Analysis of the Post-Mainshock Behavior of Reinforced ...
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Jordan Journal of Civil Engineering, Volume 15, No. 2, 2021
‐ 193 - © 2021 JUST. All Rights Reserved.
Received on 28/8/2020. Accepted for Publication on 3/2/2021.
Analysis of the Post-Mainshock Behavior of Reinforced Concrete
Bridge Pier Columns Subjected to Aftershocks
Youcef Youb 1)*, Abdelkrim Kadid 2) and Hanane Lombarkia 3)*
1) Ph.D. Candidate, LGC-ROI Civil Engineering Laboratory - Risks & Interacting Structures, Department of Civil Engineering, Faculty of Technology, Batna2 University, Batna 05078, Algeria.
E-Mail: [email protected]; * Corresponding Author. 2) Professor, LGC-ROI Civil Engineering Laboratory - Risks & Interacting Structures, Department of
Civil Engineering, Faculty of Technology, Batna2 University, Batna 05078, Algeria. 3) Ph.D., Department of Hydraulics, Faculty of Technology, Batna2 University, Batna 05078, Algeria
ABSTRACT
The cumulative damage caused by aftershocks has become an important area of research to ensure the safety
of bridges in post-mainshock scenarios. This study analyzes the evolution of the seismic rigidity relationships
of reinforced concrete (RC) bridge pier column systems subjected to mainshock–aftershock (MS–AS)
sequences. Material non-linearity has been considered through lumped plasticity models for different
percentages and grade types of the reinforcing steel bars. The RC bridge pier columns are simulated by using
the SAP 2000 package software and subjected to a set of ground motion sequences. The results indicate that
the characteristics of the aftershocks significantly influence the damaged state of the RC bridge pier columns
after a mainshock. The additional damage caused by aftershocks to the pre-damaged RC bridge pier column in
the plastic region is minimized by substituting a few ordinary longitudinal steel-reinforced bars with identical
tubular bars, characterized by their high expected yield stress. This technique can decrease the vulnerability of
the bridge to additional aftershock damage by enhancing the post-yielding stiffness, thereby improving the
post-mainshock behavior of the bridge.
KEYWORDS: RC bridge pier column, Non-linear behavior, Aftershocks, Rigidity degradation, Cumulative damage, Post-yield stiffness.
INTRODUCTION
Various construction guidelines have been recently
developed according to the seismic assessment of
structures. The mainshock caused by a powerful
earthquake is always followed by a series of aftershocks.
Some of them can cause additional damage to structures
in a post-disaster situation. The Mw9.0 Tohoku ground
motion was one of the most severe earthquakes to have
occurred recently. The earthquake, which took place on
March 11th, 2011, triggered over 100 aftershocks with
magnitudes greater than 6.0. Several major aftershocks,
such as the Mw7.1 aftershock that occurred on April 7th,
2011, led to additional damage and widespread disorder
in the Tohoku region (Pomonis et al., 2011). This study
investigated the impact of aftershocks on the ductility
demand of elastic-perfectly plastic systems with a single
degree of freedom by using real or artificial mainshock–
aftershock sequences. Several studies have reviewed the
various effects of aftershocks on pre-damaged structures
(Goda et al., 2012; Iervolino et al., 2014; Ruiz-Garcia,
2012; Shen et al., 2015; Zhai et al., 2015).
Displacement-based methods, which are also known as
pushover analyses, account for the nonlinearity of the
material of these structures, provide an alternative to
force-based methods and usually have a better capacity
to simulate the real behavior of a structure subjected to
an earthquake loading in addition to generating accurate
results. We used the nonlinear static (pushover)
procedure in conjunction with the nonlinear dynamics
procedure as a dynamic integrated time history analysis
to assess the nonlinear behavior evolution of a pier
column highway bridge subjected to strong earthquakes.
Analysis of the Post-Mainshock… Youcef Youb, Abdelkrim Kadid and Hanane Lombarkia
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One of the aims of this study is to estimate the
probability of the failure of mainshock-damaged
structures subjected to an aftershock sequence. This
allows us to monitor the variation of its structural
performance due to the increased vulnerability caused
by the cumulative damage. The nonlinearity of the
material is considered through concentrated plasticity
type to predict the behavior of a reinforced concrete
(RC) column pier bridge by utilizing the two analysis
methods mentioned above. We aim to study the
evolution of curvature variation, dissipated energy and
ductility element variation after the mainshock and
aftershock waves to analyze the cumulative damage
progression and contain or limit the failure of the bridge
pier column due to second stiffness degradation. The
damage progression is minimized by utilizing a fixed
amount of substitute bars, characterized by their high
expected yield stress, instead of ordinary longitudinal
reinforcing bars.
The following studies analyzed the cumulative
damage evolution caused by aftershocks, modeling
aspects and the post-earthquake parameters used as
performance indicators in seismic assessments. Qiao et
al. (2020) highlighted the effects of mainshock–
aftershock (MS–AS) sequences on a 5-story RC frame
sample. Ren et al. (2020) conducted a numerical
analysis of the plastic hinge lengths of ultra-high
performance concrete columns subjected to acyclic load.
FEM simulations were performed by using the open-
source software OpenSees and further validated by
experimental tests. A parametric analysis was also
performed to assess the influence of major parameters
on the length of the plastic zone.
Olinei et al. (2019) studied the effect of the
frequencies of earthquakes on the forces and
displacements in the tunnel lining. The results
demonstrated that the forces and displacement in the
tunnel lining increased as the difference between the
frequencies of an earthquake and the natural frequency
reduced. Abdollahzadeh et al. (2019) demonstrated the
effect of the MS–AS sequences by developing the
performance-based plastic design technique to account
for the effects of aftershocks. A disproportional
relationship was obtained between the impact of the
MS–AS sequence and the increasing number of frame
stories. Polimeru et al. (2019) analyzed two hollow RC
bridge columns subjected to reversed cyclic loads by
using 1D and 2D numerical simulation models. Pang
and Wu (2018) explored the effect of aftershocks on the
seismic responses of multi-span RC bridges by adopting
a fragility-based numerical approach.
Omranian et al. (2018) examined the effects of
aftershocks on the seismic vulnerabilities of two kinds
of skewed bridges, such as an original bridge and a
bridge retrofitted with Fiber-Reinforced Polymer (FRP).
These bridges were subjected to a series of earthquake
ground motions. It was observed that the FRP
confinement decreased the probability of failure in the
skew bridge and had a more significant effect on the
higher levels of damage state. Yu et al. (2018)
investigated the collapse capacity of inelastic single-
degree-of-freedom (SDOF) systems subjected to MS–
AS earthquake sequences. They used an extended
incremental dynamic analysis method to determine the
collapse capacity of nonlinear SDOF systems subjected
to a series of MS–AS earthquakes by scaling the entire
earthquake sequence. Monteiro et al. (2018) compared
common structural analysis software tools used in the
nonlinear analyses of bridge structures. Alternative
adaptive pushover procedures are presented and applied
to a case study involving a bridge based on a lumped
plastic hinge model.
Several studies (Shatarat, 2012; Shatarat et al., 2017;
Botez et al., 2014; Monteiro et al., 2008; Su et al., 2017;
Kaptan et al., 2017) have analyzed the modeling aspects
that can impact structural vulnerability by comparing
different modeling approaches to determine the ideal
nonlinear properties in terms of lumped or distributed
plasticity cases. Grecho et al. (2016) investigated the
impact of the post-yielding stiffness ratio on nonlinear
seismic response parameters by employing a stochastic
approach. They concluded that the post-yield stiffness
must be considered while determining the inelastic
response of the structure. Fu and Liu (2013) analyzed
the first exceedance failure and cumulative damage
through the modified Park and Ang’s method. Their
proposed seismic damage model provided an accurate
prediction of the damage caused to RC columns
subjected to a load sequence.
Purpose and Objectives of the Study The objectives of the current study are two-fold. The
first objective involves conducting a parametric study to
understand the effects of uncertain parameters on the
Jordan Journal of Civil Engineering, Volume 15, No. 2, 2021
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nonlinear behavior of the bridges. According to the
results obtained from the parametric analysis, the second
objective is addressed; i.e., ensuring that the bridge
structures remain operational after a strong earthquake.
This study is based on the nonlinear static and dynamic
analyses performed in the SAP 2000 package software
by using a bridge pier with variable hollow column
sections. The elasto-plastic behavior is modeled by a
combination of the concentrated plasticity concept and
the plastic hinges model.
Thus, the primary purpose of this study is the
investigation of the most important ground motion
characteristics that influence the dynamic response
behavior of a bridge pier column. This is followed by
quantifying the level of damage caused by the MS–AS
earthquake sequence in terms of rigidity degradation.
Attempts are then made to control the structural seismic
damage by improving the post-yield stiffness of the pier
column. This improvement is conducted by allocating a
certain number of finishing bars characterized by their
relatively greater strength, instead of ordinary
reinforcing steel, thereby ensuring that the bridge has an
improved resistance to strong aftershocks and meets the
requirements for emergency use.
Description of the Bridge Pier Column The structure studied in this paper is a (RC)
reinforced concrete single column pier highway bridge
crossing Oued El-Rekham river in the Wilaya of Bouira
in Algeria country. As shown in Fig. 1, the highest pier
column is 92 m high with a variable hollow rectangular
cross-section, its outline dimension is 8 m (along the X-
axis denoted as the longitudinal direction of the bridge)
x 9 m (transverse direction) and variable wall thickness
of: 120 cm; 80 cm and 60 cm with corresponding height
of 25 m; 25 m and 42 m respectively from bottom to top.
The reinforcing longitudinal steel bars of 1% in all
variable sections are disposed in double layers near the
outside wall face and single layer near the inside wall
face with a spacing of 20 cm over all sides of the wall.
The cover concrete thickness protecting the reinforcing
steel bars is 30 mm. The top of the pier is subjected to
98000 kN as a dead load. The bottom pier has a fixed
boundary condition.
BOUIRA Highway box-girder bridge
Figure (1): Main bridge spans and pier column sections
Analysis of the Post-Mainshock… Youcef Youb, Abdelkrim Kadid and Hanane Lombarkia
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MODELING ASPECTS
Finite Element Model
The pier column was modeled as FEMA column
element with multilinear uniaxial Mx; hinges model
accounted for the bridge longitudinal direction. FEMA
columns consist of elastic segments and two plastic
hinges in their end zones. These features were
introduced through [SAP 2000 - 2017] which has been
selected as a software tool due to its widespread use
among practitioners and is commonly used for nonlinear
static and dynamic analyses of structures. Non-linear
properties of the moment-rotation relationships may be
defined and assigned automatically from the element
material and section properties to the hinges as a
backbone curve, as illustrated in Fig. 2 according to
FEMA-356 [FEMA, 2000].
Fig. 3 describes the Takeda hysteretic model (Takeda
et al., 1970) which was used to model the nonlinear
hysteretic behavior of the bridge pier column. Rayleigh
damping was applied as 5% of critical damping. Except
in the plastic hinge, the cracked section properties were
used throughout the length of the column. The effective
section properties were calculated from the yield moment, yield curvature and concrete elastic modulus : 𝐼
∅ .
. ACI 318-14[ACI, 2004] section 6.6.3.1.1 suggests
a value of 0.7Ig for the effective moment of inertia, which
is independent of any parameters or load level and will be
used below for defining the curvature of the fiber model.
The section of this model was divided into several fibers.
The core and the cover concrete fibers were assigned the
constitutive stress–strain relationships proposed by
Mander et al. (1988), as shown in Fig. 4 (a) & Fig. 4 (b),
while the steel fibers were assigned the bilinear
constitutive stress–strain relationships, as shown in
Fig. 4 (c).
Figure (2) : FEMA plastic hinge model of column
Figure (3) : Modified Takeda hysteresis
(a) Confined concrete
(b) Unconfined concrete
(c) Bilinear steel
Figure (4) : Mander constitutive stress-strain
relationships
Jordan Journal of Civil Engineering, Volume 15, No. 2, 2021
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Earthquake Database For illustration purposes, six seismic mainshock-
aftershock sequences taken from the Pacific Earthquake
Engineering NGA Ground Motion Database (PEER,
2010) were used in this study. The following criteria
were employed for identifying and selecting these
seismic sequences: 1) magnitude of main aftershock
event equal to or greater than 6.0; 2) seismic sequences
having PGA of the mainshock and the aftershocks
greater than 200 cm/s2 ; 3) some stations have been
chosen with aftershocks’ intensity, measured by the
PGA, greater than that of their corresponding
mainshocks, although the magnitude and seismic
moment of the mainshocks were greater than those of
the aftershocks; and 4) sequences have been assembled
with different signals, taking into account different
predominant periods "Tg". Under the above criteria, a
total of six recorded ground motions taken from three
earthquakes and five recording stations were identified
and selected for developing this study. To perform the
dynamic analysis, a time gap having zero acceleration
ordinates between the mainshock and the aftershock
acceleration time history has been adopted to ensure that
the system reaches its rest position. Intensity measures
of selected time history accelerations are shown in
Table 1.
Table 1. Relevant information on a few selected seismic records
Earthquake Record Designation Station Magnitude Mw PGA (g) Tg (s)
KOBE 1101 Amagazaki 6.9 0.276 1.00
KOBE 1116 Shinozaka 6.9 0.225 0.7
KOBE 1119 Takarazuka 6.9 0.697 1.8
NORTHRIDGE PUL 104 Pacioma Dam (Upper Left) 6.69 1.585 0.49
NORTHRIDGE PUL 194 Pacioma Dam (Upper Left) 6.69 1.285 0.73
SAN FERNANDO PUL 164 Pacioma Dam (Upper Abut) 6.61 1.219 1.19
Nonlinear Analysis Methods A modal analysis was performed to determine mode
shapes and their corresponding natural periods.
Pushover analysis was then carried out in the
longitudinal direction, as per the requirements of the
recommendations of the Seismic Retrofit Manual by the
Federal Highway Administration (FHWA, 2006).
For automated plastic hinge properties, the moment
curvature relationship of the potential plastic hinges is
determined by the software SAP 2000 based on the
column cross-section geometry, longitudinal and
transverse reinforcement details, confined and
unconfined concrete and steel stress-strain curve
parameters. Concrete cracking and reinforcement
yielding were considered by taking into account
effective moments of inertia. The capacity curve using
plastic hinge properties was obtained by pushing
monotonically the bridge pier column, through the well-
known nonlinear static pushover analysis method.
The direct-integration time-history analysis used in
this study is a nonlinear dynamic analysis method, in
which the equilibrium equations of motion are fully
integrated as a structure is subjected to dynamic loading.
Analysis involves the integration of structural properties
and behaviors at a series of time steps which are
relatively small regarding to loading duration. The
motion under evaluation is described by the equation
given as follows: 𝑀𝑢 𝑡 𝐶𝑢 𝑡 𝐾𝑢 𝑡 𝐹 𝑡 . For stability conditions, the Hilbert-Hughes-Taylor
(HHT) method with 0 < α ≤ -1/3 was adopted, which is
more appropriate for nonlinear time history cases
characterized by difficult convergence.
RESULTS AND DISCUSSION
Cumulative Damage Caused by the Aftershock on the
Post-mainshock Response The strength and stiffness degradation of the pier
column due to the additional and permanent damage
caused by an earthquake motion, especially an
Analysis of the Post-Mainshock… Youcef Youb, Abdelkrim Kadid and Hanane Lombarkia
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aftershock, is analyzed in this section. The bridge pier
column was subjected to a sequence of ground motions
obtained from the 1101 KOBE and1116 KOBE
earthquakes, as shown in Fig. 5.
Figure (5): ACC. 1101-1116
(a)
(b)
Figure (6) : Evolution of (a) rotation and (b)
dissipated energy
It is evident from Fig. 6 (a) that additional damage
of approximately 77 %, which is expressed in terms of
increased rotation, is observed at the end of the
aftershock, in comparison to the damage observed after
the main shock. Further, it can be seen from Fig. 6 (b)
that although the Peak Ground Acceleration of the
aftershock has a ratio of 0.81, which is lower than that
of the mainshock, the 1116 KOBE ground motion can
absorb more energy than its corresponding mainshock,
with the latter accounting only for 9 % of the total
dissipated energy. These observations are explained by
the effects of the dynamic aftershock features, some of
which are elaborated upon below.
Effect of the Aftershock Intensity on the Post-
mainshock Response
The effects of the magnitude and frequency are
neglected by comparing the real and artificial MS–AS
ground motion sequences with identical magnitudes.
The transient variations of the acceleration for these
sequences are shown in Fig. 7 and Fig. 8. The sequences
are chosen such that the ratio of their PGAs is relatively
large and equal to 3.11, thereby eliminating probable
influence of the frequency content. The energetic
approach was used to assess the pier column damage
level caused by the load sequence.
Figure (7): ACC. 1119-1116
Figure (8): ACC. 1116-1119
X= 10.25Y= -2.76
X= 78.79Y= -2.25
-4
-3
-2
-1
0
1
2
3
0 20 40 60 80 100 120
1101 - 1116
Acc
eler
atio
n (
m/s
2 )
Time(s)
-0.000005
0
0.000005
0.00001
0.000015
0.00002
0.000025
0.00003
0.000035
0 20 40 60 80 100 120
1101-1116
Time (s)
Rot
atio
n(R
ad)
0
20
40
60
80
100
120
0 20 40 60 80 100 120
1101-1116
Time (s)
Dss
ipat
ed E
ner
gy (
KN
.M)
Time (s)
X= 6.0Y= -6.97
X= 65.75Y= -2.25
-8
-6
-4
-2
0
2
4
6
0 10 20 30 40 50 60 70 80 90 100
1119-1116
Acc
eler
atio
n (
m/s
2 )
Time (s)
X= 14.79Y= -2.25
X= 56.95Y= -6.97
-8
-6
-4
-2
0
2
4
6
0 20 40 60 80 100
1116 - 1119
Acc
eler
atio
n(m
/s2 )
Time (s)
Jordan Journal of Civil Engineering, Volume 15, No. 2, 2021
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(a)
(b)
Figure (9): Moment-rotation curve due to (a)
sequence N°01 and (b) inverse of sequence N°01
(a)
(b)
Figure (10) : Evolution of (a) rotation and (b)
cumulative dissipated energy
(a)
(b)
Figure (11) : Evolution of energy due to (a)
sequence N°01 and (b) its inverse
The hysteretic curves shown in Fig. 9 (a) and Fig. 9
(b) confirm that the structural damage may be affected
by the load sequence. The permanent displacement
(Fig.10 (a)) and cumulative dissipated energy (Fig.10
(b)) curves indicate that a relatively higher amount of
damage is caused by the aftershocks when the bridge is
subjected to relatively greater damage from the
mainshock.
It is evident from Fig.11(a) and Fig.11(b) that the
ratio between the dissipated and input energy increases
with increasing displacement amplitude. The ratio is
equal to 34 % and 30 % for the real and inverse
sequences, respectively.
Effect of the Aftershock Frequency Content on the
Post-mainshock Response The influence of the frequency of the aftershock on
the dynamic post-mainshock response during the
dominant period is studied by subjecting the bridge pier
column to a real ground motion sequence composed by
the KOBE 1101 and KOBE 1116 earthquakes and their
inverses. These sequences were recorded during
-6
-4
-2
0
2
4
6
-0.0004 -0.0003 -0.0002 -0.0001 0 0.0001 0.0002 0.0003
SEQ N°01 (1119-1116)SEQ N°01
Rotation (Rad)Fle
xura
l Mom
ent
(KN
.m)
x 10
5
-6
-4
-2
0
2
4
6
-0.0004 -0.0003 -0.0002 -0.0001 0 0.0001 0.0002 0.0003
INV SEQ N°01
Rotation (Rad)Fle
xura
l Mom
ent
(KN
.m)
x 10
5
-0.0004
-0.0003
-0.0002
-0.0001
0
0.0001
0.0002
0.0003
0 20 40 60 80 100
INVERSE SEQ. N° 01
SEQ. N° 01
Time (s)
Rot
atio
n(R
AD
)
-500
0
500
1000
1500
2000
2500
3000
3500
0 20 40 60 80 100
INVERSE SEQ.N°0
SEQ.N°01
Time (s)
Dis
sip
ated
En
ergy
(K
N.M
)
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0 20 40 60 80 100
INPUT ENERGY
HYSTERETIC ENERGY
En
ergy
(K
N.M
)
Time (s)
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0 20 40 60 80 100
INPUT ENERGY
HYSTERETICENERGY
En
ergy
(K
N.M
)
Time (s)
Analysis of the Post-Mainshock… Youcef Youb, Abdelkrim Kadid and Hanane Lombarkia
- 200 -
the1995 Kobe–Japan earthquake and are characterized
by their identical magnitudes, as shown in Fig. 12 (a)
and Fig. 12 (b).
(a)
(b)
Figure (12): (a) ACC. 1101-1116 and (b) ACC. 1116-1101
(a)
(b)
Figure (13): (a) Rotation evolution and (b) signal predominant periods
X= 10.25Y= -2.76
X= 78.79Y= -2.25
-4
-3
-2
-1
0
1
2
3
0 20 40 60 80 100 120
1101 - 1116
Acc
eler
atio
n (
m/s
2 )
Time(s)
Tg = 0.67
Tg = 1.01
X= 14.78Y= -2.25
X= 61.21Y= -2.76
-4
-3
-2
-1
0
1
2
3
0 20 40 60 80 100 120
1116 - 1101
Acc
eler
atio
n (
m/s
2 )
Time(s)
Tg = 0.67
Tg = 1.01
-0.000005
0
0.000005
0.00001
0.000015
0.00002
0.000025
0.00003
0.000035
0 10 20 30 40 50 60 70 80 90 100 110 120
1116-1101
1101-1116
Rot
atio
n (
Rad
)
Time(s)
Tg = 0.67
Tg = 1.01
0
20
40
60
80
100
120
140
160
0.01 0.1 1 10
1116
1101
Periods (s)Pse
ud
o-S
pec
tral
Vel
ocit
y (c
m/s
)
Jordan Journal of Civil Engineering, Volume 15, No. 2, 2021
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(a)
(b)
Figure (14) : Evolution of (a) dissipated energy and (b) cumulative dissipated energy
The transient evolution of the rotation generated due
to the ground motion of the 1101–1116 sequence is
shown in Fig.13 (a). Although the PGA of the aftershock
has a ratio of 0.82, which is lower than that of the
mainshock, it is evident that such an artificial aftershock
not only causes additional damage, but also increases the
peak and residual bottom pier rotation. This behavior is
attributed to the dominance of the high-frequency
aftershock during its dominant period, which is shorter
than that of the mainshock, as shown in Fig. 13 (b).
The curves of the dissipated energy and cumulative
dissipated energy are shown in Fig. 14 (a) and Fig. 14
(b). Although the PGA and duration of the aftershock
are smaller than those of the mainshock, the latter
dissipated lesser energy than the former, because the
latter's low-frequency content was more dominant in
comparison to that of the corresponding aftershock.
The above results demonstrate that despite having a
lower PGA than the second component of the sequence,
the 1116 KOBE ground motion can be more harmful
either as being mainshock or aftershock due to its high-
frequency content, which is more dominant than the
corresponding low-frequency content.
Difference between the Bridge Pier Column's
Response under Real Near-Fault and Artificial
Sequences
Although the near-fault mainshock has the
maximum PGA, it is composed of lengthy periods of
dominance that might not lead to inelastic behavior or a
significant amount of accumulated damage. The impact
of the aftershock frequency content is further explored
by subjecting the bridge pier column to two ground
motion sequences that consist of an identical main shock
and different aftershocks with varying periods of
dominance. The first real sequence was obtained from
the Northridge earthquake, which was recorded at the
Pacioma Dam (Upper Left) Station. The artificial
sequence was assembled with the main shock wave
obtained from the San Fernando earthquake, which was
recorded at the Pacioma Dam (Upper Abut) Station as
an aftershock, as shown in Fig. 15 (a) and Fig. 15(b).
0
20
40
60
80
100
120
140
0 10 20 30 40 50 60
1116
1101
Dis
sip
ated
En
ergy
(K
N.M
)
Time (s)
0
50
100
150
200
250
0 10 20 30 40 50 60 70 80 90 100 110 120
1116-1101
1101-1116
Dis
sip
ated
En
ergy
(K
N.M
)
Time (s)
Analysis of the Post-Mainshock… Youcef Youb, Abdelkrim Kadid and Hanane Lombarkia
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(a)
(b)
(c)
Figure (15): (a) ACC. 194-104, (b) ACC. 194-164 and (c) top displacements’ evolution
(a)
(b)
Figure (16): Predominant period of (a) 194-164 sequence and (b) 194-104 sequence
X= 4.54Y= -12.850
X= 54.58Y= 15.849
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100
194-104
Time (s)
Acc
eler
atio
n (
m/s
2 )
Tg =0.49
Tg =0.73
X= 4.56Y= -12.8501
X= 57.76Y= 12.19037
-15
-10
-5
0
5
10
15
0 10 20 30 40 50 60 70 80 90 100
194-164
Time (s)
Acc
eler
atio
n (
m/s
2 )
Tg =0.73
Tg =1.19
-0.4
-0.2
0
0.2
0.4
0.6
0.8
0 20 40 60 80 100
194-164
194-104
Time (s)
Dis
pla
cem
ent
(m)
Tg = 0.73 Tg = 1.19
0
50
100
150
200
250
0.01 0.1 1 10
194
164
Pse
ud
o-S
pec
tral
Vel
ocit
y (c
m/s
)
Periods (s)
Tg = 0.73
Tg =0.49
0
50
100
150
200
250
0.01 0.1 1 10
194
104
Periods (s)Pse
ud
o-S
pec
tral
Vel
ocit
y (c
m/s
)
Jordan Journal of Civil Engineering, Volume 15, No. 2, 2021
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(a)
(b)
(c)
Figure (17): Evolution of (a) dissipated energy; (b) energy due to 194-104 sequence and
(c) energy due to 194-164 sequence
The transient variation of the displacement of the top
tier for each seismic sequence is shown in Fig.15(c). It
is evident that the bridge column has exhibited inelastic
behavior, which has resulted in permanent displacement
at the end of the mainshock of the first sequence.
However, there was no significant increment in the peak
or the residual displacement at the end of the following
aftershock, despite the relatively large sequence (PGA)A
/(PGA)M ratio, which was equal to 1.23.
The second sequence was characterized by its
relatively low aftershock PGA, which was equal to 0.94
with respect to its corresponding mainshock. However,
this sequence reported a different response, wherein
there was a clear rise in the peak and residual top pier
displacement. This behavior was attributed to the
artificial aftershock effect.
This difference between the responses is further
explained by the relatively longer dominant period of the
aftershock, which is more similar to the period of the first
mode of vibration of the bridge pier column
(Tg/T1 =0.9) shown in Fig. 16 (a) than that of the real
aftershock shown in Fig. 16 (b). Thus, despite experiencing
strong aftershocks, response accumulation does not
necessarily occur. It is heavily dependent on the dominant
period of the aftershock and the first natural period of the
bridge pier column at the end of the mainshock.
The curves plotted in Fig. 17 (a) confirm the above-
mentioned conclusion. A rise in the dissipated energy
0
1000
2000
3000
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6000
0 20 40 60 80 100
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194-104
Time (s)D
issi
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ner
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KN
.M)
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6000
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12000
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INPUT ENERGY194-104
HYSTERESISENERGY 194-104
Dis
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En
ergy
(K
N.M
)
Time (s)
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INPUT ENERGY194-164
HYSTERETICENERGY 194-164
En
ergy
(K
N.M
)
Time (s)
Analysis of the Post-Mainshock… Youcef Youb, Abdelkrim Kadid and Hanane Lombarkia
- 204 -
due to the aftershock of the second sequence is more
important than that of the first sequence, despite its weak
PGA in comparison to the corresponding mainshock.
Further, it can be seen from Fig. 17 (b) and Fig. 17 (c)
that the input energy of the second sequence is larger
than that of the first one.
Hence, we can conclude that a randomized approach
can lead to a higher peak and larger residual
displacement demand than those of the real approach,
despite the structure being subjected to a stronger
aftershock during the real approach than the aftershock
applied during the artificial one.
Effect of Substituting Ordinary Reinforcing Bars by
High-strength Reinforcement
A simulation was conducted to illustrate the
behavior of the pier column of the bridge upon
increasing the yield strength of its bottom section
without altering the percentage of longitudinal steel.
Hence, ordinary bars were replaced with high-yield steel
bars at 531 MPa and an enhanced elastic modulus of 210
GPa. This was accomplished by inserting tubular steel
bars with a reinforcement ratio of (5, 10 and 15%) in the
bottom of the pier along the expected plastic hinge zone,
as shown in Fig. 18 (FEMA, 2000). The bars were
produced by a cold rolling process to attain high yield
strength and minimize the yielding plateau of the stress–
strain relationships, as shown in Fig. 19. The impact of
aftershocks on the post-mainshock response was
minimized and the post-yielding stiffness of the pier
column improved, which helped preserve the post-
earthquake functionality of the bridge. This practical
method was tested by subjecting the pier column to the
two loading sequences shown in Fig. 7 and Fig. 12 (a).
An analysis of the hysteretic behaviors of seismically
loaded pier column allows us to compare the advantages
and disadvantages of these reinforcements.
Figure (18): High-strength rolling bars in
bottom section
Figure (19): Idealized stress-strain curve indicating strength and ductility proprieties (not to scale)
Jordan Journal of Civil Engineering, Volume 15, No. 2, 2021
- 205 -
(a)
(b)
Figure (20): Actual (a) and idealized (b) moment-curvature curve of
the bottom pier column section (fiber model)
Figure (21) : Post-mainshock pushover curves
Figure (22): Hysteretic moment-rotation curve of the pier column bottom section with
different rates of finishing rolling rebars
0
1
2
3
4
5
6
7
8
9
0 0.01 0.02 0.03 0.04 0.05
0%
5%
10%
15%
Curvature (Rad)F
lexu
ralM
omen
t (
KN
.M)x
105
0
1
2
3
4
5
6
7
8
9
0 0.002 0.004 0.006 0.008 0.01
0%
5%
10%
15%
Flu
xura
lMom
ent
(KN
.m)
x 10
5
Curvature (Rad/m)
0
2000
4000
6000
8000
10000
12000
14000
‐0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0% Rolling Bars
5% Rolling Bars
10% Rolling Bars
15% Rolling Bars
Displacement (m)
Sh
ear
(KN
)
-6
-4
-2
0
2
4
6
-0.0004 -0.0003 -0.0002 -0.0001 0 0.0001 0.0002 0.0003
0%
5%
10%
15%Rotation (Rad)
Fle
xura
l Mom
ent
(Kn
.m)x
105
Analysis of the Post-Mainshock… Youcef Youb, Abdelkrim Kadid and Hanane Lombarkia
- 206 -
Figure (23): Rotation evolution with different rates of finishing rolling rebars
The actual and ideal moment-curvature curves are
shown in Fig. 20 (a) and Fig. 20 (b), respectively. The
secondary stiffness can be enhanced by substituting
ordinary reinforcing bars with geometrically identical
bars that are stronger than the former. The enhancement
of rigidity was first observed during the appearance of
the first plastic hinge and kept increasing until failure.
This conclusion is confirmed by Fig. 21, which
demonstrates the evolution of the post-mainshock push-
over curves. These curves indicate that the improvement
in the post-yield stiffness can be attributed to the
replacement of the original bars with stronger ones.
This design method can also analyze the elastic–
plastic seismic response by tracking and controlling the
seismic evolution damage of the pier column. The
hysteretic curves shown in Fig. 22 indicate that an
increment in the number of finishing high-strength bars
leads to a reduction in the curvature, which corresponds
to a rise in rigidity. It is also shown in Fig.23 that an
increment in the number of substitution bars leads to a
reduction in the post-earthquake residual deformation.
However, the substitution of ordinary bars beyond a
certain limit may reduce the ductility of the structure.
Therefore, this technique must be undertaken cautiously
to avoid failure due to lack of ductility.
CONCLUSIONS
This study aims to analyze the contributions of
various parameters to the nonlinear behavior of an RC
bridge pier column system. Following the results of the
parametric study, a technique is developed to ensure that
the bridges remained operational after an earthquake.
The RC bridge pier column system was simulated on
SAP 2000 package software and subjected to a series of
mainshocks, followed by aftershocks. The results
indicate that the varying characteristics of the multiple
sequences of ground motion significantly affected the
vulnerability relationships of the bridge pier column.
Additional emphasis is placed on the impact of the
aftershocks on the post-mainshock responses. The
findings of our study are consistent with the results
obtained from other studies. The following conclusions
can be drawn from this study.
The effect of the aftershock features on pre-damaged
bridge pier columns was explored in the first part of
this study. It was observed that the dominant period
of the mainshock ground motions, which was a
measure of the frequency content, was a pertinent
characteristic that could define the damage level of a
structure. Thus, the nonlinear dynamic response of
bridge pier columns is significantly affected by the
frequency content of the ground motion sequence of
the earthquake.
The response of the structure under artificial
sequences was unlike the response obtained under
real sequences, especially when a real mainshock
was followed by an artificial aftershock with
different ground motion features.
It was observed that a ground motion sequence
composed of an aftershock with a shorter dominant
period than its corresponding mainshock
significantly influenced the response of a pre-
damaged structure, despite the mainshock having a
higher PGA than that of the aftershock.
However, an aftershock with a larger dominant
period than that of its mainshock could also cause
significant damage if the dominant period of the
aftershock was identical to the period of the
fundamental vibration mode of the bridge pier
column at the end of the mainshock.
The final part of this study proposed an alternative
reinforcement configuration by substituting a few
ordinary reinforcing bars with geometrically
-5E-06
0
5E-06
1E-05
1.5E-05
2E-05
2.5E-05
3E-05
3.5E-05
4E-05
0 20 40 60 80 100 120
0%
5%
10%
15%
Rot
atio
n (
Rad
)Time (s)
Jordan Journal of Civil Engineering, Volume 15, No. 2, 2021
- 207 -
identical bars with a higher expected yield stress than
their ordinary counterparts. However, it is important
to strike a balance between the rigidity and ductility
of the structure by applying a moderate percentage
of this reinforcement to avoid failure due to lack of
ductility.
Although the tested design approach, under certain
dynamic environments, is more advantageous than
the conventional design approach, the numerical
results presented in this paper indicate that the
overall behavior of bridge piers, subjected to under
earthquake sequences, is heavily influenced by the
strength, duration and the spectral content of the
dynamic environment. Thus, it is difficult to attest to
the viability of this approach in improving the
designs of bridge piers in seismic zones.
Conflict of Interest On behalf of all authors, the corresponding author
states that there is no conflict of interest.
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