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Structure and Infrastructure Engineering
Maintenance, Management, Life-Cycle Design and Performance
ISSN: 1573-2479 (Print) 1744-8980 (Online) Journal homepage: https://www.tandfonline.com/loi/nsie20
Toward life-cycle reliability-, risk- and resiliencebased design and assessment of bridges and
bridge networks under independent and
interacting hazards: emphasis on earthquake,
tsunami and corrosion
Mitsuyoshi Akiyama, Dan M. Frangopol & Hiroki Ishibashi
To cite this article: Mitsuyoshi Akiyama, Dan M. Frangopol & Hiroki Ishibashi (2020) Toward lifecycle reliability-, risk- and resilience-based design and assessment of bridges and bridge networks
under independent and interacting hazards: emphasis on earthquake, tsunami and corrosion,
Structure and Infrastructure Engineering, 16:1, 26-50, DOI: 10.1080/15732479.2019.1604770
To link to this article: https://doi.org/10.1080/15732479.2019.1604770
Published online: 11 May 2019.
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STRUCTURE AND INFRASTRUCTURE ENGINEERING
2020, VOL. 16, NO. 1, 26–50
https://doi.org/10.1080/15732479.2019.1604770
Toward life-cycle reliability-, risk- and resilience-based design and assessment of
bridges and bridge networks under independent and interacting hazards:
emphasis on earthquake, tsunami and corrosion
Mitsuyoshi Akiyamaa, Dan M. Frangopolb and Hiroki Ishibashia
a
Department of Civil and Environmental Engineering, Waseda University, Tokyo, Japan; bDepartment of Civil and Environmental
Engineering, Engineering Research Center for Advanced Technology for Large Structural Systems (ATLSS Center), Lehigh University,
Bethlehem, PA, USA
ABSTRACT
ARTICLE HISTORY
After recent large earthquakes, field investigations confirmed that several bridges were severely damaged and collapsed not only due to the earthquake, as an independent hazard, but also to the subsequent tsunami, landslide or fault displacement. In addition, long-term material deterioration might
have an important impact on seismic damage to bridges. Therefore, it is important to study both independent and interacting hazards and their effects on the reliability and risk of bridges and bridge networks. Although earthquake is still a dominant hazard to bridges in many earthquake-prone countries,
a life-cycle reliability and risk approach has to consider both independent and interrelated hazards
causing bridge failure. Such an approach is presented in this paper. In addition, issues related to lifecycle analysis, design, risk, resilience and management of bridges under earthquake and other hazards
are discussed. Finally, the concepts and methods presented are illustrated on both single bridges and
bridge networks.
Received 23 September 2018
Revised 5 December 2018
Accepted 9 January 2019
1. Introduction
Bridges may be susceptible to damage during an earthquake
event, particularly if they were designed without adequate
seismic detailing. Bridge columns built using earlier design
codes (i.e. without proper seismic detailing) often lack
adequate flexural strength and ductility capacity, and/or
shear strength. When subjected to strong ground motions,
they have the potential to exhibit brittle failure. Several
destructive earthquakes in Japan inflicted various levels of
damage on the structures and infrastructure systems. The
investigation of these negative consequences gave rise to serious discussions about performance indicators and seismic
design philosophy, and to extensive research activity on the
retrofit of as-built bridges (Akiyama, Frangopol, &
Mizuno, 2014).
There are several performance indicators that can be
related to the possible occurrence of local and global failures, including system ductility, failure times, redundancy,
robustness and resilience (Biondini & Frangopol, 2016).
These performance indicators need to be included into the
practical design and assessment for bridges (Biondini &
Frangopol, 2018). A review of performance indicators and
metrics is available in Barone and Frangopol (2014),
Frangopol and Saydam (2014), Ghosn et al. (2016), Saydam
and Frangopol (2011) and Zhu and Frangopol (2012).
Reliability-based performance indicators, which account
for the uncertainty in both resistance and load, have been
the basis for establishing the safety levels of structural
CONTACT Mitsuyoshi Akiyama
[email protected]
ß 2019 Informa UK Limited, trading as Taylor & Francis Group
KEYWORDS
Life-cycle; reliability; risk;
resilience; hazard;
earthquakes; bridge;
bridge network
design codes. Although reliability-based performance indicators can provide adequate information on the safety of
bridge components and individual bridges, they lack the
ability to reflect the outcome of a failure event in terms of
economic losses. On the other hand, risk and risk-based
performance indicators offer additional information on the
performance of structural systems under various hazards.
Risk allows combining the probability of component or system failure with the consequence of the event.
As observed in recent disasters (e.g. 2011 Great East
Japan earthquake and 2016 Kumamoto earthquake in
Japan), because the transportation networks, including
bridges, play a crucial role in the evacuation of affected
people and the transportation of emergency goods and
materials, the functionality of the network after a disaster
must be investigated (Unjoh, 2012). A significant amount of
research efforts has shifted the focus from the investigation
of the performance of individual components of the infrastructure to that of entire distributed civil infrastructure
systems and networks (Frangopol & Estes, 1997; Akg€
ul &
Frangopol, 2003; Biondini, Frangopol, & Restelli, 2008;
Ghosn, Moses, & Frangopol, 2010; Bocchini, Frangopol, &
Deodatis, 2011; Dong & Frangopol, 2017; Saydam, Bocchini,
& Frangopol, 2013; Stergiou & Kiremidjian, 2010; Torbol &
Shinozuka, 2014).
The prompt restoration of critical infrastructure facilities
after an extreme event is always a goal of paramount
importance (Bocchini & Frangopol, 2012a, 2012b). To
STRUCTURE AND INFRASTRUCTURE ENGINEERING
27
Figure 1. Recent large earthquakes in Japan after the 1995 Hogoken-Nanbu (Kobe) earthquake.
quantify the promptness of the restoration, it has become
customary to use the concept of resilience. Even though
there are several definitions of resilience in the literature,
the most widely accepted definition is provided by Bruneau
et al. (2003): ‘resilience is defined as the ability of social
units (e.g. organisations, communities) to mitigate hazards,
contain the effects of disasters when they occur, and carry
out recovery activities in ways that minimise social disruption and mitigate the effects of future earthquake’.
Resilience emphasises the impact of infrastructure damage, failure and societal recovery under hazards with a low
probability of occurrence and high consequences. On the
other hand, sustainability concentrates on current and
future resource management, and addresses the impacts of
planning and development on the economy, society and the
environment. A sustainable infrastructure system needs to
include resilient and adaptive capabilities for ensuring its
long-term sustainability. Some of the most promising solutions for resilience are actually also sustainable in nature
(Mackie, Kucukvar, Tatari, & Elgamal, 2016). Meanwhile,
Bocchini, Frangopol, Ummenhofer and Zinke (2014) proposed a unified approach by combining resilience and sustainability and concluded that a systematic unification of
resilience and sustainability is mandatory.
Design and assessment of structures have been geared
towards addressing the most dominant hazard at the location of interest. However, the possibility of structures experiencing multiple hazards of different types during their
lifetime needs to be considered. The design methodology of
bridges must shift towards a more comprehensive approach
of addressing multiple hazards to ensure adequate performance under different mechanical and environmental scenarios (Chulahwat & Mahmoud, 2017; Gidaris et al., 2017).
Quantification of the reliability and risk associated with
damage to each bridge under multiple hazards can help in
prioritising retrofit activities for bridges in a network.
Significant advances have been accomplished in the field
of earthquake engineering. However, there is a need to promote further research for developing concepts and methods
in order to design and assess resilient and sustainable
bridges and bridge networks in a life-cycle context. This
paper provides an overview of life-cycle design and assessment methodologies of bridges under multiple hazards with
an emphasis on earthquake, tsunami and continuous deterioration based on the lessons from recent large earthquakes
in Japan. Several performance indicators necessary to be
implemented into the practical design and assessment are
introduced. Finally, the concepts and methods presented are
illustrated in two case studies on bridges under independent
hazards and bridge networks under interacting hazards.
2. Lessons from recent large earthquakes in Japan
Figure 1 shows several recent destructive earthquakes in
Japan after the 1995 Hyogoken-Nanbu (Kobe) earthquake.
Lessons from these earthquakes have demonstrated that not
only seismic safety, but also other performance indicators
for both individual bridges and bridge networks have to be
taken into consideration. Based on the field investigations
conducted after the recent large earthquakes in Japan,
important lessons are introduced herein.
2.1. Typical failure modes of as-build RC columns
designed before 1990
In Japan, seismic design specifications for structures and
civil infrastructure systems have been significantly revised.
The first seismic design code for road bridges, which
included the seismic analysis considering the inelastic bridge
behaviour and seismic design actions for the verification of
the no-collapse requirement (i.e. Level 2 Ground Motion),
28
M. AKIYAMA ET AL.
Figure 2. Typical failure mode of RC columns designed before the 1990s: shear failure of RC columns of Shinkansen viaducts [photographs (a) and (b) taken by the
first author and photograph (c) courtesy of Dr. Takahashi at Kyoto University].
Figure 3. Typical failure mode of RC columns designed before the 1990s: damage to RC columns with the cut-off of the rebars [photographs (a) and (b) taken by
the first author and photograph (c) courtesy of East Japan Railway Company].
was issued in Japan in 1990 (Japan Road Association, 1990).
Before 1990, the designers did not predict the whole behavior of bridges under seismic excitation and did not identify
the most probable failure modes of these bridges (Akiyama,
Matsuzaki, Dang, & Suzuki, 2012). Also, there was a lack of
proper knowledge on structural details.
Figures 2 and 3 illustrate typical failure modes of RC columns designed according to the old design code. RC bridge
piers had insufficient shear reinforcement and/or have cutoffs of longitudinal rebars without adequate anchorage
length at the midpoint of bridge pier. These deficiencies
caused several damages to RC columns during the past
large eartquakes.
2.2. Ductility design and seismic retrofit
Based on the experience of seismic damage to bridges and
research progress on earthquake resistance, shear and ductility design methodologies of RC components were modified.
Figure 4 depicts the relationship between horizontal load
and displacement of a bridge pier. According to the revisions of seismic design codes, lateral strength and displacement ductility have been improved (Kawashima, 2000).
In addition, several seismic retrofitting methods have
been developed. Figure 5 presents the damaged states of the
Shinkansen viaducts taken after the 2003 Sanriku-Minami
earthquake and the 2011 Great East Japan earthquake. The
retrofitted columns of the viaducts performed well, with
almost no damage during the 2011 Great East Japan earthquake (Akiyama & Frangopol, 2012b). There have been no
reports on the damage of retrofitted RC columns or on the
undesirable consequences elsewhere in the retrofitted bridge.
2.3. Effect of damage to bridge on the network
functionality
An example of post-disaster functionality deterioration of a
road network is shown in Figure 6. Figure 6(a) displays the
collapse of as-build bridges over the Kyushu Expressway
preventing traffic passage after the 2016 Kumamoto earthquake. Since the old overpass bridge did not have a substantial daily traffic, this bridge was not retrofitted to meet
the current seismic design requirements. Seismic retrofit
strategy must be established considering the consequences
associated with the bridge failure. In Figure 6(b), the damage of the embankment is shown. Although the nearby
bridge did not have any damage, the functionality of the
post-disaster road network deteriorated severely. Reliable
and efficient frameworks for quantifying the functionality
loss of road networks involving bridges and other road
structures (e.g. tunnels and embankments), and for identifying the most vulnerable structure in the network
are needed.
2.4. Bridge damages due to independent hazards
(seismic damages of corroded bridges)
The effect of corrosion on the deterioration of the capacity
of bridges under seismic hazard has to be considered. Field
investigation conducted after the 2011 Great East Japan
earthquake confirmed that some of RC structures and steel
bearings were severely deteriorated due to chloride-induced
corrosion as shown in Figure 7. It is important to understand that the seismic demand depends on the results of
seismic hazard assessment, whereas the seismic capacity
STRUCTURE AND INFRASTRUCTURE ENGINEERING
29
Figure 4. Improvement of seismic capacities associated with horizontal strength and displacement.
Figure 5. No. 5 Inohana viaduct taken after the 2003 Sanriku-Minami earthquake and after the 2011 Great East Japan earthquake (Note: the viaduct was retrofitted
before the 2011 Great East Japan earthquake) (both photographs taken by the first author).
Figure 6. Example of post-disaster functionality deterioration of road network [photograph (a) courtesy of Mr. Matsunaga at Kyodo Engineering Consultant Co.
Ltd. and photograph (b) taken by the first author].
Figure 7. Material deterioration observed in the field investigation after the 2011 Great East Japan earthquake (all photographs taken by the first author).
depends on the other hazard, such as hazard associated with
airborne chlorides. The seismic performance of existing
bridges in a harsh environment cannot be expected to be
the same as that at the time of construction.
2.5. Bridge damages due to interacting hazards
Several bridges were severely damaged and collapsed not
only due to the strong ground motion, but also to the
30
M. AKIYAMA ET AL.
Figure 8. Matsurube bridge collapsed due to the land slide during the 2008 Iwate-Miyagi earthquake (both photographs taken by the first author).
Figure 9. Koizumi bridge collapsed due to the tsunami during the 2011 Great East Japan earthquake (both photographs taken by the first author).
Figure 10. Utatsu bridge collapsed due to the tsunami during the 2011 Great East Japan earthquake (all photographs taken by the first author).
subsequent tsunami, landslide or fault displacement. Figure
8 shows the collapse of Matsurube bridge during the 2008
Iwate-Miyagi Nairiku earthquake. The abutment was displaced by the landslide due to the strong ground motion.
Figures 9 and 10 present the photographs of Koizumi bridge
and Utatsu bridge, respectively, taken after the 2011 Great
East Japan earthquake. Koizumi bridge had the superstructure supported by five RC bridge piers. The superstructure
was displaced more than 400 m from the original position.
The concrete superstructure of Utatsu bridge was
washed away.
Koizumi bridge has been retrofitted by a seismic damper
to prevent the excessive superstructure response under
strong excitations. Also, RC bridge piers of the Utatsu
bridge were retrofitted by jacketing to improve their capacity against the strong ground motions (Akiyama,
Frangopol, Arai, & Koshimura, 2013). Retrofitted bridges
could prevent failures from a strong ground motion; however, they could not prevent the washout of superstructure
due to a giant tsunami. For these bridges, tsunami was the
dominant hazard.
Figure 11 presents the photograph of the Aso bridge
taken before and after the 2016 Kumamoto earthquake. This
bridge was constructed in 1970. The central part of this
bridge is an arch with a simple span and continuous threespan girders on both sides. The Aso bridge was seismically
STRUCTURE AND INFRASTRUCTURE ENGINEERING
31
Figure 11. Aso bridge collapse due to the ground motion, land slide and/or fault displacement during the 2016 Kumamoto earthquake [photograph (a) taken
before the bridge collapse (courtesy of Dr. Yabe at Chodai Co. Ltd.) and photograph (b) taken after the bridge collapse by the first author].
Figure 12. Okirihata bridge damaged due the ground motion and/or land slide (all photographs taken by the first author).
retrofitted before the 2016 Kumamoto earthquake; however,
for this bridge, the ground motion was not the dominant
hazard. In fact, this bridge was completely destroyed due to
a huge landslide or fault displacement caused by the 2016
Kumamoto earthquake.
Figure 12 shows the photograph of the Okirihata bridge
taken after the 2016 Kumamoto earthquake. This bridge was
designed based on the design code revised after the 1995
Hyogoken-Nanbu earthquake. Rubber bearings, including
elastomeric bearings and seismic isolators, had been
installed to improve the seismic performance. All rubber
bearings at the abutments and three piers were ruptured.
Since the landslide occurred in the mountains directly
beside the bridge, this damage might have been caused by
not only the ground motion but by landslide effects. Please
note that the causes of the collapses of the Aso bridge and
Okirihata bridge are still under investigation.
2.6. Examples of robust and resilient bridges against
unexpected actions
Compared with the conventional girder bridges, a rigid
frame bridge under seismic action has less damage due to
the effect of tsunami or landslide as presented in Figures 13
and 14. The rigid frame structure could be appropriate for
the bridge under the hazards associated with tsunami and
landslide. As shown in Figure 13, since the rigid frame
structures do not have bearings between the superstructure
and substructure, they could prevent the washout of superstructure due to the tsunami attack compared with the conventional girder bridge.
Figure 14 depicts that the abutment of Aso-Choyo bridge
could not support the PC box girder after it was transversely
displaced by the landslide. However, since both the superstructure and the substructure were rigidly connected and
behaved as a continuous unit, the severe damage to the
Aso-Choyo bridge due to this landslide was not observed.
2.7. Sustainability issues (debris caused by tsunami)
In Japan, following the tsunami due to the 2011 Great East
Japan earthquake, large areas of farmland were flooded with
salty water and contaminated by sea sediments, which led to
long-term soil contamination of high fertile agricultural land
by metal and metalloid compounds (Portugal-Pereira & Lee,
2016). As a result of the earthquake and subsequent tsunami, approximately 23 million tons of disaster debris was
generated (Figure 15), with more than 12 million m3 of tsunami deposits left in the flooded area.
The structural and geotechnical utilisation of the concrete
and soil fraction in the disaster debris and tsunami deposits
has presented a huge challenge to engineers since: (a) the
clearance of debris and tsunami deposits is an urgent task
which must be completed within a few years and (b)
although a large amount of waste-mixed concrete and soil
can be recycled and used in the reconstruction, their properties have temporal and spatial variations (Inui, Yasutaka,
Endo, & Katsumi, 2012). If poorly managed, the waste can
have significant environmental and public health impacts
and can affect the overall recovery process (Brown, Milke, &
Seville, 2011).
32
M. AKIYAMA ET AL.
Figure 13. Rigid frame in the tsunami affected region taken after the 2011 Great East Japan earthquake (all photographs taken by the first author).
Figure 14. Rigid frame in the landslide affected region taken after the 2016 Kumamoto earthquake (both photographs taken by the first author).
Figure 15. Debris generated by the tsunami due to the 2011 Great East Japan earthquake [photograph (a) taken by the first author and photograph (b) courtesy
of Dr. Takahashi at Kyoto University].
Figure 16. Progress of structural design methodology: from the classical allowable stress design method toward the life-cycle-based design and assessment of network involving bridges under multiple hazards.
3. Toward life-cycle-based design and assessment
of bridges and bridge networks under independent
and interacting hazards
Figure 16 illustrates the progress of structural design methodology from the deterministic allowable stress design
(ASD) toward the life-cycle-based design and assessment of
transportation networks involving bridges. The structural
safety in design is traditionary quantified by comparing the
structural capacity, R, with the load, L. In the ASD method,
the designer must size the structural components such that
their service loads do not exceed a certain fraction of elastic
STRUCTURE AND INFRASTRUCTURE ENGINEERING
limit. Static and linear elastic analysis are performed to estimate R at the component-level.
With the development of computer technology and computer simulation capability, and with the lessons from the
disasters as described in Section 2, structural design methodology has progressed so that consequences caused by the
structural failure, several performance indicators, and lifecycle concepts of bridges and bridge networks under multiple hazards are being developed. These progresses are
overviewed herein.
3.1. Progress of structural design methodology
3.1.1. Reliability-based design
In current semi-probabilistic load resistance-factored design,
the concept of the reliability index is introduced in code
calibration. The uncertainties in R and L are considered separately by assigning different load factors and resistance factors through rational calibration procedures, where the
target reliability index for each type of structural element is
assigned to maintain an acceptable probability of failure
(Liu, Frangopol, & Kim, 2009). The structural components
are designed based on ultimate limit states, or serviceability
limit states, or both (Estes & Frangopol, 2001).
Evolution of structural design methodologies from allowable structural design (ASD) method to load and resistancefactored design (LRFD) method has revealed the importance
of uncertainty consideration in balancing economical and
safety aspects of structural designs (Liu et al., 2009). Along
with the improvement of computer performance, R and L at
the structure-level could be evaluated by the nonlinear and
dynamic analysis considering uncertainties and correlations.
A reliability-based capacity design procedure was proposed
to obtain the hierarchy of resistance of the various structural
components and failure modes necessary to ensure a suitable plastic mechanism and avoid brittle modes (Akiyama
et al., 2012). Although the capacity design method has been
developed to maximise post-event operability and minimise
the cost of repairing bridges after a severe earthquake, consequences associated with functionality and recovery cannot
be explicitly incorporated in the reliability-based
design method.
3.1.2. Risk-, reslience- and sustainablity issues
Performance-based engineering has gained significant attention and is being used in many areas of structural engineering. Performance-based earthquake engineering has been at
the frontier among natural hazards (Attary et al., 2017).
This framework is based on the total probability theorem
and can be disaggregated into different analysis phases that
include hazard analysis, structural analysis, fragility analysis
and loss analysis. When the limit states of the structure are
mutually exclusive, the probability of losses due to failure
can be determined by multiplying the probability of failure
by the probability of losses (Ellingwood, 2006a, 2006b):
XX
P½Loss > LjLSP½LSjH P½H (1)
P½Loss>L ¼
LS
H
P½Loss>L ¼
X
P½Loss > LjLSP½LSjHs 33
(2)
LS
where P [H] is the probability of occurrence of hazard H, P
[LS | H] is the conditional probability of the limit state LS
given the occurrence of H, P [Loss > L | LS] is the probability of loss exceeding L given the limit state LS and P [LS |
Hs] is the conditional probability of the limit state LS given
the postulated hazard scenario Hs.
Consequences have been quantified in terms of several
measures, e.g. monetary loss, human fatalities and environmental damage (ISO13824, 2009). Lounis and McAllister
(2016) reported that the consequences associated with sustainability can be grouped as follows:
Social consequences: fatalities, injuries, and reduction/
loss of service.
Economic consequences: loss of income, loss of productivity, delays in service delivery and user’s costs.
Environmental consequences: irreversible and reversible
environmental damages.
With regard to resilience, there may be similar social and
economic consequences of failure. Additional consequences
associated with resilience may include (Lounis &
McAllister, 2016):
Functionality consequences: loss of other systems or
services due to dependence on damages system.
Recovery consequences: time to restore system functionality
causing delays and losses in restoration of other systems.
In addition to studies investigating the risk, resilience
and sustainability through quantitative approaches and
application to case studies to bridge structures, studies on
the contribution to risk reduction and resiliency coming
from structural control have been provided. For example,
enhancing the robustness of bridge can improve the resiliency of not only the bridge itself but also the surrounding
community by reducing repair costs and downtime after an
extreme event. Several interesting structures, and their
design methodologies have been developed experimentally
and computationally (Akiyama, Abe, Aoki, & Suzuki, 2012b;
Brito, Ishibashi, & Akiyama, 2018; Domaneschi & Martinelli
2016; Eatherton & Hajjar, 2011; Echevarria, Zaghi,
Christenson, & Accorsi, 2016; Iqbal, Fragiacomo, Pampanin,
& Buchanan, 2018; Lehman et al., 2015; Loli, Knappett,
Brown, Anastasopoulos, & Gazetas, 2014; Mitoulis &
Rodriguez, 2017; Rodgers, Mander, Chase, & Dhakal, 2016).
3.1.3. Life-cycle perspective
A life-cycle approach is needed in the risk assessment, mitigation
procedure, and quantification of resilience and sustainability,
because the effect of aging and environmental aggressiveness
can reduce the structural performance and functionality, and it
depends on the time of occurrence of the event (Biondini,
Camnasio, & Titi, 2015; Frangopol, 2011; Frangopol & Soliman,
2016). The classical time-invariant structural design and
34
M. AKIYAMA ET AL.
hazards is useful for identifying significant threat scenarios.
A discussion on various design and analysis aspects for
bridges under multiple hazards in a life-cycle context is provided herein.
Figure 17. Bridges belonging to a network under independent and interacting hazards.
assessment methods need to be revised to account for a proper
modelling of the structural system over its entire life-cycle by
taking into account the effects of deterioration process, timevariant loadings, and maintenance and repair interventions,
among others (Liu & Frangopol, 2005; Sanchez-Silva,
Frangopol, Padgett & Soliman, 2016; Yang & Frangopol 2019a;
Biondini & Frangopol, 2016; Frangopol, 2011).
It is crucial to implement rational management strategies
that maintain performance of bridges within acceptable levels
through their life-cycle. As shown in Figure 16, life-cycle
design and assessment methodology can encompass all the key
concepts such as risk, resilience and sustainability. However,
there is still a need to fill the gap between theory and practice
by incorporating life-cycle concepts in structural design and
assessment codes (Sabatino, Frangopol, & Dong, 2016; Yang &
Frangopol, 2019b; Biondini & Frangopol, 2018; Frangopol &
Kim, 2014; Frangopol & Soliman, 2016). Moreover, as provided in the lessons learnt from the past seismic disasters,
more comprehensive multiple hazards have to be taken into
consideration in the life-cycle design and assessment for ensuring the adequate life-cycle performance.
3.2. Life-cycle design and assessment of bridges under
multiple hazards
As mentioned in Sections 2.4 and 2.5, a strong earthquake
could cause multiple disasters, including damage to structures due to strong ground motions and/or liquefaction and
the washout of structures due to subsequent tsunamis and
landslides. In addition, seismic capacity would deteriorate
due to the material corrosion, fatigue and scour caused by
the flood, among others. Figure 17 presents an example of
an individual bridge and road network near a coast line.
Comparing life-cycle reliabilities and risks among structures
belonging to a network under independent and interacting
3.2.1. Literature review on multi-hazard analysis
Different types of hazard such as independent hazards, correlated hazards, concurrent hazards and cascading hazards
have been investigated in the literature (Akiyama &
Frangopol, 2012b, 2013; Asprone, Jalayer, Prota, &
Manfredi, 2010; Kameshwar & Padgett, 2014). Life-cycle
performance approaches of RC structures exposed continuously to the chloride ions in earthquake-prone regions were
proposed in several studies (Akiyama, Frangopol, &
Matsuzaki, 2011; Alipour, Shafei, & Shinozuka,
2011;Biondini, Camnasio, & Palermo, 2014; Rao, Lepech, &
Kiremidjian, 2017a, 2017b, among others).
Several researchers estimated the seismic risk or resilience
of road network taking into consideration the effect of corrosion on the bridge performance deterioration (Alipour &
Shafei, 2016; Biondini et al., 2015; Kurtz, Song, & Gardoni,
2016; Rokneddin, Ghosh, Duenas-Osorio, & Padgett, 2013;
Zanini, Faleschini, & Pellegrino, 2017). The influence of the
climatic changes, and in particular of the temperature and
humidity on the corrosion rate has been reported in the literature (e.g. Andrade, Alonso & Sarrıa, 2002). Recently, several advanced simulations for investigating the effect of the
temperature and humidity, and the concentration of CO2 in
the atmosphere due to the climate change on the probability
of reinforcement corrosion of RC structures have been performed (Bastidas-Arteaga & Stewart, 2015; Stewart, Wang,
& Nguyen, 2011, 2012; Yooh, Çopuroglu & Park, 2007).
Zhang, Cai and Pan (2013) presented a framework for
fatigue reliability analysis of long-span bridges under combined dynamic loads from vehicles and wind. Even though
the stresses from either the vehicle loads or wind loads may
not be able to induce serious fatigue problems alone, the
superposed dynamic stress ranges cannot be ignored for
fatigue reliability assessment of long-span bridges.
A multi-hazard optimisation framework for wind and
seismic loading for two suspended floor slab isolation system was proposed by Chulahwat and Mahmoud (2017).
Their results highlighted the effectiveness of tuning the suspended slab system to meet the wind and seismic performance objectives.
Scour plays an important role in the seismic response of
bridges since it weakens the lateral strength of the foundation. A multi-hazard reliability-based or risk-based framework for evaluating the structural response of bridge under
the combined effects of scour and earthquake events has
been investigated (Alipour, Shafei, & Shinozuka, 2013;
Banerjee & Prasad, 2013; Chandrasekaran & Banerjee, 2016;
Dong, Frangopol, & Saydam, 2013; Yilmaz, Banerjee, &
Johnson, 2016).
Structural damage accumulation resulting from the action
of sequences of seismic excitations has been investigated in
the assessment of life-cycle system reliability and performance optimization (e.g. Esteva, Campos, & Dıaz-Lopez,
STRUCTURE AND INFRASTRUCTURE ENGINEERING
2011; Esteva, Dıaz-L
opez, Vasquez, & Le
on, 2016).
Meanwhile, the aftershocks have the potential to cause more
severe damage to bridges, since the bridges damaged due to
a mainshock cannot be repaired under high aftershock hazard. Seismic hazards associated with aftershocks are not
explicitly accounted for in modern bridge design codes, nor
in emerging methodologies such as performance-based seismic design.
Nazari, van de Lindt and Li (2015) developed a methodology that can quantify the changes that would be needed in
the structural design of a building to account for aftershock
hazards and illustrate it by using a basic nonlinear model of
a building. Probabilistic risk and resilience of highway
bridges under mainshock and aftershock sequences were
estimated for implementing risk mitigation strategies and
equipping decision makers with a better understanding of
structural performance (Dong & Frangopol, 2015).
3.2.2. Life-cycle performance of bridges under independent hazards
For bridges under independent hazards, the effect of material corrosion due to mechanical and/or environmental stressors on the structural performance deterioration needs to be
taken into consideration. As mentioned in Section 3.2.1,
seismic reliabilities of corroded bridges or bridges damaged
by the scour due to flood are examples of independent hazards. Structural capacity larger than structural demand has
to be ensured for a whole lifetime. However, further
research is needed to develop the numerical model of the
structural fragility of corroded or damaged bridges.
Structural reliability can be evaluated based on the multiple
independent hazard curves and fragility curves.
For new bridges, it could be possible to provide higher
structural performance and durability. For example, RC
structures designed with high quality concrete and adequate
concrete cover prevent the steel corrosion causing the
deterioration of structural performance during whole lifetime of these structures. An alternative approach is to use
corrosion-resistant stainless steel or epoxy-coated reinforcement. In this case, even when a bridge using durable materials is located in an earthquake prone region and marine
environment, it’s not necessary to consider the effect of
material corrosion on the seismic capacity in the fragility
analysis. Life-cycle reliability can be estimated only considering a dominant hazard. Although the initial cost of a
bridge designed with high durability would be expensive,
this can be justified on a life-cycle cost basis.
For existing bridges, visual inspections, field test data
regarding structural performance and/or monitoring play an
important role in the bridge performance assessment. This
information helps engineers to update the variables associated with prediction of current and future structural capacity, and to confirm whether the structural capacity
deteriorates and it’s necessary to be repaired. Maintenance
strategy of existing bridges under independent hazards has
to be developed considering which hazard is dominant on
the basis of the significance and how the structural capacity
could deteriorate before the occurrence of the identified
35
dominant hazard. A case study of bridges under independent hazards is illustrated in Section 4.
3.2.3. Life-cycle performance of bridges under interacting hazards
It is not feasible to design a bridge that will remain intact
under all hazards that might impact its performance
(Ellingwood, 2006a, 2006b). Under excessive interacting hazards on bridges such as seismic and tsunami hazards, and
seismic and landslide hazards, it is quite difficult to identify
the solution in terms of structural control for preventing the
failure of bridges with damage due to the strong ground
motion under the cascading giant tsunami or huge landslide
shown in Figures 8–12. Damaged structures are more vulnerable, since the damage cannot be repaired before the
occurrence of the cascading hazard. The technology may
not exist for enhancing the structural ductility and integrity
of bridge against damage and collapse even if additional
requirements beyond those provided in the current structural codes are required.
For new bridges under excessive interacting hazards, conceptual design plays an important role in reducing the risk
and in enhancing the resilience of bridge and bridge network. When determining the structural form (e.g. girder
bridge versus rigid frame) and alignment of roads and structures, various circumstantial conditions such as geological
and geographical conditions, environmental conditions, disaster history, and specific characteristics of the expected disasters have to be investigated. Additionally, attention should
be paid to a wider spectrum of factors such as the regional
disaster management plan, and expected recovery process of
structures (Honda et al., 2017).
For existing bridges under excessive interacting hazards,
it is quite difficult to reduce the probability of bridge failure and the associated risk with a limited budget. As
observed in 2011 Great East Japan earthquake and 2016
Kumamoto earthquake, large-scale hazards can damage
many bridges in an existing transportation system simultaneously. It is of vital importance to develop a management plan to recover structures and civil infrastructure
systems in terms of resilience and sustainability.
Accelerated bridge construction (ABC) technology and
disaster waste management system have to be established
for the networks under the excessive interacting hazards.
Prefabrication of structural component using ABC technology is a resilient solution that decreases on-site construction time and help roads and road structures reopen
soon after a disaster.
The environmental impacts of a disaster is substantial as
mentioned in Section 2.7. For example, Hurricane Katrina
in 2005 resulted in debris management costs exceeding USD
4 billion, accounting for more than a quarter of the total
cost associated with disaster response and recovery according to Lorca, Çelik, Ergun, & Keskinocak (2017). They presented a decision-support tool employing analytical models
to assist disaster and waste management with decisions
regarding collection, trasportation, reduction, recycling and
disposal of debris. It is very important before the occurrence
36
M. AKIYAMA ET AL.
Figure 18. Flowchart for evaluating the deterioration process of RC structures
in a marine environment (adapted from Miyamoto et al., 2015).
Figure 19. Cracked area patterns of RC slabs in Niigata City.
Figure 20. Cracked area patterns of RC slabs in Uwajima City.
of the disaster to develop the tool for optimising and balancing the financial and environmental costs, duration of
the collection, and disposal operations, landfill usage, and
the amount of recycled materials (FEMA, 2007; Kim,
Deshmukh, & Hastak, 2018). A case study of bridges and
bridge networks under interacting hazards is illustrated in
Section 5.
4. Life-cycle reliability of bridges under
independent hazards: mechanical and
environmental hazards
Time-dependent models have been developed that can simulate all stages of corrosion including corrosion initiation,
crack initiation and propagation (Akiyama, Frangopol, &
Suzuki, 2012c; Akiyama, Frangopol, & Takenaka, 2017;
Akiyama, Frangopol, & Yoshida, 2010; Papakonstantinou &
Shinozuka, 2013). Regarding the life-cycle reliability estimation of RC structures in an aggressive environment, the
exact influence of environmental factors affecting degradation mechanisms is difficult to predict as they vary in time
and space. Probabilistic hazard assessment associated with
environmental stressors has to be included in the life-cycle
reliability analysis of RC structures. Figure 18 shows the
flowchart for evaluating the degradation process of RC slab
in a marine environment (Miyamoto, Akiyama, &
Frangopol, 2015). Several challenges for enhancing the lifecycle structural reliability estimation of bridge in an aggressive environment are introduced herein.
It is well-recognised that the material properties of a RC
structure and structural dimensions are random due to the
spatial variability associated with workmanship and other
factors. This randomness cause spatially corrosion damages
such as corrosion cracks and cover spalling. It is of great
importance to simulate deterioration processes in a stochastic field context. Modeling the spatial variability of model
parameters gives one the ability not only to quantify the
probability of degradation but the extent of damage as well.
As an example, based on the formulations presented by
Papakonstantinou and Shinozuka (2013), spatial variability
associated with the random variables used in the degradation process of a RC slab is represented by a 2D Gaussian
stochastic field. The power spectral density is:
" 2 2 #
b
b
b
j
b
j
1
2
1
1
2
2
Sf0 f0 ðj1 ; j2 Þ ¼ r2
exp (3)
4p
2
2
where b1 and b2 are proportional to the correlation distance
of the stochastic fields along the x1 and x2 axes, respectively.
Figures 19 and 20 illustrate examples of RC slab plan
views in Niigata City and Uwajima City, respectively, and
present the elements with corrosion cracks from a random
realisation at 30 years and 60 years after the construction
(Miyamoto et al. 2015). Due to the difference of airborne
chloride hazard, RC slab in Niigata City has more elements
with corrosion cracks. For this case study, it was simply
assumed that the concrete element cracks when the tensile
stresses due to the volume expansion of corrosion products
reach the tensile strength of concrete. If a bridge is located
in earthquake-prone region or heavy traffic route, or both,
it is necessary to consider the effect of material corrosion
on life-cycle structural performance considering the spatial
distribution associated with the material properties and
mechanical stressors.
In Figures 19 and 20, the difference of wind speed, distance from coast line and percentage of time during one
day when the wind is blowing from sea toward land
between two cities are considered when quantifying the airborne chloride hazard. A calculation model for predicting
concentration of airborne chloride ion at an arbitrary time
and location has to be developed considering the transportation and adhesion processes of airborne seawater particles.
STRUCTURE AND INFRASTRUCTURE ENGINEERING
37
Figure 21. Buckling model of a longitudinal rebar in the plastic hinge of corroded RC column subjected to cyclic loading.
Figure 22. Estimation of steel weight loss distribution based on limited inspection results.
Studies on spatial variability associated with the airborne
chloride over the bridge are scarce.
In the seismic probabilistic risk assessment, the annual
probability of exceedance of seismic capacity is:
ð1 dp0 ðcÞ pfa ¼
(4)
dc P½De Ca jC ¼ cdc
0
where p0 ðcÞ is the annual probability that the seismic intensity, C, at a specific site would exceed a value c and P½De Ca jC ¼ c is the fragility, which is the conditional probability of the seismic demand De exceeding the seismic capacity
Ca conditioned upon the seismic intensity c.
In the calculation of the conditional probability P½De Ca jC ¼ c of bridge piers in a marine environment, the
effect of corrosion has to be taken into consideration. As
the steel weight loss of rebars increases, the seismic capacity
decreases. Using the total probability theorem, the annual
probability of exceedance of seismic capacity Ca under
earthquake excitation at t years after construction can be
expressed as:
ð 100 ð 1 dp0 ðcÞ pfa ðt Þ ¼
dc 0
0
P De Ca jC ¼ c; Cw ¼ cw ðt Þ f ðcw ðt ÞÞdcdcw
(5)
where P [De Ca| C¼c, Cw ¼ cw (t)] is the probability of
the seismic demand De exceeding the seismic capacity Ca
conditioned upon the seismic intensity c and steel weight
loss cw (t), and f (cw (t)) is the probability density function
(PDF) of cw (t).
In the calculation of P [De Ca| C ¼ c, Cw ¼ cw (t)],
the effect of steel corrosion, cover cracking and debonding
between concrete and rebar on the deterioration of lateral
strength and ductility capacity of RC columns needs to be
considered in the non-linear analysis as shown in Figure 21.
Performing the structural analysis using the reduced steel
rebar cross-section is an oversimplification for evaluating
the relationship between load and displacement of deteriorating RC components.
For existing bridges, what is actually important and difficult in their life-cycle reliability estimation is how to accurately predict the degree and location of the current material
deterioration and how to adequately quantify this deterioration in terms of input data in the fragility analysis
(Akiyama & Frangopol, 2014; Yanweerasak, Akiyama, &
Frangopol, 2016). As shown in Figure 22, identifying the
possible spatial distribution of material corrosion over a
large-scale structure based on the limited number of inspection results and updating the life-cycle reliability are
demanding and challenging problems. Owing to the uncertainties, the predicted life-cycle performance, despite how
accurate or advanced the tools used to obtain this performance were, may deviate from the actual performance exhibited by the structure over time. A frequent updating of the
life-cycle performance is required as new information (e.g.
monitoring results) becomes available (Okasha &
Frangopol, 2011).
Yanweerasak et al. (2016) presented a procedure for estimating the mean and variance of steel weight loss in the
plastic hinge of corroded RC structures based on inspection
results. Variance of steel weight loss depends on the number
and space interval of inspection locations based on the statistical estimation error process (Honjo & Otake, 2013). The
variance is used as the observation noise during the updating process. P [De Ca| C¼c, Cw ¼ cw (t)] in Equation (5)
is estimated using the updated random variables.
As an illustrative example, the locations of the steel
weight loss measurements are assumed as shown in Figure
23. The simple average is almost the same among Cases 2, 3
and 4; however, the number of inspection points are different. Figure 24 displays the updated cumulative-time failure
probability based on the inspection data using Sequential
Monte Carlo Simulation (SMCS) (Akiyama et al., 2010).
The cumulative-time failure probabilities of Cases 2, 3 and 4
at Year 30 are smaller compared with that of Case 1. From
Figure 24, although the cumulative-time failure probabilities
are nearly identical for Cases 2, 3 and 4 because the magnitudes of steel weight loss from the inspection results are
38
M. AKIYAMA ET AL.
Figure 23. Assumed location of the steel weight loss measurements in the plastic hinge.
Figure 24. Relationship between the cumulative-time failure probability and
the time after construction (years).
almost identical, a significant difference in the correlation
among random variables can be confirmed.
Figure 25 depicts the correlations between x3 and x5 using
100,000 samples of SMCS, where x3 and x5 are random variables
associated with airborne chloride and surface chloride concentration relation, and associated with estimation by diffusion
equation, respectively. Before updating, the random variables are
assumed statistically independent. After updating, all random
variables related with the prediction of the steel weight loss were
updated simultaneously by SMCS. These results illustrate that,
as expected, having more inspection locations can provide a
more accurate reliability assessment.
To understand the steel corrosion growth process and
the change in the spatial variability of steel corrosion with
time, continuous monitoring is necessary. X-ray photography has been applied to observe steel corrosion in RC
beams (Akiyama & Frangopol, 2014; Lim, Akiyama, &
Frangopol, 2016; Lim, Akiyama, Frangopol, & Jiang, 2017;
Zhang, Song, Lim, Akiyama, & Frangopol, 2019). They estimated the steel weight loss by the digital image processing
of the X-ray photograms. The non-uniform distribution of
steel weight loss along rebars inside RC beams determined
using X-ray radiography and its correlation with longitudinal crack widths and loading capacity were experimentally
investigated (Figure 26). Although Gumbel distribution
parameters were derived from the experimental data of steel
weight loss to model spatial steel corrosion (Lim et al.
2016), further experimental research is needed to determine
whether these parameters are stationary over the steel corrosion process, and to investigate the effect of concrete quality,
rebar amount and arrangement, and climatic condition
on them.
A finite element (FE) analysis method has been used to
simulate the structural responses of the corroded beams
when considering two different inputs (i.e. uniform and
non-uniform cross-sectional area of rebars over the beam).
Comparing the numerical results of the flexural responses of
the simulated beams to those of the test beams in the
experimental study, the effect of mesh size on the accuracy
of the FE model was investigated.
Figure 27 presents the comparison of computational and
experimental results of the relationship between load and
deflection, and the comparison of contour of the principal
tensile strain obtained from the FE analysis, flexural cracking caused during the bending test, and steel weight loss.
Average steel weight losses over RC beam shown in Figure
27(a, b) are 12.1 and 25.5%, respectively. As presented in
Figure 27, when the spatial distribution of steel weight loss
seems to be more uniform, the effect of mesh size on the
computational results can be ignored. However, when the
spatial variability becomes larger, the computational results
depend on the mesh size.
Spatial distributions associated with the bond properties and
internal and external cracks due to the volume expansion of
corrosion products are not taken into consideration in the computational results shown in Figure 27. More studies on this
topic are needed for further improvement in FE modeling
(Zhang et al. 2019). In addition, because of the budget shortage,
the number of inspection and/or monitoring results to understand the corrosion condition inside existing RC component
has to be limited. Further research is needed to develop a procedure of providing the possible input data for FE analysis (e.g.
material properties and constitutive models of corroding RC
component) based on the limited number of inspection results.
5. Life-cycle reliability of bridges under interacting
hazards: seismic and tsunami hazards
Frameworks for multi-hazard risk assessment have been
reported in the literature as described previously. Tsunami
intensity is correlated with the magnitude of the oceanic
earthquake, and a bridge may have severe damage due to
the strong ground motion before the tsunami arrives.
STRUCTURE AND INFRASTRUCTURE ENGINEERING
39
Figure 25. Effect of the number of inspection locations on the variability associated with random variables used in the prediction of steel weight loss (adapted
from Yanweerasak et al., 2016).
Figure 26. X-ray machine at Waseda University to visualise the corroded rebars embedded in the concrete beam.
Difficulties in estimating the reliability of bridges under tsunami hazards are similar to those associated with bridges
under aftershocks. Strong aftershocks have the potential to
cause extensive structural damage. Damaged structures due
to mainshock are even more susceptible to incremental
damage due to aftershocks because their reduced structural
capacity decreases the threshold of the ground motion
intensity needed to cause further damage.
Yeo and Cornell (2005) divided the seismic performance
assessment and design process into simpler components in
terms of the description, definition and quantification of
earthquake intensity measures (IMs), engineering demand
parameters (EDPs), damage measures (DMs) and decision
variables (DVs). Commonly used examples of the above
parameters are peak ground acceleration (PGA) and firstmode spectral acceleration (IMs), interstory drift ratios,
inelastic component deformations and floor acceleration
spectra (EDPs), damage states of structural and non-structural elements (DMs) and fatalities, financial losses and
downtimes (DVs). Based on the total probability theorem,
the mean annual rate t(DV) of exceeding a given level of
DV ¼ x, is Yeo and Cornell (2005):
ððð
tðDV Þ ¼
GðDVjDMÞdGðDMjEDPÞdGðEDPjIMÞdkðIM Þ
(6)
where k (IM) is the mean annual rate of exceeding a given
IM and is obtained from a conventional probabilistic hazard
analysis. G(EDP | IM) is the complement of the cumulative
distribution function of EDP conditioned by a given level of
IM (i.e. G(EDP | IM) ¼ P[EDP y | IM ¼ x] while in the
continuous case G(EDP | IM) ¼ fEDP|IM (y | x) dy is the
conditional probability density function times dy).
Based on Equation (6), Yeo and Cornell (2005) discussed
the reliability of structures under aftershock hazard. If a
structure had the mainshock with the intensity MI and
damage state SI due to the mainshock, the mean rate
exceeding a given DV in post-mainshock time interval [0,
tmax] is Yeo & Cornell (2005):
ð ð ð ð
ttamax ðDVjMI; SI Þ ¼
Ga ðDVjDM; iÞ
DM EDP IM i
dGa ðDMjEDP; iÞdGa ðEDPjIM; iÞdktamax ðIM; ijMI ÞdGa ðijMI; SI Þ
(7)
where the subscript a refers to the aftershock environment,
ktamax is the mean number of aftershocks exceeding a given
IM in post-mainshock time interval and Ga (i | MI, SI) is
the probability that the structure is in damage state i after
the mainshock given MI and SI. The inclusion of Ga (i | MI,
SI) means an additional integral over all possible post-mainshock damage states i.
Equation (7) can be used for estimating the reliability of
bridges under tsunami hazards. IM could be the hydrodynamic features such as tsunami wave velocity and height,
and EDP and DM could be the tsunami demands and structural damage states due to the tsunami in the estimation of
dGa in Equation (7). In addition, if reliability will be estimated given the occurrence of the earthquake, Equations (6)
40
M. AKIYAMA ET AL.
Figure 27. Effect of element size in FE model on the computational results of corroded RC beam: (a) average steel weight loss over RC beam ¼ 12.1% and (b)
average steel weight loss over RC beam ¼ 25.5%.
and (7) can be simplified because it is not necessary to consider the earthquake occurrence rate.
It is expected that the damage and the economic loss
resulting from the anticipated Nankai Trough earthquake
and its associated tsunami would be larger than those resulting from the 2011 Great East Japan earthquake. As an illustrative example, reliabilities, economic loss and recovery
time of road networks including bridges and embankments
in Town A in Kochi-Prefecture and Town B in MiePrefecture under both seismic and tsunami hazards due to
the anticipated Nankai trough earthquake are computed.
Figure 28 displays the schematic layouts of the investigated
networks in Towns A and B.
Akiyama and Frangopol (2016) estimated the reliabilities
of individual bridge and embankment under seismic and
tsunami hazards based on the parameters associated with
the fault movement caused by the anticipated Nankai trough
earthquake provided by Central Disaster Management
Council (2003). Taking into consideration the lessons from
the 2011 Great East Japan earthquake, these parameters
were updated by Cabinet Office, Government of Japan
(2012a, 2012b). In this case study, these updated parameters
are used to estimate the seismic and tsunami intensities.
It is difficult to evaluate the exact fault movement during
the seismic event since uncertainties associated with fault
movement vary in time and space. The average stress drop
at the seismic fault is assumed to be random. Seismic intensity at the bridge site given seismic event is estimated by the
attenuation relation. In this case study, the relationship
between the seismic intensity and the distance from seismic
fault taking into consideration the effect of seismic fault
type and soil condition on the attenuation rule provide by
Si and Midorikawa (1999) was used to estimate the PDF of
the PGA given the occurrence of the anticipated Nankai
Trough earthquake.
Figure 29 displays an example of tsunami propagation
computation to obtain the PDF of the tsunami wave height
and velocity at the locations of bridges and embankments
analysed. Horizontal 2D tsunami analysis based on non-linear long-wave theory (Goto, Ogawa, Shuto, & Imamura,
1997) is performed in this simulation. The PDF is calculated
by Monte Carlo Simulation (MCS) using the random variables associated with the seismic fault and considering the
difference of roughness coefficient among the locations
of interest.
Figures 30 and 31 present an example of PDF of PGA
and tsunami height at the Towns A and B, respectively. As
the difference of distances between each structure and seismic fault is negligible, PDFs of PGA shown in Figures 30
and 31 are applied to all structures in Towns A and B
STRUCTURE AND INFRASTRUCTURE ENGINEERING
41
Figure 28. Example of road network affected by the anticipated Nankai Trough earthquake.
Figure 29. Propagation analysis of tsunami caused by the anticipated Nankai
Trough earthquake.
(Figure 28), respectively. Since tsunami intensities depend
on the location of structures (e.g. distance from the coastline), tsunami fragility is estimated by using the PDF considering the location of each structure.
In this case study, it was assumed that the sea level around
Japan is not changing over time (i.e. time-independent).
However, since sea level rise appears to be a real and longterm effect observed around the world (FEMA, 2016), further
research is needed to consider non-stationarity in tsunami
intensities in the structural reliability and risk analysis. Li,
Wang and Ellingwood (2015) proposed a life-cycle reliability
estimation method in the presence of non-stationary loads.
Seismic fragility curves are developed by comparing the seismic demand and capacity. The demands of bridge and
embankment are estimated using non-linear time history analysis and Newmark’s method, respectively. In this case study,
three damage states (i.e. no, moderate and complete) are considered and related to an anticipated level of post event functionality (Padgett, Dennemann, & Ghosh 2010). Details of the
methodology used for obtaining the seismic fragility are found
in Akiyama et al. (2014). Figure 32 presents an example of seismic fragility curves of hypothetical bridge and embankment.
The PDF of the hydrodynamic forces given the tsunami
height can be identified based on MCS. Then, the hydrodynamic horizontal and uplift forces are applied to bridges.
When estimating the tsunami fragility of bridges, a push-over
analysis using hydrodynamic forces given tsunami height is
performed to compare the tsunami capacity with the tsunami
demand in MCS. A detailed procedure for developing the tsunami fragility is described in Akiyama & Frangopol (2013).
Figure 33(a) depicts an example of tsunami fragility curve
of bridges assuming that the bridge has no damage before the
tsunami arrive. It is necessary to develop the tsunami fragility
curve of bridges and embankments given seismic damage
state Dss ¼ ds1, Dss ¼ ds2 and Dss ¼ ds3 where ds1, ds2 and ds3
are no damage state, moderate damage state and complete
damage state due to the ground motion, respectively. Recent
studies have attempted to model the degradation of physical
42
M. AKIYAMA ET AL.
Figure 30. Example of probability densities of peak ground acceleration and
tsunami height at the Town A in Figure 28.
Figure 32. Example of seismic fragility curves: (a) bridge and (b) embankment.
damage caused by a ground motion (Jalayer, Asprone, Prota,
& Manfredi, 2011; Nogami, Murono, & Sato, 2008).
Figure 33(b) displays an example of tsunami fragility curve
associated with the complete damage state given Dss¼ds1 and
Dss¼ds2. It is confirmed in Figure 33(b) that the damaged
bridge due to the ground motion is more vulnerable to the
tsunami attack. For the embankment, tsunami fragility can be
developed by comparing the heights of embankment and tsunami considering the residual displacement due to the ground
motion based on the Newmark’s method.
Equation (4) for estimating the failure probability can be
rewritten to include the damage state of structure k due to a
ground motion:
ð1
PðDSs ¼ dsi jC ¼ cÞ fC ðcÞdc
(8)
pfs;k ðiÞ ¼
0
Figure 31. Example of probability densities of peak ground acceleration and
tsunami height at the Town B in Figure 28.
vulnerability over a seismic sequence (Amadio, Fragiacomo,
& Rajgelj, 2003; Li & Ellingwood, 2007; Polese, Ludovico,
Prota, & Manfredi, 2013). Cyclic stiffness degradation model
needs to be used for the bridge to evaluate the residual
where DSs is the seismic damage state, and fC(c) is the PDF
of seismic intensity c (i.e. PGA) due to the anticipated
Nankai Trough earthquake. The probability that the structure k is in damage state DSt¼dsj after the tsunami taking
into consideration the seismic damage DSs¼dsi is:
Ð Ð Ð1 P DSt ¼ dsj jFW ¼ f w ; DSs ¼ dsi pft;k ði;jÞ ¼
0
(9)
fFW jH fw jh fHjC ðhjcÞ fC ðcÞ dfw dh dc ðj iÞ
where DSt is the tsunami damage state, fH|C (h|c) is the PDF
of the tsunami wave height H given c and fFW|H (fw|h) is the
conditional density function of the wave load Fw given H.
Since the wave load depends not only on the tsunami wave
height but also on the tsunami velocity and tsunami features
(e.g. hydraulic bore), fFW|H (fw|h) was evaluated using several types of tsunami waves using MCS.
STRUCTURE AND INFRASTRUCTURE ENGINEERING
Finally, the probability that the structure k is in damage
state DS¼dsj after the occurrence of both the seismic and
tsunami events is provided by:
j
X
pfs;k ðiÞ pft;k ði;jÞ
pfk DS ¼ dsj ¼
(10)
i¼1
Table 1 lists an example of failure probabilities of bridges
and embankments at the Towns A and B in Figure 28.
Because of the difference of seismic and tsunami intensities
between Towns A and B, the probabilities associated with
the complete damage state at Town A are higher than those
at Town B. As listed in Table 1, the seismic and tsunami
reliabilities depend on the locations of bridge and embankment in the road network. When the structure is located
near the coast line, the failure probabilities need to be estimated considering the effect of both seismic and tsunami
hazards on the structural performance.
The ground motion induced- and/or tsunami induceddamage to bridges and embankments cause the deterioration
Limit state probability
(a) 1.0
Moderate damage state
0.8
0.6
0.4
0.2
Complete damage state
0.0
0
10
20
Tsunami height (m)
30
Limit state probability
(b) 1.0
0.8
0.6
0.4
0.2
0
k¼1
k¼1
where nb and ne are the number of bridges and embankment located in the investigated link, and BDI and EDI are
the damage index of bridge and embankment and classified
as shown in Table 2.
Chang et al. (2000) define the damage states of the link
according to LDI. The increase in the damage state of the
link will reduce the link traffic capacity and speed limit. In
this case study, the relationship between damage state and
residual percentage of traffic-carrying capacity and free-flow
speed listed in Table 3 (Guo, Liu, Li, & Li, 2017) was used.
The consequences associated with each damage state corresponding to a bridge and embankment are evaluated and
quantified by the expected economic loss and full recovery
time (Dec
o, Bocchini, & Frangopol, 2013; Dong &
Frangopol, 2016; Dong, Frangopol, & Saydam 2014).
The expected economic loss of the investigated link can
be provided by:
10
20
Tsunami height (m)
Rdir ¼
nb X
mb
X
ne X
me
X
pfk;b DS ¼ dsj Cdsj;b þ
pfk;e DS ¼ dsj Cdsj;e
k¼1 j¼1
k¼1 j¼1
30
Figure 33. Example of bridge tsunami fragility curves: (a) fragility curves
assuming that bridge has no damage before the arrival of the tsunami and (b)
fragility curves associated with complete damage state due to tsunami assuming that the bridge has moderate or no damage due to ground motion before
tsunami will arrive.
Rindir ¼ Rrun þ Rtl
Town A
Town B
Damage state
A
C
F
G
Moderate
2.21 101
2.95 101
2.29 101
1.16 101
1.54 101
7.33 102
3.29 102
2.11 102
Complete
7.99 101
5.01 101
5.44 101
3.11 101
4.96 101
4.39 101
8.72 101
2.17 101
(13)
(14)
Cdsj;b and Cdsj;e are the direct repair costs associated with a
given damage state of bridge and embankment, respectively,
mb and me are the number of damage statues of bridge and
Table 1. Example of failure probability of bridges and embankments under seismic and tsunami hazards.
Bridge 1
Bridge 5
Bridge 8
Bridge 12
Embankement
Embankement
Embankement
Embankement
(12)
where
With no damage
due to ground motion
d
0.0
of the post-disaster road network functionality. The damaged structures can be open, closed or partially open within
a road network. Consequently, traffic flow in the links can
be different and speed limits might be reduced for various
damage conditions of the link (Frangopol, Dong, &
Sabatino, 2017). The damage state and the number of each
bridge and embankment can affect the functionality of the
investigated link. Chang, Shinozuka, and Moore (2000) proposed the performance indicator of a link including bridges
after an earthquake which is expressed in terms of link
damage index (LDI). In this case study, to evaluate a link
performance including bridges and embankments after the
seismic and tsunami events, LDI is modified by:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u nb
ne
X
uX
ðBDIk ðtÞÞ2 þ
ðEDIk ðtÞÞ2
LDI ðtÞ ¼ t
(11)
Re ¼ Rdir þ Rindir
With moderate damage
due to ground motion
d
43
Damage state
Bridge 4
Bridge 5
Bridge 6
Bridge 7
Embankement
Embankement
Embankement
Embankement
A
B
D
E
Moderate
1.34 101
8.98 102
9.90 102
4.51 102
1.11 101
1.33 101
7.43 102
6.33 102
Complete
3.46 101
2.01 101
2.13 101
9.29 102
3.98 101
3.11 101
1.12 101
1.10 101
44
M. AKIYAMA ET AL.
Table 2. Damage index of bridge and embankment.
Damage state
BDI
EDI
No
Moderate
Complete
0
0.3
1.0
0
0.3
1.0
Table 3. Damage state and residual percentage relation (after Guo
et al., 2017).
Residual percentage (%)
Link status (LS)
LI
LI
LI
LI
LI
¼
¼
¼
¼
¼
1
2
3
4
5
LDI
Traffic-carrying capacity
Free-flow speed
0 LDI < 0.5
0.5 LDI < 1.0
1.0 LDI < 1.5
1.5 LDI < e
1
100
100
75
50
0
100
75
50
50
0
Figure 34. Expected economic loss and full recovery time of links at the Towns
A and B.
Table 4. Assumed recovery time from a damage state.
Damage state
Network component
Bridge
Embankment
Moderate
Complete
30 days
5 days
180 days
60 days
Table 5. Information on links and traffic at Town A.
Average daily traffic
Average daily traffic ratio
Length of link (km)
Link speed (km/h)
Link 1
Link 2
Link 3
Detour
10,000
30%
7.3
40
6000
20%
7.1
40
5000
10%
9.1
40
19.0
40
Estimated in Equations (15) and (16).
Table 6. Information on links and traffic at Town B.
Average daily traffic
Average daily traffic ratio
Length of link (km)
Link speed (km/h)
Link 1
Link 2
Link 3
Link 4
Detour
6000
10%
5.5
40
4000
10%
4.1
40
6000
10%
5.0
40
6000
10%
3.5
40
7.8
40
Estimated in Equations (15) and (16).
embankment, respectively (mb ¼ me ¼ 3 in this case study),
and Rrun and Rtl are the economic loss associated with running vehicles on detour and monetary value of the time loss
for users traveling though the detour and damaged link at a
given damage state, respectively.
In addition, Rrun and Rtl depend on the link status LS
listed in Table 3 (Dong et al., 2014):
Rrun ¼
(
tIL
X
i¼1
CRun;car
5
X
PðLS ¼ lÞ
)
l¼1
T
T
þ CRun;truck
Dld ADTDði; lÞ
1
100
100
(
tIL
X
(15)
T
T
cAW Ocar 1 þ cATC OTruck
100
100
i¼1
i¼1
)
Dld
ll
ll
þ ADTEði; lÞ ADTDði; lÞ S
SD S0
5
X
Rtl ¼
PðLS ¼ lÞ Figure 35. An example of a temporary bridge using precast girder, column
and foundation.
(16)
where P(LS ¼ l) is the probability that the link is in status
of l (l¼ 1, 2, … , 5) listed in Table 3, tIL is the time interval
until all structures in the investigated link reaches full functionality, CRun,car and CRun,truck are the costs for running
cars and trucks per unit length, respectively, Dld is the
length of the detour, ADTD (i, l) is the average daily traffic
to detour at time i given LS¼l; T is the average daily truck
traffic ratio, cAW and cATC are the wage per hour and compensation per hour, respectively, ADTE (i, l) is the average
daily traffic remaining on the damaged link at time i given
LS ¼ l; Ocar and OTruck are the average vehicle occupancies
for cars and trucks, respectively, ll is the link length, S0 and
STRUCTURE AND INFRASTRUCTURE ENGINEERING
45
Figure 36. An example of flowchart managing the debris generated by the anticipated Nankai Trough earthquake.
SD are the average speed on the intact link and damaged
link, respectively and S is the average detour speed.
The expected full recovery time FRT is estimated as:
FRT ¼ maxfT1b ; T2b ; . . . ; Tnb ; T1e ; T2e ; . . . ; Tne g
(17)
where
Tib ¼
mb
X
pfi;b DS ¼ dsj CFRT;dsj;b ði ¼ 1; 2; . . . ; nb Þ
(18)
pfi;e DS ¼ dsj CFRT;dsj;e ði ¼ 1; 2; . . . ; ne Þ
(19)
j¼1
Tie ¼
me
X
j¼1
CFRT;dsj;b and CFRT;dsj;e are the recovery times associated with
a given damage state of bridge and embankment,
respectively.
In this case study, the expected economic loss and full
recovery time are estimated by Equations (8)–(19), and
parameters associated with the consequence evaluations
including damage index BDI and EDI of bridge and
embankment listed in Table 2, relationship between link
damage state and traffic-carrying capacity and free-flow
speed given in Table 3, recovery time of each network component from a damage state listed in Table 4, information
on link and traffic at Towns A and B provided in Tables 5
and 6, respectively, and direct and indirect cost information
provided by Shinoda, Miyata, Yonezawa and Hironaka
(2010); Shoji, Fujino and Abe (1997) and Ministry of Land,
Infrastructure, Transport and Tourism in Japan (2008).
Figure 34 illustrates the expected economic loss and days
necessary to be fully recovered from the event of all links at
the Towns A and B. The bridges and embankments belonging to Link 1 at both Towns A and B have higher failure
probabilities, resulting in higher economic loss and larger
days necessary to be fully recovered. In addition, because of
higher seismic and tsunami hazards, and larger daily traffic
at the Town A, the expected economic loss and FRT at the
Town A are larger than those at the Town B. Reliability and
risk approaches are useful to identify the dominant hazard
and most vulnerable structure, and to make the decision on
the priority for upgrade and/or repair actions.
Hypothetical bridges and embankments were used in this
case study. As shown in Figure 32, it was assumed that their
fragility curves shift right compared with the structures
designed according to the old design specification (Akiyama
et al., 2014). However, the probabilities associated with the
complete damage state are extremely large given the occurrence of the Nankai Trough earthquake. Constructing or retrofitting all structures with high-performance requirements
46
M. AKIYAMA ET AL.
that prevent any damage or failure due to strong ground
motion and giant tsunami caused by the anticipated Nankai
Trough earthquake would be too expensive and impractical.
Before the occurrence of Nankai Trough earthquake,
structural engineers in Japan have to contribute to resilience
and sustainability considering the very high failure probability of individual structures in the region where the effects of
both seismic shaking and the tsunami waves would be very
intense. Recently, in very populated urban centres and a
critical network location an ABC methodology which combines durable materials and low-damage technology has
been developed for minimising the traffic disruption.
Although there have been several reports on seismic damage
resistant technology for ABC (El-Bahey & Bruneau, 2012;
Mehrsoroush & Saiidi, 2016; Palermo & Mashal, 2012; Varela &
Saiidi, 2017), ABC technology taking into consideration the situation after the catastrophic event has to be developed for
enhancing the resilience. Using precast members as structural
elements is the integral part of ABC. Making precast element
lighter, providing constructible beam-column and column-foundation connections and assembling the elements without heavyconstruction-equipment are the primary challenge for ABC in
the affected regions. Figure 35 presents an example of a temporary bridge using precast girder, column and foundations.
As already mentioned, it is very important before the
occurrence of the anticipated Nankai Trough earthquake to
establish the procedure of how the estimated debris generated by the disaster will be managed. In the case study, the
consequences in Equation (12) were associated with the
monetary loss and recovery time. Based on the estimated
amount of debris in the affected regions under seismic and
tsunami hazards, a procedure for optimising the localisation
of processing sites, selection of processing capacities, and
debris flow decisions encompassing collection, transportation and disposal with balancing the cost and duration of
the operations is needed (Lorca et al., 2017). Figure 36
depicts an example of flowchart managing the debris generated by the anticipated Nankai Trough earthquake.
shock and subsequent cascading hazard events. A risk-based
decision-making approach at the network-level is necessary
for identifying the dominant hazard and vulnerable structures requiring strengthening and retrofit.
After a catastrophic event, the functionality of transportation networks can be significantly affected, leading to disastrous effects on the economy. To quantify the promptness
of the restoration, it has become customary to use the concept of resilience. In addition, the economic, environmental
and social impacts of disaster debris need to be investigated
in terms of sustainability. Consequences associated with the
resilience and sustainability must be studied and implemented into the risk estimation of bridge network under
multiple hazards. Life-cycle design and assessment methodology can encompass all the key concepts such as risk, resilience, sustainability and multiple hazards learning from the
past disaster lessons.
Finally, the concepts and methods presented are illustrated on both single bridges and bridge networks with an
emphasis on earthquake, tsunami and continuous deterioration. Further research is needed to enhance the framework
for estimating the reliability and risk of bridges under multiple hazards. Specifically, the integration of bridge performance under multiple independent or interacting hazards in a
comprehensive life-cycle infrastructure network in terms of
performance, management and optimisation under uncertainty (Frangopol, 2011; Frangopol & Soliman, 2016) must
be investigated.
Acknowledgments
The authors express sincere appreciation to Dr. Masayuki Yoshimi,
National Institute of Advanced Industrial Science and Technology of
Japan, for his suggestions related to seismic fault parameters. The
authors also thank Prof. Shunichi Koshimura at Tohoku University for
many suggestions on the topic of tsunami propagation analysis. Special
appreciation is extended to Dr. Sopokhem Lim and Mr. Kengo
Nanami at Waseda University.
Disclosure statement
6. Conclusions
This article presents an overview of the progress of structural design methodology from the deterministic ASD
method toward the life-cycle-based design and assessment
of bridges and bridge networks under multiple hazards.
Field investigations after recent large earthquakes in Japan
confirmed that several bridges were severely damaged and
collapsed not only due to the earthquake, as an independent
hazard, but also due to the subsequent tsunami, landslide or
fault displacement. Material corrosion caused further damage to structures under earthquake excitations. In addition,
the collapse of as-built bridges over highways prevented the
traffic passage. Even if the bridge has no damage during the
seismic event, damage to embankment can substantially
decrease the functionality of the post-disaster road network.
A probabilistic life-cycle framework for quantifying the
functionality loss of road networks involving bridges and
other road structures is needed for the occurrence of a main
No potential conflict of interest was reported by the authors.
Funding
This work was financially supported by JSPS KAKENHI [Grant
Number JP 16H02357, 16KK0152 and 16H04403], the Institute for
Research on Safety and Security of Greater Tokyo, US National
Science Foundation Award [CMMI-1537926] and the US Federal
Highway Administration Cooperative Agreement Award [DTFH61-07H-00040]. The opinions and conclusions presented in this paper are
only those of the authors.
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