seismic damage evaluation of highway viaducts equipped
TRANSCRIPT
Journal of Structural Engineering Vol.61A (March 2015) JSCE
Seismic damage evaluation of highway viaducts equipped with FPS bearings
subjected to level II earthquake ground motions
Javier Lopez Gimenez*, Toshiro Hayashikawa **, Takashi Matsumoto ***, Xingwen He ****
* Graduate Student, Graduate School of Eng., Hokkaido University, Nishi 8 Kita 13 Kita-ku, Sapporo 060-8628
** Dr. of Eng., Professor, Faculty of Eng., Hokkaido University, Nishi 8 Kita 13 Kita-ku, Sapporo 060-8628
*** Ph.D., Associate Professor, Faculty of Eng., Hokkaido University, Nishi 8 Kita 13 Kita-ku, Sapporo 060-8628
**** Dr. of Eng., Assistant Professor, Faculty of Eng., Hokkaido University, Nishi 8 Kita 13 Kita-ku, Sapporo 060-8628
During the last decades, the need for safer bridges has led to high level aseismatic design of
bridges including the use of base isolation bearings. This study numerically evaluates the
effectiveness of a promising base isolation bearing, the Friction Pendulum System (FPS),
used to improve the seismic performance of highway bridges under strong earthquakes.
Nonlinear dynamic analysis and parametric studies are conducted with three-dimensional
viaduct models subjected to near-fault earthquakes. The results show that FPS supports can
effectively reduce the seismic response at the piers of both straight and curved viaducts.
However, curved viaducts subjected to extreme earthquakes may suffer from damage at the
expansion joint. In such cases, the seismic performance can be improved by installing
unseating prevention cable restrainers as well as changing the bearing arrangement of FPS.
Keywords: curved bridge, friction pendulum system, cable restrainer, near-fault earthquake
1. INTRODUCTION
Past earthquakes, such as the 1995 Hyogo-ken Nanbu
earthquake, and more recent seismic events have exposed the
seismic vulnerability of highway bridges, which can
detrimentally affect the rescue and evacuation activities in the
aftermath of a seismic disaster1). According to these past
experiences, such vulnerability may be magnified in structures
with irregular and complex geometries like curved viaducts2), or
in those equipped with an expansion joint3), especially when it
separates two bridge sections with different characteristics4).
During the last decades, the use of base isolation bearings has
been implemented to improve the seismic performance of such
bridges, changing their fundamental frequencies to avoid
resonant vibration with the predominant energy-containing
frequencies of the earthquake. Isolation bearings are basically
classified into rubber and sliding bearings. Throughout the last
years rubber bearings have been extensively used, but recently
sliding supports have been found more applicable for economic
reasons5). Sliding systems filter out seismic forces via frictional
interface and rarely have re-centering capability, except the
Friction Pendulum System (FPS)6). Due to its curved sliding
surface, relative movement of the FPS resembles pendulum
motion, providing isolation effects and gravity restoring force.
This makes FPS a viable option for bridge seismic isolation7).
While the response of FPS supports has been widely studied on
straight viaducts5, 8), there is still a necessity of further research on
their performance when applied to complex structures subjected
to extreme earthquakes. Regarding this topic, several studies in
the past reported that the performance of FPS under near-fault
motions was not very satisfactory, due to significantly large
bearing displacements9). This fact can increase the risk of damage
at the expansion joint and instability in the isolation system. In
order to improve the performance at the expansion joint, the use
of unseating prevention cable restrainers is an economic and
widely used seismic protection strategy in Japan. Previous
researches have studied the efficiency of the combination of
isolators with cable restrainers10), but there is still a necessity of
evaluating this strategy in complex structures equipped with
highly flexible bearings such as FPS supports.
Therefore, the purpose of the current research is to analyze
the benefits of FPS supports as seismic isolators in viaducts
subjected to critical conditions. In this research the adopted
numerical models possess various unfavorable characteristics that
will increase the vulnerability of bridges in earthquakes. These
characteristics include high piers, curved alignment, the presence
of an expansion joint, and adjacent bridge sections with different
sizes and types of bearing supports. The evaluation on the seismic
performance of the structure is carried out by adopting three-
dimensional modeling and nonlinear dynamic analysis. Five
near-fault earthquake ground motion records are used to assess
the risk of loss of serviceability or structural collapse under these
critical conditions that will induce the structure to beyond its
elastic limits.
The current analysis of the overall seismic response of the
viaduct focuses on two aspects. Firstly, this paper presents a study
of the effectiveness of FPS supports when applied to viaducts
with critical conditions including two different superstructure
configurations, i.e. straight and curved ones. The comparison of
the responses of these two models is accompanied with a
parametric study to investigate the role that FPS design
parameters play in the seismic response of the structure. Secondly,
different and economic solutions in order to improve the seismic
performance of the viaducts with a higher risk of seismic damage
are explored. The proposed solutions include the combination of
FPS supports with unseating prevention cable restrainers, a
device widely used in Japan to protect bridges against extreme
seismic loads, as well as the confirmation on the restraint effect of
out-of-plane displacements of the FPS supports. The conclusions
of this study can assist engineering practice in designing effective
protection strategies against strong earthquakes, providing a
better understanding of the behavior of viaducts isolated by FPS
with different characteristics, and further choices to combine it
with other seismic protection devices.
2. NUMERICAL MODEL OF VIADUCT
2.1 Superstructure and piers
The widely recognized susceptibility to earthquake damage
of bridges is even more amplified with the rupture of continuity
of the superstructure at expansion joints. In addition, the
difference in the vibration properties of two adjacent bridge
components is a dominant factor which causes out-of-phase
vibration, differential displacements, and increases the risk of
structural seismic damage. In the current study, the considered
viaduct is composed by a three-span continuous seismically
isolated section connected to a single simply supported non-
isolated span. Such configuration has been selected in order to
analyze the overall response of a substantially adverse case of
viaduct under critical demands. The overall viaduct length of 160
m is divided into four spans of 40 m each, as shown in Figure 1.
The bridge superstructure consists of a concrete deck slab
resting on three I-shape steel girders equally spaced at an interval
of 2.1 m, and interconnected by steel diaphragms. Full composite
action between the slab and the girders is assumed for the deck
model. In order to evaluate the benefits of the seismic isolation,
two different bridge configurations, straight and curved, have
been studied and their dynamic responses have been compared.
(1) Straight viaduct: The bridge alignment is straight and the
deck longitudinal axis coincides with the global X-axis as
described in Fig. 1(a).
(2) Curved viaduct: The bridge alignment is horizontally
curved in a 100 m radius of curvature, measured from the origin
of the circular arc to the centerline of the bridge deck (Fig. 1(b)).
Tangential configuration for both piers and bearing supports is
adopted with respect to the global coordinate system, in which
the X- and Y-axes lie in the horizontal plane while the Z-axis is
vertical.
The superstructure weight is supported by five hollow box
section steel piers of 20 m height (Fig. 2 and Table 1), designed
according to the Japanese seismic code11). Characterization of the
(a) Straight viaduct
(b) Curved viaduct
Fig. 1 Plan view of viaduct models
Fig. 2 Elevation view of viaduct models
Table 1 Cross section properties of piers
Pier A Ix Iy
(m2) (m4) (m4)
P1 0.4500 0.3798 0.3798
P2 0.4700 0.4329 0.4329
P3 0.4700 0.4329 0.4329
P4 0.4700 0.4329 0.4329
P5 0.4500 0.3798 0.3798
non-linearity of the piers is based on the fiber flexural element
modelization. Each pier is divided in five longitudinal parts
which, as well are subdivided in 12 transverse divisions. The
selected number of divisions is considered appropriate and
optimum in the model of this study. The element stress resultants
are determined by integration of the fiber zone stresses over the
cross section of the element. The non-linear behavior of the piers
derives entirely from the non-linearity of the fibers.
2.2 Bearing supports
The non-isolated approach span (S1) is supported by
traditional steel fixed bearings resting on Pier 1 (P1), while steel
roller bearings are placed at the right end on Pier 2 (P2), allowing
for movements in the in-plane tangential direction while
restrained by stoppers in the out-of-plane radial direction. The
isolated continuous span (S2) is supported on pier units P2, P3,
P4 and P5 by base isolation bearings. The seismic isolation of S2
is achieved by placing FPS supports under each of the three
girders resting on each pier. Displacements of FPS isolators have
been limited in the out-of-plane radial direction through the
installation of single rail bearings, permitting sliding movements
only in the in-plane tangential direction. This arrangement
represents the most commonly used bearing configuration
method for bridges in Japan. The behavior of FPS is modeled by
a simplified bilinear force-deformation relationship6) as
represented in Fig. 3. FPS bearings are modeled with a high
vertical stiffness, and the normal force acting on each device (N)
is considered as a constant value obtained after gravity load
analysis. The principal design parameters that characterize the
numerical model of FPS are the radius of curvature (RFPS) and the
friction coefficient (μ) of the sliding surface. In the current
research, their significance on the overall seismic response of the
viaduct is analyzed through an extensive parametric study.
Values of RFPS equal to 0.75 m, 1 m, and 1.5 m, and μ equal to
5%, 12% and 20% are selected for comparison.
2.3 Expansion joint
The isolated and non-isolated viaduct sections are separated,
introducing a gap equal to the width of the expansion joint
opening between both spans. A critical separation gap of 0.1 m
has been selected to study the interaction between adjacent
segments of the bridge and its effect on the bridge response. This
gap could be closed, resulting in collisions between both sections
of the viaduct. These impacts have been modeled using impact
spring elements with a stiffness Ki=980.0 MN/m, that acts when
the gap between the adjacent decks is completely closed. On the
other hand, there is no limitation in the longitudinal displacement
of the superstructure at the right end of the isolated span, since no
expansion joint is considered on top of P5.
3. METHOD OF ANALYSIS
The bridge model of the current study has been developed by
the authors using Fortran programming language. In order to
analyze the elasto-plastic dynamic response, as well as to assess
seismic damage of bridge frame structures when subjected to
strong earthquakes, a non-linear dynamic finite element
technique has been applied. The analysis is conducted through a
numerical method that considers both geometrical and material
nonlinearities, being the characterization of the non-linear
structural elements based on the fiber flexural element modeling.
Table 2 Characteristics of the earthquake ground motion records
Earthquake record Component PGA (gal) PGV (cm/sec) PGD (cm) T1 (sec)
TAK L 599.58 127.15 35.77 1.24
(JR Takatori Station record T 603.61 120.69 32.73 1.20
1995 Kobe Earthquake) V 266.36 16.02 4.47 0.13
KOB L 805.45 81.27 17.68 0.68
(Meteorological Agency record T 586.94 74.33 19.95 0.71
1995 Kobe Earthquake) V 336.13 38.30 10.29 1.02
RIN L 821.37 165.98 28.14 1.32
(Rinaldi Station record T 463.28 72.94 19.96 0.30
1994 Northridge Earthquake) V 835.62 50.60 11.98 0.13
SYL L 826.99 129.32 31.89 1.57
(Sylmar Hospital record T 592.80 78.08 16.81 0.63
1994 Northridge Earthquake) V 525.10 18.80 9.33 0.77
CHI L 555.02 176.59 324.16 2.64
(TCU068 Station record T 452.78 263.03 429.80 8.19
1999 Chi-Chi Earthquake) V 476.99 187.31 266.60 3.41
Fig. 3 Analytical model of FPS supports
The damping mechanism is introduced in the analysis through
the Rayleigh damping matrix. Additionally, the governing
equations of motion are solved in incremental form using
Newmark’s method (β=0.25), and Newton-Raphson iteration
method is selected to achieve the acceptable accuracy in the
response calculations. Regarding the materials, the steel is
modeled using a bilinear model with yield strength of 245.4 MPa,
elastic modulus of 200 GPa and a strain-hardening ratio of 0.01.
To assess the seismic performance of the viaduct, the bridge
model is subjected to the longitudinal (L), transverse (T), and
vertical (V) components of different strong earthquake ground
motions. The longitudinal earthquake component shakes the
viaduct parallel to the global X-axis, while T and V components
act in the Y- and Z-axes, respectively. Since the seismic
performance can be strongly influenced by the properties of the
applied wave, a group of near-fault ground motion records has
been employed for simulations to ensure the applicability of the
conclusions of this study. Table 2 summarizes the characteristics
of the 5 records obtained from the 1994 Northridge Earthquake,
the 1995 Kobe Earthquake, and the 1999 Chi-Chi Earthquake.
Due to their high intensity and low probability of occurrence, the
adopted records are considered as level II earthquakes in the
Japanese seismic code11). The frequency contents of the
earthquakes are composed predominantly of long vibrational
periods, indicating that flexible structures will be especially
exposed to their destructive potential. Among the selected records,
JR Takatori Station (TAK) and Chi-Chi earthquake (CHI)
records show higher values in both horizontal directions of the
peak ground velocity (PGV), a parameter which is representative
of earthquake intensity since it is directly correlated with energy
demands. The 5%-damped earthquake acceleration spectra
presented in Fig. 4 for both longitudinal and transverse
components, show peak accelerations for periods between 0.3
and 1 sec. for the majority of the employed records. However, the
above mentioned TAK and CHI records present maximum or
very large spectral accelerations in larger periods. These records
would be expected to develop extensive damage to structures
with longer natural periods, such those using base isolation
systems or with increasing size of the spans.
4. NUMERICAL RESULTS
The overall three-dimensional seismic response of the bridge
is examined in detail through non-linear dynamic response
analysis. The results of the free vibration analysis show that the
natural periods of the isolated span for the straight and curved
configurations are 0.86 sec and 0.84 sec, respectively. On the
other hand, the selected design parameters of the FPS supports
effectively provide a degree of isolation of more than two12).
Since the considerable period shift can lead to a substantial
increase of deck displacements13), particular emphasis has been
focused on the expansion joint performance, expecting that the
flexibility of the superstructure increases the possibility of deck
collisions.
4.1 Classification of seismic damages
Post-earthquake evaluation of the damage sustained by
bridges in recent strong seismic events provides one of the best
means of assessment of seismic resistance capability for new
constructions, as well as for retrofitting of existing bridge
structures10). For this reason, some of the most concerned types of
earthquake damages, which also exist in this study, are thus
focused on and evaluated in this and the following sections of this
paper, as enlisted below.
(1) Expansion joint impact forces: The added flexibility as
a consequence of the installation of base isolation bearings can
result in a detrimental increase of collisions between adjacent
decks. High impact forces should be avoided, since they not only
cause localized damage at the colliding girders but also transmit
detrimental forces to the bearing supports located in the proximity
of the expansion joint.
(2) Deck unseating: One of the most catastrophic seismic
damages to bridge superstructures is the collapse due to deck
unseating. During a strong earthquake, adjacent spans vibrate out
of phase resulting in relative displacements at the expansion joint.
This possibly allows the deck to become unseated from the
supporting substructure if the induced displacements are
excessively large. Unseating damage can thus occur when the
roller bearing relative displacement exceeds the seating length.
0 1 2 3 4
0
1000
2000
3000
Sp
ectr
al a
ccel
erat
ion
(g
al)
Period (sec)
TAK
KOB
RIN
SYL
CHI
0 1 2 3 4
0
1000
2000
3000
Sp
ectr
al a
ccel
erat
ion
(g
al)
Period (sec)
TAK
KOB
RIN
SYL
CHI
(a) Longitudinal component (b) Transverse component
Fig.4 5%-damped earthquake acceleration spectra
This is a potential cause of seismic damage and structural
collapse especially in old bridge constructions, usually designed
with short seat widths. To evaluate this damage in the presented
models, the maximum displacement of the roller bearing (B2) in
the negative tangential direction has been designated as the
damage index. In this study, even though the Japanese
Specifications11) consider a minimum seat width of 0.70 m, a
limit of 0.45 m has been fixed in order to determine the high
unseating probability for existing bridges with narrow steel pier
caps that provide short seat widths.
(3) Tangential horizontal joint residual opening: In the
aftermath of a seismic event, the magnitude of the permanent
tangential offset at the expansion joint can disrupt the usability of
the bridge, causing traffic closure. This is considered a critical
issue since it may affect first-aid, firefighting, rescue and
evacuation activities. In this research, the residual joint opening is
mainly caused by the final position of the roller bearing support,
which is related to the residual pier inclination of Pier 1. In order
to evaluate the possibility for vehicles to pass over the tangential
gap length, a residual tangential opening of 0.15 m, which
represents the contact length of a truck tire, has been selected as
limiting value14).
(4) Bridge pier damage: In the current paper, the
evaluation of the seismic damage at the bridge substructure is
carried out by analyzing two different features, i.e. the bending
moment-curvature relationships at bottom of the piers, and the
residual pier inclination (RPI) after the seismic event. During an
earthquake, the bottom section of the pier suffers larger bending
moments, thus the maximum curvatures transmitted to the base
of the pier can be considered as an appropriate measure of the
seismic damage of the bridge. Secondly, the inelastic cyclic
strains supported by the piers during a seismic event can lead to
significant residual deformations. This fact could affect the
serviceability and safety of the structure, and lead to costly repair
and strengthening operations. Therefore, RPI is taken into
account in this study as an important variable for seismic damage
evaluation. It has been computed as the average pier position in
the orbit of the two horizontal directions during the last 3 seconds
of the earthquake record. As a limiting value, a maximum RPI
equal to 1% of the height of the pier has been considered11).
4.2 Evaluation of seismic damage
Firstly, in order to evaluate and to compare the seismic
damage in straight and curved viaducts isolated by FPS supports,
the performance of the expansion joint is discussed. Fig. 5 and
Fig. 6 show, in descending order, the time histories of pounding
forces, roller bearing displacements, and expansion joint
tangential opening. These graphs provide valuable information to
evaluate the impact forces, the risk of unseating damage, and the
risk of loss of serviceability of the bridge due to excessive
residual opening, respectively. The presented results belong to
straight and curved models equipped with FPS bearings with
RFPS=1 m and μ=12%, and subjected to JR Takatori Sta. record,
which represents the worst scenario for the studied viaducts.
The obtained results show a correlation between the three
time-histories presented here. The flexibility added to the
superstructure as a consequence of the installation of FPS
supports increases the magnitude of the collisions at the
expansion joint, resulting in two main problems. Firstly, the
impact forces at the expansion joint push the roller bearings and
increase their displacements in the negative tangential direction
and thus, raise the risk of deck unseating. Secondly, impact forces
are transmitted to Pier 1 via the fixed bearings, which can induce
damage at the pier and increase its residual inclination. As a
consequence, residual displacements in the roller bearings can be
affected and this could lead to excessive residual joint opening.
For the straight viaduct, the largest impact forces, which take
place between seconds 5 and 10 (Fig. 5(a)), lead to the maximum
roller bearing displacements in the negative direction (Fig. 5(b)).
However, in this case the proposed threshold of -0.45 m is not
exceeded. Similarly, for the expansion joint tangential opening
(Fig. 5(c)), maximum values are also correlated to the timings
when maximum impact forces occur, but the residual opening
limit is not overpassed and the usability of the bridge is not at risk.
(c) Expansion joint tangential opening
0 10 20 30-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
opening limit
time (s)
Tan
gen
tial
op
enin
g (
m)
(b) Roller bearing displacements
0 10 20 30-0.6
-0.4
-0.2
0.0
0.2
unseating limit
time (s)
Ro
ller
bea
rin
g d
isp
l. (
m)
0 10 20 30-25
-20
-15
-10
-5
0
time (s)
Po
un
din
g f
orc
es (
MN
)
(a) Pounding forces
(c) Expansion joint tangential opening
0 10 20 30-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
opening limit
time (s)
Tan
gen
tial
open
ing (
m)
(b) Roller bearing displacements
0 10 20 30-0.6
-0.4
-0.2
0.0
0.2
unseating limit
time (s)R
oll
er
bear
ing d
ispl.
(m
)
0 10 20 30-25
-20
-15
-10
-5
0
time (s)
Poundin
g f
orc
es (
MN
)
(a) Pounding forces
Fig. 5 Expansion joint response Fig. 6 Expansion joint response
of the straight viaduct of the curved viaduct
80%
20%
�B2 Displacement > -0.45 m
�B2 Displacement < -0.45m
73.33%
26.67%
�Residual Opening < 0.15m
�Residual Opening > 0.15m
(a) Risk of unseating (b) Residual joint opening
Fig. 7 Evaluation of the risk of expansion joint damage for curved
viaducts
The performance of the curved viaduct does not seem to be
as satisfactory as the straight case, since the higher impact forces
at the expansion joint (Fig. 6(a)) lead to excessive residual and
maximum roller bearing displacements (Fig. 6(b)), as well as
large joint residual opening, as shown in Fig. 6(c). For curved
viaducts, the proposed limits are clearly exceeded, increasing the
risk of collapse or loss of serviceability of the structure. The
directional effects of near-fault motions and the orientation of the
expansion joint respect to the strike fault, would explain the
difference in the response of the expansion joint between the
straight and the curved viaducts.
In order to broaden the analysis scope of the detrimental
response of curved viaducts, the effect that both design
parameters of FPS supports and the earthquake inputs have on
the performance of the bridge is analyzed. Fig. 7(a) shows the
evaluation of the risk of unseating damage for the studied curved
viaducts. In this case, the ratios are derived from the response of
bridges equipped with FPS supports with RFPS equal to 0.75 m, 1
m, and 1.5 m, and μ equal to 5%, 12% and 20%.
After subjecting these models to the 5 earthquake ground
motion records, 20% of the cases present maximum roller
bearing displacements that overpass the proposed limit. This
percentage represents only the study cases subjected to TAK
input, which highlights the severe conditions that this record
implies for the proposed model. It can also be concluded that for
the most demanding case (TAK input) the variation of FPS
supports design parameters is not effective in reducing the risk of
unseating damage, since all the cases subjected to TAK exceed
the proposed unseating limit. Similar conclusions can be drawn
from the evaluation of the risk of excessive residual joint opening.
In this case, the 26,67% of cases that present detrimental values,
which are shown in Fig. 7(b), belong to those models subjected
to TAK input and some subjected to CHI input. These two
records were previously characterized as those with the highest
potential damage for the proposed models.
On another note, the performance of the piers of the viaducts
is firstly evaluated in terms of maximum curvatures transmitted
to the substructure. Fig. 8 presents the bending and yielding
moments ratio (M/My) – curvature relationships at the bottom of
the five piers of the viaduct. The bending moments are shown for
two rotating directions. In the first row, results related to the in-
plane bending moments (MX) are presented, while the graphs
located in the lower row display the out-of-plane bending
moments (MY). The displayed results belong to straight and
curved viaducts equipped with FPS supports with RFPS=1 m and
μ=12%, and subjected to JR Takatori Station earthquake record.
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P5
-0.005 0.000 0.005
-1
0
1Μ
Y
curvature (1/m)
M/M
y
P5
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P4
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P3
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P2
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P1
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P4
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P3
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P2
-0.01 0.00 0.01
-1
0
1M
X
M/M
y
P1
(a) Straight viaduct
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P5
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P5
-0.005 0.000 0.005
-1
0
1Μ
Y
curvature (1/m)
M/M
yP4
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P3
-0.005 0.000 0.005
-1
0
1Μ
Y
curvature (1/m)
M/M
y
P2
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P1
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P4
-0.005 0.000 0.005
-1
0
1M
X
M/M
yP3
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P2
-0.01 0.00 0.01
-1
0
1Μ
X
M/M
y
P1
(b) Curved viaduct
Fig. 8 Bending moment – curvature relationships at the bottom of the piers
Firstly, focusing on the straight viaduct case described in Fig.
8(a), detrimental plastic deformations in Pier 1 can be observed.
This is due to the fact that the bearings located on top of P1 are
fixed supports, which transmit large seismic forces to the bottom
of the pier. On the other hand, piers equipped with FPS supports
show elastic bending moments, highlighting the effectiveness of
these isolators in reducing the seismic forces transmitted to the
substructure even when subjected to level II earthquakes. The
response of the piers in the out-of-plane direction (MY) is not
directly related to the differences in the supports, but to the fact
that bearing displacements are restrained in that direction in all
the units. In the out-of-plane direction, the supports can be
considered as fixed, and thus they increase the transmission of
seismic forces. This affects the out-of-plane bending moments
which present higher values, especially in the inner piers that
support more dead load. A similar behavior can be observed in
curved viaduct models, as shown in Fig. 8(b). Thereby, piers
equipped with FPS bearings safely remain inside the elastic range
in the in-plane direction, even in this bridge configuration that
proved to be more vulnerable to seismic damage. However,
there is a remarkable difference regarding the in-plane bending
moments induced to P1. Pier 1 presents plastic deformations but,
unlike the straight viaduct case, the hysteretic loops observed in
MX are not centered near the zero curvature, but present large and
detrimental values in the negative x-direction. This response leads
to important residual pier inclinations (RPI) that can increase the
displacements of the roller bearing and thus, the risk of excessive
residual joint opening.
A more detailed insight in the RPI response can be obtained
by analyzing Fig. 9, which presents the obtained values related to
curved viaducts equipped with FPS with different characteristics
and subjected to TAK record. According to this, Pier 1 is the only
one that presents residual inclinations that exceed the proposed
limit. These high values can be moderately reduced by increasing
the coefficient of friction of the FPS, but not to an extent that will
assure the serviceability of the structure. Pier 5, equipped with
isolation bearings, shows elastic moments in both horizontal
directions, but present negligible values of RPI slightly different
from zero. The slight ground displacements during the last
seconds of the considered earthquake record would explain that,
in the moment of the evaluation, piers had not reached an
absolute rest position.
4.3 Seismic performance improvement of curved viaducts
equipped with FPS bearings
After analyzing and comparing the performance of the
analyzed bridge models, the case of curved viaducts subjected to
TAK input appeared to be especially vulnerable to seismic
damage. In the current section, different seismic protection
strategies involving the use of FPS supports are proposed and
analyzed. The objective is to improve the seismic performance of
the curved viaduct in a more effective way than the one obtained
through the variation of the design parameters of the FPS
supports. Two different measures are proposed in order to
achieve this goal.
(1) Unseating prevention cable restrainers: In order to
provide additional fail-safe protection against extreme seismic
loads, models where unseating prevention cable restrainers are
installed at the expansion joint to provide a link between adjacent
decks have been proposed. The installation of these restrainers is
an economic and widely used seismic protection strategy in
Japan, which reduces the risk of unseating of the superstructure
and avoids excessive joint opening. Cable restrainers are
anchored to the three girder ends (1 unit per girder), and they
have been modeled as tension-only spring elements10) with a
slack of 25 mm to accommodate thermal movements (Fig.
10(a)). Restrainers with high mechanical properties were selected,
expecting large load carrying capacity of them due to the
remarkable flexibility added by FPS to the superstructure.
(a) Unseating prevention cable restrainers (b) FPS bearings arrangement
Fig. 10 Proposed measures for seismic response improvement
5% 12% 20% 5% 12% 20% 5% 12% 20%
0.0
0.5
1.0
1.5
2.0
2.5
RFPS
µ
1.00 m 1.50 m
Resi
du
al P
ier
Incl
inati
on
(%
)
0.75 m
P1 P2 P3 P4 P5
damage limit
Fig. 9 Residual pier inclination in curved viaducts
Initially, restrainers behave elastically with a stiffness K1
(K1=157 MN/m), while their plasticity is introduced by the yield
force F1 (F1=4.2 MN), the post-yielding stiffness K2 (K2=0.05K1),
and the ultimate strength F2 (F2=4.7 MN). In order to simplify,
the effects of the expansion joint in the transverse direction and
the shear forces acting on the cable restrainers are neglected.
(2) Modification of the arrangement of FPS supports: In
the models analyzed in the previous section, FPS supports were
allowed to move only in the longitudinal direction, following the
most common configuration for bridge bearings in Japan. The
proposed arrangement for the current section, presented in Fig.
10(b), consists of restraining the radial displacements only to the
end-span bearings (B3 and B6). This is done to limit the
expansion joint displacements only in the tangential direction,
since the expected large radial displacements of the deck would
be difficult to accommodate by the expansion joint. On the other
hand, radial and tangential displacements are allowed for the FPS
bearings located in the inner piers (B4 and B5). The objective is
to increase the benefits of the seismic isolation, expecting to
reduce seismic damage in the out-of-plane direction of the piers.
In order to analyze the effectiveness of the above proposed
seismic protection strategies, four different cases are studied.
These cases are enlisted below.
Case 0: This model is the same as studied in section 4.1,
where FPS supports can move only in longitudinal direction and
cable restrainers are not installed at the expansion joint.
Case 1: This model analyzes the effectiveness of the
installation of cable restrainers. FPS bearings can move only in
the longitudinal direction.
Case 2: The objective of this model is to study the
effectiveness of allowing the FPS supports of the inner piers to
move in both horizontal directions. In this case, cable restrainers
are not installed at the expansion joint.
Case 3: This model aims to analyze the effectiveness of the
combination of both proposed strategies. The curved viaduct of
this study case allows the FPS bearings of the inner piers to move
in both horizontal directions. In addition, both deck sections are
connected through the expansion joint by the installation of
unseating prevention cable restrainers.
In the first place, the effectiveness of the proposed measures
is evaluated through the comparison of the seismic responses of
the expansion joint obtained for the four study cases. For the
current section, the analyzed models are isolated with FPS
supports with a friction coefficient equal to 12%, and a radius of
curvature of the sliding surface equal to 1 m. Besides, the four
cases have been subjected to the JR Takatori Station earthquake
record since, as it was previously ascertained, it represents the
most critical condition.
Fig. 11 shows the results for Case 0. As explained in the
preceding section, the non-satisfactory response of the expansion
joint increases the risk of lost of serviceability and collapse of the
structure. This is due to the excessive induced displacements to
the roller bearing, as well as to the large residual opening at the
deck discontinuity.
The connection provided by the installation of cable
restrainers seems to be beneficial for the seismic response of the
curved viaduct subjected to TAK input, as it can be seen in the
results presented in Fig. 12. The impact forces, represented in the
negative y-axis in Fig. 12(a), are reduced in magnitude when
compared to Case 0, although the number of impacts is clearly
increased. Another important magnitude that can be observed in
this graph is the value of the tensile forces supported by the cable
restrainers, which are plotted in the positive y-axis. The high
flexibility of the superstructure isolated by FPS supports induces
large tensile forces in the cable restrainers, which overpass the
yielding force, but in any case the ultimate strength of the device
is reached.
(c) Expansion joint tangential opening
0 10 20 30-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
opening limit
time (s)
Tan
gen
tial
openin
g (
m)
(b) Roller bearing displacements
0 10 20 30-0.6
-0.4
-0.2
0.0
0.2
unseating limit
time (s)
Ro
ller
bea
rin
g d
isp
l. (
m)
0 10 20 30-25
-20
-15
-10
-5
0
5
time (s)
Po
un
din
g f
orc
es (
MN
)
(a) Pounding forces
(c) Expansion joint tangential opening
0 10 20 30-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
opening limit
time (s)
Tangenti
al o
pen
ing (
m)
(b) Roller bearing displacements
0 10 20 30-0.6
-0.4
-0.2
0.0
0.2
unseating limit
time (s)
Roll
er b
ear
ing d
ispl.
(m
)
0 10 20 30-25
-20
-15
-10
-5
0
5
time (s)
Poundin
g f
orc
es
(MN
)
(a) Pounding forces
(c) Expansion joint tangential opening
0 10 20 30-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
opening limit
time (s)
Tangenti
al o
pen
ing (
m)
(b) Roller bearing displacements
0 10 20 30-0.6
-0.4
-0.2
0.0
0.2
unseating limit
time (s)
Roll
er b
ear
ing d
ispl.
(m
)
0 10 20 30-25
-20
-15
-10
-5
0
5
time (s)
Poundin
g f
orc
es
(MN
)
(a) Pounding forces
(c) Expansion joint tangential opening
0 10 20 30-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
opening limit
time (s)
Tan
gen
tial
open
ing (
m)
(b) Roller bearing displacements
0 10 20 30-0.6
-0.4
-0.2
0.0
0.2
unseating limit
time (s)
Roll
er b
ear
ing d
ispl.
(m
)
0 10 20 30-25
-20
-15
-10
-5
0
5
time (s)
Poundin
g f
orc
es (
MN
)
(a) Pounding forces
Fig. 11 Expansion joint response Fig. 12 Expansion joint response Fig. 13 Expansion joint response Fig. 14 Expansion joint response
of Case 0 of Case 1 of Case 2 of Case 3
In addition, the induced negative displacements at the roller
bearings are reduced (see Fig. 12(b)), although the peak negative
displacement still remains close to the proposed limit. The
installation of cable restrainers can help to transmit the re-center
capability of FPS supports to the roller supports that show a more
centered behavior than the one observed in Case 0, in which
most of the displacements took place in the negative direction.
Moreover, the decrease of the magnitude of the impact forces
influences the residual displacements of the roller bearings, which
present a remarkable decrease. As a consequence, the residual
opening at the expansion joint (Fig. 12(c)) shows values that are
clearly below the proposed limit. If cable restrainers do not fail,
the maximum expansion joint opening allowed by the restrainers
will be smaller than the proposed opening limit, ensuring the
bridge serviceability.
By allowing some of the FPS supports to move in both
horizontal directions (Case 2) the magnitude of the impact forces
can be moderately reduced, as observed in Fig. 13(a). The
comparison between the roller bearing time-histories of Case 0
and Case 2 show some similarities, but by allowing radial
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P5
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P5
-0.005 0.000 0.005
-1
0
1Μ
Y
curvature (1/m)
M/M
y
P4
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P3
-0.005 0.000 0.005
-1
0
1Μ
Y
curvature (1/m)
M/M
y
P2
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P1
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P4
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P3
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P2
-0.01 0.00 0.01
-1
0
1Μ
X
M/M
y
P1
(a) Case 0
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P5
-0.005 0.000 0.005
-1
0
1Μ
Y
curvature (1/m)
M/M
y
P5
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P4
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P3
-0.005 0.000 0.005
-1
0
1Μ
Y
curvature (1/m)
M/M
y
P2
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P1
-0.005 0.000 0.005
-1
0
1Μ
X
M/M
y
P4
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P3
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P2
-0.01 0.00 0.01
-1
0
1M
X
M/M
y
P1
(b) Case 1
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P5
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P5
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P4
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P3
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P2
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P1
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P4
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P3
-0.005 0.000 0.005
-1
0
1Μ
X
M/M
y
P2
-0.01 0.00 0.01
-1
0
1M
X
M/M
y
P1
(c) Case 2
displacements in some supports, maximum displacements of the
roller bearing in the negative direction can be decreased, reducing
at the same time the risk of unseating of the approach span (Fig.
13(b)). However, residual displacements of the roller bearing
shows remarkably high negative values that, as it can be observed
in Fig. 13(c), lead to expansion joint openings slightly larger than
the limiting value of 0.15 m.
Finally, the combination of both seismic protection strategies,
i.e. installation of cable restrainers and allowance of some
isolators to move in both horizontal directions, is evaluated. The
impact forces time history presented in Fig. 14(a) is very similar
to the one obtained in Case 1, in terms of magnitudes of the
impact forces and tensile forces sustained by the cable restrainers.
Similarly, the response of the roller bearing (Fig. 14(b)) is
comparable with Case 1, but as a consequence of the release of
radial displacement restraint of the inner bearings, the magnitude
of the displacements is beneficially reduced. Besides, the
response in terms of tangential opening of the expansion joint
(Fig. 14(c)) is also enhanced. The favorable performance of the
cable restrainers, which work in the plastic range, avoids
excessive joint opening. In general, Case 3 proves to be the most
effective strategy in improving the seismic performance of the
expansion joint, combining the advantages of both proposed
measures.
Following the same order as in the previous section, the
evaluation of the seismic performance of the piers of the curved
viaduct is conducted via the evaluation of both, the bending
moment – curvature relationships at the pier bottoms, and the
residual pier inclinations. When comparing the results obtained
from Case 1 (Fig. 15(b)) with the previously discussed results of
Case 0 (Fig. 15(a)), two main differences can be observed. Firstly,
in-plane bending moments of P1, which still show high values
inside the plastic range, also present hysteretic loops located in the
area of positive curvatures. As a consequence, residual
displacements of both the first pier, and the roller bearing support,
exhibit values in the positive direction of the x-axis. Therefore,
the initial joint gap is closed and the risk of excessive residual
joint opening, that was previously observed, is eliminated. The
second difference is the increment of the out-of-plane bending
moments of P2, the pier located under the expansion joint. The
inter-span connection provided by the cable restrainers installed
on the top of this pier, which transmits seismic forces and
increases the effects of the curvature, can be the main reason of
this increase in the bending moments.
On the other hand, Case 2 (Fig. 15(c)) presents an
improvement in the response of all the piers. By allowing FPS
supports located on top of piers P3 and P4 to move in both
horizontal directions, the beneficial effects of the isolation can
also be observed in the out-of-plane bending moments. Out-of-
plane bending moments of P3 and P4 are now inside the elastic
range, and the response of P2 in this direction is also improved.
In-plane bending moments (MX) for Case 2 also present some
differences when compared to the original model. While piers
equipped with FPS supports still remain inside the elastic range,
the maximum curvatures observed for P1 are decreased. When
compared to Case 0, the magnitude of the impact forces
transmitted to this pier through the fixed bearings is decreased,
and therefore the maximum curvatures at the base of the pier
show more moderate values. However, this reduction is not
enough to effectively reduce the risk of loss of serviceability due
to excessive joint opening, as it was previously discussed.
Finally, Case 3 (Fig. 15(d)) combines the advantages
observed in Case 1 and Case 2 when compared to the original
study case. In-plane bending moments of P1 are reduced and the
hysteretic loops are mainly localized in the area of positive
curvatures, reducing the risk of excessive expansion joint residual
opening. Moreover, out-of-plane bending moments of P3 and P4
show the same beneficial response observed in Case 2. At the
same time, this seismic protection strategy is able to reduce the
increment of MY in P2 that takes place as a consequence of the
installation of cable restrainers. It is also noteworthy that in none
of the proposed cases the satisfactory response of MX in the piers
equipped with FPS supports is affected, since they present elastic
behavior in all the studied cases.
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P3
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P2
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P5
-0.005 0.000 0.005
-1
0
1Μ
Y
curvature (1/m)
M/M
y
P5
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P4
-0.005 0.000 0.005
-1
0
1M
Y
curvature (1/m)
M/M
y
P1
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P4
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P3
-0.005 0.000 0.005
-1
0
1M
X
M/M
y
P2
-0.01 0.00 0.01
-1
0
1Μ
X
M/M
y
P1
(d) Case 3
Fig. 15 Bending moment – curvature relationships at the bottom of the piers
The analysis of the seismic performance of the piers is
complemented with the study of the residual pier inclinations of
the substructure units (Table 3). From the observed results, it can
be concluded that the performance of the piers equipped with
FPS supports is satisfactory in all the study cases. Those cases
where FPS supports can move in the radial direction present
remarkable lower values due to the extent of the isolation effects
to both horizontal directions. Case 0 is the only model that
presents residual pier inclinations higher than the proposed limit
of 1%, which can imply loss of structural serviceability and
reparations of the pier. This performance can be improved by
following the seismic protection strategies proposed in cases 1, 2,
and 3. The reduction in RPI observed in these three cases can be
a consequence of the reduction of the pounding forces occurring
after installing cable restrainers and/or allowing some FPS
supports to move in the radial direction.
5. CONCLUSIONS
The seismic response of critical cases of viaducts isolated by
FPS supports and subjected to great earthquake ground motions
has been analyzed. Firstly, the dynamic behavior of isolated
straight and curved viaducts is discussed in terms of seismic
damage of the expansion joint and of the bridge piers. Special
attention has been paid to the effect of FPS support design
parameters on the dynamic behavior of the most unfavorable
cases. Finally, in order to improve the seismic performance of
those cases in which the damage limits where overpassed,
extended seismic protection strategies involving the use of FPS
supports have been examined. The obtained results provide
sufficient evidence for the following conclusions.
(1) FPS supports beneficially reduce the seismic forces
transmitted to the piers of the viaducts and thus, reduce their
plastic deformations and structural damage. In-plane bending
moments in those piers equipped with the sliding isolators remain
inside the elastic range, even when viaducts are subjected to the
selected level II earthquake ground motion records.
(2) Seismic isolation with FPS supports leads to high impact
forces in the studied viaducts. In the case of straight viaducts the
pounding forces at the expansion joint do not compromise the
stability or serviceability of the bridge. However, the larger
pounding forces observed in curved viaducts subjected to JR
Takatori Station earthquake record lead to an unfavorable
response of the expansion joint. The evaluation of the
performance in terms of unseating damage, and excessive
residual joint opening indicates that there is a clear risk of
structural seismic damage.
(3) The risk of loss of stability or serviceability, observed in
curved viaducts subjected to the most extreme earthquake records,
is not effectively reduced through the modification of the design
parameters of the FPS supports. The radius of curvature and the
coefficient of friction of the sliding surface of the FPS supports do
not have a clear influence on the seismic performance of these
critical study cases.
(4) Unseating prevention cable restrainers installed in curved
viaducts equipped with FPS supports prove to be an effective
strategy to improve the seismic performance of these viaducts.
The impact forces that take place at the deck discontinuity are
reduced, leading to a moderate decrease of the risk of deck
unseating and to a clear reduction of the joint residual opening.
However, out-of-plane bending moments are increased
especially in the pier located under the expansion joint, due to the
transmission of seismic forces as a consequence of the inter-span
connection.
(5) When installed in highly flexible structures like viaducts
isolated with FPS supports, cable restrainers are subjected to high
structural demands. If these devices fail, the viaduct will behave
in the same way as an unrestrained case, which increases the risk
of seismic damage at the expansion joint. Therefore, it is
important to carefully consider the mechanical characteristics of
cable restrainers, especially when they are installed in bridges
isolated with flexible bearings.
(6) The allowance for the FPS supports located in the inner
piers to move in both tangential and radial directions improves
the seismic performance of the piers of the curved viaduct models,
especially in the out-of-plane direction. The release of the
restraint of the radial movements of the base isolation systems
seems also beneficial for the seismic response of the expansion
joint. This measure leads to a clear reduction in the risk of
unseating damage by decreasing the maximum displacements of
the roller bearing supports.
(7) For most of the study cases, seismic isolation by FPS
supports seems to be an effective way to protect the analyzed
viaducts against the extreme aseismic demands that level II
earthquake ground motions induce. For the reduced number of
study cases that present a risk of seismic damage, a remarkable
improvement of the seismic performance can be obtained by
allowing some of the FPS supports to move in both horizontal
directions, and by the installation of unseating prevention cable
restrainers in the expansion joint.
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Table 3 Evaluation of RPI
Study Case
RPI P1 (%)
RPI P2 (%)
RPI P3 (%)
RPI P4 (%)
RPI P5 (%)
Case 0 1.61 0.41 0.37 0.26 0.05
Case 1 0.59 0.18 0.23 0.16 0.04
Case 2 0.42 0.04 0.05 0.05 0.03
Case 3 0.37 0.16 0.06 0.05 0.03
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(Received September 24, 2014)
(Accepted February 1, 2015)