Seismic protection measures for bridges can be used both for obtaining acceptable performances from new structures that for retrofitting existing ones. With the modern design philosophy based on probabilistic Performance-Based Earthquake Engineering (PBEE) approaches, the engineers are allowed to investigate different design solutions in terms of vulnerability assessment. However, if probabilistic PBEE approaches are nowadays well established and widely studied also for bridges, the topic of using the PBEE frameworks for the evaluation of the effectiveness of seismic protection devices for bridges is not extensively treated in literature. The first objective of this work is to deal with the problem of assessing the earthquake performance of an highway bridge equipped with different bearing device: the elastomeric bearings (ERB) and the friction pendulum systems (FPS). The second purpose is to evaluate the efficiency of a structure-dependent IM in case of isolated system. The examined structure is an highway bridge with concrete piers and steel truss deck. A FE model of the bridge is developed by using nonlinear beam-column elements with fiber section and the devices are modeled by specific elements implementing their nonlinear behavior. The effectiveness of the different retrofitting strategies has been carried out in terms of damage probability. Choosing the example of slight damage, and referring to the curvature ductility as EDP, the probability of damage during a period of 50 years is: 23% for the structure without isolation, 7% for the structure equipped with ERB, and 3% for the structure equipped with FPS isolation.

1. Effectiveness Evaluation of Seismic Protection Devices for Bridges in
the PBEE Framework
Paolo Emidio Sebastiani1, Jamie E. Padgett2, Francesco Petrini3*, Franco Bontempi4
1,3,4
Department of Structural and Geotechnical Engineering, Sapienza University of
Rome, Rome, Italy
2
Department of Civil and Environmental Engineering, Rice University, Houston, TX,
USA
*corresponding author. E-mail: francesco.petrini@uniroma1.it
ABSTRACT
Seismic protection measures for bridges can be used both for obtaining acceptable
performances from new structures that for retrofitting existing ones. With the modern
design philosophy based on probabilistic Performance-Based Earthquake Engineering
(PBEE) approaches, the engineers are allowed to investigate different design solutions
in terms of vulnerability assessment. However, if probabilistic PBEE approaches are
nowadays well established and widely studied also for bridges, the topic of using the
PBEE frameworks for the evaluation of the effectiveness of seismic protection devices
for bridges is not extensively treated in literature.
The first objective of this work is to deal with the problem of assessing the earthquake
performance of an highway bridge equipped with different bearing device: the
elastomeric bearings (ERB) and the friction pendulum systems (FPS). The second
purpose is to evaluate the efficiency of a structure-dependent IM in case of isolated
system. The examined structure is an highway bridge with concrete piers and steel truss
deck. A FE model of the bridge is developed by using nonlinear beam-column elements
with fiber section and the devices are modeled by specific elements implementing their
nonlinear behavior. The effectiveness of the different retrofitting strategies has been
carried out in terms of damage probability. Choosing the example of slight damage, and
referring to the curvature ductility as EDP, the probability of damage during a period of
50 years is: 23% for the structure without isolation, 7% for the structure equipped with
ERB, and 3% for the structure equipped with FPS isolation.
KEYWORDS
Bridges, PBD, fragility, seismic protection, friction pendulum, elastomeric bearings.
1 INTRODUCTION
Earthquake damages in last decades showed the bridges as the most vulnerable elements
of the transportation network. In order to mitigate potential damage, bridges with
insufficient seismic performance may be seismically retrofitted (Imbsen 2001). At the

2. same time, through the modern design philosophy based on probabilistic PerformanceBased Earthquake Engineering (PBEE) approaches, the engineers are allowed to
investigate different design solutions in terms of vulnerability assessment. However, if
probabilistic PBEE approaches are nowadays well established and widely studied for
bridges and also extended to other kind of hazards (Ciampoli & Petrini 2012), the use of
the PBEE frameworks for the evaluation of the effectiveness of seismic protection
devices for bridges is not so extensively treated in literature (Zhang & Huo 2009).
This research aims to provide enhanced understanding of the impact of various retrofit
strategies on the seismic performance of a bridge through the use of PBEE approach.
Two kinds of seismic isolation devices are considered: the elastomeric bearings (ERB)
and the friction pendulum system (FPS). The examined structure is an highway bridge
with a steel truss deck which is continuous over the concrete piers. Therefore fragility
curves are obtained for the bridge equipped with the two above mentioned type of
devices, in order to assess the effect of retrofit measures on the seismic performance of
bridge under a range of seismic demand levels (Padgett & DesRoches 2009). The
comparison of the relative performance of the bridge piers under various retrofit
measures in terms of fragility is carried out. Some issues related to the implementation
of the PBEE for assessing the effectiveness of the considered isolation devices are
highlighted.
2
CASE STUDY, MODELING AND GROUND MOTIONS
2.1 Case study
The case study bridge "Mala Rijeka" is one of the most important bridges on the
Belgrade - Bar International Line. The bridge was built in 1973 as the highest railway
bridge in the World (Worlds Record Lists) and it is a continuous five-span steel frame
carried by six piers of which the middle ones have heights ranging from 50 to 137.5 m
measured from the foundation interface. The main steel truss bridge structure consists in
a continuous girder with a total length L=498.80 m. Static truss height is 12.50 m, and
the main beams are not parallel, but are radially spread, in order to adjust to the route
line. The bridge longitudinal profile and the deck cross-section are shown in figure 1.
2.2 Ground motion database
Current PBEE practice selects ground motions whose intensity (measured by an
Intensity Measure or IM) is exceeded with some specified probability at a given site, and
whose other properties are also appropriate (as typically determined by probabilistic
seismic hazard and disaggregation calculations). For this study two unscaled ground
motion sets prepared by N. Jayaram and J. Baker have been selected
(peer.berkeley.edu/transportation/). The first set consists of 40 ground motions selected
so that their response spectra match the median and log standard deviations predicted for
the following scenario: magnitude = 6, source-to-site distance = 25 km. The range of
spectral acceleration is between 0 to 0.6 g. The second set (not shown here for sake of
brevity), consists of 40 ground motions which similarly are referred to the following

3. scenario: magnitude= 7, source-to-site distance = 10 km. For both sets it results: Vs30 =
250 m/s, earthquake mechanism = strike slip and the range of Sa is up to 1.5g; response
spectra predictions are from the Boore and Atkinson (2008) ground motion model.
Figure 1. Bridge longitudinal profile and bridge-deck cross section.
2.3 Bridge column modeling
As well known, bridge columns are among the most important components in the
seismic design of bridge structures given their role in resisting lateral seismic loads and
in transferring vertical loads. The main purpose of this study is to compare two retrofit
(or design) methodologies in terms of performance, therefore a simple model of a
cantilever column with lumped mass is used to analyze the seismic behaviour of the
bridge. The response of the pier III in figure 1 is evaluated via non-linear dynamic
analyses run in OpenSees 2.2.2 (McKenna, 1997). The column is modelled with a
nonlinear element with fiber-section distributed plasticity. Although the large
displacements of the pile can significantly affect the design, as a rough approximation,
and just for simplification purposes, the geometric non-linearity is not considered here,
with the aim to provide a very first insight on the effects of the different isolation
devices. The material properties are assumed as deterministic and are shown in tables 1,
2 and figure 2, where b is the strain-hardening ratio and R is a parameter to control the
transition from elastic to plastic branches. According to geotechnical field test the
column is assumed to be founded on rock (Radosavljevic & Markovic 1977). The
superstructure is idealized as a lumped mass connected to the column top through
specific elements implementing nonlinear behavior of the devices: fix restraint in the asbuilt case, the single FPBearing element in case of friction pendulum device and
elastomeric Bearing element in case of elastomeric device. The column is 137 m height,
with a tube variable section as shown in figure 3. The mass is distributed among the
column nodes and the geometry is shown in figure 3.
fpc
-37050 kN/m2
Table 1. Concrete properties
fpcU
εc0
εU
λ
0.2 fpc
-0.0025
-0.01
0.1
ft
-0.14 fpc
Table 2. Steel properties for rebars
fy
E
b
440000 kN/m2 2.1 E+08 kN/m2
0.01
R
18
Ets
ft / 0.002

4. fy
λE0
ft
Ets
Ep
Ets
(U, f pcU)
(c0 , f pc)
E0=2f pc/c0
Figure 2. OpenSees uniaxial materials: Concrete02 and Steel02
Figure 3. Bridge pier details (sizes are in meters). The longitudinal section is rotated of 180°
2.4 Isolation system modeling
ERB and FPS are quite common isolation devices. Figure 4 shows the sketches and the
correspondent behaviors of these isolators modelled by a bilinear constitutive law. The
bilinear model can be completely described by the elastic stiffness k1, characteristic
strength fy and post-yielding stiffness k2. Table 3 summarizes the parameters and
formulas for bilinear modeling of these two isolation devices. For the FPS, the friction
coefficient (m) and sliding surface radius (R) determines the characteristic strength fy
and the post-yielding stiffness k2=W/R, where W is the deck weight. The FPS has a very
rigid initial stiffness k1 which is taken as 75 times the post-yielding stiffness k2 (Zhang
& Huo 2009). For elastomeric bearings, the post-yielding stiffness k2 is determined by
the area (A), total thickness (L) and shear modulus (G) of the rubber layers, i.e.
k2=GA/L.
Figure 4. Bilinear relationship to model the isolation devices

5. The characteristic strength fy can be obtained by assuming a yielding displacement dy
(equal to 6 mm in this paper) and the initial stiffness k1 is taken as 10 times of postyielding stiffness k2 (the value of a in the figure is 0.1).
FPS
Table 3. Properties of isolation devices
initial stiffness k1
strength fy
k1=75 k2=160000 kN/m
fy=mW= 256.1 kN
ERB
k1=10 k2=50200 kN/m
fy= k1dy =301.2 kN
post-yielding stiffness k2
k2=W/R=2134.5 kN/m
k2=5020 kN/m
3 SEISMIC DEMAND MODELS
The traditional probabilistic seismic demand model (PSDM) offers a relationship
between an engineering demand parameter EDP (e.g., column curvature) with one type
of ground motion IM or with vector-valued IMs. In both cases, the seismic demands are
determined by the parameters of the ground motion and of the structural system, which
means that the PSDM is structure specific. Therefore, when the structural design
parameters change, new nonlinear time-histories analyses have to be performed. The so
called Probabilistic Seismic Demand (PSDA) method utilizes regression analysis to
obtain the mean (mIM) and the standard deviation (z) by assuming the logarithmic
correlation between median EDP and an appropriately selected IM:
where the parameters "a" and "b" are regression coefficients obtained by the nonlinear
time history analyses. The remaining variability in ln(EDP) at a given IM is assumed to
have a constant variance for all IM range, and the standard deviation can be estimated:
3.1 Engineering demand parameters and intensity measure
Object of this work is to focus on simple engineering demand parameters well correlated
to the structural damage. For simplicity, two of the most common EDPs are adopted: the
curvature ductility at the base of the pier mc and the top displacement ductility dc. In the
PBEE procedures the most efficient IM should be chosen on the basis of the relationship
between the structural response and the intensity of the seismic action. PGA is one of the
most commonly implemented IM. However, especially in case of isolation systems, the
PGA could not be the most reliable parameter. In fact the structural response is heavily
influenced by the dynamic behavior of the system. For this reason in this study the
spectral acceleration Sa(T1) evaluated at the first modal period T1 is adopted. However it
is not easy to evaluate a suitable T1 for an isolated system. For instance, in case of base
isolation, the T1 of the isolated structure can be evaluated exclusively according to the
isolation device properties. On the contrary, when the isolation device is located on the
top of the pier and the pier mass is considerable, the stiffness and the mass of the pier
can not be neglected. At the same time, as additional modelling issue, the nonlinear

6. element for the isolation device is not operative in case of modal analysis, therefore an
equivalent model need to be used to calculate the T1 value. The bearing is modeled by a
linear spring with a secant equivalent stiffness to approximate the real nonlinear
behavior of the device. For comparison purpose, a not-cracked stiffness has been used
for the piers, in order to clearly quantify the influence of the isolation on the T1 value.
Thus T1 has been evaluated through a linear dynamic analysis. The efficiency of the IM
is here evaluated (as usual) on the basis of its correlation with the pertinent EDP. The
vibrational periods of the examined bridge column in the three examined configurations
are shown in Table 4.
Table 4. Dynamic properties after gravity loads application
Typology
Period of the first mode [s]
No isolation
T1 = 1.72
FPS
T1= 4.20
ERB
T1 = 2.90
3.2 Regression results
In the as-built case (without isolation), Sa(T1) as IM provides a better correlation than
the case when the IM is assumed to be the PGA.
No isolation
FPS
ERB
Table 5. Regression parameters
EDP
INT
SLOPE
mc
1.67
0.92
PGA
dc
1.15
0.81
mc
1.74
0.76
Sa(T1)
dc
1.82
0.92
mc
1.75
1.33
PGA
dc
1.10
1.12
mc
1.30
0.61
Sa(T1)
dc
1.21
0.65
mc
1.83
1.34
PGA
dc
1.11
1.14
mc
1.57
0.78
Sa(T1)
dc
1.13
0.74
R2
0.54
0.35
0.86
0.92
0.72
0.63
0.58
0.68
0.67
0.63
0.64
0.75
z
0.59
0.77
0.29
0.26
0.58
0.60
0.65
0.56
0.64
0.61
0.67
0.49
The table 5 shows the IM-EDP correlation parameters for all the cases, while in the
figure 5 one can see the graphical results in the case without isolation and with m c as
EDP. As shown in table 5, when the isolation devices are included in the model, the
differences between the dispersion (factors R2 and z) obtained by adopting the two
different IMs is not as clear as in the previous case. To this regard, in figure 6 the
regression results for the bridge pier equipped with FPS isolation device are also shown.
The two dispersions (by assuming either the PGA or the Sa(T1) as IM) are very similar,
this indicate that additional studies should be conducted in order to find an IM that is

7. clearly efficient in both cases of not isolated and isolated structures. Additional
comments regarding these aspects are provided in the conclusions.
Figure 5. IM-EDP regression results for the bridge pier without isolation. PGA as IM (left), Sa(T1)
as IM (right); EDP= curvature ductility at the pier base.
Figure 6. IM-EDP regression results for the bridge pierequipped with FPS isolation device. PGA as
IM (left), Sa(T1) as IM (right); EDP= curvature ductility at the pier base.
4
FRAGILITY CURVES AND HAZARD
4.1 Damage states
The EDPs or functions of EDPs are generally used to derive the damage index (DI) that
can be compared with the limit states (LS) correspondent to various damage states (DS)
dictated by a capacity model. For simplicity, the DI is chosen as same as the EDP in this
study. A number of studies have developed the criteria for the LS and corresponding DS
based on damage status of load-carrying capacity. Three damage states DS namely
slight, moderate and complete damage are adopted in this study and their concerning
limit values are shown in tab. 6. Through a pushover analysis, the slight damage has
been associated to the achievement of maximum tensile strength of concrete, while the
moderate one to the yielding of the steel rebar. A comparison between the values
adopted by Choi et al. (2004) and the ductility factor defined in the EC8 for piers, has
allowed us to define also limit values referred to the collapse.

8. Table 6. Summary of EDPs and corresponding LSs
Slight damage DS1
Moderate damage DS2
Cracking
Cracking and spalling
Curvature ductility mc
mc> 1
mc> 2.48
Displacement ductility dc
d c> 1
dc> 1.47
EDP
Complete damage DS3
Failure
mc> 7.44
dc> 4.40
4.2 Fragility results
Fragility curves are here developed using a 3D nonlinear time-history analysis for
probabilistic seismic demand modeling. Assuming a log-normal distribution of EDP at a
given IM, the fragility functions (i.e. the conditional probability of reaching a certain
damage state ith for a given IM) can be written as:
where F is the standard normal distribution function.
Table 7. Fragility parameters (in units of g) for case study for each damage state
EDP
DS1
DS2
DS3
z
z
z
mIM(g)
mIM(g)
mIM(g)
No
isolation
FPS
ERB
mc
dc
mc
dc
mc
dc
0.103
0.137
0.122
0.156
0.133
0.216
0.299
0.267
0.658
0.565
0.671
0.496
0.337
0.208
0.531
0.281
0.424
0.363
0.299
0.267
0.658
0.565
0.671
0.496
1.408
0.687
3.127
1.517
1.727
1.584
0.299
0.267
0.658
0.565
0.671
0.496
Figure 7. Fragility, with mc as EDP, for as-built (no isolation), FPS and ERB models respectively
The fragility curves obtained for the three configurations of no isolation, FPS and ERB
are shown in Figure 7, with mc as EDP and Sa(T1) as IM. The mean and dispersion
values for all the other cases are summarized in the table 7.
4.3 Hazard and rate of failure
For the structure-dependent IM selected, three different hazard curves (Fig. 8) have been
evaluated, related to the three periods of vibration as illustrated below (tab. 4). In this
study seismic hazard curves for Los Angeles are adopted, and calculated by the
OpenSHA software (Field et al. 2003).

9. Figure 8. Hazard curves:Los Angeles, CA
Table 8 -T-year probabilities of damages
EDP
PTf1
PTf2
PTf3
mc
2.34E-01 1.35E-02 3.87E-05
No
isolation
dc
1.31E-01 4.95E-02 9.30E-04
mc
3.63E-02 4.33E-04 1.31E-07
FPS
dc
1.37E-02 2.13E-03 1.32E-06
mc
6.95E-02 3.35E-03 1.73E-05
ERB
dc
1.10E-02 1.98E-03 2.50E-06
The seismic fragility can be convolved with the seismic hazard in order to assess the
annual probability PAi of exceeding the ith damage state:
where H(a) is the hazard curve that quantifies the annual probability of exceeding a
specific level of IM at a site. Additionally, it is possible to evaluate the T-year
probability PTfi of exceeding the damage state ith, estimated as:
Assuming a T=50 years period, the probabilities of exceeding the different damage
states are shown in tab.8.
5 CONCLUSIONS
A comparison of the relative performance of the bridge piers under various retrofit
measures in terms of fragility and probability of damage is carried out. The adoption of a
structure-dependent IM, namely Sa(T1), poses some issues since the first period of
vibration T1 changes in the different examined retrofitting strategies. Therefore a direct
comparison of the fragility curves obtained for different retrofitting strategies on a single
chart is not allowed. Sa(T1) results to be more efficient than the PGA when the isolation
is not present, however this result can not be extended to the case with isolation. An
explanation of that can be found in the uncertainty which affects the evaluation of a
suitable T1 for the case of high pier with isolated deck. As already mentioned, the
isolation device is located on the top of the pier, and also the mass of the pier is

10. considerable with respect to the mass of the deck portion relying on it. Thus a linear
equivalent model has been developed to take into account the whole system: pier, device
and deck. Moreover, due to the choice of using a structure-dependent IM, also the
seismic hazard has been evaluated case by case for the three examined structural
configurations. In terms of damage probability, choosing the example of slight damage
and referring to the curvature ductility as EDP, the probability of damage during a
period of 50 years is: 23% for the structure without isolation, 7% for the structure
equipped with ERB, and 3% for the structure equipped with FPS isolation.
6 ACKNOWLEDGEMENTS
This work was partially supported by StroNGERs.r.l. from the fund “FILAS - POR
FESR LAZIO 2007/2013 - Support for the research spin-off”.
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