Fragility Analysis of Deteriorating Bridge Components Subjected to Simulated Ground-Motion Sequences

Abstract

This study assesses the impact of corrosion deterioration on the seismic performance of bridge components during a sequence of ground motions. Specifically, a simplified methodology is proposed to derive state-dependent fragility relationships for bridge components (i.e., fragility relationships that explicitly depend on the damage state achieved by the component during a first shock) subjected to chloride-induced corrosion and 500 simulated mainshock-induced ground-motion sequences. Specifically, vector-valued probabilistic seismic demand models are derived for various corrosion levels. Those models relate the dissipated hysteretic energy in the sequence to a deformation-based engineering demand parameter induced by the first shock and a ground-motion intensity measure of the second shock, calibrated via sequential cloud-based time-history analyses. For each corrosion level, fragility relationships are first derived for a single ground motion; state-dependent fragility relationships are then derived by considering the additional damage induced by a second ground motion within the simulated sequence (structure-specific damage states are considered). Finally, continuous functional models are developed from the analysis results to estimate the fragility relationships at a given corrosion level. The results demonstrate the significant impact of environmental deterioration in seismic-prone regions, emphasising the necessity of accounting for deteriorating effects in current practice.

Full text

Otárola K, Fayaz J, Galasso C. Fragility analysis of deteriorating bridge components subjected to simulated ground-motion
sequences. Proceedings of the 12th National Conference in Earthquake Engineering, Earthquake Engineering Research
Institute, Salt Lake City, UT. 2022.
Fragility Analysis of Deteriorating Bridge Components
Subjected to Simulated Ground-Motion Sequences
K. Otárola
1
, J. Fayaz
2
and C. Galasso
3
ABSTRACT
This study assesses the impact of corrosion deterioration on the seismic performance of bridge components during a sequence
of ground motions. Specifically, a simplified methodology is proposed to derive state-dependent fragility relationships for
bridge components (i.e., fragility relationships that explicitly depend on the damage state achieved by the component during a
first shock) subjected to chloride-induced corrosion and 500 simulated mainshock-induced ground-motion sequences.
Specifically, vector-valued probabilistic seismic demand models are derived for various corrosion levels. Those models relate
the dissipated hysteretic energy in the sequence to a deformation-based engineering demand parameter induced by the first
shock and a ground-motion intensity measure of the second shock, calibrated via sequential cloud-based time-history analyses.
For each corrosion level, fragility relationships are first derived for a single ground motion; state-dependent fragility
relationships are then derived by considering the additional damage induced by a second ground motion within the simulated
sequence (structure-specific damage states are considered). Finally, continuous functional models are developed from the
analysis results to estimate the fragility relationships at a given corrosion level. The results demonstrate the significant impact
of environmental deterioration in seismic-prone regions, emphasising the necessity of accounting for deteriorating effects in
current practice.
Introduction
Earthquake-induced ground motions lead to intermittent shocks to a structure during its lifetime, while ageing
and deteriorating effects constitute a continuous mechanism of environmentally-induced damage accumulation
[1]. Currently, it is known that a considerable proportion of the civil infrastructure systems/infrastructure
components across the globe shows visible signs of ageing and deterioration, especially while approaching the
end of their design lifetime [2]. Therefore, the simultaneous consideration of infrequent ground-motion
sequences and ageing and deteriorating effects in seismic-prone regions is critical for risk preparedness and
risk-informed decision making. Among the various mechanisms that structures are likely to experience when
exposed to environmental hazards, chloride-induced corrosion deterioration is of particular interest from the
structural performance standpoint [3]. The significance of considering primary and secondary effects of
chloride-induced corrosion deterioration on structural material properties (e.g., percentage of area loss of steel
1
PhD student, Dept. of Science, Technology and Society, Scuola Universitaria Superiore (IUSS) Pavia, Pavia, PV 27100
(email: kenneth.otarola@iusspavia.it)
2
Research fellow, Dept. of Civil, Environmental and Geomatic Engineering, University College London, London, WC1E 6BT
(email: j.fayaz@ucl.ac.uk)
3
Full professor, Dept. of Civil, Environmental and Geomatic Engineering, University College London, London, WC1E 6BT
(email: c.galasso@ucl.ac.uk)

rebar) for lifetime structural response and damage/loss have been addressed by several authors [4–6],
highlighting the potential underestimation of seismic fragility/losses when not accounting for this threat [7–
10]. Depending on the severity of the environmental exposure, these mechanisms may lead to loss of structural
capacity of structural components [11–13]. Therefore, efforts towards a structural performance-based
assessment framework under joint - yet uncorrelated - seismic and environmental hazards are imperative. Here,
a simplified methodology is presented to derive state-dependent fragility relationships under mainshock-
induced ground-motion sequences for a given corrosion deterioration level of interest. In the context of this
paper, state-dependent fragility relationships explicitly express the dependency on the damage state achieved
by a bridge component during a first shock. Specifically, the proposed methodology is exercised using the
physics-based hybrid ground-motion simulations of Cybershake 15.12 and a real ordinary bridge structure
designed for southern California (La Veta Avenue, Orange, California). The ground-motion sequences are
utilised to perform nonlinear time-history analyses of the case-study bridge structure. The results of the
analyses are then used to derive structure-specific fragility relationships for different corrosion levels under
single ground motion and state-dependent fragility relationships to model the increased damage caused by the
following ground motions in the sequences. The results emphasise the necessity to incorporate deteriorating
effects in structural performance-based assessments to account for the accelerated deterioration of structures
during their lifetime.
State-dependent Fragility Analysis
A two-spanned double-column ordinary bridge structure (i.e., Bridge B [14]) is selected as a case study to
investigate the effects of the mainshock-induced seismic sequences on the fragility of deteriorating structural
components. The structural performance of ordinary bridge structures is mainly inferred by the response of
their columns [14,15]. Therefore, in this study, the assessment is conducted primarily on the columns of the
bridge’s sole bent. The proposed state-dependent fragility relationships are not explicitly conditioned on time;
instead, they are conditioned on a corrosion deterioration parameter () that implicitly depends on time [3].
Here,  corresponds to the percentage area loss of steel rebar [16], denominated arbitrarily as corrosion
deterioration level. The corrosion deterioration level depends directly on the type of environmental exposure.
Therefore, unlike exposure-specific time-dependent fragility relationships, the developed fragility
relationships dependent on the percentage of area loss of steel rebar are more applicable and generic for
different exposure scenarios. In total, six equally spaced deterioration levels are considered ranging from 0%
up to 25%. Along with the percentage area loss of rebar steel, corrosion results in various secondary effects.
These secondary effects are accounted for in terms of reductions in structural material properties such as cover
concrete strength [17], core concrete strength [18], steel yield strength [19], steel ultimate strength [19], and
steel ultimate strain [20]; all been reduced as a function of the deterioration level . For each of those levels,
a bridge computational model is developed; the adopted nonlinear modelling strategy implemented via the
software framework OpenSeesPy [21] is consistent with the work of Fayaz et al. [14].
Monte-Carlo simulation is used to obtain catalogues (with interarrival times following the Poisson
assumption) of simulated ground motions (hybrid simulations) from the CyberShake 15.12 [22,23] database,
representing a 100-year bridge lifetime. In this study, among the ~900 southern California sites available in
CyberShake [22], the simulations are obtained for Los Angeles Downtown (LADT) because of its proximity
to seismic sources coupled with a large inventory of buildings and bridge structures. The simulated ground
motion set is limited to the seismic sources [22] that lie within 100 km from the LADT site. Within this setting,
the simulated ground motions for LADT are randomly sampled using the annual probabilities of occurrence
of the corresponding rupture variations, ruptures and sources [22,23]. Ground-motion sequences are then
assembled using consecutive simulated ground motions with a maximum interarrival time of 12 months
between the events. This assumption is to select seismic sequences occurring between the probable
decision/repairing actions after a significant earthquake event [9]. Finally, the 500 ground-motion sequences
(i.e., a first mainshock, , followed by a second mainshock, ) with higher  (denoted

herein as  for brevity) in both shocks are arbitrarily selected (with a minimum threshold of 0.1g). The
previous intensity measure () is estimated as the geometrical mean of seven equally-spaced 
pseudo-acceleration spectral ordinates [24] within the range [,2.5] including the fundamental structural
period, where  (i.e., 0.37 s) is the dominant structural period in the transversal direction [25]. Note that the
first three modal periods of the bridge structure are 0.83 s, 0.44 s and 0.37 s, respectively.
Sequential cloud-based nonlinear time-history analyses are performed using the above inputs for the
various corrosion deterioration levels. For each considered ground-motion sequence, an analysis is conducted
by rotating the two orthogonal components of the ground motions on the bridge structure through 180 degrees
at 30 degrees intervals. From the six rotated responses, the median value of the maximum curvature (),
as well as the column associated median of the dissipated hysteretic energy () are derived for
both and . This data is used to calibrate probabilistic seismic demand models (s), represented
by a surface depending on the deformation-based engineering demand parameter () from the  and
the selected intensity measure () from the . The s are derived by fitting the response surface
󰇛󰇜 as per Gentile and Galasso [26].  is the total dissipated hysteretic energy
in the sequence (i.e., in  and ; that is the summation of );  is the dissipated hysteretic
energy during  (i.e.,  due to );  is the dissipated hysteretic energy during  (i.e.,
 due to );  is the associated deformation-based  for  (); and  is the
associated  for  (). A five parameter (i.e., , , , , and ) functional form is fitted as shown
in Eq. 1, for each deterioration level of the analysed structural component (i.e., the bridge column).
    󰇛  󰇜
(1)
Using the deformation-based  thresholds (





) for  (estimated via pushover analyses) and the
energy-based  threshold (







) for  (obtained using s), and inverting Eq. 1, the median and
dispersion of the desired fragility relationship are computed. A total of four  are selected to perform the
state-dependent fragility analyses, which are: a) slight damage (); b) moderate damage (); c) extensive
damage (); and d) complete damage (). No damage is defined as . Continuous functional models
are fitted using the previously obtained values using a quadratic functional form to predict the median and
dispersion at any deterioration level of interest.
Results
The fitted continuous functional models and the derived fragility relationships are first presented for the
component in pristine conditions to display the influence of the chloride-induced corrosion deterioration. After
performing a stepwise regression, a polynomial quadratic functional form is selected for the median fragility
and dispersion prediction models (Fig. 1a). The fitted models explain a high proportion of the variance (above
95% in every case). It can be observed that the deteriorating effects are more apparent at , with a difference
in the fragility median of the model of about 67% between the pristine and deteriorated ( =25%) conditions.
It is also noticeable that the impact of corrosion on  and  can be negligible for engineering purposes.
This is more easily observable in the fragility relationships (Fig. 1b), where the relationship correspondent to
and  are more apparently affected by the deterioration mechanisms.
Similarly, to understand the combined effects of ground-motion sequences and corrosion-induced
deterioration effects, state-dependent fragility relationships are shown for pristine (Fig. 2a) and deteriorated
( =25%) (Fig. 2b) conditions. As expected, the observed difference in the median fragility values indicates
that the deteriorated component is more fragile than the pristine component. Moreover, higher reductions in
the median fragility values are attained when conditioning on the various s, in the deteriorated component.
For instance, differences up to 35% are observed between the structural component in pristine and deteriorated

( =25%) conditions for  given no damage. Differences up to 49% are observed for the same conditions
for  given . In general, the median fragility values reduce as the corrosion deterioration level increases,
and the differences between the undamaged and the damaged (conditioned on a previous ) median fragility
values are higher in a deteriorated component rather than one in pristine conditions, given the ground-motion
sequence.
Figure 1. a) Median fragility values as a function of the deterioration level ; and b) fragility relationships
under various (i.e., 0%, 12.5% and 25%) deterioration levels ; of the bridge column.
Figure 2. a) State-dependent fragility relationships in pristine conditions; and b) state-dependent fragility
relationships for =25% deterioration level; of the bridge column.
Conclusions
A simplified methodology to derive state-dependent fragility relationships for structural components subjected
to mainshock-induced ground-motion sequences while experiencing chloride-induced corrosion deterioration
along their lifetime was presented. It was demonstrated that seismic and environmental multi-hazard
mechanisms could negatively impact the fragility of structural components. It was further observed that the
components become weaker following earthquake-induced damage, and corrosion-induced deterioration can
accelerate this loss of structural capacity. Therefore, the combined consideration of infrequent earthquake-
induced ground-motion sequences and environmentally-induced corrosion deterioration in seismic-prone
regions is critical for risk preparedness and decision making to minimise societal losses.

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