THESIS Seismic Assessment-libre
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Transcript of THESIS Seismic Assessment-libre
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UNIVERSITY OF PERADENIYA
SRI LANKA
SEISMIC ASSESSMENT OF SCHOOL BUILDINGS
IN
SRI LANKA
BY
MARASINGHA MUDIYANSELAGE
JANAKA KUSUMSIRI MARASINGHA
A thesis submitted to the Faculty of Engineering, University of Peradeniya,
Sri Lanka in partial fulfillment of the requirements for the Degree of
Master of the Science of Engineering
December, 2013
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DECLARATION
I,
"Marasingha Mudiyanselage Janaka Kusumsiri Marasingha",
hereby declare that the work presented herein is genuine work done originally by me for the
partial fulfillet of Masters Degree i trutural Egieerig at Uiersity of Peradeiya and
has not been published or submitted elsewhere for the requirement of a degree programme.
Any literature, data or works done by others and cited within this dissertation has been given
due acknowledgement and listed in the reference section.
Signature :- .
Student's name :- Marasingha Mudiyanselage Janaka Kusumsiri Marasingha
Date :- .
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ACKNOWLEDGEMENTS
I would like to express my deepest gratitude to my advisor, Dr. K.K.Wijesundara, for his
excellent guidance, caring, patience, and providing me with an excellent atmosphere for
carrying out his research. I would like to thank Dr. U.I.Dissanayake who provided all his support
guiding with supportive background in coordinating with the University and scheduling
progress meetings as well as publication of technical papers in different events using the
results of this research.
I would thank all the other lecturers in the Department of Civil Engineering, Faculty of
Engineering including the examiners panel who patiently corrected my thesis for the kind
support gie i folloig y Bahelors Degree ad Masters Degree up to this leel.
My thanks goes to all of the colleagues followed this degree helping and giving suggestions to
success this research.
I would also like to thank my parents, two elder sisters. They were always supporting me and
encouraging me with their best wishes.
Finally, I would like to thank my wife, Anushka Rajapaksha. She was always there cheering me
up and stood by me through the good times and bad.
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ABSTRACT
Considering the occupancy of future generation and the vulnerability of their lives in school
time, it is considered being a timely requirement to assess the performance levels of school
buildings for different return period earthquakes which happens without any advance
notification. For this purpose, the Incremental Dynamic Analysis (IDA) is performed using
nonlinear finite element model of two storey 8 classroom type plan building developed in
Opeees oputer progra. The daage idies ased o the iter-storey drift are evaluated for immediate occupancy and collapse prevention performance levels. The
corresponding drift ratios for immediate occupancy and collapse prevention performance
levels are calculated using the resultant IDA curves drawn for past 30 earthquake records with
0.2 scale increments for each earthquake. The past 30 earthquake records selected from PEER
database are scaled to match their average response spectrum with the response spectrum
which can be considered as spectrum corresponding with an earthquake having 475 years
return period according to the Indian Standards. Finally, the damage index which is close to the
collapse prevention performance level is observed in the school building for an earthquake
with the return period of 2500 years highlighting the importance of designing school buildings
to resist the lateral load induced by earthquakes.
Furthermore corresponding inter-storey drift ratios were obtained using static push over (SPO)
analysis also. Since the pushover analysis is a static analysis, it cannot take into account the
effects of energy content, duration and frequency content of an accelerograme as IDA analysis.
In IDA analysis it performs a series of dynamic analyses on structure under input real
accelerograme. Then the effect of above parameters could be interpreted towards the
ultimate drift. Therefore, this study extended to compare those effects in estimation of
ultimate drift ratio by comparing the ultimate drifts obtained from IDA analysis and the
pushover analysis.
Finally, the research is concluded with highlighting the importance of designing school
buildings for rare earthquakes by improving reinforcing detailing to assure the essential criteria
provided by FEMA guidelines. That is because the assessed type plan has a very low ductility
and unfavorable drift concentration at the first storey level leading to a soft-storey failure
mechanism. Further the effect of masonry in-fill walls and bi-directional earthquake loads are
to be considered in future.
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TABLE OF CONTENT
List of Tables
List of Figures
CHAPTERS
1. Introduction 1
2. Literature Review 6
2.1 Earthquakes and wave propagation
2.2 Seismicity of Sri Lanka
2.3 Damages on gravity design frames
2.3.1 Joint failures
2.3.2 Shear failures
2.3.3 Flexural failures
2.3.4 Combined failure of shear and flexure
2.4 Damage Indices used for assessment of a structure
2.4.1 Non-modal parameter based damage indices
2.4.1.1 Ductility based damage index
2.4.1.2 Inter-storey drift based damage index
2.4.1.3 Park and Ang damage index
2.4.1.4 Modified Park and Ang damage index
2.4.1.5 Mahin and Bertero damage index
2.4.1.6 Damage index based on the wavelet energy
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2.4.2 Modal parameter based damage indices
2.4.2.1 Damage index based on the natural period
2.5 Incremental Dynamic Analysis (IDA) Method
3. Building Description and Finite Element modeling 28
3.1 Typical School Buildings in Sri Lanka
3.2 Nonlinear Finite Element model
3.2.1. Fibre Sections
3.2.2 The force formulation
3.2.3 Concrete Material Model
3.2.4 Reinforcement Steel Material Model
4. Analysis and Results 41
4.1 Selection of accelerograms
4.2 Response spectra
4.3 Incremental Dynamic Analysis (IDA)
4.3.1. Nonlinear dynamic analysis
4.4 Results of IDA
4.4.1 Estimation of Immediate occupancy (IO) and Collapse
prevention (CP) performance points in IDA curves
4.5 Static Pushover curve and results
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5. Assessment and Evaluation 58
5.1 Comparison of results
5.2 Performance Based Assessment
6. Conclusions and Future Recommendations 62
Appendices
A. Detail drawings
B. Selected Accelerograms
C. Response spectra
D. OpenSees Scripts for IDA & SPO
References
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List of Tables
Table 2.1 Details of earthquake recoded very close to Sri Lanka 13
Table 4.1 Peak ground accelerations 45 Table 4.2: Average Inter-storey Drift ratios by IDA 55 Table 4.3: Inter-storey drift ratios- Pushover analysis 57
Tale 5.: Copariso of Iter-storey drift ratios 58 Table 5.2: Damage indices by IDA 60
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List of Figures
Fig.1.1: Effect of the Sichuan earthquake 3
Fig 2.1: Tectonic plates of earth 7 Fig..: Propagatio of a P ae 7 Fig..: Propagatio of a ae 8 Fig 2.4: Rayleigh and Love wave propagation 9 Fig 2.5: Identification of different wave patterns in a time series 10 Fig. 2.6: Recorded earthquake events around Sri Lanka 12 Fig 2.7: Beam-column joint failures 15 Fig 2.8: shear failures due to lack of confinement 15 Fig 2.9: Cushing of concrete in plastic hinge regions 17 Fig 2.10: Buckling of longitudinal reinforcements 17 Fig 2.11: Short column effect 18 Fig 2.12: Soft storey effect 19 Fig 2.13: An example IDA curve 27
Fig 3.1: 8 class room block type plan 2 storey 28 Fig 3.2: 12 class room block type plan 3 storey 29 Fig 3.3: Selected school building type 30 Fig 3.4: Sectonal view of the building 31 Fig .5: Opeees -D finite element model 32
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Fig 3.6: Fibre section assigned to 1st storey column of 375 x300 mm 34 Fig 3.7: Material assignment in a fibre section 34 Fig 3.8: Assignment of fibre sections in each element 35 Fig 3.9: flow diagram of force formulation 37 Fig.3.10: Uniaxial concrete material, stress-strain relationship 38 Fig 3.11: Typical hysteretic stress-strain relation of concrete 38 Fig 3.12: Uniaxial Steel material, stress-strain relationship 40 Fig 3.13: Hysterisis model of Steel material 40
Fig 4.1: Three of the selected accelerograms 42 Fig 4.2: Definition of a response spectrum 45 Fig 4.3: Graphs for Site response spectrum from Indian code 46 Fig 4.4: Site response spectra 47 Fig 4.5: 5% Response spectra of 30 earthquakes 48 Fig 4.6: Comparison of response spectra 48 Fig 4.7: Algorithm of IDA 50 Fig 4.8: IDA curves for 30 earthquakes 52 Fig 4.9: Defined point of flexural yielding 53 Fig 4.10: Moment-curvature diagrams 54 Fig 4.11: Example for defined failure point 55 Fig 4.12: Pushover curve and equivalent bi-linear curve 56
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Fig 5.1: Average IDA curve 59 Fig. 5.2: Relationship between Earthquake Design Level and
Performance Level 61
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Chapter 1 Introduction Most of the building structures in Sri Lanka are designed only to bare the gravity loads, as there
have no severe winds or earthquake events frequently been affected in the island. The lateral
load resisting systems are applied mostly only on high-rise buildings which are more
concentrated around the commercial center of Colombo. The pattern of earthquakes has now
been changed a little as per the records after the tsunami event on December 2004.
Majority of government buildings in Sri Lanka are similar in architectural features. They are
designed by departments or ministries considering only few site changes for foundation
designs to construct island wide. This could be effective by reducing the cost of design and
construction monitoring all over the island since most of the site factors are common inside
this small Island having only 65,610 km2 area. The type plans for the school buildings are
developed by the Ministry of Education. As mentioned earlier these buildings have been
designed only to bare gravity loads neglecting the effect of applicable lateral loads.
According to the census data published in 2012, out of 20,263,723 of Sri Lankan
population,(Population Atlas of Sri Lanka, 2012) there are 3,973,847 of students and 219,886
of teachers (Sri Lanka Education Information, 2011), studying and working in government
schools in Sri Lanka. This is about 20 per cent of the total population. They occupy in school
buildings at day time, which highlights the importance of assessing building performance to
protect students.
During the recent earthquakes in China, Pakistan and India, the complete collapse of school
buildings, which were gravity designed reinforced concrete frame buildings, were observed
causing thousands of deaths of school children. Even though, there were few earthquakes
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recorded within Sri Lanka, historical records indicate that there was a devastating earthquake
(Mw=6.4) in Colombo 1615.
An earthquake measuring eight on the Richter scale struck Sichuan province in China on 12th
May 2008, reporting a massive death toll over 70,000, affecting over 45.7 million people and
causing disruption to daily operations amounting to a reported economic loss of $1000 billion.
Reportedly more than 80 per cent of buildings in the area collapsed including a large number
of school buildings. Not only did this inhibit the rescue operations, a large number of young
children were buried under the debris adding to the extensive death toll and causing severe
trauma to the nation.
Schools were amongst the most damaged structures during the Sichuan earthquake. About
7000 schools were seriously affected; some collapsed, others were seriously damaged.
Collapse of Juyuan Middle School and Dujiangyan School, burying many young children and
teachers in the debris caught national and international attention calling for the need for
immediate investigations.
According to records nearly 2million square meters of school areas crumbled in the
earthquake, killing 4737 studentsand injuring more than 16,000. Sichuan Construction Bureau
reported that 6898 classrooms collapsed across Sichuan (Dr Derry Yu. et al, Woods Bagot, Issue
0902).Fig: 1.1 illustrate the severity of Sichuan earthquake.
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Fig:1.1:Effect of the Sichuan earthquake.
[Source:http://www.drgeorgepc.com/Earthquake2008ChinaSichuan.html
http://www.foreigners-in-china.com/sichuan-earthquake-facts.html]
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In referring to those kind of devastations, occupancy of school children and the vulnerability
of their lives in school time in Sri Lanka, it is considered being a timely requirement to assess
the performance levels of school buildings for different return period earthquakes which
happens without any advance notification.
There are several type plans of single storeyed to four storeyed school buildings, prepared by
the Ministry of Education, Sri Lanka. The most common from them all over the island can be
considered as the two-storeyed 8 class room type plan. When referred to the detailed
drawings of the building structure, it is a concrete moment frame building structure with brick
in-fill walls. Further the partition walls to separate each class room are placed along shorter
direction of the building, as there are half walls opened to the corridor along the longer side of
the building. This gives an initial sense of weaker direction of the building which will be
discussed later.
The unrecoverable damage to the society from any devastating earthquake event could only
be addressed by assessing existing structures considering their performance in a predictable
intensity of earthquake in Sri Lankan vicinity. It can be considered as a duty towards the future
generation assuring their life safety in a hard time.
To overcome the task, the common type plan of two storeyed school building was modeled in
Opeeesoputer progra (PEER, 2006). This program was selected considering its
exclusive capacity in handling complex numerical approaches to perform a non-linear dynamic
analysis using time history inputs of real earthquakes.
A 3-Dimensional finite element model of the school building was then developed in the
Opeees progra, considering material nonlinearity through force-based frame elements
defined using fiber sections and geometric nonlinearity through co-rotational transformations.
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The 30 numbers of real accelerograms were selected from the PEER database and scaled to
match in average with the design response spectrum corresponding to an earthquake having
475 year of return period. Then these ground motions were used to perform inelastic dynamic
analysis. Furthermore the input ground motions were scaled in 0.2 scale intervals to perform
an Incremental dynamic analysis (IDA). The inter-storey drift was considered to be the suitable
damage measure for this analysis.To develop IDA curve for each accelerogram, the recorded
maximum inter-storey drift ratios for different scale factors were plotted against the
corresponding spectral accelerations.
While analyzing the model, moment-curvature plots at different locations were observed using
Opeees reorder to ealuate the strutural perforae leels. In this study, the two
structural performance levels were considered as immediate occupancy performance level and
the collapse prevention performance level. Immediate occupancy performance level is defined
as the point of losing the linear relationship of moment-curvature plots at the plastic hinge
locations of the structure. Most of the time, it was observed that the plastic hinges were
formed in first storey transverse beams. Thecollapse prevention performance level is defined
as the point where the drop of 30 per cent moment capacity at the plastic hinges was observed
in the first storey transverse beam.
For each IDA curve, the inter-storey drift ratios relevant to the points of the immediate
occupancy performance level and the collapse prevention performance level were calculated
and averaged to obtain the normalized results at immediate occupancy and collapse
prevention performance levels, respectively. Then the results are compared in an average IDA
curve for different return period earthquakes predicted by other studies.
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Chapter 2 Literature Review 2.1 Earthquakes andWave Propagation
According to the tectonic plate theory, the earth crust is consisting of 13 major tectonic plates
(Kramer, 1996)as shown in Fig: 2.1. These plate boundaries have been identified considering
the places where the Earthquakes occurred so far. So majority (around 90%) of the
earthquakes which has happened around the world has occurred in these boundaries. Those
earthquakes are called interplate earthquakes. However, intraplate earthquakes or in other
words the earthquakes which are occurring far away from the plate boundaries could be
considered as less than 10% of the total number of earthquakes (Stein, 2007).
Characteristics of Intraplate Earthquakes are that, recurrence intervals of intraplate
earthquakes are higher than interplate earthquakes, the faults of intraplate Earthquakes is very
rarely recognized, intraplate Earthquakes release more stress than the interplate Earthquakes.
One of the most important points of intraplate earthquakes are that the seismic wave
generated by the intraplate earthquakes dissipates more slowly compared to the Interplate
earthquakes. One reason for this is that the strong, coherent rock beneath the interiors of the
plate, transmit the seismic energy more efficiently over a long distance than the weaker rocks
which are beneath the plate boundaries.
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Fig: 2.1: Tectonic plates of earth
Thus, when either an interplate or intraplate earthquake occurs many different types of
seismic waves are generated and travel through the earth crust. There are two main types of
waves. They are called body waves and surface waves. Body waves can be further categorized
in two groups as P waves and S waves. When P waves travel in the media, materials move back
and forth in the direction which the wave propagates as shown in Fig:2.2. Therefore, P waves
are induced volumetric deformations but not the shearing deformations while travelling
through the media. P waves travel faster than the S waves and follows a direct path. The
reason for the P waves to travel faster is that usually the geologic materials are stiffer in
volumetric compression than in shear.
Fig: 2.2: Propagatio of a P ae
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Shear waves, as the name describes are involved in shear deformations but not in volumetric
deformations. When S waves travel in the media, materials move at right angles to the wave
propagation direction as shown in Fig: 2.3.
The surface waves arrive after the body waves.They have low frequencies and high amplitudes.
They travel same as ripples on water and the damages caused on structures are mainly due to
these waves.
Fig:2.3: Propagatio of a ae
Surface waves which are not initiated at the source or at the beginning of the earthquakes.
They occur because of the interaction between body waves and the surface and layers of the
surface of the earth. These surfae aes trael alog the earths surfae hile dereasig the
amplitude exponentially with respect to depth. Since it is necessary to have the interactions
with layers for the surface waves to be generated these surface waves are dominating quite far
away from the source of the earthquake. Surface waves will be producing the peak ground
otio at a distae ore tha to ties of the thikess of the earths rust ad are
concentrated in a shallow zone near the surface. In the Engineering point of view, the
important surface waves are Rayleigh waves and Love Waves.
Rayleigh waves could be considered as the most important type of surface waves, especially in
terms of earthquake engineering applications. The medium has to be a homogeneous elastic
half space where Rayleigh waves would travel a bit slower than the S waves. Rayleigh waves
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will produce both the vertical and horizontal particle motions which are a point which should
be considered in terms of earthquake resilient structures as illustrated in Fig: 2.4. Low
frequency Rayleigh waves can produce particle motions at larger depth and travels faster, but
the high frequency waves are confined to shallow depths and travels slower.
Basically Love waves are developed in the presence of a soft surficial layer and their velocities
vary with frequency between the shear wave velocity of the surficial layer and the shear wave
velocity of the underlying material. Love waves only has horizontal component of particle
motion as shown in fig: 2.4.
Fig: 2.4:Rayleigh and Love wave propagation
Thus the ground motion generated due to earthquake waves sways all the structures on
groud. The aordig to the Netos la, a iertia fore ats o the struture hih
relates with the mass (m) of the building andthe accelerations (a)applied by the ground
motion. Because mass is constant when the ground acceleration increases the force acting also
increases on the structure.The energy waves of an earthquake travel all the directions, but it is
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more dangerous when it moves ground parallel to the surface. This is dangerous for buildings
which are designed to resistvertical gravity loads only.
Fig: 2.5: Identification of different wave patterns in an accelerogram
Above described wave forms are illustrated in the graph on fig:2.5. That helps us to identify the
pattern and different properties of such earthquake in after processing stage.
2.2 Seismicity of Sri Lanka
Sri Lanka is located within the Indo- Australian plate of the above mentioned tectonic plates of
the earth crust. Therefore, the earthquakes occur around Sri Lanka can be considered to be
intra plate earthquakes which are not very high magnitude in general. However considering
past records and studies on earthquakes around Sri Lanka, the effect of earthquakes on
designing buildingscannot be ignored.In the past many moderate earthquakes have been
occurred in the vicinity of Sri Lanka. It was found in literature that the earthquake catalog for
Sri Lanka was first compiled by Abayakoon,(1998). It was used by many other researchers to
prepare the seismic hazard map for Sri Lankan cities by either using Probabilistic or
Deterministic seismic hazard assessment approach. However, new composite earthquake
catalog has been compiled for Sri Lanka by (Uduweriya and Wijesundara, 2013) elaborating the
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completion period and including the recent earthquakes (after 2000) which were recorded at
stations installed at pallekele, Hakmana and Mahakanadarawa demarcated by the
geographial oordiates 20.7 N latitude and 6888 E longitude, from different sources.
Past earthquakes recorded in South Indian Peninsula were taken from the earthquake catalog
of agitude .5 for outh Idia Regio furished y Chadra ,Rao and Rao
(1984),Guha and Basu (1993),Iyengar et al. (1999),Rajendran and Rajendran (2005), and Jaiswal
and Sinha (2007).
Furthermore, internationally recognized earthquake databases, such as the National
Earthquake Information Center (NEIC), the International Seismological Center (ISC), and the
Incorporated Research Institutions for Seismology (IRIS), the Indian Meteorological
Department (IMD) and the United States Geological Survey (USGS) have also served as sources
for historical and instrumental data. Duplicate events were eventually eliminated from the
newly compiled catalog. The composite catalog spans a period of 946 yrs from 1063 to July
ad iorporates earthuakes ith M :5. All these data ere take usig the
renowned data bases and from the Journal papers which are published internationally after
reviewing.
When the catalog is closely analyzed it is clearly observed that the earthquakes of magnitude
6.5 in 1615 and 5.5 in 1938 have happened near Colombo. The earthquake in 1615 in Colombo
with a magnitude around 6.5 is suspected as killed around 2000 people.
Fernando and Kulasinghe(1986), states the clear set of data which can be found by the
measurements taken within the country. This starts with the implementation of micro-
earthquakes recording stations in Kothmalearea in 1982 under the Kothmale reservoir project.
These are also included in the earthquake catalog. Until year 2000, there werehardly any
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records of the earthquakes as there were no any measuring stations in Sri Lanka. But after the
establishment of measuring stations in 2000 at Pallekele and in 2010 at Mahakanadarawa and
Hakmana, there are records of few minor earthquakes occurred in Sri Lanka.Fig:2.6 shows
recorded earthquake events around Sri Lanka.Few recorded earthquakes are shown in above
Table 2.1
Fig: 2.6: Recorded earthquake events around Sri Lanka
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Table 2.1 Details of earthquake recoded very close to Sri Lanka
Date
Time
UTC+05:30 Location Magnitude Depth/km
1 31-Aug-1973 1:20:02 Bay of Bengal 5.9 33
2 30-Oct-1987 11:12:36 North Indian Ocean 5 10
3 31-Oct-1987 11:44:05 Bay of Bengal 4.5 33
4 7-Dec-1993 2:24:45 Laccadive Sea 5.2 10
5 17-Nov-1998 19:45:18 Laccadive Sea 4.5 10
6 12-Dec-2000 6:53:58
near the coast of Kerala,
India - 10
7 25-Sep-2001 20:26:44
near the coast of Tamil
Nadu, India 5.2 10
8 5-Aug-2004 8:45:55 Laccadive Sea 4.7 10
9 7-Jul-2005 18:43:23 North Indian Ocean 4.6 10
10 18-Jul-2007 9:57:24 Bay of Bengal 5.2 10
11 15-Apr-2009 8:47:58
near the east coast of Sri
Lanka 4.5 10
12 25-Jul-2010 15:05:02 Laccadive Sea 4 10
13 19-Nov-2011 16:10:15 Laccadive Sea 4.7 10
14 6-Jul-2012 19:48:28 Laccadive Sea 4.2 10
2.3Damages on Gravity designed frames
When we consider post disaster studies of seismic events all over the world many authors have
recorded that the majority of collapsed or heavily damaged structures are reinforced concrete
frames and masonry in fill walls (Saatcioglu et al., 2001). The reinforced concrete generally
preferred over other construction materials due to economic reasons and availability. Heavy
damages inflicting most of the casualties had been observed due to poor performance of
gravity designed reinforced concrete frame elements and masonry infill walls followed by very
poor regulatory control over both structural design and construction. Especially lack of proper
lateral load resisting system in gravity designed reinforced concrete frames leads to a soft-
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storey failure resulting due to the low ductile failure modes of structural members undergoing
inelastic deformations. Different low ductile failure modes were observed in gravity designed
concrete frame structuresare:
Joint failures Shear failures Flexural failures and Combined failure of shear and flexure
Mostly on the column elements these common types of failure modesare identified.
2.3.1 Joint failures
Behavior of beamcolumn joints in frames subjected to lateral loading is a complex
phenomenon, as a number of parameters affect the strength of joints. Further, there is
significant difference in the mechanism of shear resistance in case of exterior and interior
beamcolumn joints. Shear strength of beamcolumn joints is mainly influenced by
compressive strength of concrete, joint aspect ratio, amount of longitudinal reinforcement in
beams connected to the joint and axial force in column. Considering uncertainties regarding
role of transverse reinforcement in failure mechanism of joints, the joint shear strength models
prescribed assuming that the internal forces in the joint are to be transferred by diagonal
compression strut of concrete core alone. The model proposed by Hegger et al, (2004),
considers the number of parameters influencing the shear strength of joints, including the role
of transverse reinforcement, and is applicable for all types of joints. Most of the other
proposed models are not applicable to the non-ductile gravity designed buildings, where no
transverse reinforcement is provided in the joint region.
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Fig: 2.7: Beam-column joint failures
As shown by fig: 2.7, in most places poor detailing are seenin beamcolumn joints, which may
lead tofail in joint shear strength. Then due to the applied compression and tension cycles of
loading it produces diagonal direction cracks in joint and lead to a failure.
2.3.2 Shear failures
Most of the failures in RC frame buildings during past earthquakes and experimental studies
have been mainly attributed to shear failure of columns as shown in Fig:2.8. Brittle shear
failure of beams and columns occurs due to strut action of in-fills, especially, in case of weak
frames with strong in-fills and frames with in-fills of partial height.
Fig: 2.8: shear failures due to lack of confinement
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Shear failure of Reinforced Concrete (RC) columns in in-filled frames is observed particularly in
buildings designed solely for gravity loads due to lack of sufficient transverse reinforcements.
The transverse reinforcements used were 6mm -10 mm mild steel with smooth surface placed
at wider spacing. They were also limited to be perimeter ties with 900 hooks in detailing
providing lack confinement effect.
For inference about possibility of shear failure in columns, reliable estimation of column shear
strength is a prerequisite. Researches on this have revealed that the shear strength (Vn) of a
column can be considered to have distinct contributions from concrete (Vc) and transverse
reinforcement (Vs). Contribution of concrete inshear strength is rather complex and is
influenced by several factors including axial compressive force, column aspect ratioand
deformation ductility demand. A number of models are available for evaluation of shear
strength of RC columns.
As masonry walls participated in lateral load resistance of the frame system, short column
effect was created around windows and other openings. Even some nonstructural elements
reduce the deformation capacity of structural elements. Sometimes the landing slabs of
staircases connected at column mid height lead to apply unexpected lateral forces or cause
short column effect. That may associate with reduced unsupported height of column element
suffering brittle shear failures described which shown in fig:2.8.
2.3.3 Flexural failures
Flexural failure occur due to either compression crushing of concrete or due to yielding of
reinforcement steel accompanied by tensile cracking of concrete. Typical bending failure
caused by yielding of bars on the tension face near the top and bottom joints of the column.
Cracks will appear on both sides symmetrically because the reversible nature of seismic
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loading. Fig: 2.9 shows the compression crushing of concrete due to flexural deformation at
the plastic hinge region.
Fig: 2.9: Cushing of concrete in plastic hinge regions
In flexure increased confinement pressure will lead to break of hoop reinforcements and when
they fail the buckling of main reinforcement occurs illustrates in fig:2.10. Finally failure with
crushed concrete and exposed broken stirrups and buckled main bars may see in failed
sections of the elements.
Fig: 2.10: Buckling of longitudinal reinforcements
Flexural yielding of columns is observed in case of frames with weak in-fills. This leads to make
the short column effect as shown in Fig:2.11. Failure of the tension side columns due to
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excessive overturning moment in in-filled frames has been observed in case of infill panels with
large aspect ratio. Failure of compression side columns due to crushing of concrete has also
been reported in frames having very high gravity loads.
Fig: 2.11: Short column effect
2.3.4 Combined failure of shear and flexure
With very complex behavior of buildings under seismic actions, it may mostly occurrence of
combined failures of above described modes in shear and flexure. The severe among these will
be soft storey mechanism shown in fig: 2.12 which always lead to more casualties with heavily
damaged structure.
Beams may also fail either in shear or in flexure. Shear failure is undesirable as it limits the load
resisting capacity and prevents the yielding of longitudinal reinforcements. Shear failures occur
mainly due to inadequate lateral ties provided. Flexural failures occur due to inadequate
amount of main horizontal steel bars or inadequate anchorage of the bars especially at the
bottom near the beam column joint. Sometimes it may be due to poor quality of concrete.
Even the beams can have reversal of stresses in top bottom faces in a seismic action which
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have to be considered in design. Since the failure of a beam is less catastrophic than a column
the designs should be so as to have strong supporting columns than beams.
Fig: 2.12:Soft storey effect
As explained earlier the worst is soft storey effect on first storey columns as shown in fig:2.12
considering the overall damage and casualties.
Above mentioned reasons for the seismic damages can be categorize in to two groups.
1. Factors contributing to increased seismic demand
2. Factors contributing to reduced ductility and energy absorption
Factors contributing to increased seismic demand
The unreinforced brick and block walls act as lateral bracings for reinforced concrete frames
often damage prematurely developing diagonal tension and compression failure or out of
plane failure in most of the seismic events. In most of the buildings masonry were used
extensively for interior partitioning as well as exterior enclosure increasing wall to floor area
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ratio. That does not make effective lateral load resisting system with sufficient stiffness in brick
walls which causes high drift demands on frame members.
Most commercial buildings generally use parking spaces at the ground floor level and
sometimes stores at first storey level providing larger floor area above ground floor. These
factors result in forming soft storey at leading to extensive deformation demands on the highly
critical fist storey columns.
Majority of the reinforced concrete frame structures have violated the philosophy of Strong-
column Weak-beam causing high deformation demands on columns especially in first storey
level which increases the storey drift and force to form hinge on the column.
Factors contributing to reduced ductility and energy absorption
Lack of transverse reinforcements is the most common case to sustain heavy damages on
columns. Even the transverse reinforcements limiting to perimeter with 900 hooks also result in
poor confinement effect on structural elements.
Very few or no transverse reinforcements in beam-column joints are the next observation on
reducing the strength and deformability of structural system. Openings of the masonry infill
walls and staircase landing slab connection at mid height of the columns lead to short column
effect reducing the strength of structural system.
Considering all of these post disaster studies, we can configure that most of our school
buildings having structural systems with weak beams and strong columns designed may have
very low capacity on drift demands in a seismic event. As well as most of the masonry walls of
the sides of those buildings in longitudinal face are half walls as often observed. And they can
easily make the short column effect.
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21
Some school buildings have libraries or auditoriums at ground floors having wider spaces which
can obviously form soft storey mechanism at seismic events.
In detailing structural elements commonly provided transverse reinforcements on columns are
6 mm mild steel ring type stirrups having only perimeter tie shape with 900 hooks leading very
low confinement effect. Even at joints it could not observe any special detailing to increase the
ductility. Hence the structural system of these school building type plans can categorize in just
gravity design frames with no considerations on lateral load resisting system which can lead to
structural and non-structural failures at an unexpected seismic event.
2.4 Damage Indices used for assessment of a structure
To measure the damage state after a seismic event on a structure, several damage indices have
been introduced in the literature. They can categorize in to two different groups as non-modal
parameter based and modal parameter based damage indices depending up on the parameter
or parameters used to define the index (Cosenza et. al. (1993) and Bozorgnia and Bertero
(2001)).Commonly, most of those indices are equal to zero when structure remain in elastic
range during seismic event and they are equal to 1 at complete collapse of the structure.
Damage parameters such as ductility, displacement, inter-storey drift and energy or
combination of them can be used to define non-modal parameter based indices. Ductility
based damage index introduced by Powel and Allahabadi, (1988), Inter-storey drift based
damage index, Park and Ang, (1985, 1987), damage index and modified Park and Ang damage
index are few of non-modal parameter based damage indices.
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22
2.4.1 Non-modal parameter based damage indices
2.4.1.1 Ductility based damage index
11maxmax monymon yuu uuDI Where umax is the maximum displacement, uy is the yield displacement, umon is the monotonic
displacement, max=umax/uy is the displacement ductility imposed by an earthquake and
mon=umon/uyis the monotonic ductility capacity of the structure.
When the ductility is defined in terms of the top displacement of a multi degree of freedom
frame, this damage index fails to identify the concentration of damage in a single storey.
2.4.1.2 Inter-storey drift based damage index
umIDIDDI WhereID mis the Inter-storey drift at the center of mass, ID uis ultimate inter-storey drift which
usually corresponds to the 30% strength drop of the storey.
This damage index is used as a better non-modal parameter based damage index to quantify
the damage of a structure.The ductility and the drift based damage parameters do not account
themselves the accumulation of damage due to the number of inelastic cycles that the
structure is subjected and the energy dissipation demand. Hence they could not estimate the
actual damage state of a structure (Mahin and Bertero,(1981);Mahin and Lin, (1983)).
2.4.1.3 Park and Ang damage index
This index which is the linear combination of the ductility defined in terms of displacement and
the hysteretic energy dissipation as expressed in the following form
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23
yuy hyu y F EDI parameter is calibrated using the experimental data.
This index includes the cumulative effect of repeated cycles of inelastic response to the
damage with the consideration of the hysteretic energy (Eh) dissipation. Due to the difficulty of
parameter determination the methodology was modified by Kunnathet al, (1992) basically by
referring the moment curvature response of plastic hinge region instead of the force-
deformation response of a structural member.
2.4.1.4 Modified Park and Ang damage index
uy
h
yu
y
MEDI
Both Park and Ang damage index and the modified damage index by Kunnath et al,(1992)are
calibrated for the concrete member experimentally, they might not be appropriate for
assessing the damage state of only gravity design structures with poorly confined reinforced
concrete members.
2.4.1.5 Mahin and Bertero damage index
A damage index by combining of displacement ductility and the hysteretic ductility H which is
defined as the ratio of hysteretic energy EH to energy capacity EHmon under monotonically
increasing lateral deformation has proposed by Mahin and Bertero (1981) as:
11111 111 HmonHmonDI This damage index is further improved by Bozorgnia and Bertero, (2001) as:
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24
2/1222 11111 HmonHmonDI Where1and 2are constants and mon is the ductility defied under the monotonically
increasing lateral deformation.
2.4.1.6 Damage index based on the wavelet energy
The proposed damage index based on wavelet energy by Wijesundara et al, (2011)can be
expressed as:
utEEDI Where Et is the total wavelet energy and Eu is the ultimate wavelet energyassociated with the
acceleration response at the top storey of a structure during the seismic excitation. Since this
damage index is based on energy of the response, it is capable to take into account the effect
of inelastic cyclic loading on the damage.
2.4.2 Modal parameter based damage indices
Natural periods, mode shapes, modal damping ratio and inelastic period are some of damage
parameters which can be used to define modal parameter based damage indices. However,
there is only few modal parameter based damage indices found in literature.
2.4.2.1 Damage index based on the natural period
Damage index based on the natural period of vibration proposed by Dipasquale and Cakmak,
(1990) is expressed as:
d
e
TTDI 1
Where Te and Td are the natural periods of undamaged and damaged structures, respectively.
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25
Comparing all of those damage indices described above, it can be noted that the inter-storey
drift based damage index is the most commonly used damage index by Engineers and
researchers, considering its simplicity in estimation of global damage status of the structure.
Damage index based on ductility which defined in terms of top displacement would not
identify the concentration of damage in a single storey. Therefore inter-storey drift based
damage index can be considered as a better non-modal parameter to quantify the damage of
structure.
2.5 Incremental Dynamic Analysis (IDA) method
Incremental Dynamic Analysis (IDA) is a parametric method which can be used for the
assessment of structural performance under seismic loads using the inelastic dynamic analyses
rather than using static pushover analysis methods. This method is proposed by Vamvatsikos
and Cornell, (2002). From the inelastic dynamic analysis, the resultant damage parameter
defined earlier in this section with assigning one or more accelerograms (recorded real ground
motions) each scaled to multiple levels of intensity, on the structure can be obtained. The
resultant curve of the response parameter verses the intensity level for a given accelerogram is
called the incremental dynamic analysis curve.
Then,the resultant IDA curves are observed to obtain the different performance levels of the
structure within the Performance Based Earthquake Engineering (PBEE) frame work. With the
use of computer programs, nonlinear dynamic analyses for each accelerograme for different
scaling intervals can be performed and relevant response results can be obtained. Selecting
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26
suitable scaling intervals, continuous curve can be developed to observe the structural
behaviour from elastic yielding to complete collapse facilitating the understanding.
In this method, the fundamental concept is to scale an accelerogram. Different earthquake
acceleration records can be found in many databases which are pre processed by baseline
correction, filtering, rotation etc. There are three ways to select ground motion records:
Select from a database perfectly match with site response spectrum Create an artificial earthquake record Select several real records from a database and process them by scaling magnitudes to
match their average response spectrum with the expected site response spectrum.
The last method is very much suitable because it can interpret the real frequency content and
energy content all over the analysis giving better acceptable results. (D. Vamvatsikos and C.
Allin Cornell, (2002))
The selected accelerogram is a vector with elements
a(ti) ti= 0, t1, t2, t3 , t(n-1) For simplicity, a scalar , + ) can be introduced to uniform scaling up or down to account more severe or milder ground motions. Therefore, the scaled accelerogram can be represented
as:
a= {a, (ti) }
This operation can also be conveniently considered as a scaling of elastic acceleration spectrum
byin Fourier domain as amplitudes across all frequencies keeping phase information intact.
Hence, in this study the spectral acceleration is taken as the intensity measure parameter.
-
27
Performing inelastic dynamic analyses of a structural model with assigning accelerations in
multiple scales, inter-storey drift as the selected damage index parameter in this study at each
storey levelcan be obtainedand, subsequently, the IDA curves for each acceleration record can
be developed as plots of maximum Inter-storey drift against the spectral acceleration.
An example of IDA curve is shown in Fig: 2.13. Each point of the curve explains the maximum
inter-storey drift value obtained from nonlinear dynamic analysis of the model structure by
assigning the acceleration record with the scaled intensity represented by spectral acceleration
on the structure.
Then this curve facilitates our understanding on structural behavior at different earthquake
magnitude levels. Parallel observations of moment-rotation curves of beams and columns will
illustrate the damage status of the structure, which can be used to define the performance
levels of Immediate Occupancy (IO) and Collapse Prevention (CP) in the PBEE frame work.
Fig: 2.13: An example IDA curve
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Sp
ect
ral
Acc
l / (
Sa
/g)
Inter-Storey Drift Ratio %
-
28
Chapter 3 Building Description and Finite Element modeling 3.1Typical School Buildings in Sri Lanka
School works division of Ministry of Education has developed several type plans for school
buildings since 1984.Considering requirements, availability of lands & financial allocations of
government, the ministry will decide the suitable type plan out offollowing two configurations:
8 class room block type plan 2 storey 12 class room block type plan 3 storey
Fig: 3.1 and 3.2 illustrate the plan view, elevation and sectional view of the two configurations;
respectively.Some special designs also have been done for several schools when it is required
to combine class rooms and libraries or assembly halls (Auditorium).
Fig: 3.1: 8 class room block type plan 2 storey
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29
Fig: 3.2: 12 class room block type plan 3 storey
From various type plans designed by the Ministry of Education Sri Lanka, the two storey 8
classroom type plan was selected for this study.This type of buildings, shown by fig: 3.3, is very
common in schools in all over the Island.
The building consists of reinforced concrete framed structure designed to resist the gravity
loads. The structure could be considered as symmetric in plan and elevation. The floor plan is
rectangular with dimensions of 27.9 m in length and 9 m in width. The building has 9 bays with
equal span of 3.1 m in longitudinal direction while it has only single span of 9 m in its
transverse direction.
When the architectural features are considered, there is a stair void in middle bay of the
longitudinal direction and four class rooms besides the stair void sizing of 6.2 m x 7.5 m
separated using infill brick walls in each floor. There are corridors of 1.5 m wide in front of each
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30
floor. The roof covered with Calicut tiles has wooden frame work mounted on roof beams
combined with reinforced concrete posts and gabled infill walls.
Fig: 3.3:Selected school building type
The superstructure of the building consists of 20 columns of 300 mm x 375 mm along two
edges of the 9 m spanning direction (transverse direction). The columns hold 300 mm x 650
mm beams spanning on transverse direction while they are tied together using 225 mm x 225
mm tie beams. The floor slab is 115 mm thick and has only one void for stair case. All columns
are tied around using a 225 mm x 225 mm tie beam at roof level also while the 225 mm x 450
mm roof beams host the roof spanning on transverse direction.Fig:3.4 shows a section of
selected building.
Other architectural and structural drawings are included in the appendix A.
-
31
Fig: 3.4:Sectonal view of the building
3.2 Nonlinear Finite Element model
A 3-Dimmensional (3D) finite element model is developed for damage assessment ofthe
building when it subjects to an earthquake usig Opeees Fiite Eleet progra. The
objective is to develop the finite element model which is capable of taking into account
material andgeometric nonlinearities in dynamic response of the building induced by an
earthquake. The Opeees progra proide wide range of facilities for nonlinear structural
modeling.
Fig:3.5 illustrates the 3-D model of the building. It consists of frame elements to represent all
the beams and columns. As in most of the finite element analysis programs initially the nodal
coordinates were input to the program referring the actual design and then combining nodes,
the elements were added in the model. The base nodes were then assigned with fixed single
point constraints. All frame (beams and columns) elements in the models are inelastic beam-
olu eleets aailale ithi Opeees fraeork (PEER, 2006). They are based on the
-
32
force formulation (Spacone et al., (1991). The force formulation method will be described in
detail later.
Fig: 3.5: Opeees -D finite element model
The first floor slab and the roofwere modeled using rigid diaphragms.A Diaphragm Constraint
causes all of its constrained joints to move together as a planar diaphragm that is rigid against
membrane deformations. All constrained joints are connected to each other by links that are
rigid in the plane, but do not affect the out-of-plane deformation. This is required to define a
master node and name other all slave nodes to link with master node. The Opeees
program provides this facility under multi point constraint. In this model, the master node at
each floor is added at the centre of the mass of the floor and the rigid diaphragm was defined
connecting all slave nodes around the perimeter to the master node.
-
33
The force-displacement relation is then transferred to the global reference system
considering of nonlinear geometry of large displacements in accordance with the corotational
theory.
This model is capable to take into account the axial force and bending moment interaction,
since, the inelastic beam-column element accounts for the interaction along the beams or
columnsby integrating of uniaxial hysteretic material models over the cross section of the
beam or column. Each inelastic beam-column element is assigned five integration points and
each integration point represents a fibre section.
3.2.1.Fiber Sections
The fibre section assigned to an element is constructed using a patch and reinforcement
layers. The size of the patch and the number of reinforcement layers vary depending on the
cross sectional size and the reinforcement detailing of the element, respectively. Fig:3.6
illustrates the fiber sections assigned to the first storey column (C1).
To define a fibre section 2D coordinate system is considered having its origin in the
geometric center of the section. According to above example of defined section, the
coordinates of the four corner points of the concrete patch and starting and end points of the
steel layers are to be set. The total areas of reinforcements in each layer are also required. The
shapes of concrete can be varied according to difference of confined and unconfined concrete
material assignments on core and cover concrete patches, but in this model the concrete
material considered to be single patch having unconfined concrete material which is further
described below.
-
34
Fig: 3.6: Fibre section assigned to 1st storey column of 375 x300 mm
The concrete patch can be divided in to a mesh having different number of fibers in both ways.
In this model all the sections are defined to have a 10 x 10 grid referring to the study of
sectional sensitivity conducted by Spacone et al (1991) which has shown to be a good number
in converging response pattern. An example of material assignment is shown in below
fig:3.7.More details of material models are described later.
Fig: 3.7: Material assignment in a fibre section
Stre
ss
Strain
Concrete
-
35
All the beam column elements are defined to have 5 integration points, which also defined
referring to the study of Spacone et al. (1991) on element sensitivity with different number of
integration points. Though different fibre sections can be assigned in each integration points,
here it has been considered same section all through the element and integration points are
used to increase the element sensitivity as well as to obtain outputs of moment-curvature
curves of sections which are very important outputs in this analysis described in later chapters.
Furthermore Fig: 3.8 illustrates how beam and column elements are assigned the fiber sections
in the model.
Fig: 3.8: Assignment of fibre sections in each element
3.2.2 The force formulation
The most important aspect in modeling is the availability of elements based on force
formulation. In the force-formulation the force-displacement relation is established in the
basic element without rigid body modes.The force formulation offer many advantages over the
typical displacement formulation such as:
-
36
The force-interpolation functions are always exact in the absence of 2nd order effect A single element can be used to represent the curvature distribution along the entire
member with sufficient accuracy through selection of sufficient number of
integration points
The formulation has proven numerically robust and reliable, even in the presence of strength softening as it is noticed in the compression crushing of elements.
In this method, the force shape function is assumed first and then stresses are derived
satisfying equilibrium condition and by the stressStrain relationship the strain values are
obtained. Two of those operations are closedform approaches and more accurate results could
obtain even though the last step of displacement calculation is done in weak form
compatibility equations. Forced-based formulations yield the element flexibility matrix rather
than the element stiffness matrix. However, there are some cases where it is worth to
compute the element flexibility matrix without rigid body modes and to invert it to get the
corresponding element stiffness matrix. This is particular interesting in those instances where
displacement-based beam formulations are approximate and force-based formulations are
exact for example tapered elements, material nonlinear elements. Fig: 3.9 illustrates the flow
diagram of the force formulation.
Furthermore, the force formulation method has more advantages than displacement based
formulation such as:
Drastic reduction in number of structural degree of freedoms can handle softening members Element loads are easily considered
-
37
The ea ad olu are assiged ith fire setios defied usig failities i Opeees
program. The materials use to define the section are nonlinear as describe bellow.
Fig: 3.9: flow diagram of force formulation
3.2.3 Concrete Material Model
Since there are no adequate shear reinforcement provided for column and beams in this
gravity design structure the confinement effect of the core is minimized. Therefore concrete is
considered to be unconfined concrete material.
To defie uofied orete the Opeees fraeork proides aterial type aed
Corete hih represet the uiaial Kent-Scott-Park, (1971)nonlinear concrete material
model. Further degraded linear unloading/reloading stiffness according to the work of Karsan-
Jirsa with no tensile strength also has been taken in to account in this material model.
Fig: 3.10 illustrates the monotonic curve of stress-strain in concrete material while Fig: 3.11
shows the hysteretic response of the concrete material under the cyclic loading indicating the
loading and unloading and reloading branches at different levels of strains.
-
38
Fig: 3.10: Uniaxial concrete material, stress-strain relationship
Fig: 3.11:Typical hysteretic stress-strain relation of concrete
The strai opoet, c at the peak compressive strength and u at the concrete crushing are
estimated using following equations as specified in uniaxial Kent-Scott-Park (1971) nonlinear
concrete material model.
euS
Str
ec
fc
fu
Strain
Stre
ss
-0.002 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016
Concrete Strain [mm/mm]
Co
ncr
ete
Str
ess
[M
Pa
]
7
14
21
28
35
42
49
-
39
'1
002.0
c
yhs
c
ff
k
k
kSh
ffz
kz
hs
c
c
m
m
u
002.043
100014529.03
5.0
002.08.0
'
'
Where fc is concrete compressive cylinder strength, fyh is Yield strength of hoop reinforcement,
s is ratio of volume of hoop reinforcement to volume of concrete core, h is the width of concrete core measured outside of the hoops and Sh is the spacing between hoop
reinforcement. Aordig to the aoe defiitio ad gie desig details, the Corete
material is defined with properties of compressive strength, f pc = - 20 MPa, crushing strength, f
pcu= - 1MPa and corresponding strains are c = -0.004 and u = - 0.006.
3.2.4 Reinforcement Steel Material Model
The nonlinear material for reinforcement is defined using the uniaxial bilinear steel material
aed teel ithi the Opeees fraeork. I this aterial kieati hardeig and
optional isotropic hardening are describe by a nonlinear evolution equation. The relevant
stress strai ure for teel is sho i folloig fig:3.12 while Fig: 3.13 shows the
hysteretic response of the steel material under the cyclic loading.
-
40
Fig: 3.12:Uniaxial Steel material, stress-strain relationship
Fig: 3.13:Hysterisis model of Steel material
Where Fy is the yield strength, E is the Initial elastic tangent (modulus of elasticity) and b is the
strain hardening ratio. According to the design information, the properties of steel material are
defined as Fy = 460 MPa, E = 200 GPa and b = 1%
Fy
Fy
E0
Str
ess
or
Fo
rce
Strain or
Deformation
840
700
560
420
280
140
0
-140
-280
-420
-560
-0.010
0.000
0.010
0.020
0.030
0.040
0.050
0.060
Strain [mm/mm]
Str
ess
[M
Pa
]
-
41
Chapter 4 - Analysis and Results
4.1 Selection of accelerograms
To perform nonlinear dynamic analyses of structures, the seismic input needs to be specified in
terms of accelerograms. Accelerograms which represent the variation of ground acceleration
with respect to the time during an earthquake, maybe either in terms of
Artificial accelerograms (i.e. generated by using stochastic algorithms), Natural accelerograms (that is selected from real earthquakes) or Simulated accelerograms (i.e. generated by a numerical simulation of the rupture and
travel path mechanisms).
The latter option is fairly complex to be implemented, requires a large number of input
parameters and a comprehensive knowledge of the seismotectonic setting of the area under
study. Therefore, simulated accelerograms are usually employed to a lesser extent in the
engineering practice when compared with real and artificial records.
Nonlinear dynamic analyzes were performed using real accelerograms. The use of real
accelerograms rather than artificial accelerograms as seismic input has the important
advantage to account for amplitude, frequency content, energy content and duration
characteristicsof the real ground shaking.
All of the above characteristics are of primary importance in the assessment of non-linear
response of structures. Furthermore, accelerograms recorded during real earthquakes are
preferable as they possess realistic low frequency content and proper time correlation
between horizontal and vertical components of motion as well.
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42
For the seismic assessment of a structure, it is specified to use at least 7 accelerograms to
obtain the average response. But in literature it has shown that using 30 records it gives more
accurate fig: as the average response. Hence, for this analysis, 30 real accelerograms are
selected from PEER database (http://peer.berkeley.edu/peer_ground_motion_database)
recorded in different locations all over the world. Each earthquake has its own characteristic
properties of duration, frequency content and energy content. Fig:: 4.1showfew of the
selected real accelerograms.
Then these earthquake records are scaled to match their average response spectrum with the
site response spectrum according to following procedure.
Fig: 4.1: Three of the selected accelerograms
Note that all selected accelerograms and their response spectra are attached in Appendix B
and C, respectively.
-4.0
-2.0
0.0
2.0
4.0
0 10 20 30 40Acc.
(m/s
2 )
Time (s)
-5.0
0.0
5.0
0 5 10 15 20 25Acc.
(m
/s2 )
Time (s)
-10.0
-5.0
0.0
5.0
10.0
0 10 20 30 40
Acc.
(m
/s2 )
Time (s)
-
43
4.2 Response Spectra
A response spectrum is a plot of the peak values of the response(displacement, velocity, or
acceleration) of a number of Single Degree of Freedom (SDOF) systems with different
naturalvibration periods subjected to the same seismic input. Therefore, an acceleration
response spectrumrepresents the peak accelerations that a suite of SDOF systems with a range
of natural periods mayexhibit when subject to a given ground motion component.In general,
the acceleration response spectrum associated with a specific time-history recorded at agiven
location has a jagged shape with significant peaks and valleys. The response spectrum
foranother ground motion recorded at the same site during a different earthquake will exhibit
also anirregular shape, but the peaks and valleys will not necessarily coincide with those in the
previousone. Therefore, appropriately smoothed spectra are usually defined for design and
evaluationpurposes. Thesespectra are termed as design response spectra. They do not
represent the particularaccelerationresponse from a single ground motion time-history, but
rather they are intended to bemore representative of general characteristics for a reasonable
range of expected ground motions at agiven site. There are two basic approaches for the
development of design response spectra: site-specificor standard procedures.
Site-specific response spectra are developed using source to site distances, appropriate
attenuationrelationships, expected magnitudes, and actual local site conditions. Therefore, it is
typicallyassumed that site-specific studies will provide more accurate acceleration spectra than
using thecodified standard acceleration spectra. Site-specific response spectracan be
generated by means of a deterministic seismic hazard analysis (DSHA) or a probabilisticseismic
hazard analysis (PSHA). In the DSHA, the site ground motions are estimated for a
-
44
specificearthquake scenario, defined as a seismic event of a certain magnitude for a particular
seismic sourceoccurring at a certain distance from the site. The representation of the ground
motions in terms of thecorresponding site-specific response spectra is achieved by using
appropriate attenuation relationships, (Anil K. Chopra, (2006).
The PSHA is anapproach that uses the likelihood (probability) that a given level of ground
motion will occur duringa specific exposure period. In the PSHA, the site ground motions are
defined for selected values of the probability of exceedance in a given time exposure period, or
for selected values of annualfrequency or return period for ground motion exceedance. This
approach considers all potential earthquake sources that may be significant to the site
underconsideration. This approach incorporates the frequency of occurrence of earthquakes
ofdifferentmagnitudes on the seismic sources, the uncertainty of the earthquake locations on
the sources, andthe ground motion attenuation including its uncertainty.
On the other hand, standard response spectra are based on a general characteristic shape that
isdefined in terms of estimates of selected ground motion parameters, which can be effective
peak ground accelerations or spectral accelerations. The approach proposed by Newmark and
Hall (1982), to develop design response spectra using peak ground motion parameters (peak
ground acceleration, velocity and displacement), multiplied by a series of appropriate spectral
amplificationfactors that depend on the damping level.Above description is simply illustrated
in following fig:4.2
-
45
Fig: 4.2: Definition of a response spectrum
For this study the site response spectrum is developed using the criteria and equations given in
the Indian code IS 1893 (Part 1) 2002, Clause 6.4. The three different response spectra with 5%
damping are developed in Indian Code for rock or hard soil, medium soil and soft soil as shown
in Fig:4.3. However, this study assumes the site to be located in the hard soil. Peak ground
accelerations at the site on hard soil in Colombo are given as in Table 4.1.
Table 4.1 Peak ground accelerations
Return period / years Peak Ground
Acceleration / g
50 0.05
475 0.10
2500 0.35
Peak ground acceleration values at three return periods are taken from study conducted by
Uduweriya et al. (2013),based on the probabilistic seismic hazard assessment.
-
46
Fig: 4.3: Graphs for Site response spectrum from Indian code
The equations of three main stages of response spectrum for hard soil are given in the
following equations as:
1 + 15 T . T .
= 2.50 . T . 1.00/ T . T .
The relevant plots of spectra are developed as shown by Fig:4.4.
Type II (Medium Soil)
Type I (Rock or Hard Soil)
Type III (Soft Soil)
Period (s)
2.0
2.5
3.0
Sp
ect
ral
Acc
ele
rati
on
Co
eff
icie
nt
(Sa
/g)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0
0.5
1.0
1.5
3.5
4.0
-
47
Fig: 4.4: Site response spectra
The selected real accelerograms are then scaled to match their average response spectrum
with site response spectrum using different scale factors. Fig: 4.5 illustrates the 5% damped
response spectra of scaled 30 accelerograms. The SeismoSignal (Version
5.0.0)(www.seismosoft.com)computer program was used to obtain these response spectra by
feeding each selected earthquake as an input. Furthermore, Fig: 4.6, Compares the site
response spectrum (475 Y) and the averaged response spectrum obtained from 30 real
accelerograms.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 1 2 3 4
Spe
ctra
l A
cce
llera
tio
n (
Sa/g
)
Period (s)
475 Y
50 Y
2500 Y
-
48
Fig: 4.5: 5% Response spectra of 30 earthquakes
All 30 response spectra are attached separately in Appendix - C.
Fig: 4.6: Comparison of response spectra
Finally, the matched set of earthquake records can be considered equal to recorded
earthquakes in Sri Lanka, hence their scale values are considered as equal to scale 1.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 1.0 2.0 3.0 4.0 5.0
Spe
ctra
l A
cce
lera
tio
n (
Sa /
g)
Period (S)
Avg R S
Site R S 475 Y
Site R S 50 Y
Site R S 2500 Y
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49
4.3 Incremental Dynamic Analysis (IDA)
As discussed earlier the Incremental Dynamic Analysis (IDA) curve is simply a plot of one
damage measurement with increment to intensity of an earthquake applied on the structure
(D.Vamvatsikos and C.A.Cornell, (2002)). In this study, the inter-storey drift is selected as the
damage measurement considering its simplicity and applicability as explained in early section.
The intensity of an earthquake can be interpreted by different measurements. In many
researches it has shown that the spectral acceleration is a better measurement to represent
the intensity.
IDA curve is obtained from appropriately scaling each accelerogram to cover the entire range
of structural response, from elasticity, to yielding, and finally global dynamic instability. Scaling
of an accelerogram is started from factor 0.2 and increased by 0.2 factors until failure of the
structure is observed. The maximum inter-storey drift corresponding to a given scale factor of
the selected accelerogram is obtained from nonlinear dynamic analysis of the model.It must be
noted that input ground acceleration is applied in longitudinal direction of the school building
model to perform the inelastic dynamic analysis. From the modal analysis of the building
without including the masonry walls, it is observed that first translational modes in the
longitudinal and the transverse directions are quite close to each other. Even these period
values in both directions are verified using a similar modal analysis for elastic finite element
model of the structure using SAP 2000 (Version 10) computer program. As a consequence of
that, input accelerations are applied in slightly weaker longitudinal direction.
Then by repeating the non-linear dynamic analysis of the model for different scale factors of an
earthquake, inter-storey drifts for different scale factors can be obtained. The corresponding
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50
spectral accelerations for different scale factors are taken from their response spectra. Once
the inter-storey drifts and corresponding spectral accelerations are obtained for different scale
factors of acceleration, the IDA curve for the selected accelerogram can be drawn as variation
of spectral acceleration against the inter-storey drifts. This procedure is simply explained by
following algorithm in fig:4.7
Fig: 4.7: Algorithm of IDA
To make this analysis process easier, a MATLAB (Version 7.6.0.324 (R2008a)), (2008),
(http://www.mathworks.in)code was developed to ru the Opeees progra. The MATLAB
code opens the model and then performs the nonlinear dynamic analysis calling the ground
motion text path file with 0.2 scale increment at each step. Finally,the plotsof the relevant
moment-curvature curves and the maximum inter-storey drift are obtained and saved for
future references. This process was repeated until the failure of the structure is observed for
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51
each accelerogram. Altogether 793 inelastic dynamic analyses are performed for the school
building to develop the 30 IDA curves for the 30 ground motion records.
4.3.1.Nonlinear dynamic analysis
A Newmark acceleration time integration scheme with beta and gamma 0.25 and 0.5
respectively and tangent stiffness proportional damping equal to 5% of critical damping were
adopted in this analysis in verifying the incremental dynamic equilibrium. Furthermore, it must
be noted that the energy convergence criterion is used with Krylov Newton Raphson
incremental iterative procedure for checking the convergence of the model.
4.4. Results of IDA
The IDA curves start as straight line in the elastic range and then show the softening by
displaying a tangent slope less than the elastic and also indicate the significant softening
displaying the effect of yielding. They also display the record-to-record variability. This can be
observed in following fig:4.7 with 30 IDA curve plots after the analysis.
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52
Fig: 4.8: IDA curves for 30 earthquakes
4.4.1Estimation of Immediate occupancy (IO) and Collapse prevention (CP) performance
points in IDA curves
The immediate occupancy performance level is defined as the elastic limit of a structure while
the collapse prevention performance level is defined based on the type of the failure mode
observed in the critical elements in which larger plastic deformation is expected.
The immediate occupancy performance level of a structure is defined as the end of the elastic
limit. For the building, immediate occupancy performance point on each IDA curve is defined
corresponding to the flexural yielding at the first storey beam as shown by fig:4.9.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Spe
ctra
l A
cce
lera
tio
n
(Sa
/g)
Inter-Storey Drift Ratio %
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53
Fig: 4.9: Defined point of flexural yielding.
According to the study by Vamvatsikos and Cornell (2002), the collapse prevention
performance point on an IDA curve is defined for this study, incorporating the element
performance.
From the numerical investigation, it is evidenced that the global failure of the building results
in the failure of the first storey beam elements in flexure due to the excessive deformation. As
the result of the gravity design of the frames, effective depths of the tie beams are lower than
the columns and, in turns, this results beam sections have less strength and stiffness than the
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54
corresponding column sections. Therefore, plastic deformations are concentrated at the first
storey tie beams. As a consequence of this, the global failure points on IDA curves of the
buildings corresponds to the 30% drop from the moment capacity of 1st storey beam element
calculated using moment-curvature curves shown in Fig:4.10and 4.11.
Fig: 4.10: Moment-curvature diagrams
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55
Fig: 4.11: Example for defined failure point
For each IDA plot, the inter-storey drift ratios related to both flexural yielding and failure
(immediate occupancy and collapse prevention performance points, respectively) are found.
Then the inter-storey drift ratios are averaged to normalize the result and tabulated in Table
4.2. It is important to note that the inter storey drift ratio at the first storey was higher for all
the cases proving the soft-storey mechanism developed due to the structural configuration of
the building. Further, the resultant average inter-storey drift ratios for immediate occupancy
and collapse prevention performance levels are also tabulated in Table 4.2.
Table 4.2: Average Inter-storey Drift ratios by IDA
Immediate occupancy
performance level
Collapse prevention
performancelevel
Average Inter-storey
Drift ratio (%)
1.2 1.9
30%
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56
4.5 Static Pushover curve and results
Pushover analysis is performed using a displacement control by triangular distribution with the
effect of gravity load acting on the structure. For this 0.00001m displacement increments in
40000 steps on Node 62 of the model was applied and corresponding base shear values with
drift ratios were recorded.
The blue curve in Fig:4.12 shows the resultant pushover curve while the red line represents
the equivalent bi-linear approximation to the pushover curve considering equivalent energy to
define the yield drift or the inter-storey drift corresponding to the immediate occupancy
performance point.
Fig: 4.12: Pushover curve and equivalent bi-linear curve
Fro Fig: ., the orrespodig iter-storey drifts for iediate oupay ad ollapse
preetio perforae leels are foud adtaulated ello iTale ..
0
200
400
600
800
1000
1200
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Bas
e Sh
ear
/ kN
Drift Ratio %
SLS ULS
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57
Table 4.3: Inter-storey drift ratios- Pushover analysis
Immediate occupancy
performance level
Collapse prevention
performancelevel
Inter-storey
Drift ratio (%) 0.95 2.40
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58
Chapter5 - Assessment and Evaluations
. Copariso of results The opared resultat iter-storey drift ratios orrespodig to iediate oupay ad
ollapse preetio perforae leelsotaied fro ireetal dyai aalysis ure ith
those otaied fro pushoer ure are taulated i Tale 5.. It a e oeted that
pushoer ure uder estiate the iter-storey drift deads for IO perforae leel ad
oerestiate the iter-storey drift deads for CP perforae leel. Oerestiatio of CP
leel drift dead ould e due to the fat that stati pushoer aalysis aot take ito
aout the effets of eergy otet, duratio ad the freuey otet of a
aelerograe.
Tale 5.:Copariso of Iter-storey drift ratios
Inter-storey Drift ratio (%)
Immediate occupancy
performance level
Collapse prevention
performancelevel
IDA 1.2 1.9
SPO 0.95 2.4
%Difference -21% +26%
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59
. Perforace Based Assesset The damage indices of the school building for different return period earthquakes according to
the procedure are calculated using selected damage measure parameters in chapter 2.4.
Fig:5.1 illustrates the average curve of 30 IDA curves indicating the immediate occupancy and
collapse prevention performance points.
Fig: 5.1: Average IDA curve
The inter storey drift (ID) based damage index is defined as
umIDIDDI ID m - Inter storey drift at the center of mass
ID u Ultimate Inter storey drift
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.5 1 1.5 2 2.5 3 3.5
Spe
ctra
l A
cce
lera
tio
n /
(Sa
/g)
Inter-Storey Drift Ratio %
CP
50Y
475Y
2500Y
IO
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60
When, IDu = 1.9, resultant damage indices can be calculated and tabulate as shown in Table
5.2
Table 5.2: Damage indices by IDA
Return Period /
(years) 50 475 2500
Damage Index 0.15 0.25 0.87
It shows that the damages on the school building would be very slight bythe earthquake having
50 or 475 years return period occurring in Sri Lanka, while it may nearly in complete collapse
by an earthquake having 2500 year return period.
In FEMA guide lines (FEMA 356, November 2000), four performance levels and four levels of
seismic excitation are considered. The performance levels are designated as operational,
immediate occupancy, life safety and collapse prevention. Operational performance level is
satisfied when facility continues in operation with negligible damage after the
earthquake.Immediate occupancy performance level is satisfied when the facility continues in
operation with minor damage and minor disruption in non-essential service.Life safety
performance level is satisfied when life safety is essentially protected and the damage is
moderate to extensive. Collapse Prevention performance level is satisfied when the life safety
is at risk and damage is severe and structural collapse is prevented.The relationship between
these performance levels and earthquake levels is summarized in Fig:5.2.
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61
Fig: 5.2: Relationship between Earthquake Design Level and Performance Level
Most of the guidelines including FEMA specify the school buildings as essential buildings.
According to the results obtained from IDA curves, the school building satisfies the basic
objective for rare or 475 years return period earthquake as the building remains in immediate
occupancy performance level. However, the school building does not satisfy the essential
objective for very rare or 2500 years return period earthquakes as the building reach collapse
prevention performance level.
Operational Immediate
Occupancy Life Safety
Near
Collapse
Frequent
(43 years)
Occassional
(72 years)
Rare
(475 years)
Very Rare
(2500 years)
Ea
rth
qu
ake
De
sig
n L
eve
l
System Performance Level
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62
Chapter - Coclusios ad Future Recoedatios Fro the results of ireetal dyai aalysis of to storey 8 lassroo type pla shool
uildig, folloig olusios a e dra.
Whe the shool uildig sujets to a earthuake ith retur period of 5 or 5 years, it
auses ery ior daage to the uildig satisfyig the asi ojeties as suggested y FEMA
guidelies. Hoeer, the shool uildig leads to the oplete ollapse durig a earthuake
ith the retur period of 5 years forig the ufaorale drift oetratio at the first
storey leel ithout satisfyig the essetial ojetie. ie the shool uildigs are lassified
as iportat lass of uildigs, they should at least satisfy the essetial ojetie. Therefore,
the shool uildig is uale to satisfy the essetial perforae ojetie for 5 years
retur period of earthuake as suggested y the FEMA guidelies.
By opariso of iter-storey drift liits orrespodig to iediate oupay ad
ollapse preetio perforae leels otaied fro ireetal dyai aalysis ures, it
is lear that the to storey 8 lassroo type pla shool uildig has lo leel of dutility of
.=./. resultig fro lo dutile fleural failure odel of the strutural eleets due to
the lak of ofieet of orete. Hoeer, Euro ode 8 suggests usig a fator of .5, hih
diretly relates to the strutural dutility, for the graity desig reifored orete strutures.
Therefore, the resultat .5 strutural dutility of the shool uildigs is uite ell athed the
Euro ode 8 suggestio. Furtherore, the strutural dutility leel a e iproed sigifiatly
y proidig adeuate ofieet to the orete at the plasti hige regios.
As above mentioned, this study investigates the performance of the school building ignoring
the effects of masonry infill walls on the response. As a consequence of ignoring the masonry
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63
walls, the stiffness in longitudinal and transverse directions of the building model are quite
similar. This is conformed in observing that the first translation modes effective in longitudinal
and transverse directions of the building are almost same. However, in adding the masonry
infill walls which were mainly placed in the transverse direction of the building model, there
will be a significantly high stiffness in the transverse direction compared to the stiffness in
other direction and in turn, it causes significant change of the response. Investigation on
effects of adding infill walls in the response of the building along with bi-directional earthq