
system under
each ground motion
The mean
1
thespectral
PEER
NGA strong
motions
database.
elastic
acceleration,
considering
all the records
for a
Accelerograms
target
PGA,
at
0.30
s
is
considered
as
the
intensity
measure
The acceleration response spectrum of the
0.5
in the present study. Figure 10 shows the response curves obThe
NDRM
method
requires
selected
accelerograms
is The
compatible
tained
for the considered
structure class.
drift demand with
for
accelerograms to perform the nonlinear
the building
code
specified
a specified
shaking level
takes into
account allspectrum
the uncertain-for
0
ties, type
material
and record-to-record
variability.
0
0.5
1
1.5
2
1
dynamic time
history
analysis
as2.5 part3 of
D uncertainties
soil of NEHRP
classification
(BCP,
Peak Normalized Drift(%)
For the fragility functions derivation, the NDRM method
the IDA
of structures. A suite of ten
2007). The accelerograms were also
computes the limit state probability of exceedance for a spec(Randomly Generated, Fifty Simulations)
ve law of DS masonry structures. From left to right: constitutive ified ground motion through the integration of the joint probFig. 8. Lateral force-deformation constitutive law of DS masonry
enerated forstructures.
SDOF mechanical
model.constitutive
The lateral
in experthe later ability density function of the drift demand and drift capacFrom top to bottom:
law force
obtained
ity. The First Order Reliability Method, FORM, approximah.
imentally and randomly generated for SDOF mechanical model.
tions (Der Kiureghian, 2005; Pinto et al., 2004) are employed
The lateral force in the later case is normalized by the peak lateral
to obtain the limit state exceedance probability. A damage
strength.
natural accelerograms are obtained from scale was developed as per recommended of FEMA (2003)
of
the PEER NGA strong motions database. for the derivation of fragility functions (see Table 2). The
idealized yield drift limit θy was selected such that the damThe randomly
simulated constitutive
lawsspectrum
assigned to each
The acceleration
response
of the age state between 0.7θy and
1.5θy is a slight damage, as
of the fifty SDOF systems are also shown in Fig. 8.
quires
selected accelerograms is compatible with per FEMA (2003) recommendation, which is roughly simSelection
and scaling
of accelerograms
inear 3.3 the
building
code
specified spectrum for ulated compared to the observed behavior. The ultimate drift
limits θu corresponds to the lateral deformation when the
art of The NDRM
type Dmethod
soil of
NEHRP
classification
requires
accelerograms
to perform(BCP,
the
lateral force drops by 20 %, as proposed by Magenes and
f ten nonlinear
2007).
The
accelerograms
also Calvi (1997), which corresponds to the near collapse limit
dynamic
time history
analysis as part were
of the IDA
of structures. A suite of ten natural accelerograms are obstate. This limit state in our study approximately corresponds
tained from the PEER NGA strong motions database. The acto the near collapse limit state as the strength drops very
celeration response spectrum of the selected accelerograms
rapidly after the ultimate limit state (see Fig. 8).
is compatible with the building code specified spectrum for
The FORM approximation is used to obtain the limit state
type D soil of NEHRP classification (BCP, 2007). The acprobability of exceedance for various target ground motions.
celerograms were also selected and used elsewhere (Ahmad
A lognormal cumulative distribution function is assumed,
et al., 2012a, b, c; Menon and Magenes, 2011). The acceleroas employed elsewhere (Kircher et al., 1997; Porter et al.,
grams are normalized, anchored to common PGA, and lin2007), and fitted to the observed points. The median and logearly scaled to multiple shaking levels for IDA of each SDOF
arithmic standard deviation of each limit state are obtained,
system.
which can be used for fragility derivation (see Fig. 11):
Base Shear Coefficient
Normalized
Drift (%)
(Experimentally Derived)
www.nat-hazards-earth-syst-sci.net/12/3441/2012/
Nat. Hazards Earth Syst. Sci., 12, 3441–3454, 2012
N. Ahmad et al.: Seismic vulnerability of the Himalayan half-dressed rubble stone masonry structures
2
1.5
BCP-2007, D Soil
Mean Spectrum
4.5
Individual Record
4
3.5
BCP-2007, D Soil
Mean Spectrum
Individual Record
2
BCP-2007, D Soil
Mean Spectrum
Individual Record
Spectral Displacement (1/PGD)
3450
Spectral Acceleration (1/PGA)
7, D Soil
ctrum
Record
scaled to multiple shaking levels for IDA
of each SDOF system.
Spectral Displacement (1/PGD)
genes,
lized,
1.5 employed elsewhere (Kircher et al., 1997;
approximations (Der Kiureghian, 2005;
3
Porter et al., 2007), and fitted to the
1 Pinto et al., 2004) is employed to obtain
2.5
the limit state exceedance probability. A
points. The median and
1 observed
2
damage
scale was developed as per
logarithmic standard deviation of each
0.5
1.5
limit state are obtained which can be used
recommended
of FEMA (2003) for the
0.5
1
derivation of fragility functions (see Table
for fragility derivation (see Figure 11):
0.5
2).
The
idealized
yield
drift
limit
θ
was
⎛ 1 ⎛ SA ⎞ ⎞
y
0
⎟⎟ ⎟
P[D ≥ d LS / SA = sa ] = Φ ⎜⎜ Ln ⎜⎜
0
1
2
3
4
5
(2)
5
0
⎟
selected
such
that
the3 damage
state
0
0
1
2
3 ⎝β
4⎝ sa LS ⎠ ⎠5
0
1 Period (sec)
2
4
5
Period (sec)
between
and
1.5θy
isSpectrum)
a slight
(EC8 Specified
PGD at 0.7θy
Target PGA
0.4g-Normalized
Period
(sec)
where
P
represents
the Spectrum)
limit state
(EC8
Specified
PGD
at
Target
PGA 0.4g-Normalized
(PGA-Normalized
damage,
as
per Spectrum)
FEMA
(2003)
probability of exceedance;
represents
recommendation, which is roughly
the
standard
normal
cumulative
simulated compared to the observed
distribution function; β represents the
behavior. The ultimate drift limits θu
logarithmic standard deviation of fragility
corresponds to the lateral deformation
function; SA represents the seismic
when the lateral force drops by 20%, as
intensity; sa LS represents the median
proposed by Magenes and Calvi (1997),
estimate of the distribution. The values of
which corresponds to the near collapse
β and sa LS are also provided in Figure 11.
limit state. This limit states in our study
The functions can be employed in future
approximately corresponds to(Detailsnear
of Individual Record)
Details of Individual Record)
applications for the damageability
collapse limit state as the strength drops
Fig.
9.
Characteristics
of
the
accelerograms
used
in
the
present
study.
From
left
to right and top to
acceleration
response
spectrum,
assessment
ofbottom:
considered
DS
masonry
s used in the present vary
study.rapidly
From left
to right
and top tolimit
bottom:
after
the ultimate
states
displacement
response
spectrum
and
details
of
the
individual
record.
t response spectrum and
details
of the
structures during earthquake induced
(see
Figure
8).individual record.
ground
motions.
3.4 Fragility Functions
0.8
2 Damage scale considered for fragility
function;
β represents
the logarithmic
standard deviation
Order
Reliability
Method
FORMof
fragility function;
SA
represents
the
seismic
intensity;
The FORM approximation is usedandto
obtain the limit state probability of
exceedance
various
target
Nat. Hazards
Earth Syst. for
Sci., 12,
3441–3454,
2012ground
motions.
A
lognormal
cumulative
distribution function is assumed, as
Probability of Exceedance
0.7
SA(g)@0.30sec
functions
derivation
Each
SDOF
system is analyzed using the
0.7
Limit States
(LS)motions
versus scaled to multiple
selected
ground
Drift Limits
0.6 Damage State (DS)
PGA levels. The drift demand for each
LS1: Damage
level PGA
Grade-1
0.5
record
and target
is obtained
θ 1 = 0for
.7 θ yall
DS1 will be attained.
the
SDOF
systems.
The
drift
demand
is
0.4 LS2: Damage level Grade-2
θ
=
1
.
5
θ
correlated
with
the
corresponding
ground
2
y
0.3 DS2 will be attained.
LS3: Damage
level
motion
intensity
to Grade-3
derive response
curves
θ = 0 .5 (θ y + θ u )
0.2 DS3 will be attained.
for each SDOF system under 3each ground
LS4: Damage level Grade-4
0.1
motion
record.
The mean elastic
θ 4 spectral
= θu
DS4 will
be attained.
acceleration,
considering
all
the
records
0
0
0.1
0.2
0.3
0.4
0.5
0.6
for
a target
PGA,
at (%)
0.30sec
is considered
Drift
where
θi represents
the mean
target drift
as 10
the Structure
intensity response
in the obtained
present
Figure
curves
limit
states;
θy measure
represents
the
idealized
Fig. 10. Structure
response
curves
obtained
through
IDA
of SDOF
study.
Figure
10
shows
the
response
through
IDA
of
SDOF
systems.
yield drift limit derived from the possible
systems. curves
obtained for the considered
bi-linearization
of
lateral
forceclass.functions
The driftderivation,
demand forthea
For structure
the
fragility
deformation
specified
shakingresponse
level takesofintomodel;
account θu
NDRM
methodthecomputes
the limits.
limit A
state
represents
ultimate
drift
mean
all the uncertainties,
material
uncertainties
1 is SA
probability
of
exceedance
for
a
specified
value
of
0.16%
considered
for
θ
y and
and
record-to-record
P [D ≥ dLS
/SA
= sa] 8
Ln variability.
,
(2)
ground
motion
of
0.60%
for through
θβu. Asathe
logarithmic
standard
LS integration
deviation
0.20
isprobability
considered
forofeach
theP joint
probability
density
function
the of
where
represents
theof
limit
state
of exceedance;
driftstandard
limit
drift the
demand
and sates.
drift
First
8 represents
the
normalcapacity.
cumulativeThe
distribution
SA(g)@0.30sec
g the
ultiple
each
or all
nd is
round
urves
round
ectral
cords
dered
resent
ponse
dered
for a
count
inties
0.8Table
1
0.6
0.5 0.8
0.4
0.3
0.2
0.6
0.4
0.1
0 0.2
0
0.1
0.2
0.3
0.4
LS1(0.15,0.31)
LS2(0.25,0.31)
LS3(0.33,0.31)
0.5
0.6
LS4(0.45,0.31)
NDRM
Drift (%)
Figure 10
Structure response curves obtained
0
0
0.2
0.4
0.6
0.8
through IDA of SDOF systems.
SA(g)(0.30sec,5%)
1
Figure 11 Fragility functions for Himalayan DS
Fig.
11.
Fragility
functions
for Himalayan
DS NDRM.
masonry
For
the
fragility
functions
derivation,
the structures
masonry
structures
obtained
through
obtained
through
NDRM.
NDRM
method
computes the limit state
probability
of exceedance
for a specified
3.5 Vulnerability
Functions
ground motion through the integration of
the The
joint impact
probability
density
functiononofthe
the built
of an
earthquake
driftenvironment
demand andisdrift
capacity.
The
First
computed in terms of the
Reliability
Method
saOrder
represents
the
median
estimate
of casualties.
the FORM
distribution.
LS monetary losses and
human
TheThe
valuesmonetary
of β and sa LSlosses
are also provided
in
Fig.
11.
The
funccorrespond to the
tions economic
can be employed
in
future
applications
for
the
damlosses the authority has to bear
ageability assessment of considered DS masonry structures
to bring the devastated society to habitable
during earthquake induced ground motions.
condition. It includes the direct losses due
to building damage and indirect losses
www.nat-hazards-earth-syst-sci.net/12/3441/2012/
including
business downtime and loss of
means of income besides the response and
relief expenditure. The direct economic
Economic Loss Ratio (%)
The impact of an ELR(0.38,0.37)
earthquake on the built environment is computed in terms
of
monetary losses and human casualties. The
80
monetary losses correspond to the economic losses the authority has
to bear to bring the devastated society to habit60
able condition. It includes the direct losses due to building
damage and indirect losses, EL
including
business downtime and
= (ELR/100)xNxC
40
loss of means of income besides the response and relief exwhere
penditure. The direct economic
losses Losses
related to the buildEl = Economic
20
ELR = Economic
Loss Ratio
ing damage represent the amount
required
to pay for the reN = Number of Buildings
pair, demolishment and replacement
of structures
C = Replacement
Cost of Buildingdamaged
0
in earthquakes
(Bal0.2et al., 2008;
FEMA,
2003).
0
0.4
0.6
0.8 Only1 the direct economic losses are
considered in the present research
SA(g)(0.30sec,5%)
study. The human casualties include the number of people
injured and trapped in the collapsed buildings which are essential for rescue operation soon after the earthquake (Erdik
et al., 2011; Hancilar et al., 2010). The casualties may be further classified into minor, moderate and serious injuries and
deaths (Spence, 2007b).
Vulnerability function for economic losses is derived from
the building fragility functions. It included the estimation
of probability of building damages at a specified shaking
intensity, which are convolved with the economic consequence factor ECF (Ahmad, 2012c), where ECF refers to
the scale relating building damage with the monetary losses.
The FEMA model which assigns a cost ratio (the ratio of
damaged building repair to replacement cost) of 0.02 for
DS1, 0.10 for DS2, 0.50 for DS3 and 1.0 for DS4, is employed herein to derive vulnerability curve for the considered DS masonry building. Figure 12 reports the vulnerability curve for the considered DS masonry structures where the
losses are represented in terms of the economic loss ratio.
The function can be used to compute the economic losses for
the structures during earthquake given the shaking intensity
(SA @ 0.30 s).
www.nat-hazards-earth-syst-sci.net/12/3441/2012/
Human Loss Ratio (%)
Economic Loss Ratio (%)
functions. It included the estimation of
Figure 13 Vulnerability functions for Himalayan
Human
loss ratio which can provide
economic loss ratio. The function can be
DS masonry structures obtained using the Spence
probability of building damages at a
used to compute the economic losses for
estimates
of human
casualties
(2007b) human
consequence
factor. in collapsed
specified shaking intensity which are
the structures
during
earthquake
given the
buildings during earthquake given 3451
the
N. Ahmad
et al.: Seismic
vulnerability
the Himalayan half-dressed rubble stone masonry structures
convolved
with the
economicofconsequence
shaking intensity ([email protected]).
shaking
intensity
([email protected]).
4 Seismic
Risk
of DS Masonry
factor ECF (Ahmad 2012c), where ECF
Structures
in
Scenario
Earthquakes
100
50
refers to theELR(0.38,0.37)
scale relating building damage
Slight Injuries
HL = (HLR/100)xNxO
with the monitory losses. The FEMA
80
40
The present studywherealso included case
model which assigns a cost ratio (the ratio
Hl = Human Injuries
studies for risk assessment
ofRatioconsidered
HLR = Human Loss
of damaged
building repair to replacement
60
N = Number of Buildings
30
DS masonry structures
in large
scenario
O = Occupants
Per Building
cost) of 0.02 for DS1, 0.10 for DS2, 0.50
earthquakes.
Three
scenario
earthquakes
= (ELR/100)xNxC
Moderate Injuries
40
for DS3
and 1.0 ELfor
DS4, is employed
20
Critical Injuries
with
Mw
7.0,
7.5
and
8.0Injuries
are &considered
where
Serious
Fatalities
herein to derive vulnerability
curve for the
El = Economic Losses
20
for
which
building
damageability
is
ELR = Economic Loss Ratio
10
considered DS masonry
Figure
N = Numberbuilding.
of Buildings
assessed
at
various
source-to-site
C = Replacement Cost of Building
12 reports
the vulnerability
curve for the
0
distances.
Each
of the1 scenario
earthquake
0
0.2
0.4
0.8
1
0
considered DSSA(g)(0.30sec,5%)
masonry0.6structures
where
0
0.5
1.5
2
ground motions
is simulated with 1000
SA(g)(0.30sec,5%)
the losses are represented in terms of the
different
motion
fields,for
considering
Figure
13 ground
Vulnerability
functions
Himalayan
Fig. economic
12. Vulnerability
function
for The
Himalayan
DS masonry
loss
ratio.
function
canstrucbe
Fig. 13. Vulnerability functions for Himalayan DS masonry strucDS masonry structures obtained using the Spence
tures obtained using the FEMA (2003) economic consequence factures obtained using the Spence (2007b) human consequence factor.
used to compute the economic losses for
(2007b) human consequence factor.
tor.
the structures during earthquake given the
shaking intensity ([email protected]).
4 Seismic
Risk
of casualties
DS Masonry
Vulnerability
functions
for human
are derived
3.5 Vulnerability functions
from
the
collapse
fragility
function
of
the
buildings.
For this
Structures in Scenario Earthquakes
100
purpose the human consequence factor (HCF) developed by
Spence (2007b) is employed in the present study. It includes
present
case
the The
convolution
of the study
collapse also
fragilityincluded
function with
the
forSpence
risk model.
assessment
of assigns
considered
lossstudies
ratio of the
This model
ratio of
slight
with 0.50,
moderate injuries
withscenario
0.12, seriDSinjuries
masonry
structures
in large
ous earthquakes.
injuries with 0.08Three
and critical
injuries
and
deaths
with
scenario earthquakes
0.064 in collapsed buildings. Figure 13 reports the vulnerawith
Mwderived
7.0, 7.5
and
8.0 are
considered
bility
functions
for the
casualty
estimation
in earthfor
which
building
damageability
is
quakes. The losses are represented in terms of the Human
lossassessed
ratio, which canatprovide
estimates ofsource-to-site
human casualties
various
in collapsed
buildings
during
earthquake
given
the shaking
distances. Each of the scenario earthquake
intensity (SA @ 0.30 s).
ground motions is simulated with 1000
different ground motion fields, considering
4
Seismic risk of DS masonry structures in
scenario earthquakes
The present study also included case studies for risk assessment of considered DS masonry structures in large scenario
earthquakes. Three scenario earthquakes with Mw = 7.0, 7.5
and 8.0 are considered, for which building damageability is
assessed at various source-to-site distances. Each of the scenario earthquake ground motions is simulated with 1000 different ground motion fields, considering uncertainties in the
ground motions estimate. Empirical ground motion prediction equations (GMPEs) are used to estimate ground motions
(Abrahamson and Silva, 2008; Boore and Atkinson, 2008;
Campbell and Bozorgnia, 2008).
Damageability of structures is assessed using the previously derived fragility function. For a given earthquake and
specified source-to-site distance, the corresponding seismic
intensity is obtained using the GMPEs. The associated limit
state probability of exceedance is obtained to compute the
percentage of structures in various damage states. Figure 14
reports the damage probability matrix, showing the mean
Nat. Hazards Earth Syst. Sci., 12, 3441–3454, 2012
Campbell and Bozorgnia, 2008).
various damage states. Figure 14 reports
the damage probability matrix, showing
Damageability of structures is assessed
the mean estimate of the percentage of
3452using the N.previously
Ahmad et al.:derived
Seismic vulnerability
of
the
Himalayan with
half-dressed
stone
masonry structures
fragility
structures
variousrubble
damage
levels.
function. For a given earthquake and
Rjb = 0 – 10km
Rjb = 10 – 20km
Rjb = 20 – 30km
Rjb = 30 – 40km
Rjb = 40 – 50km
DS1 DS2 DS3 DS4
DS1 DS2 DS3 DS4
DS1 DS2 DS3 DS4
DS1 DS2 DS3 DS4
DS1 DS2 DS3 DS4
DS1 DS2 DS3 DS4
DS1 DS2 DS3 DS4
DS1 DS2 DS3 DS4
DS1 DS2 DS3 DS4
DS1 DS2 DS3 DS4
DS1 DS2 DS3 DS4
DS1 DS2 DS3 DS4
DS1 DS2 DS3 DS4
DS1 DS2 DS3 DS4
DS1 DS2 DS3 DS4
100
Mw = 7.0
80
60
40
20
0
100
Mw = 7.5
80
60
40
20
0
100
Mw = 8.0
80
60
40
20
0
Figure 14 Damageability (percentage of total stock) of DS masonry structures in scenario earthquakes. DS1
Fig. 14. Damageability (percentage of total stock) of DS masonry structures in scenario earthquakes. From top to bottom: Damageability
represents slight damages; DS2 represents moderate damages; DS3 represents heavy damages; DS4 represents
for Mw = 7.0, Damageability for Mw = 7.5 and Damageability for Mw = 8.0. DS1 represents slight damages; DS2 represents moderate
near-collapse/collapse
limit
state.
damages;
DS3 represents heavy
damages.
The
observed
damageability
of
the
estimate
of the percentage
of type
structures
withvery
various
damage
considered
structure
seems
high.
levels.
It can be observed that more than 40
The observed damageability of the considered structure
percent of the stock may collapse during
type seems very high. It can be observed that more than
earthquake
withmay
Mwcollapse
equal during
or greater
thanwith
40 percent
of the stock
earthquake
buildings
located
in the
nearinand
Mw7.0,
equalfor
or greater
than 7.0,
for buildings
located
the near
field.
The percentage
and intermediate
intermediate field.
The percentage
of collapsedof
structurescollapsed
can even rise
to
70–80
during
large
earthquakes
structures can rise even up to 70- and
for buildings
located
in close
source-to-site and
distance.
80 during large
earthquakes
forThis
huge percentage of damageability will consequently result in
buildings located in close source-to-site
highly associated socio-economic losses. This high vulneradistance. This huge percentage of
bility of the considered building type gives merit to the use
damageability
will consequently
resultbyinAli et
of simple
retrofitting interventions,
as investigated
high toassociated
losses.
al. (2012),
mitigate the socio-economic
risk of vulnerable stone
masonry
buildings
the future
expected large
This inhigh
vulnerability
of earthquake.
the considered
building type gives merit to the use of
simple retrofitting interventions, as
5 Conclusions
investigated by Ali et al. (2012), to
the a risk
vulnerable
The mitigate
paper presents
study of
carried
out as part stone
of the research
aiming buildings
towards riskinmitigation
and disaster
risk remasonry
future expected
large
duction
in
the
Himalayan
region,
which
could
be
subjected
earthquakes.
to very large earthquakes in the future. Half-dressed masonry structures representing public critical facilities in the
region are considered for investigation, a very common type
in the region. Fragility functions are derived for the considered construction type using experimental and numerical
investigations. Furthermore, vulnerability functions are derived for economic loss estimation and human casualty estimation. The derived fragility and vulnerability functions are
employed for earthquake scenario risk assessment considNat. Hazards Earth Syst. Sci., 12, 3441–3454, 2012
moderate and large magnitude earthquakes. The con5ering
Conclusions
sidered construction type exhibits high vulnerability against
earthquakes. Up to 40 percent of building stock can collapse
The
paper presents a study carried out as
in large earthquakes, where the percentage of collapse can
part
the
research
aiming
towards
rise asof
high
as 70–80
for large
earthquakes
with risk
close sourcemitigation
and
riskcan
reduction
in for comto-site distance.
Thedisaster
present study
be employed
the
Himalayan
region,
could authorities
be
municating
the expected
risk which
level to public
to
take
measures
aiming
towards
risk
mitigation
and
disaster
subjected to very large earthquakes in the
risk reduction.
This can in turn
result in the
mitigation of ecofuture.
Half-dressed
masonry
structures
nomic losses from future earthquakes. The findings from the
representing public critical facilities in the
present study can also be employed for rapid earthquake loss
region
are considered for investigation, a
estimation within the context of prompt response to disaster
very
common
inoperation
the region.
Fragilityplanning
sites, essential fortype
rescue
and emergency
functions
arehuman
derived
for the
considered
that can reduce
casualties
in earthquakes.
construction
using
experimental
and
Supplementarytype
material
related
to this article
is
numerical
investigations.
Furthermore,
available online
at:
vulnerability
functions are derived for
http://www.nat-hazards-earth-syst-sci.net/12/3441/2012/
nhess-12-3441-2012-supplement.zip.
economic loss estimation and human
casualty estimation. The derived fragility
and
vulnerability
Acknowledgements.
Thefunctions
reviewers’ are
effortemployed
in evaluating the
for
earthquake
risk assessment
manuscript
and kindlyscenario
providing encouraging
remarks is highly
appreciated. The experimental study presented herein is financially
supported by the Board of Advanced Studies and Research
(BOASAR) of the University of Engineering & Technology
(UET) Peshawar and the Higher Education Commission (HEC) of
Pakistan, which are gratefully acknowledged.
Edited by: M. E. Contadakis
Reviewed by: J. M. Dulinska, T. Makarios, and
one anonymous referee
www.nat-hazards-earth-syst-sci.net/12/3441/2012/
N. Ahmad et al.: Seismic vulnerability of the Himalayan half-dressed rubble stone masonry structures
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