analysis of the post-mainshock behavior of reinforced

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

- 194 -

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


- 195 -

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


- 196 -

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


- 197 -

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


- 198 -

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)


- 199 -

(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)


- 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

)


- 201 -

(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)


- 202 -

(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

)


- 203 -

(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

4000

5000

6000

0 20 40 60 80 100

194-164

194-104

Time (s)D

issi

pat

edE

ner

gy (

KN

.M)

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4000

6000

8000

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12000

0 20 40 60 80 100

INPUT ENERGY194-104

HYSTERESISENERGY 194-104

Dis

sip

ated

En

ergy

(K

N.M

)

Time (s)

0

2000

4000

6000

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12000

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20000

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INPUT ENERGY194-164

HYSTERETICENERGY 194-164

En

ergy

(K

N.M

)

Time (s)


- 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)


- 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


- 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)


- 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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