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

i

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 :- .

ii

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.

iii

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

v

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

vi

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

vii

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

viii

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

ix

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

x

Fig 5.1: Average IDA curve 59 Fig. 5.2: Relationship between Earthquake Design Level and

Performance Level 61

1

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

2

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.

3

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]

4

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.

5

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.

6

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.

7

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

8

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

9

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

10

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

11

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

12

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

13

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-

14

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.

15

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

16

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

17

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

18

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

19

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

20

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.

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.

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

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:

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.

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

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

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

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.

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

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

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

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.

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 %

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

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

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%

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

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

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%

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

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.

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

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

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