seismic risk assessment for simply … · · 2017-10-04steel material of bridge is st37. this...

4th International Conference on Earthquake Engineering and Seismology

11-13 October 2017 – ANADOLU UNIVERSITY – Eskisehir/TURKEY

SEISMIC RISK ASSESSMENT FOR SIMPLY SUPPORTED STEEL RAILWAY

BRIDGES IN TURKEY

M. F. Yılmaz 1,2 and B. Ö. Cağlayan 3

1 Research Assistant, Civil Engineering Department, Ondokuzmayıs University, Samsun

2 Doctoral Student, Civil Engineering Department, İstanbul Technical University, İstanbul

3 Assistant Prof. Dr, Civil Engineering Department, İstanbul Technical University, İstanbul

Email: [email protected]

ABSTRACT:

For seismic risk assessment of bridges, probabilistic based approaches become more popular day by day. In

seismic risk assessment, fragility analyses are extensively used as an effective tool. There are various research

studies for highway bridges and different type of structures; however, there is not enough background to

determine earthquake performance of railway bridges which is different from highway bridges. Earthquake

behavior of these bridges is unlike each other. With considering geometric differences of the railway bridges’

structural systems, it is a necessity to define the earthquake performance of the railway bridges in detail. To

demonstrate the seismic risk assessment of railway bridges in Turkey, a representative bridge is selected that is a

common steel bridge type in Turkey. The total length of the selected simply supported bridge is 22.4m and

height of main beams is 1.83m. Stringers and transverse beams were constructed with IPN450, IPN300, and

UPN240 steel profile. Steel material of bridge is ST37. This bridge is a riveted bridge. 3D Finite Element Model

of the bridge was built for the nonlinear analyses. 30 real ground motion data were chosen with different

characteristics. And they are scaled for 0.1g PGA to 1.0g PGA to separately. Totally 300-time history analyses

for 10 different PGA values are done. Nonlinear time history analyses were used to determine the earthquake

response of the bridge. Using the result of analyses, fragility curves of the bridge were constructed and discussed

in detail.

KEYWORDS: Railway Bridges, Nonlinear Analysis, Earthquake Performance Of Railway Bridges, Fragility

Analyses

1. INTRODUCTION

Fragility curve is a most commonly used effective tool to determine the seismic behavior of structure and its

components. Fragility is conditional probability clarify that structure or structural component will exceed a

certain damage level for a given ground motion intensity. Fragility curve can be derived with expert-based,

empirical or analytical way.(Shinozuka et al. 2000b) It is often not possible to collect the necessary data so that

empirical and expert opinion-based methods can be used to obtain fragility curves. For this reason, it is

important to obtain fragility curves with analytical methods. The analytical method is dependent on some

numerical analysis results such as elastic spectral analyses, nonlinear static analyses, and nonlinear time-history

analyses. These numerical analyses are used to construct a probabilistic seismic demand model (PSDM). The

most realistic result of earthquake demand is obtained by the nonlinear time-history analysis. Three different

nonlinear time-history analysis procedures are widely used. These are cloud, stripe and incremental dynamic

analysis (IDA). (Mackie and Stojadinovic 2005)(Dolsek 2009) Cloud method includes selecting different real

earthquake data and using these data without scaling, Stripe method includes scaling a group of real ground

motion data to a specific intensity measure (IMs), IDA includes scaling a group of real earthquake data for a

different IMs level. Fragility curve is generally expressed with the help of the two-parameter log-normal

probability distribution function. These parameters can be obtained by different curve fitting methods.(Cornell et

al. 2002)

Transport networks have great contributions to the country's economy. Therefore, the damages that can be

caused by the natural disasters in these networks will cause material and moral damages to the country, Kobe

mailto:[email protected]



earthquake is an example of this. The elements with the highest probability of collision damage in transport

networks are bridges. Therefore, determining the earthquake performances of bridges has great importance.

There are many different studies in the literature for determining the earthquake performances of bridges. Fragility curves of bridges were obtained by using different empirical methods and analytical

methods.(Shinozuka et al. 2000b)(Shinozuka et al. 2000a)(Pan et al. 2010) The effects of different bridge

designs on earthquake performance are also examined.(Zhang et al. 2008) One of the most important factors

affecting bridge performance is the characteristics of the earthquake. The characteristics of the earthquake are

different for small and large earthquakes. For this reason, multiple stripe analysis, which is obtained by scaling

different earthquake groups for each IMs value, can give more realistic results.(Chandramohan et al. 2013) It is

also observed that some of the bridges that suffered slight damage to the main earthquakes did not see any

damage, and some experienced more damage in the aftershocks. Therefore, determining the effects of

aftershocks is another important issue.(Dong and Frangopol 2015) Studies are also being carried out on

obtaining the fragility curves of railroad and railway bridges. (Tsubaki et al. 2016)(Kim et al. 2014)

In this paper typical simply supported steel railway bridge was chosen as a case study. The bridge location is on

the Manisa-Uşak-Dumlupınar-Afyon railway line. 30 different real ground motion data were selected for three

different soil condition. Earthquake data were scaled from 0.1g to 1.0g separately and 300 nonlinear time history

analysis were conducted. Demands of the bridge were recorded and probabilistic seismic demand model was

derived. Limit state belong to bearing were illustrated for four different HAZUS damage level. Fragility curve

for these damage levels was derived using two-parameter lognormal distribution function. The parameters were

determined by using maximum likelihood method. The results are discussed in detail.

2. DESCRIBING CASE STUDY AND 3D FINITE ELEMENT MODELLING

2.1. Describing Case Study

In Turkey, the railway construction started with the contribution of European countries such as England, France,

and German and the main aim of the railway network usage was to transport agricultural goods and valuable

mineral to the harbors for easy transferring the goods to Europe. The first railway line was constructed by an

English company between Izmir and Aydın in 1856 and the total road length is 130km (Çağlıyan and Yıldız

2013). Railway lines are divided into 7 regions in Turkey for ease of maintenance, repair, and operation. The

total length of the railway lines is 8722 km and 25443 culverts and bridges are in the inventory that %81 of them

were built before 1960. Hence the Turkish railway line includes many historical and monumental bridges.

This study focus on simply supported steel railway bridge placed on the Manisa-Uşak-Dumlupınar-Afyon

railway line. The bridge is simply supported one span bridge with 22.4 m length and the main girder of the

beam’s height is 1.83m (built up section composed of plates and angles connected to each other with rivets to

form I section) the beam with steel plate and angle elements connected to each other by using rivets. Stringers

and transverse beams are IPN450, IPN300.

Figure 1 3D model view of the bridge.



2.2. 3D Finite Element Modeling

All the elements of the bridge are modeled by 2- node beam element. According to shop drawings and site visual

inspections, the computer model is created more realistic with the elements, supports and their connections to

each other. As an example; due to the centerline differences of the connected beam members, eccentricity at the

connection points was taken into account during modeling the bridge.

The weight of the sleepers and rails were taken into account and applied to the dead load at the appropriate

nodes. And the weight of perforated plates and gusset plates were ignored. Steel materials of the bridge were

assumed as ST37 which fits for the construction years of the bridge. The only load that was considered during

the modal analysis was dead load but for the fragility analysis also the train load was taken into account as mass.

Sap2000 was used to model the bridge. Finite element model was composed of 242 frame, 40 link elements, and

152 nodes.

Time history analyses were applied to the model with considering both material and geometric nonlinearity.

Plastic hinges were defined as steel fiber PMM plastic hinges. In order to detect any hazard on bridges, plastic

hinges are defined at the start end the end points and the midpoints of all the beams. Geometric nonlinearity was

defined as Δ-δ with large displacement and Newmark direct integration was used in the analysis. Three

component of the earthquake, one longitudinal and two horizontal directions were defined in the time history

process.

2.3. Determining Nonlinear Behavior of Support Condition.

Determining nonlinear behavior of support is an important issue of developing a 3D model of a real bridge.

There are no information or experimental study on nonlinear behavior of supports of railway bridges. The most

common usage of supports at a bridges are pined and roller at opposite sides for simply supported bridges or

continues bridges. To calibrate the finite element models for the different type of supports to determine the real

behavior, scaled or in-situ tests are need to be conducted. On the other hand, nonlinear behavior of different

roadway bearing systems were investigated by Nielson.(Nielson 2005) It may be assumed, the railway bridge

supports have similar properties but more tests shall be conducted to assess. The performed studies use nonlinear

behavior of low type fixed and sliding bearing.

Low type fixed bearing: restrict translation of both longitudinal and transverse direction but allows rotation. In

longitudinal because of slot hole 2.0 mm free translation is allowed and initial stiffness of bearing is 210kN/mm.

For transverse direction because of slot 1.5mm free translation is allowed and initial stiffness of bearing is

350kN/mm. Force-displacement relation of Low type fixed bearing is illustrated by Neilson as shown in fig.(

3).(Nielson 2005)

Figure 2 Low-type fixed bearing (Nielson 2005)



(a) (b)

Figure 3 (a) Longitudinal direction force-displacement relation (b) Transverse direction force-displacement relation (Nielson 2005)

Low type sliding bearing: restrict translation of transverse direction but allows rotation. In the transverse

direction, because of slot 3 mm free translation is allowed and initial stiffness of bearing is 87.5 kN/mm. In

longitudinal friction coefficient is taken as 0.2. Force-displacement relation of Low type sliding bearing is

illustrated by Neilson as shown in fig. (4) .(Nielson 2005)

(a) (b)

Figure 4(a) Low-type sliding bearing (b) Transverse direction force-displacement relation (Nielson 2005)

Nonlinear behaviors of bearings were modeled as multilinear elastic link element and frictional link element.

Different gap distance depends on transverse direction was considered.

3. SELECTION OF GROUND MOTION AND DEVELOPMENT OF PSDM

3.1. Selecting Ground Motion Data and Scaling

Nonlinear dynamic time history analyses were performed considering both nonlinear material and effects.

Element forces, displacements, and rotations were recorded. The relation between ground motion measure IMs

and engineering demand parameter EDP can be obtained depending on the dynamic time history analyses. These

relations can be obtained by using one of the third methods named cloud (direct) method (Shome 1999) (Mackie

and Stojadinovic 2005), Incremental dynamic analysis (IDA) (Vamvatsikos and Allin Cornell 2002), and stripes

method. In this study, IDA method was used to represent the relation between IMs and EDP. IDA method lets

researchers to use scaled or unscaled, actual or synthetic ground motion records. (Mackie and Nielson B.G.

2009)(Mackie et al. 2008)



Figure 5 Moment and center displacement distribution of earthquake record

In this study, Earthquake data were selected considering different soil types, moment magnitudes, PGAs and

central distance of the earthquake records. The moment magnitudes are varying between 4.9 and 7.4 and PGAs

are changing from 0.08g-0.78g and the central distance of earthquake records are ranging from 2.5kM-69.2 kM.

the distribution of moment magnitude to central distance is shown in fig. (5) 30 different actual earthquake data

were chosen for this study for soil types A, B and C. The selected earthquake data were scaled to 10 different

PGA from 0.1g to 1.0g to to perform 300 different nonlinear time history analysis.

3.2. Developing PSDM.

When using analytical procedure PSMD describe the seismic demand of a structure or structural component in

terms of approximate intensity measure. PSDMs can be written as Eq. (1)

ln( ) ln( )[ ] 1 ( )

EDP IM

d EDPP EDP d IM (1)

Estimation of median EDP is describe as a power model as given in Eq. (2-3)(Cornell et al. 2002)

bEDP aIM (2)

ln( ) ln( ) ln( )EDP a b IM (3)

IM is the seismic intensity measure and constants a and b are the regression coefficients. is the standard

normal cumulative distribution function, EDP is the median value of engineering demand, d is the limit state to

determine the damage level and EDP IM

(dispersion) is conditional standard deviation of the regression. Eq. (4)

2(ln( ) ln( ))

2

bi

EDP IM

d aIM

N (4)

3.3. Selecting IMs.

Selection IMs is an important step to derive PSDMs. The uncertainties arising from IMs are increased dispersion

of demand so the less accurate information about the probability of exceeding of a limit state can be obtained.

There are lots of researches and studies to determine the most suitable IMs. (Padgett et al. 2008) (ÖZGÜR

4

4.5

5

5.5

6

6.5

7

7.5

8

0 20 40 60 80

Mw

Center Displacement (kM)

Earthquake Data Distribution

Earthquake Data



2009)(Yilmaz and Çağlayan 2017) Arias of spectral intensity and PGA are the most suitable IMs. This study uses PGA as IMs.

4. DERIVING FRAGILITY CURVE

4.1. Determining Limit State

Determining the limit state for a different component of the bridge is an important step to derive fragility curve.

The limit states are needed to be determined in terms of EDP metrics, such as ductility, plastic rotation or

deformation. Moreover, they need to have some qualitative or functional clarification. Four different limit states

were defined by HAZUS-MH (FEMA,2003) Slight, Moderate, Extensive and Complete. Timeline for the repair

of the bridge is the key parameter to determine the limit state. Each limit state describes the different level of

bridge functionality over time. The limit states need to be functionally equal. For example displacement limit

state of support bearing and rotation limit state of a main beam of the bridge need to be same effect on the bridge

with respect to functionality. Prescriptive approach is an effective tool to determine limit state for different

component. The prescriptive approach is an expert base approach. Different component limit state of Highway

Bridges are determined and illustrated by Mander and some of them are as given in Tab. (1).

Table 1 Quantitative limit state for bridge component (Nielson 2005)

Component Damage state

Slight Moderate Extensive Complete

Low-steel fixed bearing-long(mm) 6 20 40 255

Low-steel fixed bearing-trans(mm) 6 20 40 255

Low-steel sliding bearing-long(mm) 50 100 150 255

Low-steel sliding bearing-trans(mm) 6 20 40 255

Above limit states are determined by (Mander et al. 1996) 6 mm longitudinal deformation of low- type fixed

bearing results cracks in the concrete pier and this is supposed noticeable level of damage. At 20 mm

deformation prying of the bearings and severe deformation in the anchor bolts was detected. At 40 mm permit

toppling or sliding of the bearing was detected. At 255 mm is believed to exceed the typical seat width.

4.2. Deriving Fragility Curve

Fragility is described as probability of exceeding a limit state. There are many probabilistic approaches to obtain

more realistic and easy way to derive fragility curve. There are three way to derive fragility curve; empiric,

expert base and analytic.(Nielson 2006) Due to the lack of information obtained from past earthquakes not

enough information about the damage level of bridge expose to ground shaking, Analytical approach becomes

more important to derive fragility curve. Analytic approach depends on modeling of structure and conducting

some linear or nonlinear analysis to determine performance of structure under seismic excitation. Nonlinear

pushover analysis, nonlinear time history analysis and incremental dynamic analysis are three of them.

Fragility function is mostly defined by two parameter log normal distribution function. The parameter can be

estimated by two different statistical approaches. The method of finding the moment parameter that gives the

same moment (mean and standard deviation) as the sample moment of the observed data, the Maximum

likelihood method finds the parameter gives the highest likelihood of having produced the observed data.(Baker

2015)

ln( / )( )

xP C IM x (5)

( )P C IM x is the probability that a ground motion with IM x will cause the structure to collapse, is the

standard normal cumulative distribution function (CDF), and are median and standard deviation of the

fragility function. To derive fragility curve and are need to be determined.



One of the most effective ways to calculate moments of EDP and IMs is IDA which is scaling each ground

motion in a group until it causes structure failure. But this method has some difficulties. One of them is the need

of huge computational effort of analysis. The other one is the inapplicable results for the greater scale values

that are used during the calculation which are not possible to occure for the site, and the last one, is uncertainty

whether scaling of small and medium ground motion to large do not produce a realistic result. One of the

solutions is limiting of the ground motion scaling to a valuable IMs and it is called as truncated incremental

dynamic analysis.(Baker 2015) maximum likelihood method was used to figure the likelihood of observing the

data that were observed and a candidate fragility curve was derived.

ln( /iIMLikelihood (6)

max

,1

ln( /ln( /ˆ ˆ, argmax ln ln 1m

j

IMIMn m (7)

Using Eq (7) the fragility function parameters are obtained by maximizing the likelihood function.

(a) (b)

Figure 6 (a) Fitted fragility function for Fixed Bearing (b) Fitted fragility function for roller Bearing

Fragility function for both fixed and roller bearing are shown in fig. (6). Four different fragility curves were

obtained for slight, moderate, large and collapse damage state. The PGA values which cause the damage limits

to be exceeded by 50% probability when the fixed bearing is considered are respectively as follows 0.123g for

slight damage, 0.42g for moderate damage, 0.93g for large damage. The PGA values which cause the damage

limits to be exceeded by 50% probability when the roller bearing is considered are respectively as follows

0.086g for slight damage, 0.25g for moderate damage, 0.46g for large damage. The fragility curve shows that

roller bearing is more vulnerable component then fixed bearing.

5. CONCLUSION

There are limited studies to determine the seismic behavior of Railway Bridges, which are different from

Highway Bridges. It is clear that the seismic performance of railway bridges are needed to be determined due to

the awareness of seismically active fault lines in Turkey. Probabilistic-based approaches are the more popular

and effective way in seismic risk assessment. Many different approaches are used to derive fragility curves.

Maximum likelihood approaches are one of them. In this study simply supported steel railway bridge locating on

Manisa-Uşak-Dumlupınar-Afyon railway line in Turkey was considered. A total of 30 different real earthquake

0

0.2

0.4

0.6

0.8

1

0 1 2

Pro

bab

ility

of

Exce

ed

ance

PGA

Fixed BearingTransverse Direction

sligthmoderatelargecollepse

0

0.2

0.4

0.6

0.8

1

0 1 2

Pro

bab

ility

of

Exce

ed

ance

PGA

Roller BearingLongitutional Direction

sligthmoderatelargecollepse



records for A, B, and C type ground classes were selected. Selected earthquake records were scaled between

0.1g and 1.0g. 300 nonlinear time history analysis were performed. Damage limit cases of the bearing were

determined by using similar support properties in the literature. Fragility curve was defined as two-parameter

lognormal distribution function. The parameter of fragility function was obtained by using maximum likelihood

approach. The fragility curves of fixed and roller bearing were derived for four different limit states. The PGA

values which cause the damage limits to be exceeded by 50% probability when the fixed bearing is considered

are respectively as follows 0.123g for slight damage, 0.42g for moderate damage, 0.93g for large damage. The

PGA values which cause the damage limits to be exceeded by 50% probability when the roller bearing is

considered are respectively as follows 0.086g for slight damage, 0.25g for moderate damage, 0.46g for large

damage. The fragility curve shows that roller bearings are more vulnerable component then fixed bearings, for

higher PGA values, it is observed that probability of exceeding for collapse damage limit state is less that 50%.

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