Seismic Performance Assessment of a Retrofitted Bridge with Natural Rubber Isolators in Cold Weather Environments Using Fragility Surfaces

Bandini, Pedro Alexandre Conde; Siqueira, Gustavo Henrique; Padgett, Jamie Ellen; Paultre, Patrick

doi:10.1061/(ASCE)BE.1943-5592.0001873

Open access

Technical Papers

Apr 13, 2022

Seismic Performance Assessment of a Retrofitted Bridge with Natural Rubber Isolators in Cold Weather Environments Using Fragility Surfaces

Authors: Pedro Alexandre Conde Bandini, Gustavo Henrique Siqueira https://orcid.org/0000-0002-2416-1701, Jamie Ellen Padgett, M.ASCE, and Patrick Paultre, M.ASCE https://orcid.org/0000-0001-8111-8614 [email protected]Author Affiliations

Publication: Journal of Bridge Engineering

Volume 27, Issue 6

https://doi.org/10.1061/(ASCE)BE.1943-5592.0001873

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Abstract

Rubber-based seismic isolation has been demonstrated to be one of the most effective measures to protect structural elements from damage during earthquakes and a viable option to retrofit existing structures with poor seismic detailing. The main constituent of these isolation units is rubber, a material that is subject to stiffening when exposed to low air temperatures. In the case of isolated highway bridges, thermal stiffening might reduce the efficiency of isolators, transferring higher forces to the substructure. Assessment of the seismic response of retrofitted structures using rubber isolators in cold regions is thus necessary. Accordingly, in this study, the effect of low temperatures on the seismic performance of a highway bridge retrofitted with natural rubber (NR) isolators is quantified using a probabilistic framework based on fragility surfaces. From the component- and system-level surfaces, it is revealed that the effects of cold temperatures on highway bridges retrofitted with elastomeric isolators may be negligible, depending on the configuration of lateral restraining structures. However, when isolators are able to perform their function without impediment, their thermal stiffening might be significantly detrimental to the bridge’s substructure, mainly affecting bent columns.

Introduction

In recent decades, seismic isolation has gained attention as one of the most effective measures to mitigate or eliminate damage in the structural elements of bridges and bridge systems during severe earthquake shaking (Buckle et al. 2006). Furthermore, seismic isolation has been shown to be an efficient retrofitting measure for bridges with poor seismic detailing (Padgett and DesRoches 2009; Siqueira et al. 2014a). The rather simple concept behind seismic isolation consists of the introduction of flexibility (and damping) in the structural system of a bridge; this is typically achieved by placing isolators between the superstructure (i.e., deck and girders) and substructure (i.e., piers, bents, and abutments). Seismic isolators, therefore, decouple the bridge superstructure from the extreme lateral excitations induced at its base. This results in a significant reduction in the transmission of forces between the bridge superstructure and substructure (Naeim and Kelly 1999). This reduction in forces allows the bridge substructure to remain in the elastic range and eliminates the occurrence of plastic hinges at the top and bottom of the piers. The seismic performance of a bridge can thus be significantly improved by introducing isolators with low lateral stiffness that are capable of shifting the dominant period of the structure to the displacement sensitive region (Constantinou et al. 2011).

Laminated rubber isolators (rubber pads with reinforcing steel plates, with or without lead cores) are widely used for seismic isolation of structures (Buckle et al. 2006). While the role of steel plates is to increase the vertical stiffness by controlling the bulging of the elastomeric pads under gravity loads, the properties of the elastomeric pads highly influence the lateral response of the isolator. The mechanical properties of rubber are affected by several factors, including the temperature, aging process, strain level, loading history, and strain rate (Gent 2001). While higher temperatures have a negligible effect on reducing the stiffness of rubber, elastomers may undergo significant thermal stiffening processes when subjected to low temperatures. The following two processes are identified: (i) instantaneous stiffening, which depends only on the air temperature, and (ii) crystallization, which depends on the air temperature and on the exposure time to low temperature (Murray and Detenber 1961; Stevenson 1986; Cardone and Gesualdi 2012). For seismic applications, the effect of low levels of crystallization is highly detrimental to structural performance even after yielding occurs, owing to a large deformation cycle (Yakut and Yura 2002a, 2002b; Fuller et al. 2004). Stiffer isolators may cause the transmission of larger inertial forces to the substructure than expected when designed for a reference temperature (usually 20°C). The most commonly used elastomer in the US and Canada is NR, owing to its higher seismic performance, compared with that of synthetic rubbers, such as neoprene, when high levels of shear strain are required (Buckle et al. 2006; Siqueira et al. 2014c). Moreover, the effects of crystallization and thermal stiffening are stronger in neoprene than in NR, suggesting that the latter is better for low-temperature applications, as in the case of highway bridges in cold climates, such as in northern Canada or Alaska (Yura et al. 2001). However, NR may undergo severe stiffening at subfreezing temperatures, and these effects must be considered in the design of NR isolators.

Accordingly, to account for this phenomenon in a simplified manner, design codes such as AASHTO-14 (AASHTO 2014) and the Canadian Highway Bridge Design Code CHBDC-19 (CSA 2019) recommend the use of bounding analysis. Additionally, design standards require concomitant minimum service temperatures to be adopted for this bounding analysis, in a compromise between the expected seismic hazard and cold weather conditions. Nevertheless, Guay and Bouaanani (2016) suggested that the annual probability of the minimal average daily temperature being lower than the concomitant temperature specified by the Canadian code is greatly variable across Canada; this was attributed to the fact that the concomitant temperature considered in the code is not based on a probabilistic analysis. A probability-based framework for establishing the concomitant temperature and design earthquake action is still recommended, even if the concurrent event of prolonged low temperature and earthquake shaking is suggested as extremely improbable.

Nevertheless, substantial earthquakes have occurred during winter in North America, in such locations as Charlevoix–Kamouraska in February 1663, southern Alaska in January 1912, the southern Yukon–Alaska border in February 1979, Miramichi (New Brunswick) in January 1982, and the Ungava Region (northern Quebec) in December 1989 (Natural Resources Canada 2018; United States Geological Survey 2021). Fig. 1 links past seismic events (Halchuk 2020) and future projected coldest temperatures (Prairie Climate Centre 2019) in Canada, implying that active seismic regions could be subjected to extremely low temperatures, as in the case of eastern Canada.

Fig. 1. Canada’s (a) historical earthquakes (source: Stephen Halchuk, Natural Resources Canada, 2020. Reproduced with the permission of the Department of Natural Resources, 2020); and (b) projected annual coldest temperatures (reprinted with permission from Prairie Climate Centre 2019).

The stiffening of elastomeric isolators caused by low temperatures reduces the efficiency of isolation devices while increasing the demand on the substructure. Consequently, the question may arise of whether this effect can be harmful to the seismic vulnerability of the bridge or whether substructure components (mainly piers) are still protected when rubber isolators undergo severe stiffening. Some deterministic studies have verified the change in the elastomeric response of isolators and bridge substructure elements caused by the modification of mechanical properties at low temperatures (e.g., Warn and Whittaker 2006; Okui et al. 2019; Deng et al. 2020). Although relevant, a probabilistic framework that captures the inherent uncertainties is required for a better comprehension of the seismic performance of an isolated bridge. In this case, studies are more scarce, although Nassar et al. (2019), Billah and Todorov (2019), and Fosoul and Tait (2020) have evaluated the concurrent events of earthquake loading and thermal stiffening using either reliability or fragility analysis.

Drawbacks of the probabilistic studies are related either to the use of simplified single-degree-of-freedom models—which neglect the interaction between bridge components—or the adoption of discrete temperature scenarios (e.g., winter and summer)—which do not provide a complete portrait of the uncertainty with respect to extreme events. Moreover, none of the studies describes whether the structure under study was either originally designed as isolated or retrofitted with isolator. The retrofitting of an existing structure raises some questions with respect to the costs of intervening in other parts of the structure besides the retrofitting measure itself. For instance, the introduction of seismic isolators requires that appropriate clearances are provided so that the isolation units can perform without impediment. In addition, when investigating older structures that require rehabilitation, the capacity of the bridge components must be representative of the design era to which they belong. Finally, parametrized fragility functions have shown to be an efficient tool to assess the evolution of seismic vulnerability of bridges with age (Choe et al. 2009; Ghosh and Padgett 2010). Their application to retrofitted bridges exposed to a number of extreme environments (e.g., seismic and thermal) has not been explored yet.

By building fragility surfaces of a bridge that was designed in eastern Canada more than 40 years ago, this study addresses these gaps in the performance assessment of retrofitted bridges with elastomeric isolators during earthquakes and cold weather. Given the characteristics of the case-study bridge (i.e., age, geometry, and material), this structure is deemed representative of typical multispan continuous concrete bridges in the region. A numerical model of the retrofitted bridge, comprising its critical components (e.g., columns, abutments, and isolators) is adopted. The study leverages a multivariate seismic demand modeling approach that handles the interaction between the three critical structural components. Two scenarios are idealized to consider the case of retrofitted bridges with respect to the provided lateral clearances. Finally, fragility surfaces are constructed to assess the bridge’s seismic performance at different temperatures, based on damage state (DS) models of its components that are consistent with regional constructive systems and the design era.

Analytical Framework for Constructing Parameterized Fragility Functions

Seismic fragility analysis is a valuable tool in performance-based earthquake engineering for strategic planning of aftermath actions and for retrofitting evaluation. Seismic fragility models traditionally estimate the conditional probability of DS exceedance, DS, given the occurrence of an earthquake event with a specific intensity measure level, IM = im, as indicated by

Fragility = Pr (DS | IM = im)

(1)

Seismic fragility functions are often depicted as curves (e.g., Nielson and DesRoches 2007; Padgett and DesRoches 2008; Tavares et al. 2012; Siqueira et al. 2014a), in which the probability of exceeding a DS is only dependent on the seismic intensity. More recently, parameterized fragility functions of the form

Pr (DS | IM, P)

have been developed (Ghosh et al. 2014; Rokneddin et al. 2014; Kameshwar and Padgett 2018), in which

P = {p_{1}, p_{2}, \dots, p_{n}}

represents a set of n structural or environmental parameters (also called covariates or predictors). This approach avoids the repeated work of constructing discrete fragility functions for different system parameter values while providing a model that handles the uncertainties in the parameters of interest (Gidaris et al. 2016). The depiction of a parameterized seismic fragility function with respect to the conditioning IM and a single covariate has the form of a surface, and its visualization is useful for assessing the influence of the covariate (the structural or environmental parameter) on the structure’s seismic performance (e.g., Ghosh et al. 2014; Segura et al. 2020).

Building a parameterized fragility function can be categorized as a problem of distinguishing between two discrete regions of either structural failure (DS violation) or survival. Supervised learning techniques for discrete data (i.e., classification) are well suited to this task (Kiani et al. 2019), and logistic regression is one option that has often been adopted, owing to its simplicity and interpretability (Agresti 2002; Koutsourelakis 2010). In this case, the parameterized fragility function takes the form of the log odds (logit)

Pr (DS | IM, P) = \frac{\exp (β_{0} + β_{1} im + \sum_{i = 2}^{n + 1} β_{i} p_{i - 1})}{1 + \exp (β_{0} + β_{1} im + \sum_{i = 2}^{n + 1} β_{i} p_{i - 1})}

(2)

where β_i, with i = 0, 1, 2, …, n, is a set of model parameters that are learned from the observed data on DS exceedance. The resulting fragility model can be marginalized to incorporate the uncertainty in the system parameters (e.g., Ghosh et al. 2014), whereas further integration over seismic hazard data provides the annual frequencies of DS exceedance (e.g., Eads et al. 2013).

To generate a dataset on DS exceedance within an analytical framework, sampling techniques, such as Monte Carlo sampling, can be employed to determine the values of structural and seismic parameters used in response history analysis (RHA). These techniques may, however, be computationally expensive and time-consuming when employed to properly cover the domain of the structural and seismic parameters of interest (e.g., Nassar et al. 2019). Alternatively, probabilistic seismic demand modeling techniques can be adopted to reduce the computational cost (e.g., Nielson and DesRoches 2007; Bakalis and Vamvatsikos 2018). These techniques establish a probabilistic relationship—known as a probabilistic seismic demand model (PSDM)—between the structural responses (or engineering demand parameters, EDPs) and the seismic IM, based on the results of limited dynamic analyses.

Recently, a PSDM approach was proposed by Bandini et al. (2021) that locally considers the uncertainty of the seismic response and the correlation between pairs of structural components using Gaussian mixture models. This formulation constructs Gaussian mixture seismic demand models (GMSDMs) based on mixtures of multivariate normal distributions of the peak component seismic demands generated using multistripe analysis (MSA) (Jalayer and Cornell 2009). This density modeling approach relaxes some of the traditional assumptions made by other PSDMs and has been shown to build a more refined model that captures highly complex component interactions or a number of regimes of deformation due to the discontinuities, irregularities, and asymmetries found in structural systems. In addition to the efficiency in propagating record-to-record variability of MSA (Luco and Bazzurro 2007; Eads et al. 2013; Baker 2015), the stripe structure of the seismic demand allows one to capture the statistics of the peak component responses that depend on the observed seismic IM. In addition, this approach is suited to the selection of ground motion record techniques that are consistent with the site’s seismic hazard, such as the conditional spectrum approach (Baker 2011) or the generalized conditional IM (GCIM) approach (Bradley 2010). The joint posterior probability density function (PDF) of a vector of component EDPs (represented by the random variable X) following a Gaussian mixture (i.e., X ∼ GM(x; Ψ)) is expressed as

f (x | Ψ) = \sum_{k = 1}^{m} π_{k} f (x; μ_{k}, Σ_{k})

(3)

where

Ψ = [π^{T}, ξ_{1}^{T}, \dots, ξ_{m}^{T}]^{T}

is the vector that aggregates all the GM model parameters; π^T = [π₁, …, π_k, …, π_m−1] is the vector of mixture proportions, with

\sum_{k = 1}^{m} π_{k} = 1

; each vector ξ_k contains the model parameters related to the mean vector μ_k and the covariance matrix Σ_k of the kth mixture cluster; and f(x; μ_k, Σ_k) is the PDF of a multivariate Gaussian distribution on X with mean μ_k and covariance Σ_k. The GM model is fitted to the observed data using the expectation-maximization algorithm. Furthermore, it is challenging to find the covariance structure and the required number of clusters m to satisfactorily model this phenomenon. The Bayesian information criterion (BIC) can be used to quantify the goodness-of-fit of the model by calculating the log-likelihood of the fitted model, given the observed data, while penalizing the model complexity to prevent overfitting (i.e., preventing overcomplex models) (McLachlan and Peel 2000).

Within this framework, to evaluate the effect of thermal stiffening of NR isolators on the seismic performance of the isolated bridge, the fragility surfaces must be conditioned on a seismic intensity measure and air temperature. Therefore, the GMSDMs must also be conditioned on pairs of temperature and seismic intensity. The chosen GMSDMs are then used to draw N demand samples at a given IM level and temperature θ (i.e., D_i,im,θ = D_i | IM = im, Θ = θ) that are paired with N capacity samples C_i to generate the DS binary data: DS_i,im,θ = 1 when D_i,im,θ > C_i (i.e., exceedance of the DS) or DS_i,im,θ = 0 when D_i,im,θ < C_i (i.e., nonexceedance). Temperature is represented here by the Greek letter theta (θ) instead of T to avoid confusion with the structural vibration period. This dataset is finally used to train the fragility model given by Eq. (2). The effect of low temperatures on the global response of the isolated bridge can be incorporated in the numerical model of the isolated bridge through an analytical model that relates temperature and isolator stiffness. The formulation adopted here to represent this phenomenon is described next.

Modeling of Thermal Stiffening in Rubber Isolators

The sought mechanical properties for elastomeric seismic isolators are incompressibility (to sustain structural weight), low shear modulus (to lengthen the fundamental period), and damping (to avoid excessive displacements). The lateral stiffness K_h is the most important property of a seismic isolator. The shape factor (i.e., the ratio of the bounded and vertically loaded rubber area to the free area of one rubber layer of the bearing) of a seismic isolator typically varies between 8 and 20 (Gauron et al. 2018), allowing calculation of the lateral stiffness based on the rubber shear modulus G (instead of the effective shear modulus of the rubber layer G_eff) with negligible error

K_{h} = \frac{G A_{r}}{T_{r}}

(4)

where A_r = cross-sectional area of rubber; and T_r = total height of N rubber layers of individual thickness t_r (i.e., T_r = N t_r). For a given lateral displacement Δ_h, the shear strain in the isolator is then calculated as γ = Δ_h/T_r.

Although elastomeric isolators essentially behave as viscous–elastic materials with an elliptical hysteric curve, their lateral behavior is commonly idealized by a bilinear model for simplification (Naeim and Kelly 1999). Fig. 2 illustrates this idealization, comparing the real behavior with that of the bilinear model, which can be fully represented by the initial (elastic) stiffness K₁, the postactivation stiffness K₂, and the characteristic strength Q. The initial stiffness, the postactivation stiffness, and the characteristic strength are typically obtained from available hysteresis loops of rubber bearing tests. For NR bearings (NRBs) and high-damping rubber bearings (HDRBs), K₁ is usually assumed to be in the range of 2 to 15 times K₂ (Padgett 2007). The postactivation stiffness K₂ can also be based on the effective stiffness, characteristic strength, and design displacement (Naeim and Kelly 1999). Additionally, according to characterization tests of elastomeric bearings (HITEC 1999), the activation displacement Δ_y can be approximated as 10% of the total rubber height. The damping capacity of the isolator is intrinsically related to the energy dissipated per cycle (EDC), and the effective hysteretic damping ratio ξ_eff can be estimated as (Paultre 2010)

ξ_{eff} = \frac{EDC}{2 π K_{eff} Δ_{d}^{2}}

(5)

where K_eff = effective lateral stiffness of the ensemble isolators and substructure; and Δ_d = design displacement. When substructures present a lateral stiffness much larger than the isolation units, the effective lateral stiffness of the combination of a substructure and isolators can be approximated by the isolator lateral stiffness without introducing significant errors (i.e., K_eff ≈ K_h).

Fig. 2. Bilinear idealization of lateral hysteretic behavior of elastomeric isolator.

This approximation is useful for the preliminary design of seismic isolators using simplified methods, such as uniform-load and single-mode spectral analysis in CHBDC-19 (CSA 2019). In this case, considering the segment of the superstructure with weight W, the effective period of the isolated structure can be estimated as

T_{eff} = 2 π \sqrt{\frac{W}{K_{eff} g}}

(6)

where g = acceleration due to gravity. Based on a chosen target effective period, the effective stiffness can be estimated from Eq. (6). Furthermore, the design displacement Δ_d depends on the target effective period and damping. Hence, an iterative process may be adopted to estimate these isolator properties until convergence of the bridge displacement is achieved. Further details of the design of elastomeric isolators are discussed later, along with details of the case-study bridge.

The mechanical properties of elastomeric isolators depend intrinsically on the shear modulus of rubber, which is prone to undergo significant stiffening under low air temperatures. Thermal stiffening may significantly increase the reference temperature stiffness of rubber compounds, with two main processes distinguished: instantaneous and time-dependent stiffening. In extreme cases, the elastomer may become brittle and fail; this phenomenon is known as glass transition. All these phenomena are fully reversed once the temperature increases back to the reference conditions. The actual increase in stiffness depends on many factors, including the rubber compound, temperature, and exposure time (Murray and Detenber 1961; Derham and Thomas 1980; Stevenson 1986). Modification factors to be multiplied by nominal (at reference temperature) properties have been recommended to obtain the modified mechanical properties under the effect of low temperatures (Constantinou et al. 1999; Yakut and Yura 2002a, b; Constantinou et al. 2007). More recently, Cardone and Gesualdi (2012) conducted an extensive experimental program to assess the thermal effects on the mechanical properties of elastomeric compounds typically employed in isolation units. The following continuous empirical relationship for instantaneous stiffening was established between the rubber shear stiffness and air temperature:

G (θ) = G_{0} (0.0005 θ^{2} - 0.03 θ + 1.4)

(7)

where G₀ = secant shear modulus at the reference temperature θ₀ = +20°C.

The thermal crystallization process (or time-dependent stiffening) of rubber in seismic isolators is, however, a rather complex phenomenon to be empirically modeled, owing to in-service behavior aspects. In summary, the results reported by Cardone and Gesualdi (2012) suggest that the influence of the exposition time at low temperature on the response of rubber is conditioned on the strain amplitudes and the type of displacement protocol. In fact, thermal crystallization showed lower influence on the specimen stiffness when large shear strains (compatible with those attained by isolators subjected to strong ground shaking) were applied, compared with low strains. Regarding the displacement protocol, cyclic tests with increasing strain amplitude are deemed to be representative of the structural response to far-source earthquakes, whereas cyclic tests with constant amplitude are more suitable for simulating the seismic response under near-source conditions. Near-source earthquakes are characterized by a single large impulse of motion, which forces the structure to absorb a large amount of energy nearly instantaneously, with a few large plastic cycles (Chopra and Chintanapakdee 2001; Mavroeidis and Papageorgiou 2010). The main observed effect of rubber thermal crystallization was an increase in the force levels transmitted by the isolation system to the structure during the first loading cycle. Consequently, the relative importance of cyclic responses for structures increases at a greater distance from the epicenter, while time-dependent stiffening effects dissipate, owing to internal heating of the isolator. Conversely, the structural response is governed by the peak response in near-source conditions, which may be substantially affected by the thermal crystallization.

Finally, Eqs. (4) and (7) are coupled to the effective stiffness of NR isolators when subjected to instantaneous thermal stiffening. The presented formulation is integrated into a parameterized numerical model of the case-study bridge to modify the mechanical properties of NR isolators. Details of the case-study bridge and the seismic isolation system are described in the following section. Moreover, as is described in later sections, the ground motions used in this study are only representative of far-source earthquakes. Hence, the time-dependent stiffening of NR is neglected hereafter.

Case-Study Bridge

The seismic performance of the Chemin des Dalles overpass [Fig. 3(a)], located in Quebec, Canada, is assessed here in an idealized isolated configuration. This bridge was designed in 1975 and does not comply with current seismic design standards and detailing. The bridge has been extensively studied, and data have been gathered on its structural properties, capacity, site conditions, and numerical model (Roy et al. 2010; Tavares et al. 2013; Siqueira et al. 2014b; Zuluaga Rubio et al. 2019). It is a three-span continuous concrete girder bridge, with a

106.5 m

long and

13.2 m

wide deck, and a vertical underclearance of

6.2 m

. The superstructure is supported by two concrete piers and two seat-type wing-wall abutments. The piers are moment-resisting frames in the transverse direction, consisting of a transverse beam supported by three circular reinforced concrete (RC) columns with diameters of

0.9 m

resting on shallow foundations [Fig. 3(b)]. Therefore, this structure shares several common characteristics with typical multispan continuous concrete bridges found in the region (Tavares et al. 2012) and with the average bridge of Quebec (Tavares 2012). Details of the numerical model, design of isolation units, DSs of the critical bridge components, site consistent seismic ground motion record selection, and historical temperature data are presented hereafter.

Fig. 3. Case-study bridge over highway in Quebec: (a) overview (reproduced with permission of Canadian Journal of Civil Engineering, from “Performance-based seismic retrofit of a bridge bent: Design and experimental validation,” Nathalie Roy, Patrick Paultre, and Jean Proulx, 37, 3, 2010; permission conveyed through Copyright Clearance Center, Inc.); (b) elevation; and (c) bent details.

Numerical Modeling

The numerical model, which was originally created by Tavares et al. (2013), based on construction drawings, and calibrated with previous in situ ambient vibration tests by Roy et al. (2010), and later modified by Siqueira et al. (2014b) for the introduction of NRB isolators (without lead core), is leveraged and updated for this work. The model is built in the Open System for earthquake engineering simulation (OpenSees) (McKenna et al. 2010) and is parametrized to enable modification of the mechanical properties of the NRB isolators. Fig. 4(a) shows an overview of the three-dimensional (3D) model constructed with OpenSees, which uses beam-column elements and nonlinear zero-length spring elements to represent the behavior of this structural system. The nonlinear behavior of the bent columns and cap beams is captured with force-based beam-column elements with fiber cross sections (Neuenhofer and Filippou 1998), while concrete confinement effects are modeled according to Légeron and Paultre (2003) using Concrete02 and Steel02 prebuilt material models in OpenSees [Figs. 4(d, f, and g)]. The NR isolation units replace the original elastomeric bearings on the abutments and the pinned connections on bents, and are inserted as zero-length elements with bilinear material behavior between the six AASHTO-type V precast concrete girders and the top of the bent cap beams and the seat-type abutments [Figs. 4(b, c, and e)]. Associations of zero-length elements and zero-length elements with gaps are employed to simulate the behavior of abutments and footings [Figs. 4(b and c)]. Further details of the numerical model can be found elsewhere (Tavares et al. 2013; Siqueira et al. 2014b; Bandini et al. 2021).

Fig. 4. Numerical model of the case-study bridge: (a) model overview; (b) details of seat-type abutment with wing walls; (c) details of bent elevation; (d) details of fiber sections; (e) material laws for NRB isolator; (f) material laws for concrete; and (g) material laws for reinforcement steel.

The isolation units are redesigned according to CHBDC-19 (CSA 2019) to account for important modifications related to performance-based design requirements, recent developments of seismic hazards in Canada, and lower damping effects observed under motions rich in high frequencies (Koval et al. 2016). The shear strain of NR at the reference temperature and effective damping are set to

G_{0} = 0.75 MPa

and

ξ_{eff} = 7.5 %

, respectively. These values are representative of NR in service conditions (i.e., shear strains in the range 50%–125%) found in structural engineering applications in Quebec (Siqueira et al. 2014a). Isolation units are designed to assure a fundamental period of

2.0 s

in both the transverse and longitudinal directions. Given the target period and the effective damping ratio, the design displacement of the isolators is calculated as

Δ_{d} = 70 mm

, using the site-specific spectral data for a probability of exceedance of 2% in 50 years (Natural Resources Canada 2019) and a site class D soil. Given the different weights supported by bents and abutments, the effective stiffness of the isolators installed on the bents is

K_{eff} = 0.86 kN / mm

, whereas that of isolators installed on the seat-type abutments is

K_{eff} = 0.52 kN / mm

.

Because the isolators are preliminarily designed using the simplified approach of CHBDC-19 (CSA 2019), modal analysis of the whole bridge is performed using the effective stiffness of the NRB isolators to ensure that the first two vibration modes behave as expected. Fig. 5 illustrates the two fundamental modes of the isolated bridge, along with the first two vibration modes of the as-built bridge. Accordingly, modal information demonstrates the effective design of the isolator units in (i) lengthening the fundamental period in the two orthogonal directions, with good agreement with the target effective period

T_{eff} = 2.0 s

, and (ii) decoupling the bridge deck from the substructure, with fundamental modes mobilizing more than 90% of the modal masses in each horizontal direction. A shift in the direction of the fundamental mode from transversal to longitudinal is observed when the isolators are introduced. Motions in the longitudinal direction, however, are restricted, owing to the combined stiffness of the abutment backwall and the backfill soil. Consequently, the bridge components are more vulnerable in the transverse direction, and the bridge’s seismic performance is assessed only in this direction.

Fig. 5. First two vibration modes of the (a) as-built; and (b) retrofitted bridge with isolators.

Finally, two scenarios are idealized with respect to lateral restraining structures, represented in this case study by the abutment wing walls. CHBDC-19 (CSA 2019) requires that sufficient clearances be provided such that the isolation units can perform their function without impediment. Because this is an existing structure, two values for the gap between the deck and the abutment wing walls are considered. In Scenario I, the original

25.4 mm

gap remains unchanged and no retrofitting costs would be added, whereas pounding between the deck and the abutment wing walls would be expected because the provided clearance is not sufficient to allow the isolators to perform unrestrainedly. In Scenario II, the gap is augmented to

100 mm

, simulating a situation where the wing walls would be modified to comply with the code requirement, and intervention costs would have to be considered. A gap also exists between the deck and the abutment backwall (longitudinal direction). However, this gap is kept unchanged in both gap scenarios. Nonlinear RHAs are conducted according to the MSA technique, using the suite of seismic ground motion records described next. Although the isolated bridge has its first mode in the longitudinal direction, ground motions are only applied in the transverse direction because the bridge is restrained in the longitudinal direction by the abutment backwalls. Additionally, components are more vulnerable in the transverse direction for multispan continuous concrete bridges, such as the case-study structure (Tavares et al. 2012; Siqueira et al. 2014a).

Component Capacities and Performance Levels

An essential step in performing seismic fragility analysis is the definition of structural component capacity models. For highway bridges, these capacities are defined in terms of DSs, relating expected damage to components and the bridge’s postevent service level. Four DSs are considered in progressive order of severity: slight, moderate, extensive, and complete, and are denoted DS 1 to DS 4 hereafter for brevity. The case-study bridge includes three critical components—abutment wing walls, NRB isolators, and bent columns—while other structural components have shown negligible seismic fragility in multispan continuous concrete girder bridges in eastern Canada (Tavares et al. 2012; Siqueira et al. 2014a). The parameters associated with the engineering demand of each component are taken only in the transverse direction (Siqueira et al. 2014b) and are given in Table 1 under normal operating conditions (i.e., at the reference temperature of 20°C). For completeness, the effect of the uncertainty on the capacity should be included in the analysis (Bakalis and Vamvatsikos 2018). Therefore, the capacities of the components are assumed to follow log-normal distributions (Nielson and DesRoches 2007; Mangalathu and Jeon 2019) with median λ_C and dispersion ζ_C values fully characterizing each DS model.

Table 1. DS capacities of bridge components at reference temperature (θ₀ = 20°C)

Component EDP	DS 1		DS 2		DS 3		DS 4
	λ_C	ζ_C	λ_C	ζ_C	λ_C	ζ_C	λ_C	ζ_C
Abutment wing-wall deformation, Δ_aww (mm)	7.0	0.25	15.0	0.25	30.0	0.46	60.0	0.46
NRB isolator shear strain, γ_iso (%)	—	—	—	—	—	—	267	0.46
Column drift ratio, δ_col (%)	0.5	0.25	1.4	0.25	2.0	0.46	2.2	0.46

In this work, the main concern of the proposed retrofit approach is to protect bridge columns that were designed according to obsolete codes. Experiment-based capacity models for the columns are, therefore, adopted, instead of code-based values. These models are consistent with the design era of the bridge and more representative of the expected damage mechanics of bridge columns designed according to outdated standards. Still, the progressive damage description of the adopted capacity models is coherent with those found in the commentaries of the Canadian highway bridge design code (CSA 2019) and other performance criteria (e.g., Hose and Seible 1999). The median capacities of the columns follow the experimental findings for an exact full-scale replica of the actual bridge column, identified as specimen CH300 in the work of Zuluaga Rubio et al. (2019). These columns present poor confinement (owing to an insufficient transverse reinforcement ratio) and a lap splice at the base (a region of potential formation of a plastic hinge), justifying the smaller capacity of these components, compared with current seismic design standards. Slight damage is characterized by initial cracking and yielding of longitudinal reinforcement. Concrete cover spalling and crack opening then follow and represent moderate damage. Owing to its poor seismic detailing, an abrupt reduction in the column lateral displacement capacity is observed, which is characterized by early transverse reinforcement yielding, followed by longitudinal bar buckling and rupture for drift ratios in the vicinity of

2 %

.

The median capacities of the abutment wing walls were adapted by Tavares et al. (2013) for structures in Quebec, based on the prescriptive capacity models proposed by Choi et al. (2004) to represent first yield,

50 %

of ultimate displacement, ultimate displacement, and twice the ultimate displacement, respectively. In the case of the NRB isolators, experimental results of shear tests on rubber isolators suggest that it is very difficult to identify damage mechanisms related to intermediate damage (i.e., before failure is observed). Moreover, the damage detected prior to failure did not affect, dramatically, the functionality of the isolators in most cases (Sanchez et al. 2013; Gauron et al. 2018). For these reasons, only the complete DS is considered for the NRB isolators. Because slender isolators are designed for the case-study bridge, instability issues are more likely to take place before any sign of shear failure is observed (Siqueira et al. 2014a; Gauron et al. 2018; Saidou et al. 2021). Finally, dispersion values follow the recommendations given by Nielson (2005).

Freezing temperatures can alter a material’s response to loading and, consequently, affect an element’s capacity. For instance, experimental data on flexural-dominated columns tested at low temperatures (−40°C) exhibit an increase in flexural strength (explained by the enhancement in the mechanical properties of plain concrete and steel reinforcement in extreme cold conditions) and a decrease in displacement capacity. This decrease was attributed to a substantial reduction in the spread of plasticity of the specimens tested at low temperatures, causing an increase in the curvature demand at the base of the column (Montejo et al. 2009). A numerical parametric study was then conducted using finite-element models of bridge bents calibrated against experimental data to represent the reduction in the ductility capacity of RC columns at low temperatures. An empirical relationship between the displacement ductility

μ_{Δ}

at reference and low (−40°C) temperatures was then established (Montejo et al. 2010). The adopted engineering demand parameter for the bent columns is, however, the drift ratio δ (Table 1). Acknowledging that the slight DS (DS1) is first characterized by yielding of longitudinal reinforcement (i.e., μ_Δ,DS1 = 1), a simple conversion of the ductility levels to drift ratios is provided for each DS:

\frac{δ_{DS i (- 40)}}{δ_{DS i (+ 20)}} = 0.88 {(\frac{δ_{DS i (+ 20)}}{δ_{DS 1 (+ 20)}})}^{- 0.17}

(8)

where δ_DSi(θ) = drift ratio at temperature θ (in °C) and DS DS i. Although defined at −40°C, this relationship is recommended for temperatures below 0°C, thereby producing a conservative result (Montejo et al. 2010). Thus, the reference column drift median capacities (Table 1) are multiplied by 0.88, 0.74, 0.70, and 0.68, from slight to complete DSs, to account for the decrease in the displacement capacity at subfreezing temperatures.

Although the parametric study considered transverse reinforcement, it is worth noting that ratios as low as

0.4 %

were recorded (ratios close to

0.34 %

were found for the columns of the case-study bridge), and the flexural-dominated experimental specimens presented a transverse reinforcement ratio of

1.2 %

. In addition, the numerical model did not consider bond slip between the reinforcing bar and concrete, which was observed during laboratory tests on a replica of the actual bridge column at ambient temperature (Zuluaga Rubio et al. 2019). Therefore, the real decrease in the displacement capacity of the columns of the case-study bridge may deviate from that of the analytical model expressed by Eq. (8). This analytical model is, nonetheless, deemed adequate in this study, owing to the scarcity of more refined models.

Finally, to the best of the authors’ knowledge, no study on NRB isolators has quantitatively determined the effect of low temperatures on the shear strain capacity, except for those that undergo glass transition, which occurs at approximately −65°C for NR (Long 1974) and is beyond the scope of this study. However, one advantage of the analytical framework employed in this study is that a decrease in the shear strain capacity of the NRB isolators can be idealized and have an effortless effect on the assessed performance of the structure. Therefore, two hypothetical decreases, of

20 %

and

40 %

, in the shear strain capacity of the NRBs, owing to freezing temperatures, are investigated.

Ground Motion Record Selection

Another crucial step in seismic fragility analysis involves the selection of ground motion records that are consistent with the site’s seismic hazards, and the GCIM approach (Bradley 2010, 2012) is adopted for this purpose. For this approach, target multivariate log-normal distributions of intensity measures conditioned on the observation of earthquake events with specific values of a conditioning IM are constructed; and the ground motion records that best match these target conditional distributions are selected. Spectral acceleration at the target isolation period is discarded as a conditioning IM because the thermal stiffening on the NRB isolators causes a shift in the fundamental period of the structure. Hence, a structure-independent IM is selected instead, and peak ground velocity (PGV) is chosen, which has been recently identified as a sufficient and efficient seismic IM for the assessment of the seismic performance of highway bridge portfolios (Zelaschi et al. 2019) and isolated bridges (Avşar and Özdemir 2013), even when ordinary (non-pulse-like) ground motions are observed.

First, a probabilistic seismic hazard analysis (PSHA) is performed to determine the mean annual frequency of exceedance of the PGV (i.e., the hazard curve). The ground motion models (GMMs) of the fifth-generation hazard maps of Canada are adopted here for consistency with the design of the isolation units (Halchuk et al. 2014; Canadian Commission on Building and Fire Codes and National Research Council Canada 2015). The PSHA is followed by seismic deaggregations (Bazzurro and Cornell 1999) to define expected earthquake scenarios in terms of magnitude, distance, and ɛ, where ɛ is the deviation of the mean seismic intensity calculated from the ground motion model to the target value of the IM, divided by the standard deviation of the GMM. These steps are performed on the OpenQuake (OQ) engine (Silva et al. 2014). Target conditional distributions are then constructed based on these GMMs using a modified version of the algorithm proposed by Baker and Lee (2018) to include IMs other than spectral acceleration. Kolmogorov–Smirnov tests are finally performed to ensure the fit of the selected suites to the target conditional IM distributions for each conditioned IM. Six PGV levels are chosen, corresponding to probabilities of exceedance of 5%, 2%, 1%, 0.5%, 0.2%, and 0.1% in 50 years, and 40 records are selected for each expected earthquake scenario of interest. An example illustrating the process for record selection is shown in Fig. 6 for a 9,975-year return period of the earthquake scenario (i.e.,

0.5 %

probability of exceedance in 50 years). The process illustrated in Fig. 6 is repeated for each chosen PGV level.

Fig. 6. Example of ground motion record selection using the GCIM approach for a 9,975-year return period earthquake scenario: (a) probabilistic seismic hazard analysis (OQ); (b) seismic deaggregation (OQ); and (c) record selection via the GCIM approach.

Records are selected from the PEER NGA-West2 database (Ancheta et al. 2014), owing to the scarcity of recorded strong ground motions in eastern Canada. Two limitations are usually highlighted within this approach: (i) compared with western regions in North America, eastern events tend to generate high amplitudes at low periods; and (ii) ground acceleration attenuates more slowly in eastern North America than in western regions (Bernier et al. 2016; Segura et al. 2019). Two measures are adopted to address these limitations. First, a prescreening of the database is performed with respect to the magnitude, source-to-site distance, and soil type to limit the selection of records to those that closely match the seismic characteristics at the bridge site. Only ground motions with the following properties are available for selection after screening: 5.5 ≤ M_W ≤ 7.5,

20 \leq R_{j b} \leq 200 km

, and

200 \leq V_{S 30} \leq 760 m / s

, where: M_W = moment magnitude; R_jb = Joyner–Boore source-to-site distance; and V_S30 = shear wave velocity. This screening criterion also ensures that only far-source ground motion records are selected. Finally, the acceleration spectra of the selected suite are ensured to satisfactorily match the target GCIM distributions at low periods (Baker and Allin Cornell 2006; Luco and Bazzurro 2007).

Climate Historical Data at the Bridge’s Site

Yakut and Yura (2002a) suggest the use of historic daily low temperatures or a more conservative lower value to test instantaneous stiffening, whereas daily average (mean) temperature is suggested in the test of crystallization. However, the duration of conditioning to reach thermal equilibrium in full-scale rubber bearings (without lead core) has been reported as 3–15 h (Yakut 2000). Hence, in a compromise between the required time to reach the temperature stabilization for instantaneous stiffening and a more conservative approach that would use historic low temperature, daily mean temperature data collected at two stations in Shawinigan, Quebec, Canada (Meteorological Service of Canada, Environment and Climate Change Canada 2020) are gathered to assess the thermal effects on the seismic performance of the isolated bridge in this case study. These stations are located approximately

13.5 km

away from the bridge site and report temperature measurements from 1902 to 2020. The histograms of the daily mean temperature (

{\bar{θ}}_{daily}

) at each station are shown in Fig. 7. The climate identifiers (CIDs) of the stations are 7018000 and 7018001. The former reports temperature data from 1902 to 2004 [Fig. 7(a)], while the latter has been collecting data since 1998 [Fig. 7(b)].

Fig. 7. Mean daily temperature from two stations in Shawinigan, Quebec, Canada based on Environment and Climate Change Canada data, with identifiers: (a) 7018000; and (b) 7018001.

Despite the different time spans covered by each station, the daily mean temperatures appear to follow the same trend, with a minimum mean temperature of approximately −30°C and a maximum not exceeding +30°C. However, for a holistic seismic fragility analysis, a range from −30 to +20°C is adopted. This range is deemed adequate because the thermal effects of warmer temperatures on the seismic isolators are assumed to be negligible (Constantinou et al. 2007; Cardone and Gesualdi 2012).

Assessment of the Isolated Bridge Seismic Performance in Cold Regions

The 240 selected records were used to perform RHAs on the numerical model at six values of air temperature ranging from +20 to −30°C, for a total of 1,440 RHAs in OpenSees for each idealized scenario regarding the width of the abutment wing-wall gap. A deterministic numerical model of the isolated bridge was employed, neglecting any material uncertainty or thermal effects of the concrete and steel strengths, based on past studies that showed the low influence of these mechanical properties on the peak responses of multispan continuous concrete bridges in Quebec for both as-built and isolated configurations (e.g., Tavares et al. 2012; Siqueira et al. 2014a; Bandini et al. 2019).

PSDM

The peak responses from the nonlinear RHAs performed in OpenSees were extracted and used to build the PSDMs based on Gaussian mixtures (GMs) [Eq. (3)]. The peak demand values (conditioned on the six PGV levels and six temperature levels) were first transformed into the (natural) logarithmic space. Then 36 GMSDMs were built, considering a maximum of 10 clusters and full-unshared covariance matrices (i.e., each cluster had a full covariance matrix) to fit the observed correlated demand data. The GMSDMs were chosen according to minimum BICs and had a number of clusters varying from 1 to 4, indicating that overcomplex models were avoided. For three-variable GM models, a single cluster corresponded to nine model parameters plus its mixture proportion. Therefore, for brevity, the GM model parameters are not discussed.

These GMSDMs were used to generate 10³ correlated demand samples at each combination of temperatures and PGVs for a total of 36,000 samples for each gap scenario, which are shown along with the observed peak responses in Fig. 8. The good agreement of the sampled demands and the RHA peak responses demonstrates the refined fit of the GMSDMs, which are capable of capturing the discontinuities (caused by the abutment wing-wall gap) and the nonlinear dependence between the component responses. This feature may avoid the propagation of density modeling bias into the fragility analysis (Bandini et al. 2021).

Fig. 8. Peak responses (circles) and samples generated from GM seismic demand models (asterisks) for wing-wall gaps of (a) $25.4 mm$ ; and (b) $100 mm$ .

Construction of Component and System Fragility Surfaces

In seismic fragility analysis, performance criteria relate damage limit states to required structural functionality; for highway bridges, damage limit states are formulated at two levels, i.e., the component and system levels. Component-level damage is typically used to estimate repair actions and costs, while system-level performance combined with the component damages relates to such outcomes as lane closures, load restrictions, or speed restrictions (Mackie and Stojadinovic 2004; Padgett and DesRoches 2008; Kameshwar et al. 2020). While many alternatives exist in the literature, bridges are commonly assumed to be a series system (e.g., Nielson and DesRoches 2007; Tavares 2012; Siqueira et al. 2014a).

Adapting the methodology detailed by Ghosh et al. (2014) to the use of the GMSDMs, the generated demand samples were then paired to the same number of samples from the capacity models at each DS (Table 1). Then, binary vectors indicating component DS exceedance were built for the construction of the seismic fragility functions. To better conform the DSs of the components to the consequences to the bridge’s level of service, the components can be classified as primary or secondary, in accordance with their importance for bridge stability under traffic or subsequent seismic events (Zakeri et al. 2014). Extensively damaged columns and isolation units were classified as primary components, which are assumed to be the only components contributing to the complete DS of the bridge. Abutment wing walls were considered secondary components, contributing to the initial DSs of the whole system (i.e., slight, moderate, and extensive) because their complete damage would not have a similar consequence to that of the primary components (i.e., failure of abutment wing walls would not require bridge closure). To translate these assumptions into the fragility functions, the binary matrix in Table 2 connects the component DSs to the DS of the whole bridge.

Table 2. Adopted binary matrix relating the component DS to the overall performance of the bridge

Bridge component	DS
	DS 1	DS 2	DS 3	DS 4
Abutment wing walls	1	1	1	0
NRB isolators	0	0	0	1
Bent columns	1	1	1	1

To compare the effects of the covariates having different units on the fitted logistic regression model, covariates were first standardized with respect to their mean and standard deviation values (Agresti 2002). In this case, only the PGV and air temperature (θ) were considered predictors, and the fragility function [Eq. (2)] takes the following form

Pr (DS | PGV, θ) = \frac{\exp (β_{0} + β_{1} z_{PGV} + β_{2} z_{θ})}{1 + \exp (β_{0} + β_{1} z_{PGV} + β_{2} z_{θ})}

(9)

where z_PGV and z_θ are the standardized values of the PGV and temperature. Table 3 gives the fitted model parameters (

{\hat{β}}_{i}

) for all the components and system, at each studied scenario. The average accuracy from the five-fold cross-validation is also given, suggesting good agreement between the observed damage data and that of the fitted models. Although omitted here for brevity, the values of p of all the logistic regression coefficients are less than 0.001, demonstrating the relevance of the investigated covariates for the fragility. The resulting fragility surfaces are depicted in Figs. 9 to 12 for DS 1 to DS 4, respectively.

Fig. 9. Slight-damage (DS 1) fragility surfaces for (a) abutment wing wall; (b) bent column; and (c) system.

Table 3. Summary of fitted logistic regression models for fragility data

DS	Level^a	Scenario I ( $25.4 mm$ gap)				Scenario II ( $100 mm$ gap)
		${\hat{β}}_{0}$	${\hat{β}}_{1}$	${\hat{β}}_{2}$	Accuracy (%)^b	${\hat{β}}_{0}$	${\hat{β}}_{1}$	${\hat{β}}_{2}$	Accuracy (%)^b
DS 1	AWW	−0.693	2.168	0.127	83.79	−1.902	2.799	0.580	88.88
	ISO	—	—	—	—	—	—	—	—
	COL	−6.234	2.076	−1.484	97.90	−4.087	2.149	−1.456	92.29
	SYS	−0.667	2.169	0.139	83.58	−1.770	2.753	0.368	88.29
DS 2	AWW	−3.488	1.617	0.153	92.56	−3.388	2.097	0.188	88.59
	ISO	—	—	—	—	—	—	—	—
	COL	−10.887	2.817	−2.210	99.84	−7.057	2.331	−1.698	98.34
	SYS	−3.505	1.653	0.108	92.44	−3.358	2.095	0.145	88.33
DS 3	AWW	−5.298	1.412	0.122	98.80	−5.182	1.882	0.121	97.66
	ISO	—	—	—	—	—	—	—	—
	COL	−10.335	2.672	−1.183	99.92	−7.613	2.329	−1.724	98.95
	SYS	−5.286	1.499	0.006	98.67	−5.161	2.057	−0.215	97.01
DS 4	AWW	—	—	—	—	—	—	—	—
	ISO	−9.381	1.294	1.179	99.97	−4.629	1.236	0.357	98.04
	COL	−12.476	3.288	−1.975	99.95	−8.481	2.397	−1.913	99.38
	SYS	−8.420	1.886	−0.328	99.89	−4.799	1.598	−0.093	97.63

^aAWW: abutment wing walls; COL: bent columns; ISO: NRB isolators; SYS: system (whole bridge).

^bAverage accuracy from five-fold cross-validation.

As mentioned previously, one of the advantages of the logistic regression model is the interpretability of the model parameters. Accordingly, the positive model parameter of a given covariate indicates that the increase on this covariate increases the odds of observing damage. As expected, all the fitted model parameters related to the seismic IM (

{\hat{β}}_{1}

) are positive. In contrast, the temperature model parameter

{\hat{β}}_{2}

varies, depending on the studied level (component or system), abutment wing-wall gap length, and DS, with negative values indicating that seismic fragility increases as the air temperature decreases.

For DS 1, the abutment wing walls seem to govern the system fragility in both scenarios investigated. Indeed, the fitted model parameters at the levels of the abutment wing walls and system are close, suggesting that the first signs of yielding of the longitudinal reinforcement in the bent columns occur concomitantly with the slight damage of the abutment wing walls. This finding can also be observed through the similarity of the fragility surfaces of the abutment wing walls [Fig. 9(a)] and the whole bridge [Fig. 9(c)]. Additionally, regression coefficients and the depiction of the fragility surfaces suggest that the enlargement of the gap between the deck and the wing walls has a slight effect in reducing the seismic fragility. Indeed, the slightly larger value of

{\hat{β}}_{2} = 0.580

in Scenario II, compared with

{\hat{β}}_{2} = 0.127

in Scenario I, demonstrates the minor positive effect of colder temperatures on the system’s fragility, which can be explained by the lower lateral displacement of the stiffer NRB isolators causing less damage on the abutment wing walls.

Conversely, low temperatures are detrimental to the fragility of columns in DS 1 for both investigated scenarios, a result of the increased forces transmitted to the substructure when thermal stiffening takes place on the elastomeric isolators. At the reference temperature, the choice of retrofitting the bridge with elastomeric isolators seems effective as it is unlikely that columns will undergo slight damage even under strong shaking. The column’s seismic fragility, however, increases rapidly as temperature decreases, and the close values of the logistic regression coefficients for temperature (−1.484 and −1.456) may suggest that the effects of temperature are similar in both gap scenarios. Nevertheless, as observed in Fig. 9(b), the larger clearance (which allows the isolators to deform more freely) has a negative effect on the column’s seismic fragility. While the gap is not closed, the deck behaves as a rigid body, and the only restoring forces are provided by the isolators. When the gap is closed, the deck bends, owing to the reaction of the wing walls, and part of the energy imparted from the earthquake to the bridge is transformed into flexural strain energy during the transverse bending of the deck (which is stored as potential energy and later fully converted into kinetic energy, owing to the elastic modeling of the deck). This mechanism starts earlier in the case of the

25.4 mm

gap and limits the drift of the bent columns, compared with the

100 mm

gap, where the deck has more space to behave as a rigid body. Although this mechanism is understood, no calculation of the amount of strain energy stored by the deck is performed, for brevity.

When the isolators undergo stiffening at low temperatures, higher forces are transmitted from the deck to the substructure, and the columns become more vulnerable. Combined with the restraining action of the abutment wing walls, the fragility of the bent columns is better controlled when the wing-wall gap is smaller. It is known that elastomeric isolators can reach shear strains up to

300 %

during strong ground motions (Saidou et al. 2021). In this work, specifically, shear strains in the isolators reach up to

160 %

(Fig. 8). On the one hand, if the abutment gap were wide enough to accommodate the displacement of the isolators at a higher level of shear strain, no damage would be expected on the wing walls. Therefore, the vulnerability of the wing wall could be reduced if an even wider gap (i.e.,

> 100 mm

) were provided in this case. On the other hand, the results suggest that a smaller gap can be beneficial to the fragility of the bent columns when the isolators undergo thermal stiffening. Keeping the original clearance, however, is not detrimental to the vulnerability of the wing walls, which shows fragility levels that are comparable to those of the wider gap scenario [Fig. 9(a)].

In the case of the moderate DS, the bridge must present a limited service level, and the abutment wing walls still govern the system’s fragility [Figs. 10(a and c)]. In Scenario II, the slight reduction in the fragility of abutment wing walls at −30°C (compared with that of the reference temperature) and high PGV levels is compensated by a rapid augmentation of fragility of the columns [Fig. 10(b)]. Contrarily to the behavior observed in DS 1, the enlargement of the wing-wall gap appears to be detrimental to the abutment’s fragility, and the same phenomenon is observed at the system level. The larger PGV regression coefficient in Scenario II compared with Scenario I (2.097 against 1.617) indicates that the fragility increases more rapidly when the clearance respects the design code requirements. This phenomenon is explained by a greater velocity of the bridge deck when pounding against the abutment wing walls takes place. For a same ground motion, the deck has the space to develop a greater velocity within a wider gap, compared with the original gap. With the greater kinetic energy of the bridge deck (and therefore a greater damaging energy), the wing walls undergo larger deformations in the modified gap scenario when pounding occurs. For the bent columns, similar observations to those for the slight DSs can be drawn: lower temperatures show an adverse effect on the seismic fragility. However, the restraining effect of the wing walls at their original position results in improbable occurrence of moderate damage on the columns. When the gap increases to

100 mm

, the odds of observing inelastic behavior and moderate damage of the columns becomes larger for

PGV > 50 cm / s

and subfreezing temperatures. Similar observations can be made with respect to the fragility of the extensive DS (Fig. 11).

Fig. 10. Moderate-damage (DS 2) fragility surfaces for (a) abutment wing wall; (b) bent column; and (c) system.

Fig. 11. Extensive-damage (DS 3) fragility surfaces for (a) abutment wing wall; (b) bent column; and (c) system.

Fig. 12. Complete-damage (DS 4) fragility surfaces for (a) NRB isolator; (b) bent column; and (c) system.

Finally, for the life safety level of service, characterized by the complete DS (DS 4), the abutment wing walls present negligible seismic fragility (the fitting of the logistic regression model to the observed fragility data does not converge) in any investigated scenario (Table 3). As indicated in Tables 1 and 2, the NRB isolators are considered in this DS and may contribute to the system’s fragility. Accordingly, the isolators control the bridge fragility in the complete condition. The isolators could practically only fail by buckling when not impeded by the abutment wing walls (i.e., in Scenario II) and when subjected to severe shaking (

PGV > 75 cm / s

), which would be followed by deck unseating. In Scenario I, the restraining action of the abutment wing walls reduces the displacement amplitude of the NRB isolators, which in turn are less vulnerable than when the gap is modified to accommodate the service displacement of the isolators. As thermal stiffening takes place, the seismic fragility of the isolators is slightly reduced [as indicated by the negative temperature logistic regression coefficient in Table 3 and illustrated in Fig. 12(a)]. This phenomenon is expected as the lateral displacement of the NRB isolators diminishes for subfreezing temperatures. Buckling of longitudinal reinforcement in the RC columns is very unlikely to occur and has a slight contribution to the system’s fragility only under extremely low temperatures and severe ground shaking [Fig. 12(b)].

Potential Effect of Low-Temperature Shear Capacity Reduction on NRB

Finally, the analytical framework adopted in this study was leveraged to investigate the potential effect that a decrease in the shear strain capacity of the NRB isolators (owing to low temperatures) could have on their fragility. Accordingly, two hypothetical decreases are idealized:

20 %

and

40 %

(i.e., the median capacity in Table 1 of the NRB is multiplied by 0.8 and 0.6, respectively). The coefficients of the logistic regression models for these capacity levels are given in Table 4, along with the nominal capacity (i.e., no reduction). In both gap scenarios, the progressive decrease in the NRB capacity gradually cancels the beneficial effect of low temperatures on the fragility of the isolators, as the values of

{\hat{β}}_{2}

change from positive to negative.

Table 4. Logistic regression models for complete damage of NRB isolators, considering capacity reduction at low temperatures

Variation in	Scenario I ( $25.4 mm$ gap)				Scenario II ( $100 mm$ gap)
shear strain capacity	${\hat{β}}_{0}$	${\hat{β}}_{1}$	${\hat{β}}_{2}$	Accuracy (%)^a	${\hat{β}}_{0}$	${\hat{β}}_{1}$	${\hat{β}}_{2}$	Accuracy (%)^a
No reduction	−9.381	1.294	1.179	99.97	−4.629	1.236	0.357	98.04
$20 %$ reduction	−7.639	1.191	0.229	99.91	−3.967	1.213	−0.020	96.59
$40 %$ reduction	−6.320	1.442	−0.177	99.54	−3.061	1.176	−0.354	92.44

^aAverage accuracy from five-fold cross-validation.

The fragility surfaces indicate that the restraining action of the abutment wing walls is still beneficial to the fragility of the isolators when the original gap is maintained (Fig. 13). Conversely, the effects of the reduction in the shear capacity of the isolator are more important when the NRBs function without impediment (

100 mm

gap). Although temperature effects on the shear capacities of NRB isolators are not reported in the current literature, the results show that even a

20 %

reduction in capacity would still lead to a minimal probability of limit state exceedance [Fig. 13(b)]. A greater decrease in the NRB shear capacity would then lead to a detrimental effect of low temperatures on the isolator fragility and, consequently, to the system fragility for this case study [Fig. 13(c)].

Fig. 13. Complete-damage (DS4) fragility surfaces for NRB isolators with (a) zero; (b) $20 %$ ; and (c) $40 %$ reduction in shear strain capacity.

Conclusion

A probabilistic framework based on seismic fragility analysis was leveraged to assess the effect of thermal stiffening of NR isolators on the performance of a bridge in eastern Canada retrofitted with NR isolators designed according to CHBDC-19 (CSA 2019). Typical winter temperatures in cold regions might be detrimental to the seismic performance of elastomeric isolators, which might not function as designed at reference temperature. The poorer performance of the rubber isolators is followed by an increased displacement demand on the bent columns, which are, in turn, more prone to damage during an earthquake. This reiterates the importance of considering thermal stiffening effects in the design of rubber-based isolation systems. The reported results suggest, however, that these effects may be less important when restraining structures act in combination with the isolator. From the performance assessment, the following key findings are highlighted.

1.

An intervention on the abutment wing walls in the case of seismic retrofitting to accommodate the displacement of the isolators was shown to have negligible effect. Indeed, these components were damaged even when the clearance between the deck and the wing walls was more than 40% wider than the in-service displacement of the NRB isolators (i.e., the 100 mm gap scenario), which happens as a result of the increased velocity of the deck when pounding occurs. An even wider gap would potentially avoid damage to the wing walls by deck pounding. However, the results also revealed a beneficial aspect of the restraining action of the wing walls in protecting the bent columns when combined with the seismic isolators.

2.

Fragility models of the columns suggest that low temperatures are detrimental to the vulnerability of these components, irrespective of the DS or the gap scenario. Columns showed, however, lower fragility when the abutment gap was unchanged, compared with the modified gap scenario; this is attributed to the restraining action of the abutment wing walls. When the gap was enlarged, a poorer performance of the isolation system was observed, with larger seismic forces transmitted to the bent columns, thus increasing the displacement demand on these substructure elements. The exceedance of DSs from moderate to complete is extremely improbable when no retrofitting intervention is performed on the abutment wing walls.

3.

The system’s fragility was mainly controlled by the abutment wing walls for the slight, moderate, and extensive DSs in both gap scenarios. NRB isolators govern the complete fragility of the system only when performing without the impediment of the wing walls. In this case, thermal stiffening shows a slight positive effect on the NRBs’ fragility, owing to reduced lateral displacement. However, a potential

20 %

decrease in the shear strain capacity of the NRB isolators at low temperatures was identified as a threshold to balance out this positive effect on the fragility.

The results of this case study reveal the beneficial combination of lateral restraining structures (e.g., abutment wing walls) and elastomeric seismic isolators when the latter undergo important thermal stiffening in extreme cold weather conditions. For the case-study bridge, sacrificing the abutment wing walls reduces the probability of observing even minor damage to the bent columns, which are usually the most expensive bridge components to repair or retrofit. However, in practice, the abutment wing walls would require strengthening, and these costs should also be considered. Additionally, different deck displacement restraining mechanisms, such as keeper plates and restraining cables, have already been shown to enhance the seismic performance of bridges, and could be studied in companions of elastomeric isolators subject to subfreezing temperatures. Alternatively, a retrofitting plan could comprise the installation of NRB isolators only on top of the bents, while keeping the original elastomeric bearing pads on the abutments. This option still remains unexplored and should be investigated further. In this case, the deck would not be expected to move as a rigid body though, and its ability to remain elastic under transverse bending should be incorporated in the analysis. Given the structural system of the case-study bridge, the analysis here was limited to the transverse direction. Seismic excitation is, however, three-dimensional, and the effects on the longitudinal direction might not be negligible if other bridge types are studied. Finally, other aspects of seismic risk analysis could be incorporated to evaluate the effect of the combination of isolation and restraining structures, in terms of repair costs and return-to-service time for repair and restoration. A more thorough analysis could integrate over seismic hazard and climate data in an effort to calculate the mean annual frequency of observing each of the assessed DSs and their general acceptance by asset managers. Key findings of this study, however, are still expected to be valid as the integration of the fragility over the seismic hazard and temperature would show similar annual frequencies of DS exceedance for the wing walls, irrespective of the gap width (for gaps within the investigated range), while columns would be protected from minor to complete damage. Associated expected costs of the different retrofitting options remain unexplored.

Data Availability Statement

The following data that support the findings of this study are available from the corresponding author on reasonable request: selected ground motion records, peak demand data from RHAs, and fitted GMSDMs.

Acknowledgments

The authors gratefully acknowledge the financial support from the Natural Science and Engineering Research Council of Canada (Grant No. 37717), the Fonds de Recherche du Québec – Nature et Technologies (Grant No. 171443), and the Brazilian National Council for Scientific and Technological Development (CNPq) (Grant No. 233738/2014-2), and all the assistance provided by the Centre d’Études Interuniversitaire des Structures sous Charges Extrêmes (CEISCE). Computational resources were provided by Calcul Québec and Compute Canada for PSHA and deaggregation.

References

AASHTO. 2014. Guide specifications for seismic isolation design. 4th ed. Washington, DC: AASHTO.

Abstract

Introduction

Analytical Framework for Constructing Parameterized Fragility Functions

Modeling of Thermal Stiffening in Rubber Isolators

Case-Study Bridge

Numerical Modeling

Component Capacities and Performance Levels

Ground Motion Record Selection

Climate Historical Data at the Bridge’s Site

Assessment of the Isolated Bridge Seismic Performance in Cold Regions

PSDM

Construction of Component and System Fragility Surfaces

Potential Effect of Low-Temperature Shear Capacity Reduction on NRB

Conclusion

Data Availability Statement

Acknowledgments

References

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